Final Draft Writing Paper

  final draft writing paper: Development Writing Assessment Grade 5 Final Draft Writing Paper 50 Pack Celebration Press, 2000-12 Divided into three phases, DWA enables you to direct the initial student writing, analyze student strengths and weaknesses, and make instructional decisions based on the results.
  final draft writing paper: Kingdom Writers C. J. Hitz, Shelley Hitz, 2022-03
  final draft writing paper: The Runaway Pumpkin Kevin Lewis, 2008-08 When Buck, Billy, and their little sister Lil spy the biggest pumpkin they've ever seen, they can't resist. Buck and Billy try to roll the pumpkin down the hill, but it's too big! The giant pumpkin bumps and thumps its way through the family farm, only to end up as a sumptuous evening feast. This rollicking read-aloud picture book is guaranteed to keep children and families laughing.
  final draft writing paper: Doing Qualitative Research Using Your Computer Chris Hahn, 2008-04-11 ′I find your straightforward writing style an absolute joy, such a breath of fresh air!′ - Angie Ash, PhD student ′...thank you very much for your accessible language, clear lay out and practical applied approach. I suspect that this book will never be far from my side over the next 4 years!!′ - Mayen Konarski, PhD student Using straight-forward language Doing Qualitative Research Using Your Computer walks readers through the process of managing and streamlining research projects using commonly available Microsoft software applications. Drawing on a wide range of examples to demonstrate how easy it is to use such software, this guide is full of useful hints and tips on how to manage research more efficiently and effectively, including: - Formatting transcripts for maximum coding efficiency in Microsoft Word - Using features of Word to organize the analysis of data and to facilitate efficient qualitative coding - Synchronizing codes, categories, and important concepts between Microsoft Word and Microsoft Access - Efficiently storing and analyzing the qualitative data in Microsoft Excel - Creating flexible analytic memos in Access that help lead the researcher to final conclusions Ideal for those students or researchers who don′t want to invest in expensive specialised software packages, this guide will be an invaluable companion for anyone embarking on their own research project.
  final draft writing paper: Final Draft David Carr, 2020 A career-spanning selection of the legendary reporter David Carr's writing for the New York Times, Washington City Paper, New York Magazine, the Atlantic, and more. Throughout his 25-year journalistic career, David Carr was noted for his sharp and fearless observations, his uncanny sense of fairness and justice, and his remarkable compassion and wit. His writing was informed both by his own hardships as an addict, and his intense love of the journalist's craft. His range--from media politics to national politics, from rock 'n' roll celebrities to the unknown civil servants who make our daily lives function--was broad and often timeless. Whether he was breaking exclusives about Amazon or mourning Philip Seymour Hoffman's death or taking aim at editors who valued political trivia over substance, Carr's voice and concerns remain enormously influential and relevant. In these hundred or so articles, from a range of publications, we read his stories with fresh eyes. Edited by his widow, Jill Rooney Carr, and with an introduction written by one of the many journalists David Carr mentored and promoted, Ta-Nehisi Coates, Final Draft is a singular event in the world of writing news, an art increasingly endangered in these troubled times.
  final draft writing paper: Final Draft Level 4 Student's Book Wendy Asplin, Monica F. Jacobe, Alan S. Kennedy, 2015-09-23 Academic writing is difficult, and Final Draft gives students all the tools they need. Writing skills and in-depth analysis of models set the stage for development. Corpus-based vocabulary, collocations, and phrases, as well as detailed information on the grammar of writing, prepare your learners for college writing courses. Students learn to avoid plagiarism in every chapter of every level. This dedicated, long-term focus on plagiarism avoidance helps ensure that these students are able to use sources and highlight their own thoughts.
  final draft writing paper: Final Draft Riley Redgate, 2018-06-12 Laila Piedra doesn’t drink, doesn’t smoke, and definitely doesn’t sneak into the 21-and-over clubs on the Lower East Side. The only sort of risk Laila enjoys is the peril she writes for the characters in her stories: epic sci-fi worlds full of quests, forbidden love, and robots. Her creative writing teacher has always told her she has a special talent. But three months before graduation, Laila’s number one fan is replaced by Nadiya Nazarenko, a Pulitzer Prize–winning novelist who sees nothing at all special about Laila’s writing. A growing obsession with gaining Nazarenko’s approval—and fixing her first-ever failing grade—leads to a series of unexpected adventures. Soon Laila is discovering the psychedelic highs and perilous lows of nightlife, and the beauty of temporary flings and ambiguity. But with her sanity and happiness on the line, Laila must figure out if enduring the unendurable really is the only way to greatness.
  final draft writing paper: Mathematical Writing Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, 1989 This book will help those wishing to teach a course in technical writing, or who wish to write themselves.
  final draft writing paper: The Screenwriter's Bible David Trottier, 1998 One of the most popular and useful books on screenwriting, now greatly expanded and completely updated. This edition includes a list of resources and contains approximately 100 new entries.
  final draft writing paper: Final Draft Level 3 Student's Book Andrew Aquino-Cutcher, Wendy Asplin, Jeanne Lambert, David Bohlke, 2015-10-22 Academic writing is difficult, and Final Draft gives students all the tools they need. Writing skills and in-depth analysis of models set the stage for development. Corpus-based vocabulary, collocations, and phrases, as well as detailed information on the grammar of writing, prepare your learners for college writing courses. Students learn to avoid plagiarism in every chapter of every level. This dedicated, long-term focus on plagiarism avoidance helps ensure that these students are able to use sources and highlight their own thoughts.
  final draft writing paper: Becoming Strangers Louise Dean, 2007-01-08 After more than half a century of marriage, Dorothy and George are embarking on their first journey abroad together. Three decades younger, Jan and Annemieke are taking their last, as illness and incompatibility bring their unhappy union to an end. At first the luxury of a Caribbean resort is no match for the well-worn patterns of domestic life. Then the couples' paths cross, and a series of surprises ensues--a disappearance and an assault, most dramatically, but also a teapot tempest of passions, slights, misunderstandings, and small awakenings that punctuate a week in which each pair struggles to come to terms with what's been keeping them apart. A hit with readers and critics alike when it was published in England last year, Becoming Strangers is a different kind of love story, in which there's seldom a happy ending but sometimes a chance to redeem a life half-lived.
  final draft writing paper: Save the Cat! Blake Snyder, 2005 This ultimate insider's guide reveals the secrets that none dare admit, told by a show biz veteran who's proven that you can sell your script if you can save the cat!
  final draft writing paper: Finish Your Book in Three Drafts Stuart Horwitz, 2016-06-13 How do you write a book? Stuart Horwitz helps you do it in three drafts. Three drafts: that's all you need. - The messy draft: which is all about getting it down. - The method draft: which is all about making sense. - The polished draft: which is all about making it good. Finish Your Book in Three Drafts is for outliners who meticulously script every writing session and pantsers who pilot solely by feel. It will help you get past the fear that can land a first draft in the trashcan, and the confusion that can send a second draft into a dizzying tailspin. Because you don't want to be writing the same book for the rest of your life. You can Finish Your Book in Three Drafts provided you approach each draft in the right spirit, and know what action steps to take between drafts. With clarity, honesty, humor, and even videos, Horwitz discusses the best outlook and direction for each of the three drafts so that you can increase your efficiency, satisfaction, and engagement with both your writing process and your final product.
  final draft writing paper: Hold Back the Stars Katie Khan, 2017-05-23 A startling and evocative novel, harkening to both One Day and Gravity, a man and a woman revisit memories of their love affair on a utopian Earth while they are trapped in the vast void of space with only ninety minutes of oxygen left. After the catastrophic destruction of the Middle East and the United States, Europe has become a utopia and, every three years, the European population must rotate into different multicultural communities, living as individuals responsible for their own actions. While living in this paradise, Max meets Carys and immediately feels a spark of attraction. He quickly realizes, however, that Carys is someone he might want to stay with long-term, which is impossible in this new world. As their relationship plays out, the connections between their time on Earth and their present dilemma in space become clear. When their air ticks dangerously low, one is offered the chance of salvation—but who will take it? An original and daring exploration of the impact of first love and how the choices we make can change the fate of everyone around us, this is an unforgettable read.
  final draft writing paper: Writing Your Journal Article in Twelve Weeks Wendy Laura Belcher, 2009-01-20 This book provides you with all the tools you need to write an excellent academic article and get it published.
  final draft writing paper: The Writing Teacher's Handbook Jo Phenix, 2002 Offers practical guidance for teachers to create classrooms where pupils thrive as writers. This book helps teachers learn how to build on the experience, knowledge and ideas that students bring to the classroom, and make writing a natural part of the daily activities of any classroom.
  final draft writing paper: Writing Papers in the Biological Sciences Victoria E. McMillan, 2020-08-26 Writing in the Biological Sciences is a handy reference that new to advanced students can readily use on their own. A variety of student models prepare you for the most common writing assignments in undergraduate biology courses.
  final draft writing paper: How to Write Mathematics Norman Earl Steenrod, 1973-12-31 This classic guide contains four essays on writing mathematical books and papers at the research level and at the level of graduate texts. The authors are all well known for their writing skills, as well as their mathematical accomplishments. The first essay, by Steenrod, discusses writing books, either monographs or textbooks. He gives both general and specific advice, getting into such details as the need for a good introduction. The longest essay is by Halmos, and contains many of the pieces of his advice that are repeated even today: In order to say something well you must have something to say; write for someone; think about the alphabet. Halmos's advice is systematic and practical. Schiffer addresses the issue by examining four types of mathematical writing: research paper, monograph, survey, and textbook, and gives advice for each form of exposition. Dieudonne's contribution is mostly a commentary on the earlier essays, with clear statements of where he disagrees with his coauthors. The advice in this small book will be useful to mathematicians at all levels.
  final draft writing paper: Writing Papers in the Biological Sciences Vicky McMillan, 2012 Designed primarily for undergraduates, this self-help manual offers straightforward solutions to common problems and an overview of the diversity of writing tasks faced by professional biologists.
  final draft writing paper: The Dream Jumper's Promise Kim Hornsby, 2015-04-24 Tina Green’s husband is presumed dead from a Maui surfing accident and now she’s being haunted by otherworldly dreams. When former boyfriend, Jamey Dunn, turns up at her Lahaina dive shop and offers to help, she can’t believe his preposterous claim -- he can enter dreams. Along with her friend, Noble, they piece together clues to her husband’s disappearance, but secrets, lies, and heartbreak rise to the ugly surface to reveal that one person is an impostor, one a traitor, and one is flirting with insanity.
  final draft writing paper: Writing Science Joshua Schimel, 2012-01-26 This book takes an integrated approach, using the principles of story structure to discuss every aspect of successful science writing, from the overall structure of a paper or proposal to individual sections, paragraphs, sentences, and words. It begins by building core arguments, analyzing why some stories are engaging and memorable while others are quickly forgotten, and proceeds to the elements of story structure, showing how the structures scientists and researchers use in papers and proposals fit into classical models. The book targets the internal structure of a paper, explaining how to write clear and professional sections, paragraphs, and sentences in a way that is clear and compelling.
  final draft writing paper: Student's Guide to Writing College Papers Kate L. Turabian, 2010-04-15 High school students, two-year college students, and university students all need to know how to write a well-reasoned, coherent research paper—and for decades Kate Turabian’s Student’s Guide to Writing College Papers has helped them to develop this critical skill. In the new fourth edition of Turabian’s popular guide, the team behind Chicago’s widely respected The Craft of Research has reconceived and renewed this classic for today’s generation. Designed for less advanced writers than Turabian’s Manual of Writers of Research Papers, Theses, and Dissertations, Seventh Edition, Gregory G. Colomb and Joseph M. Williams here introduce students to the art of defining a topic, doing high-quality research with limited resources, and writing an engaging and solid college paper. The Student’s Guide is organized into three sections that lead students through the process of developing and revising a paper. Part 1, Writing Your Paper, guides students through the research process with discussions of choosing and developing a topic, validating sources, planning arguments, writing drafts, avoiding plagiarism, and presenting evidence in tables and figures. Part 2, Citing Sources, begins with a succinct introduction to why citation is important and includes sections on the three major styles students might encounter in their work—Chicago, MLA, and APA—all with full coverage of electronic source citation. Part 3, Style, covers all matters of style important to writers of college papers, from punctuation to spelling to presenting titles, names, and numbers. With the authority and clarity long associated with the name Turabian, the fourth edition of Student’s Guide to Writing College Papers is both a solid introduction to the research process and a convenient handbook to the best practices of writing college papers. Classroom tested and filled with relevant examples and tips, this is a reference that students, and their teachers, will turn to again and again.
  final draft writing paper: The Synonym Finder J. I. Rodale, 2016-04-22 Originally published in 1961 by the founder of Rodale Inc., The Synonym Finder continues to be a practical reference tool for every home and office. This thesaurus contains more than 1 million synonyms, arranged alphabetically, with separate subdivisions for the different parts of speech and meanings of the same word.
  final draft writing paper: Practical Composition Russell Brickey, Laura L. Beadling, Evelyn Martens, 2014-07-18 For English instructors at every level, the task of producing a worthwhile, workable plan for each class period can prove challenging. This invaluable work offers a vast compilation of writing exercises and in-class activities collected from professors, graduate students and lecturers from colleges and universities across the United States. Step-by-step instructions guide teachers through class discussions and exercises on topics ranging from invention, argumentation, formatting, thesis development and organization to rhetorical situation, visual rhetoric, peer review and revision. From high school teachers and first-time teaching assistants to experienced writing professors looking to enhance their courses, anyone who teaches English will appreciate the fresh ideas found in this indispensable volume. Instructors considering this book for use in a course may request an examination copy here.
  final draft writing paper: Bird by Bird Anne Lamott, 2007-12-18 NEW YORK TIMES BESTSELLER • An essential volume for generations of writers young and old. The twenty-fifth anniversary edition of this modern classic will continue to spark creative minds for years to come. Anne Lamott is a warm, generous, and hilarious guide through the writer’s world and its treacherous swamps (Los Angeles Times). “Superb writing advice…. Hilarious, helpful, and provocative.” —The New York Times Book Review For a quarter century, more than a million readers—scribes and scribblers of all ages and abilities—have been inspired by Anne Lamott’s hilarious, big-hearted, homespun advice. Advice that begins with the simple words of wisdom passed down from Anne’s father—also a writer—in the iconic passage that gives the book its title: “Thirty years ago my older brother, who was ten years old at the time, was trying to get a report on birds written that he’d had three months to write. It was due the next day. We were out at our family cabin in Bolinas, and he was at the kitchen table close to tears, surrounded by binder paper and pencils and unopened books on birds, immobilized by the hugeness of the task ahead. Then my father sat down beside him, put his arm around my brother’s shoulder, and said, ‘Bird by bird, buddy. Just take it bird by bird.’”
  final draft writing paper: Draft No. 4 John McPhee, 2017-09-05 The long-awaited guide to writing long-form nonfiction by the legendary author and teacher Draft No. 4 is a master class on the writer’s craft. In a series of playful, expertly wrought essays, John McPhee shares insights he has gathered over his career and has refined while teaching at Princeton University, where he has nurtured some of the most esteemed writers of recent decades. McPhee offers definitive guidance in the decisions regarding arrangement, diction, and tone that shape nonfiction pieces, and he presents extracts from his work, subjecting them to wry scrutiny. In one essay, he considers the delicate art of getting sources to tell you what they might not otherwise reveal. In another, he discusses how to use flashback to place a bear encounter in a travel narrative while observing that “readers are not supposed to notice the structure. It is meant to be about as visible as someone’s bones.” The result is a vivid depiction of the writing process, from reporting to drafting to revising—and revising, and revising. Draft No. 4 is enriched by multiple diagrams and by personal anecdotes and charming reflections on the life of a writer. McPhee describes his enduring relationships with The New Yorker and Farrar, Straus and Giroux, and recalls his early years at Time magazine. Throughout, Draft No. 4 is enlivened by his keen sense of writing as a way of being in the world.
  final draft writing paper: A Sequence for Academic Writing Laurence Behrens, Leonard J. Rosen, Bonnie Beedles, 2004 This brief rhetoric focuses on the key academic writing strategies of summary, synthesis, analysis, and critique. Responding to the growing interest in academic writing, this popular guide focuses on the critical reading and writing strategies necessary to help students interpret and incorporate source material into their own papers. The text employs high-interest readings from a range of disciplines to allow students to practice their summary and synthesis skills, while numerous student papers model the kinds of academic texts students are expected to produce, no matter what their area of study. Individuals who want help with writing up researched or documented papers.
  final draft writing paper: Leaders of Their Own Learning Ron Berger, Leah Rugen, Libby Woodfin, EL Education, 2013-12-30 From EL Education comes a proven approach to student assessment Leaders of Their Own Learning offers a new way of thinking about assessment based on the celebrated work of EL Education schools across the country. Student-Engaged Assessment is not a single practice but an approach to teaching and learning that equips and compels students to understand goals for their learning and growth, track their progress toward those goals, and take responsibility for reaching them. This requires a set of interrelated strategies and structures and a whole-school culture in which students are given the respect and responsibility to be meaningfully engaged in their own learning. Includes everything teachers and school leaders need to implement a successful Student-Engaged Assessment system in their schools Outlines the practices that will engage students in making academic progress, improve achievement, and involve families and communities in the life of the school Describes each of the book's eight key practices, gives advice on how to begin, and explains what teachers and school leaders need to put into practice in their own classrooms Ron Berger is Chief Program Officer for EL Education and a former public school teacher Leaders of Their Own Learning shows educators how to ignite the capacity of students to take responsibility for their own learning, meet Common Core and state standards, and reach higher levels of achievement. Video and other supplementary materials are not included as part of the e-book file, but are available for download after purchase.
  final draft writing paper: Monet Paints a Day Julie Danneberg, 2012-07-01 In November 1885, impressionist painter Claude Monet vacationed in Étretat, France, where he spent his days outside, painting scenes of the seaside village. One morning he rose early and carried all of his supplies and half-finished paintings out to the cliffs and rocky beach, finally stopping to paint the arch called Manneporte. Eager to capture the scene before him, and aware that he must work quickly to catch the light, Monet became so engrossed in his work that he forgot to watch the incoming tide. Based on a true incident, MONET PAINTS A DAY introduces readers to the life and nature of this illustrious impressionist. Interspersed throughout the story are excerpts from the painter’s notes and letters, while a second layer of text and back matter includes information about Impressionism as a whole. Lush watercolor illustrations in the Impressionist style give readers a visual for this artistic movement. A bibliography is also included.
  final draft writing paper: Save the Cat! Writes a Novel Jessica Brody, 2018-10-09 The first novel-writing guide from the best-selling Save the Cat! story-structure series, which reveals the 15 essential plot points needed to make any novel a success. Novelist Jessica Brody presents a comprehensive story-structure guide for novelists that applies the famed Save the Cat! screenwriting methodology to the world of novel writing. Revealing the 15 beats (plot points) that comprise a successful story--from the opening image to the finale--this book lays out the Ten Story Genres (Monster in the House; Whydunit; Dude with a Problem) alongside quirky, original insights (Save the Cat; Shard of Glass) to help novelists craft a plot that will captivate--and a novel that will sell.
  final draft writing paper: Research Papers For Dummies Geraldine Woods, 2002-07-05 From blank page to final draft, this is your straightforward guide to research papers You're sitting at your desk in a classroom or in an airless cubicle, wondering how many minutes are left in a seemingly endless day, when suddenly your teacher or supervisor lowers the boom: She wants a research paper, complete with footnotes and a list of sources. She wants accuracy, originality, and good grammar. And – gasp! – she wants ten pages! You may be 16 years old or 60 years old, but your reaction is the same: Help! Take heart. A research paper may seem daunting, but it's a far-from-impossible project to accomplish. Turning research into writing is actually quite easy, as long as you follow a few proven techniques. And that's where Research Papers For Dummies steps in to help. In this easy-to-understand guide, you find out how to search for information using both traditional printed sources and the electronic treasure troves of the Internet. You also discover how to take all those bits of information, discarding the irrelevant ones, and put them into a form that illustrates your point with clarity and originality. Here's just a sampling of the topics you'll find in Research Papers For Dummies: Types of research papers, from business reports to dissertations The basic ingredients of a paper: Introduction, body, conclusion, footnotes, and bibliography Note-taking methods while doing research Avoiding plagiarism and other research paper pitfalls Defining your thesis statement and choosing a structure for your paper Supporting your argument and drawing an insightful conclusion Revising and polishing your prose Top Ten lists on the best ways to begin your research online and in print Research Papers For Dummies also includes an appendix that's full of research paper ideas if you're stuck. If you're tasked with writing a research paper, chances are you already have a lot of demands on your time. You don't need another huge pile of papers to read. This book can actually save you time in the long run, because it gives you the easiest, fastest, and most successful methods for completing your paper.
  final draft writing paper: The Scribe Method Tucker Max, Zach Obront, 2021-04-15 Ready to write your book? So why haven’t you done it yet? If you’re like most nonfiction authors, fears are holding you back. Sound familiar? Is my idea good enough? How do I structure a book? What exactly are the steps to write it? How do I stay motivated? What if I actually finish it, and it’s bad? Worst of all: what if I publish it, and no one cares? How do I know if I’m even doing the right things? The truth is, writing a book can be scary and overwhelming—but it doesn’t have to be. There’s a way to know you’re on the right path and taking the right steps. How? By using a method that’s been validated with thousands of other Authors just like you. In fact, it’s the same exact process used to produce dozens of big bestsellers–including David Goggins’s Can’t Hurt Me, Tiffany Haddish’s The Last Black Unicorn, and Joey Coleman’s Never Lose a Customer Again. The Scribe Method is the tested and proven process that will help you navigate the entire book-writing process from start to finish–the right way. Written by 4x New York Times Bestselling Author Tucker Max and publishing expert Zach Obront, you’ll learn the step-by-step method that has helped over 1,500 authors write and publish their books. Now a Wall Street Journal Bestseller itself, The Scribe Method is specifically designed for business leaders, personal development gurus, entrepreneurs, and any expert in their field who has accumulated years of hard-won knowledge and wants to put it out into the world. Forget the rest of the books written by pretenders. This is the ultimate resource for anyone who wants to professionally write a great nonfiction book.
  final draft writing paper: The Hollywood Standard - Third Edition Christopher Riley Christopher, 2021-05-04 Intended to be kept at a screenwriter's fingertips, The Hollywood Standard provides what even the best script software can't: clear, concise instructions and hundreds of examples to take the guesswork out of a multitude of formatting questions that perplex even seasoned screenwriters.Contents include:* When a new scene heading is appropriate and when it isn't* How to format shot headings, dialogue, direction and transitions* How to control pace with formatting* How to make a script page visually inviting to the reader* What to capitalize and why* How to get into and out of a POV shot* How to handle text messages and Zoom meetings* How Hollywood's most innovative screenwriters are pushing the boundaries of format* How format for animation differs from live action formatsSimply put, Riley knows more about script format than anyone in Hollywood and shares it all in this indispensable guide.
  final draft writing paper: Writing a Research Paper Edward J. Shewan, 2001-02-28 This booklet is designed to guide the student through the process of writing a research paper- from selecting a topic to polishing the final draft. Writing a Research Paper will develop the skills that will benefit the student in every area of life, now and in the future.
  final draft writing paper: This Is the Story of a Happy Marriage Ann Patchett, 2013-11-07 'So compellingly personal you feel you're looking over her shoulder as she sits down to write' New York Times 'Electrically entertaining ... Funny, generous, spirited and kind' The Times This Is the Story of a Happy Marriage is an irresistible blend of literature and memoir revealing the big experiences and little moments that shaped Ann Patchett as a daughter, wife, friend and writer. Here, Ann Patchett shares entertaining and moving stories about her tumultuous childhood, her painful early divorce, the excitement of selling her first book, driving a Winnebago from Montana to Yellowstone Park, her joyous discovery of opera, scaling a six-foot wall in order to join the Los Angeles Police Department, the gradual loss of her beloved grandmother, starting her own bookshop in Nashville, her love for her very special dog and, of course, her eventual happy marriage. This Is the Story of a Happy Marriage is a memoir both wide ranging and deeply personal, overflowing with close observation and emotional wisdom, told with wit, honesty and irresistible warmth.
  final draft writing paper: Good Essay Writing Peter Redman, Wendy Maples, 2011-04-13 Lecturers, why waste time waiting for the post to arrive? Request and receive your e-inspection copy today! Writing good essays can be a real challenge. If you need a helping hand (or simply want to improve your technique) this book sets out proven approaches and techniques which can help everyone write good essays. Extensively revised and updated, this 4th edition includes new material such as: A chapter on essay planning, focusing on literature searching (using online materials), note-taking and formulating an argument A comparison of essay writing to exam writing The use of academic language, vocabulary and register, and its 'accuracy and appropriateness' A new Companion Website providing additional activities, downloads and resources. The authors focus on answering key questions you will face when preparing essays - What do tutors look for when marking my essay? What kind of skills do I need as I progress through my course? How can I avoid inadvertent plagiarism? What are the protocols for referencing? Encapsulated in easy to digest summaries, this edition shows you how to approach different types of essay questions, addresses common worries, and provides extensive use of worked examples including complete essays which are fully analysed and discussed. Visit the Companion Website at www.uk.sagepub.com/redman/ for a range of free support materials! Good Essay Writing is highly recommended for anyone studying social sciences who wants to brush up on their essay writing skills and achieve excellent grades. SAGE Study Skills are essential study guides for students of all levels. From how to write great essays and succeeding at university, to writing your undergraduate dissertation and doing postgraduate research, SAGE Study Skills help you get the best from your time at university. Visit the SAGE Study Skills website for tips, quizzes and videos on study success!
  final draft writing paper: The Thousand Lights Hotel Emylia Hall, 2017-07-01 The new pick from Fearne Cotton's Happy Place Book Club and the perfect beach read for summer 2023, set in idyllic Italy, for fans of The Garnett Girls. When Kit loses her mother in tragic circumstances, she feels drawn to finally connect with the father she has never met. That search brings her to the Thousand Lights Hotel, the perfect holiday escape perched upon a cliff on the island of Elba. Within this idyllic setting a devastating truth is brought to light: shaking the foundations upon which the hotel is built, and shattering the lives of the people within it. A heartbreaking story of loss, betrayal, and redemption, told with all the warmth and beauty of an Italian summer. Your favourite authors LOVE The Thousand Lights Hotel: 'A gloriously intoxicating fairytale - sweet, sensual and sun-drenched. You won't want to leave!' - Veronica Henry 'I loved this book. Such gorgeous, delicate writing' - Kate Riordan ''A real beautiful form of escapism' - Fearne Cotton
  final draft writing paper: Integrating Values with Communication Arts ,
  final draft writing paper: The Technique of Preparing Social Science Papers Emory Stephen Bogardus, 1921
  final draft writing paper: Building on the Past to Prepare for the Future Janina Morska, Alan Rogerson, 2022-09-01 Abstract of Book This volume contains the papers presented at the International Conference Building on the Past to Prepare for the Future held from August 8-13, 2022, in King’s College, Cambridge, UK. It was the 16th conference organised by The Mathematics Education for the Future Project - an international edu­ca­tional and philanthropic project founded in 1986 and dedicated to innovation in mathematics, statistics, science and computer education world wide. Contents List of Papers and Workshop Summaries Fouze Abu Qouder & Miriam Amit The Ethnomathematics of the Bedouin - An Innovative Approach of Integrating Socio Cultural Elements into Mathematics Education https://doi.org/10.37626/GA9783959872188.0.001 First page: 1 Last page: 6 Abstract Our study attempted to address young Bedouin (desert tribes) students’ persistent difficulties with mathematics by integrating ethnomathmematics into a standard curriculum. First, we conducted extensive interviews w 35 Bedouin elders and women to identify: 1. The mathematical elements of their daily lives- particularly traditional units of length and weight, 2. The geometrical shapes in Bedouin women’s traditional dress embroidery. Then we combined these with the standard curriculum to make an integrated 90 hours 7-8th grade teaching units that were implemented in Bedouin schools and in the Kidumatica Math Club for Excellent Students. Comparisons between the experimental groups (186) and the control group (62) showed that studying by the integrated curriculum improved:1.The cognitive aspects of the students 2.The affective aspects. Keywords: Bedouin Cultures, ethnomathematics. ======================================================= Nadine Adams & Clinton Hayes Why Everyone should know Statistics! https://doi.org/10.37626/GA9783959872188.0.002 First page: 7 Last page: 11 Abstract “Decision is the central intellectual activity in our everyday lives” and statistics is central to these activities (Longford, 2021, p. xi). The ability to manipulate and interpret data is an important component in decision making. A misunderstanding or poor grasp of data distributions and statistical methods can lead to assumptions that are not accurate. When these inaccurate assumptions are presented as factual to decision makers also possessing little or no statistical knowledge, poor decisions can be made. This paper investigates how an interpretation of statistics played a role the decision to remove multiple-choice questions from invigilated examinations at a regional Australian university. The case is further argued that it is important for everyone to have a basic understanding of statistics. ======================================================= Anita N. Alexander The Perspectives of Effective Teaching and Learning of Current Undergraduate and Graduate Mathematics Students https://doi.org/10.37626/GA9783959872188.0.003 First page: 12 Last page: 17 Abstract Some mathematics professors engage their students in discourse and explorations to promote a deep understanding of critical concepts. Still, lecture remains the norm in mathematics courses according to current mathematics students’ survey responses (Mostly Lecture 52%; Lecture & Discussions 35%; N = 89). Students were asked the best way for them to learn mathematics, whether their career plans are teaching related (Teaching Related: Yes 22%; Not Sure 36%; No 42%), as well as what they enjoy and want to change about their mathematics courses. Students requested “more discussions, and more questions to solve in class,” and described lecture as “an unacceptable way to teach,” and that “it is the worst way to learn.” Students’ perspectives on effective teaching and learning are critical for their continued passion to pursue STEM related fields, rather than stating that “I do not love mathematics anymore.” ======================================================= Clement Ayarebilla Ali & Ernest Kofi Davis Applications of Basketry to Geometric Tessellations https://doi.org/10.37626/GA9783959872188.0.004 First page: 18 Last page: 23 Abstract We present applications of basketry to geometric tessellation in the primary school mathematics. Even though there are various forms of tessellations, we present three regular and Archimedean tessellations for conceptual analysis of the geometric concepts. With a case study design of 15 pupils through interviews and observations, the findings show that pupils can apply baskets to learn geometric tessellations. It was there recommended that baskets be used to extend learning as they play, game and fun. ======================================================= Nurten Alpaslan & Emre Alpaslan Mathematics for Everybody https://doi.org/10.37626/GA9783959872188.0.005 First page: 24 Last page: 25 ======================================================= Cynthia Oropesa Anhalt, Ricardo Cortez, Brynja Kohler & Will Tidwell Interrogation of Social Justice Contexts in Mathematical Modeling: The Use of Simulations of Practice in the Mathematical Preparation of Teachers https://doi.org/10.37626/GA9783959872188.0.006 First page: 26 Last page: 31 Abstract Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. The Mathematics of Doing, Understanding, Learning, and Educating for Secondary Students [MODULE(S2)]* project developed a curriculum in modeling for teacher education that includes simulations of practice, in which prospective teachers reflect on and plan a discussion around student thinking, their models, and the contextualization of their results. We present an analysis of prospective teachers’ modeling work on the decreasing area of Indigenous reservation land in the U.S., and a simulation of practice which explores different methods for finding the area of land in connection to the injustice deeply rooted in the treatment of Indigenous people. This problem explores a critical social issue and calls for explicit attention to pedagogical knowledge in structuring discussions around the contextualization of the mathematical results. ======================================================= Takako Aoki & Shin Watanabe Find out Mathematics on a Football: Making a football with paper https://doi.org/10.37626/GA9783959872188.0.007 First page: 32 Last page: 34 Abstract We are aiming for a workshop method as a way to teach mathematics in future school education. It is important to cooperate with each other and understand mathematics. In this workshop, we aim to discover the mathematics hidden in the footballs we handle every day. As an aid to thinking, I would like to make football by paper first and learn mathematics while looking at concrete things. You need 20 equilateral triangles. A regular hexagon is made from this equilateral triangle, and a regular pentagon uses the method of making a hole. In particular, pay attention to the four-color problem in mathematics, make sure that the colours of adjacent regular hexagons are different, and use three colours (red, green, yellow). For example, in a football, how many equilateral triangles of each colour are used is one of the issues. I am looking forward to holding a workshop to see what kind of problems there are. Key words: football Introduction with paper, the truncated icosahedron, the color coding of the three colors, Euler's polyhedral formula ======================================================= Sarah Bansilal Analysing the Demands of an Assessment in a Geometry Pedagogic Content Knowledge Module https://doi.org/10.37626/GA9783959872188.0.008 First page: 35 Last page: 40 Abstract With the onset of the pandemic, universities were forced to move to online platforms for teaching and for assessments. In this paper, I reflect on the use of multiple-choice questions in a geometry PCK module for pre-service mathematics teachers. The study involves a secondary analysis of the data generated by the responses of 92 students to an assessment consisting of 25 items. The aim of the study was to distinguish between, and if possible, characterise possible levels of demands of the test items. The results suggested that there are four distinct groups of items relating to common content knowledge of early and late high school respectively, PCK related to deductive reasoning skills and critical thinking in an open book setting. ======================================================= Mike Bedwell Three or Four numbers: A Teacher’s Tale https://doi.org/10.37626/GA9783959872188.0.009 First page: 41 Last page: 43 ======================================================= Esther Billings & Lisa Kasmer Learning Experiences that Support Primary Teacher Candidates’ Understanding and Enactment of Core Mathematics Teaching Practices https://doi.org/10.37626/GA9783959872188.0.010 First page: 44 Last page: 49 Abstract In many teacher preparation programs, instruction focuses on learning about strategies and practices for teaching rather than directly enacting and honing these skills (Grossman, Hammerness, & McDonald, 2009): a corepractice approach in teacher education necessitates organizing coursework and fieldwork around practices of the teaching profession while simultaneously providing teacher candidates (TCs) ample opportunities to “practise” by enacting these teaching practices. In this paper, we share our corepractice instructional strategies, along with TC work used in our teacher preparation mathematics education courses (prior to student teaching) to engage TCs’ understanding and development of their ability to enact core practices, specifically the mathematics teaching practices outlined in National Council of Teachers of Mathematics (NCTM) (2014). ======================================================= Victoria Bonaccorso, Joseph DiNapoli & Eileen Murray Promoting Meaningful Conversations among Prospective Mathematics Teachers https://doi.org/10.37626/GA9783959872188.0.011 First page: 50 Last page: 55 Abstract Recent circumstances due to the COVID-19 pandemic and restrictions on entering public schools have created barriers for prospective teachers (PT) to gain valuable exposure to real classrooms. As a result, we have transitioned some teacher preparation from in person experiences to video case study analysis. Our research seeks to determine how this transition can foster development of critical teaching skills by infusing a model of powerful teaching with video of real classrooms. Our findings suggest that with online video case analysis PTs were able to advance their discursive conversations to strategic conversations by building on and transforming each other’s articulation of proposed teacher moves. This model for PT preparation has the potential to foster more meaningful discourse among participants by providing a space to build on and refine their understanding of mathematics teaching. ======================================================= Primo Brandi, Rita Ceppitelli & Anna Salvadori Elementary Dynamic Models: A Strategic Bridge Connecting School and University https://doi.org/10.37626/GA9783959872188.0.012 First page: 56 Last page: 62 Abstract We present an innovative educational path thought as a link between High School and University studies. The topic is the introduction to dynamic models (both discrete and continuous) which represent a key tool in a wide range of disciplines: sciences, techniques, economics, life sciences and more. ======================================================= Simone Brasili & Riccardo Piergallini Introducing Symmetry and Invariance with Magic Squares https://doi.org/10.37626/GA9783959872188.0.013 First page: 63 Last page: 68 Abstract Magic squares are key tools in mathematics teaching. They favor reasoning and creativity in problem-solving. As well, they bring students closer to the history of mathematics. Our work presents the magic squares in a learning progression introducing the symmetry linked with the idea of invariance “sameness in change” early at primary school in Montegranaro (Italy). Using the 3x3 magic square and manipulation games, a sample of 101 pupils (8 years) internalizes symmetries, reflections, and rotations associated with the square. The proposed activities provide tools and experience for geometric cognitive processes transferable from magic squares to main geometric shapes. The findings confirm that symmetry linked to the search for invariance is appropriate and accessible for primary school pupils through manipulation games. ======================================================= Angela Broaddus & Matthew Broaddus Assessing Mathematical Reasoning: Test Less – Explain More https://doi.org/10.37626/GA9783959872188.0.014 First page: 69 Last page: 74 Abstract Mathematics educational researchers have long offered recommendations for effective mathematics teaching, learning, and assessment, yet educators still struggle to implement fair and practical assessments that promote engagement and inspire students. This study describes assessments that (1) reduced anxiety, frustration, and rote imitation of procedures; (2) increased accessibility, motivation, and psychological resilience; and (3) improved engagement, strategic competence, self-assessment, and depth of understanding. Writing assignments prompted students to explain their reasoning about problems or their understanding of main ideas. Students revisited assignments in response to feedback and resubmitted them later in the course, which motivated students to deepen their understanding over time. Sample assignments, responses, and lessons learned will be shared. ======================================================= Irena Budínová & Jitka Panáčová Children with Reduced Cognitive Effectivity, their Problems and Optimal Way of Education https://doi.org/10.37626/GA9783959872188.0.015 First page: 75 Last page: 80 Abstract The contribution deals with children with reduced cognitive efficiency, their specific, and frequent difficulties in learning mathematics in the first years of education. Two examples of children with reduced cognitive efficiency will illustrate the specific ways in which reduced cognitive efficiency can manifest itself in mathematics, how children can be helped to overcome the mathematics curriculum. Problems in learning two basic arithmetic operations will be presented. The differentiation of teaching will be briefly introduced as an effective opportunity to work with these children. ======================================================= Gail Burrill Data Science and Mathematical Modeling: Connecting Mathematics to the World in which Students Live https://doi.org/10.37626/GA9783959872188.0.016 First page: 81 Last page: 89 Abstract The increasing need for statistical and quantitative thinking and reasoning makes it more important than ever that using mathematics and statistics to make sense of the world should be a central component of schooling. Data have transformed the way we look at the world. Shouldn’t this emphasis on data also impact what we teach both in mathematics and statistics? Research suggests that engaging with real data can motivate students, encourage them to take an interest in STEM fields, and allows the interests of diverse communities to be used as opportunities for learning. This paper summarizes the research looking at why connecting mathematics to the world is important for student learning, describes the role of data science and modeling in doing so, and provides examples of opportunities for students to interact with the world in which they live and work. “The development of mathematics is intimately interwoven with the progress of civilization,..” (Ebrahim, 2010) ======================================================= Gail Burrill & Thomas Dick Connecting Mathematics to the World: Engaging Students with Data Science https://doi.org/10.37626/GA9783959872188.0.017 First page: 90 Last page: 94 Abstract Mathematics and statistics can be used to describe, explore, and understand this complicated world in which we live. The workshop focus is on several potentially messy, real-world problems from predicting herd immunity, to exploring the quality of life across countries to modeling the change in CO2 levels. Each situation begins with a question and a set of data. The activities are open ended with multiple ways students might develop mathematical and statistical models, use technology to analyze the data, and make sense of terms such as herd immunity or vaccine efficacy or to investigate situations such as optimizing resources during a flood. ======================================================= Elizabeth A. Burroughs & Mary Alice Carlson Fostering Empathy in Mathematics through Mathematical Modeling https://doi.org/10.37626/GA9783959872188.0.018 First page: 95 Last page: 100 Abstract Modeling, a cyclic process by which mathematicians develop and use mathematical tools to represent, understand, and solve problems, provides learning opportunities for school students. Mathematical modeling situates mathematical problem solving squarely in the middle of everyday experiences. Modeling engenders the habits and dispositions of problem solving and empowers students to identify critical issues important to them, use their mathematical tools to address these problems, and view mathematics as a force for societal good. ======================================================= Bernardo Camou The Adventure of Learning Mathematics and Lakatos’s Legacy https://doi.org/10.37626/GA9783959872188.0.019 First page: 101 Last page: 104 Abstract Mathematics is normally described as abstract, exact, general and perfect. However, mathematics is a human creation and thus we can ask: How can humans with flaws and defects are able to create something perfect and infallible? Mathematics have its foundations in concrete problems, trials and errors approximations and representations. Learning mathematics is a fascinating trip, back and forth between concrete and abstract, between approximations and accuracy, between particular and general. Our poor representations are the road to conceptualize mathematical objects that then, seem to become perfect. In this workshop we will handle polyhedral and work with Euler’s Formula, with angular defects and its relation with surface´s curvature. In Lakato’s book Proofs and Refutations the author might have committed a mistake, though his book gives us a brilliant insight about the logic of mathematical discovery. ======================================================= Carrie Chiappetta, Christopher Walsh, Annie Smith & Javier Perez K-12 Schools after the Global Pandemic: How a Regional School District in the United States Accelerated Learning for Students, Teachers & Administrators https://doi.org/10.37626/GA9783959872188.0.020 First page: 105 Last page: 110 Abstract After the global pandemic, Regional School District 15 will start the 2021-2022 school year by accelerating learning for students, teachers, and administrators. For teachers, the focus will be on “purposeful planning,” “differentiation,” and “formative assessment” to ensure that all students learn grade level content. For administrators, the focus would be on supporting teachers in these three areas of focus. The Assistant Superintendent, the Mathematics/Science Department Chair, and the elementary and middle school mathematics instructional coaches will share the plan that they have implemented to work with K-12 teachers and administrators to ensure that students were able to learn grade level content even after the interrupted education that occurred during the global pandemic. ======================================================= Kathleen Cotter Clayton Fractions of the Future https://doi.org/10.37626/GA9783959872188.0.021 First page: 111 Last page: 116 Abstract Explore the simplicity and beauty of fractions of the future with a linear model, not with circle sets. When fractions are approached with this linear perspective, fractions can be easily taught, explored, and applied in daily life. Learn how to ask the right questions to guide your pupils to a solid understanding. Children as young as five can see that 1/3 is less than 1/2 and more than 1/4. They can also see why 9/8 is more than 1, why 1/4 plus 1/8 is 3/8, and why 1/2 × 1/2 is 1/4. Fractions are a delight when they are taught the right way. Allow the children to explore the whole picture and relationships within the whole using the linear fraction model. Learn about activities and games to build confidence and develop a deep understanding of fractions. Uncover the joy of fractions! ======================================================= Joan A. Cotter Teaching Primary Mathematics without Counting and Place Value with Transparent Number Naming https://doi.org/10.37626/GA9783959872188.0.022 First page: 117 Last page: 122 Abstract Counting - memorizing the sequence and coordinating pointing with recitation - is problematic for many children. Children with poor counting skills often struggle to learn their beginning math with various approaches. Yet, counting is unnecessary. Babies are born with the ability to subitize; that is, to detect quantities at a glance, up to three. By age 3, they can subitize up to five; by age 4 they can subitize up to 10 by grouping in fives, similar to their fingers. After children know the names for quantities 1 to 10, their next step should be place-value starting with temporary transparent number naming. For example, 11 is “ten-1”, 12 is “ten-2”, and 24 is “2-ten-4.” The counting words in Far Asian languages reflect this transparency, enhancing their pupils’ mathematics achievement. Place-value knowledge combined with subitizing gives pupils a way to master number combinations. ======================================================= Celisa Counterman M.A.T.H. = Making Algebraic Thinking Holistic https://doi.org/10.37626/GA9783959872188.0.023 First page: 123 Last page: 127 Abstract Students in mathematics often need more than just definitions and examples. The first step is leaving their anxiety at the door. Hands-on work engages students by utilizing group learning, discovery, and active learning both with and without technology lessening the fears of math. Faculty members will be given sample activities, rubrics, and sample student work. Special focus on creating Spirolaterals and quilting teach geometric movement and pattern recognition. Puzzles are created with mathematical problems in linear equations, linear inequalities, and compound inequalities bringing the focus on skills and historical facts. Faculty members will work in teams to recreate the materials themselves to see where issues in understanding come from. There will be time for both questions and answers. ======================================================= Scott A. Courtney The Impact of Remote Instruction on Mathematics Teachers’ Practices https://doi.org/10.37626/GA9783959872188.0.024 First page: 128 Last page: 133 Abstract The coronavirus pandemic has impacted all aspects of society. As the virus spread across the globe, countries and local communities closed workplaces, moved schools to remote instruction, limited in-person contact, cancelled public gatherings, and restricted travel. At one stage, over 91.3% of students worldwide, from pre-primary through tertiary education, were impacted by school closures. In the United States, many institutions continue to provide remote and hybrid learning options throughout the 2021-2022 academic year. Attempts to mitigate Covid-19 through mass remote instruction has provided unique opportunities for researchers to examine the resources teachers utilize to drive and supplement their practices. In this report, I describe remote instruction’s ongoing impact on grades 6-12 mathematics teachers and their students in rural area and small-town schools in the Midwestern United States. ======================================================= Mili Das Building on the Past to Prepare for the Future - Impact of Teaching Skills and Professionalism to Reduce Mathematics Phobia https://doi.org/10.37626/GA9783959872188.0.025 First page: 134 Last page: 138 Abstract In India mathematics is a compulsory subject for the primary, upper primary and secondary classes. In secondary school curriculum among the compulsory subjects MATHEMATICS is the most vital subject and at the same time it is the most difficult one as per the learners’ opinion as well as the parents. So, the subject is neglected by many students and as a consequence Mathematics Phobia is often developed in the students’ mind. There are many more factors which are connected to this growing distaste in learning mathematics like in appropriate curriculum organization, methodology of teaching, teachers’ knowledge, assessment techniques [Das,M.2010] and management of classroom environment. The said problem is not a new one but in present teachers’ training course special attention is given on it. In this paper author will discuss that how the teaching skills and teachers’ professionalism can create a positive environment to motivate students. Keywords: Mathematics Teacher, Learners, Curriculum, Professionalism ======================================================= Thomas P. Dick Combining Dynamic Computer Algebra and Geometry to Illustrate “the most marvelous theorem in mathematics” https://doi.org/10.37626/GA9783959872188.0.026 First page: 139 Last page: 144 Abstract Dynamic geometry software (DGS) allows for constructions and measurements that instantly update when a virtual geometric figure is manipulated. Likewise, dynamic computer algebra systems (CAS) enable symbolic calculations that instantly update when an expression or equation is altered. Linking geometric objects to symbolic parameters combines these two powerful tools together. We will illustrate a unique feature of “locked” measurement in a special DGS to create a Steiner ellipse. We then illustrate the use of a dynamic CAS to create dynamic first and second derivative zeroes of a cubic function whose zeroes can be graphically manipulated. Finally, we will link a dynamic geometric construction based on these zeroes to illustrate the Siebeck-Marden Theorem, an astounding result that has been justifiably called “the most marvelous theorem in mathematics.” ======================================================= Hamide Dogan, Angel Garcia Contreras & Edith Shear Geometry, Imagery, and Cognition in Linear Algebra https://doi.org/10.37626/GA9783959872188.0.027 First page: 145 Last page: 150 Abstract This paper discusses features of five college-level linear algebra students’ geometric reasoning, revealed on their interview responses to a set of predetermined questions from topics relevant to linear independence ideas. Our qualitative analysis identified three main themes (Topics). Each theme, furthermore, revealed similarities and differences, providing insight into technology’s potential effect. ======================================================= Ann Dowker, Olivia Cheriton & Rachel Horton Age Differences in Pupils’ Attitudes to Mathematics https://doi.org/10.37626/GA9783959872188.0.028 First page: 151 Last page: 156 This study investigated children’s and adolescents’ attitudes to mathematics, with a particular focus on whether and how these are affected by age and gender. 216 pupils from Years 2, 6, 9 and 12 participated in the study. They were given (1) the Mathematics Attitude and Anxiety’ questionnaire (Thomas & Dowker, 2000), which assesses levels of maths anxiety; unhappiness at failure in maths; liking for maths, and self-rating in maths; and (2) the British Abilities ScalesNumber Skills Test to establish actual mathematics performance. Age had a significant effect on both liking for maths and selfrating in maths: older children were lower than younger children in both. Gender had a significant effect on self-rating: boys rated themselves higher than girls, though there was no significant gender difference in mathematical performance. Self-rating, but not anxiety, predicted mathematics performance. ======================================================= Alden J. Edson & Elizabeth Difanis Phillips The Potential of Digital Collaborative Environments for Problem-Based Mathematics Curriculum https://doi.org/10.37626/GA9783959872188.0.029 First page: 157 Last page: 162 Abstract In this paper, we present an overview of the design research used to develop a digital collaborative environment with an embedded problembased curriculum. We then discuss the student and teacher features of the environment that promote inquiry-based learning and teaching. ======================================================= Belinda P. Edwards Learning to Teach Mathematics using Virtual Reality Simulations https://doi.org/10.37626/GA9783959872188.0.030 First page: 163 Last page: 168 Abstract Researchers (Lampert, et al., 2013; Zeichner, 2010; Grossman, et al., 2009a) recommend the use of rehearsals in teacher education classrooms to help preservice teachers (PST) bridge theory to practice. Rehearsals enable PSTs to practice teacher moves, such as asking purposeful questioning and engaging students in mathematical discourse during an episode of teaching a lesson (NCTM, 2014). During a rehearsal, the PST’s teacher education instructor provides coaching that helps the PST make flexible adjustments to their instruction. Using a phenomenological approach, this research investigates the use of Virtual Reality (VR) simulations to support PSTs learning to teach mathematics through rehearsals. The presentation will include samples of PSTs’ mathematics teaching episodes with attention to successes, challenges, and lessons learned from the use of VR simulations in teacher education classrooms. ======================================================= Allison Elowson, Kristen Fye, Gregory Wickliff, Christopher Gordon, Alisa Wickliff, Paul Hunter & David Pugalee Student Research in a Mathematics Enrichment Program https://doi.org/10.37626/GA9783959872188.0.031 First page: 169 Last page: 174 Abstract Increasing emphasis is placed on the development of research skills for students in STEM content areas. As part of a four-week summer enrichment program, 24 high school students participated in a mathematics course highlighting the historical development of mathematics through the lens of history and culture. Each student designed and conducted their own research study under the mentorship of instructors with expertise in mathematics, writing and technical communication, and student research. This paper presents a case study of one project selected on the basis of strong performance in meeting course goals. Data demonstrates the mathematical understanding of the student researcher, their scientific literacy and research skills, and their mathematical communication. The student prepared both a paper and a poster to report their research study. ======================================================= Antonella Fatai Improving Relational and Disciplinary Competences by Rondine Method https://doi.org/10.37626/GA9783959872188.0.032 First page: 175 Last page: 180 Abstract The present work describes an educational experience, being implemented since 2015, based on the Rondine Method application in mathematics teaching. This experience has involved 135 students from State Schools throughout Italy. The general method was developed by an Italian research team aiming at resolving conflicts in situations of contrast. The goal of the work is highlighting how the care of relationships may be a means for overcoming difficulties in mathematics. Below we describe activities referring to the general principles of active education and of socio-constructivism, which are oriented to train students both in learning by action and participation, and in bringing their own contribution to the whole class work. ======================================================= Courtney Fox Integrating Mathematics and Science: A Plan for a High School Integrated Pre-Calculus and Physics Course https://doi.org/10.37626/GA9783959872188.0.033 First page: 181 Last page: 185 Abstract This paper explores the integration of mathematics and science as a means to improve learning for high school students. Scholars have acknowledged the benefits of integration for over 50 years, but in the United States we have failed in large measure to adopt an integrative curriculum. This work provides a corrective to this problem by creating a practical curriculum for an integrated Pre-Calculus and Physics course with suggestions for implementation in any school. ======================================================= Kathy R. Fox Building an Understanding of Family Literacy: Changing Perspectives Regarding Authentic Learning Opportunities in the Home https://doi.org/10.37626/GA9783959872188.0.034 First page: 186 Last page: 191 Abstract Home to school engagement has often been a one-way path, with teachers seen as facilitators only. When schools were forced to rapidly switch to virtual instruction, teachers were suddenly entering kitchens, living rooms and other spaces to deliver virtual instruction. Findings from this qualitative study of eleven practicing teachers showed new teaching opportunities through virtual home visits. Doors were literally and figuratively opened as teachers became beneficiaries of cultural and academic practices in the home. Math instruction took on a real-world quality, as teachers were privy to home environments for authentic teaching materials. As schools open and teacher, parent, and caregiver relationships return to a more distant space, these participants described small but significant changes in the way they continued to engage parents and caregivers after the experiences of the virtual home visits. ======================================================= Grant A. Fraser Mathematics for Living: A Course that Focuses on Solving Problems in Today’s World https://doi.org/10.37626/GA9783959872188.0.035 First page: 192 Last page: 195 Abstract The author has developed and taught a course for University students who are not specializing in mathematics, science, or engineering. In contrast to traditional courses of this type, this course focuses on topics from the real world that students will encounter in later life. The aim of the course is to provide students with mathematical tools that they can use to create meaningful, practical solutions to problems that arise in these topics. Students work individually on projects and present their solutions in class. Other students then critique these solutions. With practice, students develop the skills necessary to analyze more complicated kinds of problems. A final project enables students to use their newly acquired techniques to deal with more realistic problems. The author discusses the content of the course and the impact it has had on students. ======================================================= Toshiakira Fujii Roles of Quasi-variables in the Process of Discovering Mathematical Propositions https://doi.org/10.37626/GA9783959872188.0.036 First page: 196 Last page: 201 Abstract The purpose of this paper is to clarify roles of quasi-variables by focusing on the process of discovering mathematical propositions. For this purpose, the author analyzed the assignment reports of third-year undergraduate students. As a result, the author found that looking back is important in the generalization-oriented inquiry process, but it is not enough. It is important to re-examine the found matter and its form of expression from the perspective of a new concept. In the process of looking back and re-examine, it was confirmed from the description of the metacognitive part of the students that the use of quasi-variables clarified the object of consideration and made it easier to clarify which numbers contributed to the generalization and expansion in what sense. ======================================================= Ben Galluzzo, Katie Kavanagh, Karen Bliss, Michelle Montgomery & Christopher Musco Math Modelling: Common Pitfalls and Paths for Student Success https://doi.org/10.37626/GA9783959872188.0.037 First page: 202 Last page: 207 Abstract Mathematical modelling refers to the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight. There is a distinction between applying a formula and the actual creation of a mathematical relationship. Approaching open-ended problems can be challenging for students. In this two part workshop, we first share examples of how students can get off-track while creating models, in particular making choices or assumptions that undermine the solution quality. In the second part, we demonstrate how to facilitate authentic math modelling so that students can be creative and innovative in the modelling process while having ownership over their solution. Participants will assess real student modelling solutions from Mathworks Math Modeling Challenge (M3 Challenge), a program of Society for Industrial and Applied Mathematics (SIAM), and discuss ways that they would advise teams towards improvement. ======================================================= Parker Glynn-Adey &Ami Mamolo Modelling Beauty: Hands-on Experiences in Group Theory https://doi.org/10.37626/GA9783959872188.0.038 First page: 208 Last page: 213 Abstract In the 19th century, geometric models were valued as tools for exploring complex mathematics. Quartic surfaces and hyperboloids elaborately modelled with plaster gave access to powerful ideas and brought alive wonderful new mathematics. In this workshop, we explore a diverse set of geometric models that capture mathematical beauty and we showcase how they can be used to bring alive wonderful new-for-students mathematics. We discuss the value of these experiences for fostering mathematical ways of being that can help disrupt preconceived notions about a homely, rote and rigid nature of mathematics, and capture some of the visual richness of older mathematical models. ======================================================= Gerald A. Goldin, Lisa B. Warner, Roberta Y. Schorr & Daniel Colaneri Exploring Prospective Mathematics Teachers’ Motivating Desires during Group Problem Solving Activity https://doi.org/10.37626/GA9783959872188.0.039 First page: 214 Last page: 219 Abstract Earlier research has characterized recurrent patterns of cognition, affect, and behavior during in-the-moment mathematical activity. Each pattern, termed an “engagement structure,” is named by a specific motivating desire that evokes it: e.g., Get The Job Done, I’m Really Into This, Value My Culture, etc. This study explores prospective teachers’ motivating desires as they engage in small-group problem solving sessions. Participants were enrolled in courses required for teaching certification at two eastern U.S. state universities. Based on survey, individual interview, and focus group data, we identify the most frequently occurring desires, their perceived importance and accompanying emotional feelings. We present and discuss some findings briefly, including the motivating desire to Carry My Weight with a team of peers. ======================================================= John Gordon & Kehinde Emmanuel Adenegan Are Abstract Mathematical Thinkers Born or Can They Be Trained? https://doi.org/10.37626/GA9783959872188.0.040 First page: 220 Last page: 224 Abstract Abstract mathematical thinkers in the fields of pure Mathematics and theoretical computer science have contributed significantly to the body of knowledge that has fundamentally altered the course of human civilization and technological advances. This paper explores whether these thinkers are naturally gifted or if there are pedagogical strategies that can be implemented that will bring about the same outcomes. Keywords: Abstract, critical, thinkers, Mathematics ======================================================= John Gordon Reuniting Exponents and Logarithms: Teaching Exponents, Inverse functions, and Logarithms, as one Cohesive Pedagogical Unit https://doi.org/10.37626/GA9783959872188.0.041 First page: 225 Last page: 230 Abstract Exponents, inverse functions, and logarithms are fundamentally important concepts in almost every branch of technical science. However, they are not taught together as a cohesive, comprehensive, pedagogical unit in many instances. As a result, students lose deep insight into their meaning and applicability. Additionally, particularly in the concept of the inverse function, the richness, and beauty inherent in the concept are reduced to a purely mechanical process. This paper seeks to remedy this situation by outlining a pedagogical strategy that links exponents, inverses, and logarithms together in such a manner as to preserve their natural dependence, coherency, and logic. Keywords: Exponents, inverse, functions, logarithms. ======================================================= Debra Hydorn Infographics to Develop Graphical Literacy https://doi.org/10.37626/GA9783959872188.0.042 First page: 231 Last page: 236 Abstract Tools for easily creating infographics are widely available, both online and through statistics, mathematics, and other programs. Determining the appropriate graphs to produce for different kinds of data is an important skill for students at all levels to learn, as is determining the best graph for a specific audience. With the increased availability of data comes the increased expectation that researchers in all disciplines can effectively communicate their findings to a wide range of audiences. Experts in graphical design have defined aspects of “graphical excellence,” but the effectiveness of graphically portrayed information depends a great deal on the needs and abilities of the intended audience. To create effective graphs, students not only need to be familiar with tools for creating graphs, they also need to be familiar with the communication, cognitive, and aesthetic principles associated with infographic design. ======================================================= Andrew Izsák Foregrounding Multiplicative Structure in Essential Calculus Topics https://doi.org/10.37626/GA9783959872188.0.043 First page: 237 Last page: 242 Abstract Approaches to calculus have emphasized limits, derivatives, and integrals, among other topics. Yet, across different approaches, the subject continues to pose significant challenges. The present study reports a new approach to calculus that takes multiplicative structure as an equally essential topic that is often overlooked or taken for granted. In an experimental course, 18 college students learned to reason about multiplication understood as coordinated measurement with two different units and proportional relationships understood from the variable-parts perspective. They then worked with piecewise linear functions and step functions to derive key calculus results. A first strand involved division, proportional relationships, slopes of lines, function composition, and the chain rule. A second strand involved multiplication, areas, inversely proportional relationships, and integration by substitution. ======================================================= Brian L. Johnson & Ioannis Gkigkitzis Interesting Facts about Terminating Decimals https://doi.org/10.37626/GA9783959872188.0.044 First page: 243 Last page: 248 Abstract The set of rationals is dense in R. In fact, this is even true for the smaller family of terminating decimals. Unlike density ratios in the physical world, this is an absolute property implying that infinitely many such decimals exist in even the smallest intervals we can imagine. However, it is possible to construct this infinite density in an increasing sequence of finite densities--starting with the discrete set of integers. While the terminating decimals do not seem to receive as much formal discussion as Z, Q and R, they are an essential part of the mathematics curriculum, from elementary school through college. Keywords: integers, rational numbers, algebra, density. ======================================================= Iris DeLoach Johnson Exploring a Collection of Approachable, Stimulating and Thought-Provoking Problems: Face-to-Face or Virtual? Related or not? https://doi.org/10.37626/GA9783959872188.0.045 First page: 249 Last page: 253 Abstract Students thrive when engaged in solving problems that they find to be approachable, stimulating, and thought-provoking. This workshop includes many such problems with various real-world and contrived contexts. Participants will work in groups to find the solutions as well as identify similarities and contrasts among the problems. We will explore whether there are related mathematical concepts (e.g., algebra, discrete mathematics, geometry) or mathematical processes (reasoning, connecting, communicating, representing, problem-solving, selecting tools and strategies). Many of these problems are taken from resources published broadly for students from ages 11-19+. We will compare our findings and experiences with those of school students and discuss use of technology in both face-to-face and online settings: from the past to the future! Keywords: problem-solving, reasoning, communication, collaboration, algebra, representations, Chalk Talk, Thinker-Doer problems ======================================================= Gibbs Y. Kanyongo, Nandini Bhowmick & Erika Williams Structural Equation Modeling: Focus on Confirmatory Factor Analysis https://doi.org/10.37626/GA9783959872188.0.046 First page: 254 Last page: 255 Abstract This workshop will expose participants to the statistical technique of Structural Equation Modeling (SEM), with a focus on confirmatory factor analysis (CFA), using the statistical software AMOS. Structural equation modeling is a multivariate statistical analysis technique that is used to analyze structural relationships. Confirmatory Factor Analysis examines whether collected data fit a hypothesized model of what the data are meant to measure. It is the measurement part of SEM, which shows relationships between latent variables and the observed variables. ======================================================= Anna Khalemsky & Yelena Stukalin Combining Various Data Mining Techniques in Binary Classification Teaching https://doi.org/10.37626/GA9783959872188.0.047 First page: 256 Last page: 260 Abstract Binary classification is one of the most common data analytics tasks. It appears in a wide range of applications including finance, sociology, psychology, education, medicine, and public health. In statistical and analytics courses, binary classification is usually handled by logistic regression. Other alternatives, such as decision trees, neural networks, and Naïve Bayes are not commonly taught in traditional undergraduate programs. We suggest making these methodologies accessible as alternatives or complementary approaches to binary classification. We treat the teaching of the subject as a dynamic process that involves the understanding of the analytical task, understanding terms and concepts, visualizing, analyzing, interpreting the results, and decision making. ======================================================= Richard Kitchen Leveraging Pólya’s Heuristic to Support Mathematical Reasoning and Language Development https://doi.org/10.37626/GA9783959872188.0.048 First page: 261 Last page: 266 Abstract An iteration of an instructional framework designed to provide emergent bilinguals (EBs) with opportunities to simultaneously engage in mathematical reasoning and learn the language of mathematics is illustrated in this paper. The “Discursive Mathematics Framework” (DMF) builds on Pólya’s iconic problem-solving heuristic by integrating research-based “language practices” and essential teaching practices. Videotapes and student work from problem solving lessons were examined using grounded theory methodology to illustrate the development of the DMF. Theoretically, this study contributes to the literature by providing explicit examples of how practices that promote mathematical reasoning and the learning of the language of mathematics can be taught concurrently during problem solving lessons. ======================================================= Sergiy Klymchuk An Innovative Way of Teaching and Assessing Critical Thinking in Mathematics https://doi.org/10.37626/GA9783959872188.0.049 First page: 267 Last page: 272 Abstract This paper deals with the use of deliberately misleading mathematics questions in teaching and assessment as an innovative pedagogical strategy. The intention of using such questions is to enhance students’ critical thinking. Critical thinking is understood here as “examining, questioning, evaluating, and challenging taken-for-granted assumptions about issues and practices” as defined by the New Zealand Ministry of Education. The study is based on a survey of 82 secondary school mathematics teachers who attended introductory workshops on the suggested pedagogical strategy at their regional conferences. Although the vast majority of the participants (96%) agreed to use such strategy in teaching, only 63% percent of the participants were willing to use it in assessement. Teachers’ attitudes are analysed in the paper. Key words: critical thinking, assessement, school mathematics teachers. ======================================================= Allison M. Kroesch & Albert Otto Magic Throughout the Years https://doi.org/10.37626/GA9783959872188.0.050 First page: 273 Last page: 276 Abstract Too often teachers use the word “trick” in their mathematics lessons. There are no tricks in mathematics, but there are explanations for what appears to be a trick. Throughout this paper, we will address this history of magic, including the history of playing cards. ======================================================= Aradhana Kumari Do not Teach the Symbols in Mathematics, Teach the Meaning of the Symbols https://doi.org/10.37626/GA9783959872188.0.051 First page: 277 Last page: 282 Abstract Unnecessary use of symbols in introducing ideas in mathematics makes it difficult to learn. From a student's perspective, these symbols are the hurdle for them to understand the concepts/ideas in mathematics. One example is when we ask students the following: What is the meaning of the square root of a number, often their reply is the symbol √. This shows that they did not understand the actual meaning of the square root of a number, which is the number raised to power one-half. I will present many examples and show how we can avoid using unnecessary symbols and teach the ideas and concepts in mathematics. ======================================================= Sebastian Kuntze, Marita Friesen, Jens Krummenauer, Karen Skilling, Ceneida Fernandez, Pere Ivars, Salvador Llinares, Libuše Samkova & Lulu Healy Support for Mathematics Teachers through Representations of Practice - Vignette-based Approaches in the Project coReflect@maths https://doi.org/10.37626/GA9783959872188.0.052 First page: 283 Last page: 288 Abstract Teachers' analysis of vignettes can be a key for connecting specific classroom situations with mathematics education theories. As vignettes are representations of practice with relevance for professional requirements of the mathematics classroom, vignettes also represent or portray meaningful theoretical elements. The use of vignettes in pre-service and in-service teacher professional development needs, however, conceptual and evidencebased exploration. Building on prior work with video, text, and cartoon vignettes, the project coReflect@maths aims at exploring the potentials of vignette-based work both for supporting professional learning and for research into aspects of mathematics teachers' expertise. Key aspects of the project work will be presented. ======================================================= Barbara H. Leitherer, Pankaj R. Dwarka, Entela K. Xhane & Jignasa R. Rami Undergraduate Research in a 2-Year College: Climate Change, Global Learning, Process and Observations https://doi.org/10.37626/GA9783959872188.0.053 First page: 289 Last page: 294 Abstract In order to thrive and be successful in an increasingly interconnected world, 21st century students require multiple opportunities to engage with global learning (Landorf et al., 2019). Mathematics faculty guided 2-year college honors students in the US through an independent study analyzing real-world global climate change data supplied by the World Wildlife Fund (WWF). This proposal will elaborate in depth about the undergraduate research process, lessons learned, and observations made. Presenters will reflect on strategies used to support both collaborative and independent learning; how students increased their awareness of climate change as a global problem; how this contributed to students’ ownership, success and enhancement in undergraduate research leading to preparedness for further education and a successful career in science, technology, engineering, and mathematics. ======================================================= Hadas Levi Gamlieli, Alon Pinto & Boris Koichu Secondary-Tertiary Transition and Effective Ways of Coping with it: A Perspective of Lecturers https://doi.org/10.37626/GA9783959872188.0.054 First page: 295 Last page: 300 Abstract The secondary-tertiary transition (STT) in mathematics education is a longstanding concern. This study explores university mathematics lecturers’ perspectives on the challenges underlying STT and on the effectiveness of university-level coping measures currently employed. The analysis of 311 responses to an international survey suggests that there is considerable variability regarding the prevalent perspectives on STT among university lecturers. While most respondents recognized school-related factors, the coping measures they recommended were mainly university-related. The findings stress the need to improve communication, both between university mathematics lecturers and the school mathematics education community, and across universities, for promoting comprehensive initiatives to address STT. ======================================================= Sigal Levy & Yelena Stukalin Introducing Main Statistical Concepts to Non-statisticians https://doi.org/10.37626/GA9783959872188.0.055 First page: 301 Last page: 303 Abstract In this paper we present and discuss the results of an academic open-end mid-term statistics exam given to high-school teachers qualifying to teach Mathematics at a matriculation-exam level. The exam focused mainly on defining and understanding key terms and concepts in statistical inference. The purpose of this study is to identify what questions would be good predictors of the overall score, thus indicating a good understanding of statistics. Item analysis showed that the ability to properly define a parameter, state research hypotheses and interpret the findings were more inclined to do well in the exam. Keywords: Statistical concepts, teaching statistics, non-statisticians ======================================================= Nicole Lewis, Ryan Andrew Nivens, Jamie Price, Jennifer Price & Anant Godbole Pandemic-Driven Mathematical Initiatives within the East Tennessee State University Center of STEM Education https://doi.org/10.37626/GA9783959872188.0.056 First page: 304 Last page: 309 Abstract We describe three Mathematics Education initiatives launched as a result of the global pandemic. (i) The Eastman-funded MathElites professional development (PD) program for K-8 teachers was offered online. Teachers were vastly more involved due to their greater autonomy. Old outcomes and those from 2020 will be compared. (ii) ETSU’s Governor’s School, which offers high school students Statistics and Biology college courses, went online too, and we used Columbia University Virology lessons and Covid19 data sets to make the courses more engaging to students. Student projects were assessed to be of a higher quality than in years past. (iii)With Niswonger Foundation support,we have launched a PD thrust for teachers in 2021, in the new areas of Epidemiology, Artificial Intelligence, and Statistics-with-R. ======================================================= Po-Hung Liu Students’ Perceptions of Paradoxes of the Infinity https://doi.org/10.37626/GA9783959872188.0.057 First page: 310 Last page: 315 Abstract Infinity is a significant element for understanding calculus, yet studies consistently suggest that its counter-intuitive nature confused college students. The purpose of this study was to investigate Taiwanese college students’ perceptions of paradoxes of the infinity and observe how their perspectives shifted back and forth while facing contradictory facts. It was found the 1-1 correspondence was the most used criterion for comparing the cardinality of infinite sets, which is somewhat different from previous studies, and students’ reasoning on Zeno’s paradoxes was feeble. The study suggests future research of this line should pay attention to the dialectical process of students’ discourse to detect their core beliefs about the infinity. ======================================================= Hong Lu & Xin Chen The Relationship between Teacher-student Relationship, Interest, Self-efficacy and Mathematics Achievement – Does Gender Play a Role in it? https://doi.org/10.37626/GA9783959872188.0.058 First page: 316 Last page: 321 Abstract This study compared the mechanism by which the teacher-student relationship (TSR) affects mathematics achievement in different gender groups through interest and self-efficacy in mathematics. The results suggest that (1) in both samples, TSR positively predicted interest and self-efficacy, interest positively predicted self-efficacy, and self-efficacy in turn positively predicted mathematics achievement; (2) Gender differences were also detected; The positive relationships of TSR to self-efficacy, and interest to self-efficacy, were stronger among the male than the female students. Overall, the findings confirm that TSR have an important influence on Chinese students’ mathematics academic motivation and achievement and that gender differences affect the patterns of these relationships. Possible explanations for the results and practical implications are discussed. Key words: teacherstudent relationship, interest, self-efficacy, mathematics achievement, crossgender comparison. ======================================================= Cheryl Ann Lubinski & Allison Kroesch Developing, Not Teaching, Problem-Solving Strategies https://doi.org/10.37626/GA9783959872188.0.059 First page: 322 Last page: 324 Abstract Many teachers use explicit instruction to teach students how to solve a problem and then have their students practice a specific strategy. Research indicates this type of teaching does not necessarily improve problem solving skills. Students need to solve problems using their intuitive strategies which might include pictures and concrete materials. For a specific problem, we will share the strategies used by students in the United States, 17-year-old brothers and their family in Poland, and teachers of students ages 5-17 in Zimbabwe. Findings indicate that most people do not choose a picture strategy but a trial-and-error strategy using symbols. Most are unsuccessful at solving the problem. We will share teaching strategies that encourage developing, not teaching, problem-solving strategies. ======================================================= Jürgen Maaß Professional Mathematical Modelling: What we can Learn about Teaching Real World Mathematics from the Real Application of Mathematics in our World? https://doi.org/10.37626/GA9783959872188.0.060 First page: 325 Last page: 330 Abstract lessons, more motivation and a more sustainable learning success. Professional mathematical modelling is an important foundation for modern, technology-based societies. We are all significantly influenced by the results of mathematical modelling. The decisions for lock down, masks and travel restrictions in connection with Corona are a current example. This article drafts what we as teachers & researchers can learn about successful mathematical modelling from professional working mathematicians who are using & applying mathematics in the natural sciences, technology development, medicine, economics, social and humanities research & practice, consultancy for politics, the financial world & other economic sectors). The background for this article is my research on mathematics as a technology, its acceptance as a concept and ways of technology transfer, as well as decades of experience with colleagues from industrial mathematics (https://www.indmath.uni-linz.ac.at/) and the RISC (https://www.jku.at/institutfuer-symbolisches-rechnen-risc/anwendungen/risc-software-gmbh/) who started their work here in Linz a long time ago. As a co-founder and co-organizer, I organized and enjoyed many lectures on mathematics and society, industrial mathematics, etc. at the Johannes Kepler Symposium (https://www.numa.unilinz.ac.at/JKS/2020/ ======================================================= Jodelle S. W. Magner & Susan McMillen Making Word Problems Accessible to All: Innovating through Meaningful Models https://doi.org/10.37626/GA9783959872188.0.061 First page: 331 Last page: 332 Abstract Working with a large urban district over 14 years of Mathematics Science Partnership [MSP] grants, over 500 teachers of mathematics, special education teachers, mathematics coaches and administrators have come together to create engaging mathematics within grade 3 through 12 classrooms.Workshop participants will engage with an innovative use of a mathematical model and learn how it makes mathematics more accessible to students at all levels, especially to English Language Learners. Workshop participants will experience the use of the model in a variety of problem-solving contexts. Obstacles to teachers adopting these materials to use within their instruction and strategies used to overcome these challenges will be discussed. ======================================================= Rafael Alberto Méndez-Romero & María Angélica Suavita-Ramírez The mINNga Labs: an Initiative of the Universidad del Rosario to Strengthen STEM Skills, Social Sensitivity and Youth Empowerment in Colombia https://doi.org/10.37626/GA9783959872188.0.062 First page: 333 Last page: 337 Abstract The challenge of educating the generation of the digital age leads us to resort to pedagogical innovations that are sensitive, empathetic, analytical and multidisciplinary in nature. Additionally, these new student communities are characterized by appropriating causes, mobilize, manifest and are genuinely curious, which confronts us as educators with a greater and fascinating challenge. On the other hand, the historical moment of Colombia forces us to seek the unity of the country and generate a sum of forces from the specific talents of the people in the regions, to solve, as a body, the emerging needs of the moment. In this article we show a technological pedagogical innovation designed at the Universidad del Rosario, which is based on strengthening STEM skills and youth empowerment through the use of our mINNga labs, a version of a living laboratory as a social an open innovation. ======================================================= Jennifer Missen A Process for Updating Mathematics Teaching for 21st Century Students https://doi.org/10.37626/GA9783959872188.0.063 First page: 338 Last page: 343 Abstract It is inevitable and necessary that the curriculum, pedagogy, and school and classroom structures for the teaching of Mathematics will continue to change over the next 30 years. However, teachers are time poor, there are more and more who are teaching Mathematics when it is not their primary content area, and who may have knowledge of Mathematics but not the current pedagogical knowledge. Early career teachers need support in building a portfolio of tools and resources that work for them and their students. Experienced, traditional teachers are more comfortable with direct teaching and mastery practice and, understandably, are resistant to change. Inquiry based teaching and collaborative strategies, differentiated and tailored for the class and its individuals, combined with direct teaching and mastery practice, allow for greater equity and increased preparation of students for the ever-changing workforce. This two part workshop has participants work through the process of transitioning existing, traditional or textbook units of work to flexible, differentiated units with enough detail and resources to support any teacher to walk into the classroom knowing that they will serve all the students well. ======================================================= Shelby Morge & Christopher Gordon Using Squeak Etoys to Model Mathematical Ideas https://doi.org/10.37626/GA9783959872188.0.064 First page: 344 Last page: 349 Abstract Effective mathematics instruction involves students in making sense of mathematical ideas and reasoning mathematically (NCTM, 2014). Unfortunately for many US students in grades 6-8 (ages 10-14), mathematics is a repeat of topics learned in elementary school with an emphasis on computation. For this reason, students start to see mathematics as something that is hard to understand and not enjoyable. In this workshop, we share how a technology tool, Squeak Etoys, was used in a lesson to engage grade 6-8 students in discovering the relationship between the number of sides and the angle measure in regular polygons. We describe a lesson implementation and engage participants in the development of a Squeak Etoys computer model. In addition, conclusions related to mathematics instructional practices are shared. Key words: Squeak Etoys, modeling, problem solving, lesson,geometry, polygons ======================================================= Janina Morska New Methods and Forms of Work during Online Maths Lessons https://doi.org/10.37626/GA9783959872188.0.065 First page: 350 Last page: 353 Abstract In more than 38 years as a mathematics teacher, I have always tried to look for interesting methods and new forms of work. I wondered how to explain the new material to students so that they would understand and be able to use the information in the future. The previous school year has been a huge challenge in the field of distance learning. From October 2020 to May 2021, all teachers in Poland conducted Online lessons. As a result, we had to switch from traditional classroom teaching to online teaching. So I decided to look for appropriate tools and solutions of how to conduct such lessons. Keywords: online learning, distance learning, applications, computer programs, teaching materials, virtual notes, IT tools, online mathematics. ======================================================= Patricia S. Moyer-Packenham Relationships among Semiotic Representational Transformations and Math Outcomes in Digital Games https://doi.org/10.37626/GA9783959872188.0.066 First page: 354 Last page: 354 ======================================================= Svenja Müller & Anna Fath-Streb Risk Literacy in the Context of Stochastics and Mathematical Education https://doi.org/10.37626/GA9783959872188.0.067 First page: 355 Last page: 360 Abstract The purpose of this risk literacy study was to explore the ways of integrating examples of global challenges into mathematics education. The examples follow an approach to introduce risk literacy in teacher education along with a curriculum analysis for secondary education in Germany to include risk literacy within the given requirements and constraints. Two main examples, microplastic pollution and extreme events due to climate change, are analysed in the interdisciplinary context of global challenges and their understanding of mathematical knowledge for teaching and learning stochastics. ======================================================= M. Estela Navarro Robles Elementary Teachers Reaching a Quasi-complete Knowledge of Rational Numbers through an Online Course https://doi.org/10.37626/GA9783959872188.0.068 First page: 361 Last page: 366 Abstract There is evidence that most of the Elementary Teachers in Mexico have various conceptual deficiencies in their knowledge about rational numbers; however, the deficiencies were not the same in all the cases. So, we decided to design a non-traditional-personalized online course, constructed as an adaptative system, in which it was identified if the participant covered each one of the different conceptual approaches in various contexts. When it was identified that a conceptual approach was not covered, interactive materials and videos were presented to them that allowed them to understand what they had not covered. The aim of the course is to enable teachers to reach a quasicomplete conceptualization, whose meaning for us it is to understand the topic from different conceptual approaches in a deep way. This paper presents the structure of one module of the course, one detailed example, and results of the pilot test of this module. ======================================================= Benita P. Nel Noticing through Self-reflection by Mathematics Teachers using Video Stimulated Recall https://doi.org/10.37626/GA9783959872188.0.069 First page: 367 Last page: 372 Abstract Continuous professional development should be navigated in a teacher’s own context, addressing their particular needs where timeous feedback can be of great benefit. However, the major teachers’ union in South Africa hindered government officials to enter the classroom, limiting support. Most professional development (PD) initiatives are thus off-site and not always customised to the needs of the individual teacher. In this study, the use of Video-stimulated recall (VSR) was used as a PD tool where self-reflection is foregrounded, reporting on one teacher. The research question was: What did the teachers notice and act upon when VSR was incorporated as a PD amongst mathematics teachers? Through Mason’s discipline of noticing the teacher’s noticing was investigated. Key Words: Video-stimulated recall, Mathematics education; continuous professional development; teacher noticing; in-house setting ======================================================= Zanele Ngcobo Evoking School Mathematical Knowledge among Preservice Secondary Mathematics Teachers through Error Analysis https://doi.org/10.37626/GA9783959872188.0.070 First page: 373 Last page: 373 Abstract This article explores how attention to Specialised Content Knowledge (SCK) could evoke the development of school mathematics concepts among pre-service mathematics teachers (PSMTs). At the heart of the repeated debate about the delivery of professional mathematics teacher education curricula has been the reported lack of development of PSMTs knowledge for teaching. However, discussion of what mathematical knowledge for teaching is needed by PSMTs and how it should be developed had been uneven. In South Africa, attention to improving the status quo of learners’ poor performances in mathematics has been directed toward improving in-service teachers’ mathematical knowledge for teaching. However, research has shown that the problem does not only emerge when teachers become practitioners. The problem of low levels performance and of understanding of school mathematics by pre-service teachers has been identified by many studies but is often not addressed during teacher training. This article explores an under-examined strategy for addressing the repeated concerns about the quality of pre-service mathematics teachers’ education. It examines how attention to specialised content knowledge (SCK) within a preservice teacher education curriculum could potentially influence deeper quality mathematical knowledge to pre-service mathematics teachers’ professionality. This is a qualitative study conducted in 2018 and 2019. Data was generated from (n=61) PSMTs that were enrolled for Bachelor of Education majoring in mathematics. Data was conducted using written task, open ended questionnaires and focus group interviews. The findings from this small-scale study showed that error analysis has the potential to influence the development of SMK. Furthermore, findings suggest that attention to SCK has the potential to evoke school mathematics concepts and the evolution of subject matter knowledge. Based on the findings it is recommended that future research should be conducted to determine the veracity of these conclusions and their generalization to other mathematical topics. Considering the suggestions made by in literature that the description of knowledge is only valid at the time of the investigation, there is a need of large scale to ascertain the effect of error analysis toward the development of PSMTs' SMK of other school mathematics topics. Keywords: Error analysis, Pre-service mathematics teachers, Specialised Content Knowledge. ======================================================= Jenna O’Dell & Todd Frauenholtz Recruiting Mathematics and Mathematics Education Majors to a University https://doi.org/10.37626/GA9783959872188.0.071 First page: 374 Last page: 377 Abstract This paper will present strategies used to recruit students to a four-year university to complete a double major in mathematics and mathematics education, then enter the teaching field. The recruiters are two professors who work in both the Mathematics and Education departments at a university in the United States. The mathematics department has been especially supportive of the initiative as it will double the number of mathematics majors in their programs for two years from four to nine students. The recruiting included contacting community colleges, professional organizations, word of mouth, the university marketing department, and visits to collegiate mathematics classrooms at the level of calculus and above. This project was supported by The National Science Foundation (NSF) as a Noyce project and will support students financially with full cost of attendance for the final two years of the four-year program. ======================================================= Elizabeth Oldham & Aibhín Bray Undergraduate Mathematics Students’ Reflections on School Mathematics Curricula after a Major Curriculum Change in Ireland https://doi.org/10.37626/GA9783959872188.0.072 First page: 378 Last page: 383 Abstract After decades in which the Irish post-primary (grades 7-12) mathematics curriculum changed incrementally, a major innovation project was approved in 2008, and a “reform”-type curriculum was phased in over several years. The project was controversial, and some students developed negative attitudes to the change. This paper examines recent students’ opinions: in particular, the opinions of mathematics undergraduates who had experienced the transition and who took a Mathematics Education module at one Irish university in 2019- 20. They studied old and new curriculum documents and examination papers, and watched videos of reform-type lessons; their reflective comments were posted to a discussion board. Thematic analysis of posts from the 18 (out of 25) students who gave permission for use of their work in research indicates that, by then, these students supported many aspects of the reformed curriculum. ======================================================= Nick Vincent Otuma Mismatch between Spoken Language and Visual Representation of Mathematical Concepts https://doi.org/10.37626/GA9783959872188.0.073 First page: 384 Last page: 388 Abstract This paper examines secondary students’ mismatch in meaning between spoken language and visual representation of mathematical concept of a rightangled triangle. Forty-eight students, age 16-17years participated in the case study. Students were asked to select plane figures that matched the descriptions given on each questionnaire item. In group interview, participants were asked to give properties of selected plane figures and draw a diagram representing the same plane figures. The results of this research suggested that many students had similar imperfect conception of a right-angled triangle. Keywords: Mathematical language, conceptual understanding. ======================================================= Jenny Pange & Alina Degteva Project-based Learning in Statistics https://doi.org/10.37626/GA9783959872188.0.074 First page: 389 Last page: 394 Abstract Online teaching process is triggered by the Covid-19, and project-based learning (PBL) goes through a new stage of development as it includes ICT tools and up-to-date teaching methods. We applied this approach in an online undergraduate course in statistics. This paper describes the process and evaluates the outcome of PBL in teaching statistics course to a group of undergraduate students at the University of Ioannina, Greece. Students had to attend the class and react to practical exercises according to the demands of the PBL. They were asked to use questionnaires and go through interviews to evaluate the teacher-to-student, student-to-student, and student-to-content interactions in PBL method. Data obtained from online questionnaire and were analysed. The results implied high level of interactions during PBL in statistics.Key words: project-based learning, statistics, ICT tools, interaction ======================================================= Andrea Peter-Koop School-Readiness in Mathematics: Development of a Screening Test for Children Starting School https://doi.org/10.37626/GA9783959872188.0.075 First page: 395 Last page: 400 Abstract The study reported in this paper involved the development of a screening test to be applied by teachers with the whole class at school entry. The goal of this screening instrument is the identification of children who are at risk with respect to their school mathematics learning and therefore need immediate support and intervention. The paper reports the results of a study with 1757 children from 97 Grade 1 classes in 39 primary schools in Germany that have been tested with the new screening, one month after starting school. ======================================================= Maria Piccione & Francesca Ricci The Importance of Early Developing Symbol-sense https://doi.org/10.37626/GA9783959872188.0.076 First page: 401 Last page: 406 Abstract In this paper we deal with the mathematical-objects symbolic representation, as a relevant educational problem. In particular, we refer to the semiotic approach, a teaching model caring the distinction among sign-meaning-sense, proposing its adoption since the very beginning of the school experience. Focusing on the development of symbol-sense means sharing relational learning principles, reconsidering usual instrumental learning ways. We aim at promoting students’ awareness in managing mathematical language, taking into account its widespread weakness, also shown by our investigation. Awareness is a powerful mental attitude which enables facing difficulties and generating a proper conception of what mathematics and doing mathematics really are, then enhancing affect. ======================================================= Maria Piccione & Francesca Ricci Activities and tools for Early Developing Symbol-sense https://doi.org/10.37626/GA9783959872188.0.077 First page: 407 Last page: 412 Abstract This work deals with practical aspects of semiotic and relational approaches in teaching/learning. It is based on the Early Algebra principle by which mental models of algebraic thought can be constructed starting with Primary School, by teaching Arithmetic algebraically. Here, the problem of the symbolic representation of mathematical objects is tackled. The aim is to allow students to clearly distinguish between the two worlds - the one of signs and the one of meanings - and to use signs of mathematical language with full awareness rather than just manipulating them. We present activities and tools which take into consideration different semiotic fields (gestural, iconic, natural, …) to achieve the mathematical field. ======================================================= Shelley B. Poole The “Yes, and…” Approach to Teaching Mathematical Modelling https://doi.org/10.37626/GA9783959872188.0.078 First page: 413 Last page: 417 Abstract Mathematical modelling can be a particularly creative tool when students are asked to solve open-ended problems. As instructors, when implementing mathematical modelling in the classroom, we can build on the ideas of our students. Utilizing the concept of yes, and... from improvisational theatre, we can foster students' creativity and empower them to take ownership of the mathematics when solving open-ended problems. Using this approach allows us an opportunity to let go of the structure of old and embrace new approaches and ideas in the classroom. ======================================================= Jordan T. Register & Christian H. Andersson Analysing PSTs Ethical Reasoning in a Data Driven World https://doi.org/10.37626/GA9783959872188.0.079 First page: 418 Last page: 423 Abstract The prevalence of Big Data Analytics as a proxy for human decision-making processes in globalized society, has catalyzed a call for the modernization of the mathematics curriculum to promote data literacy and ethical reasoning. To support this initiative, ten preservice mathematics teachers (PSTs) in Sweden (SWE) and the United States (US) were interviewed to identify what ethical considerations preservice teachers (PSTs) make in their mathematical analyses of data science contexts. Preliminary results indicate that teachers make a myriad of ethical considerations in their mathematical work that are tied to their critical mathematics consciousness (CMC), conceptions of data literacy, and experiences. As a result, it is imperative that educators simultaneously design educational curricula to foster students’ CMC and work to transform teacher held definitions of data literacy to reflect changes brought on by globalization. ======================================================= Sarah A. Roberts, Cameron Dexter Torti & Julie A. Bianchini A Mathematics Specialist Supporting District Shifts in Instruction for Multilingual Learners through Studio Days https://doi.org/10.37626/GA9783959872188.0.080 First page: 424 Last page: 428 Abstract Mathematics specialists fill a gap in providing individualized professional learning for classroom teachers, including furnishing much needed professional learning related to multilingual learners. This qualitative study examines the role a secondary district mathematics specialist in the United States played in supporting shifts in instruction for multilingual learners through the enactment of studio days professional learning. Interviews across two years with a mathematics specialist were examined. Using a framework of multilingual learner principles and adaptive reasoning, we share instructional shifts around the adaptive reasoning categories of flexibility, understanding, and deliberate practice, as related to multilingual learners. We conclude with implications for both research and practice related to secondary mathematics specialists, multilingual mathematics instruction, and studio day professional learning. ======================================================= Keith Robins Applying Mathematical Thinking Principles to Real Life Situations to Create an Objective Thinking Strategy https://doi.org/10.37626/GA9783959872188.0.081 First page: 429 Last page: 433 Abstract Teaching set thinking can make a great difference in teaching and learning mathematics as it demonstrates its relevance to real life. The following examples include how socialising is a mathematical process and how one can create a mathematical model for any experience or system rather than creating perceptions. ======================================================= Christine Robinson & Karen Singer-Freeman Digital Enhancements for Common, Online Mathematics Courses https://doi.org/10.37626/GA9783959872188.0.082 First page: 434 Last page: 438 Abstract The University of North Carolina System Office (UNC System) established the Digital Enhancement Project to rapidly develop high-quality, online course materials to support faculty and student success in online courses. Content was created for Calculus I, a course that is critical to student progress, is in high demand, and has large enrollments. To evaluate the usefulness and impact of the materials, project evaluators developed assessment instruments that included a survey for students enrolled in classes being taught by early adopters. Overall, students rated the quality of classes using project materials to be high. However, underrepresented ethnic minority students were somewhat less positive than other students and all students were less positive about the alignment of course content with course assessments than they were about other aspects of the course design. ======================================================= Ann-Sofi Röj-Lindberg Trends in Mathematics Education in Finland https://doi.org/10.37626/GA9783959872188.0.083 First page: 439 Last page: 444 Abstract Since PISA 2000 there has been a huge international interest towards education in Finland. Are there particular explanations to the PISA-success, a philosophers' stone, to be found? Is it possible to export innovative components found in Finnish schools to other countries and what exactly are these components? Is it about accessibility? Can the successful components be noticed and described? And why has the Finnish PISA-results in mathematics dropped lately? Questions like these have been asked over the years. In the paper I discuss trends in the Finnish public schooling that I find to be of particular importance and highlight changes in the curriculum and trends in mathematics education generally. I connect my arguments to research findings as well as to anecdotal stories. ======================================================= Sheena Rughubar-Reddy & Emma Engers Video Tutorials and Quick Response Codes to Assist Mathematical Literacy Students in a Non-classroom Environment https://doi.org/10.37626/GA9783959872188.0.084 First page: 445 Last page: 450 Abstract This paper discusses effectiveness of video tutorials, accessed via Quick Response codes, on Grade 10 mathematical literacy students’ ability to complete their homework. To assist them outside of the classroom, an intervention involving video tutorials explaining specific sections of work and how to go about solving problems, was devised. Students could access the relevant tutorials on a mobile device via the scanning of barcodes provided on the worksheets. The effectiveness of the intervention was assessed both quantitatively and qualitatively, through analysis of the participating students’ homework submissions and interviews with the students after the intervention had ended. Feedback from students via focus group interviews and questionnaires revealed that they found the tutorials helpful. This would indicate that the intervention was potentially beneficial. Keywords: Quick Response codes, video tutorials, homework. ======================================================= Sheryl J. Rushton, Melina Alexander & Shirley Dawson Mathematics to Teacher Education Persistence https://doi.org/10.37626/GA9783959872188.0.085 First page: 451 Last page: 456 Abstract In 2017, a university in Northern Utah’s Teacher Education and Mathematics Departments moved from a two-course mathematics requirement to incorporate a three-course mathematics requirement for Elementary and Special Education Teacher Education majors to satisfy university and Utah State Board of Education Quantitative Literacy graduation requirements. The proposed research seeks to determine how persistence rates differ from the original two-course math series to the new three-course destination series. ======================================================= Robyn Ruttenberg-Rozen In-the-Moment Narratives: Interventions with Learners Experiencing Mathematics Difficulties https://doi.org/10.37626/GA9783959872188.0.086 First page: 457 Last page: 462 Abstract Despite a significant amount of planning, so much of what occurs in mathematics teaching and learning intervention interactions, for both teacher and learner, are based on fleeting in-the-moment decisions and responses. At the root of these in-the-moment interactions are narratives that position the learner, teacher, and mathematics. In this paper I explore the interplay between in-the-moment decisions and responses, narratives, and positioning within a mathematical intervention for a learner experiencing mathematics difficulties. I use data from a mathematics intervention study of learners experiencing mathematics difficulties to show that interventions in mathematics can be a reciprocal and partnered activity. Importantly, since these narratives emerge in the reciprocal space of an intervention, narratives also evolve through the interaction. ======================================================= Tanishq Kumar Sah Extension of Theories https://doi.org/10.37626/GA9783959872188.0.087 First page: 463 Last page: 465 Abstract From an atom to this universe, from a bowl of water to the cosmic ocean this constant is present everywhere. This constant is π ( periodicity of the tangent function). For tangent function we know that tan(tan-1(x))=x, but the expression tan(ntan-1(x)) looks very complicated but is actually an expression of the type polynomial divided by another polynomial. The sine function is very important not only for graphs but for geometry too. There are some inputs whose behavior is very strange from the usual ones. Geometrical shapes and their relations are very important for many thing such as for vectors and many more but the triangle is very special because it is the least sided polygon. Riemann zeta function is very crucial for prime numbers. Infinite series related to them may be a game changer for it. Wallis’s integral formula is a boon but its domain is very constrained and needs another solution to it. ======================================================= Ishola A. Salami & Temitope O. Ajani Mathematics Songs to Hip-hop Music: Power to Engage Pupils and Improve Learning Outcomes in Primary Mathematics https://doi.org/10.37626/GA9783959872188.0.088 First page: 466 Last page: 471 Abstract Song-based strategy has been one of the most effective approaches of making learners remembering rule-governed educational contents like that of Mathematics. But the extent to which learners enjoy Mathematics songs and get engaged in it within and outside the school system is limited. Besides, many of the available Mathematics songs are for preschool while research studies have shown that learners’ scores in Mathematics started to decline from Primary IV class. One of the music types children love most is hip-hop and they easily memorize the lyrics. This led to the production of Mathematics hip-hop music with its lyrics being Mathematics principles, ideas, formulae and procedures for upper primary classes. This study determines the effectiveness of Mathematics Hip-hop music on improved Mathematics learning outcomes. Keywords: Hip-hop music, MATMUSIC, Upper primary Mathematics. ======================================================= S R Santhanam Teaching Mathematics using Storytelling and Technology https://doi.org/10.37626/GA9783959872188.0.089 First page: 472 Last page: 475 Abstract Storytelling coupled with technology is an attractive method to teach geometry. The following story was told to a set of students of the age group 14 – 16 years, who are familiar with the GeoGebra software. A pirate hid his treasures in an island and left a note for the treasure hunt to his son. The instructions are as follows. “Find two palm trees in the island with markings of a heart (🤍) on them. There will be a very small pond near them. From the pond go to one palm tree and turn 90 degrees and proceed equal distance to mark a point P on the ground. Do the same for the second palm tree to get another point Q. The treasure is hidden at the midpoint of PQ”. When his son went there, he could find the two palm trees but there was no pond nearby. But with his geometric knowledge, he could find the treasure. How? The students tried and some found the solution. In this short paper, this is discussed. ======================================================= Ipek Saralar-Aras & Betul Esen Designing Lessons for the 5th Graders through a Design Study on Teaching Polygons https://doi.org/10.37626/GA9783959872188.0.090 First page: 476 Last page: 481 Abstract It has been argued by researchers that learning about polygons is important. Student performance on polygons, particularly at the middle school level, was found to be lower than expected. Thus, this paper presents brief summaries of RETA-based lesson plans on polygons. The RETA is a maths model, which supports realistic, exploratory, technology-enhanced and active lessons. The participants of the study were 60 middle school students. Data was collected through lesson recordings of 5 lessons, pre-tests and post-tests to measure students’ performance on polygons, lesson evaluation forms and interviews. The findings show that students found the RETA-based lessons engaging but some of the parts were difficult for them. The lesson plans presented in this paper were the 2nd version of the plans, amended after the 1st cycle of designbased research. It is hoped that the lesson plans set an example for teachers and teacher candidates. ======================================================= Stephanie Sheehan-Braine & Irina Lyublinskaya A Framework for Online Problem-Based Learning for Mathematics Educators https://doi.org/10.37626/GA9783959872188.0.091 First page: 482 Last page: 487 Abstract Research shows that problem-based learning (PBL) has the capacity to make mathematics culturally relevant, so there is a need to adapt this successful learning model to virtual environments. This study proposes the Framework for Online Problem-Based Learning for Educators (OnPBL-E) to add this challenge. The content components of the OnPBL-E framework were developed by unpacking PBL instructional principles and identifying interactions between the essential elements of PBL: the context, the educator, and the learner. Then, the Multimodal Model for Online Education was used to identify online modules for these interactions. This study also describes an example of implementing PBL in an online mathematics modeling course. ======================================================= M. Vali Siadat Keystone Model of Teaching and Learning in Mathematics https://doi.org/10.37626/GA9783959872188.0.092 First page: 488 Last page: 493 Introduction Keystone model presents a holistic approach to math education at the college. It is a dynamic system of frequently assessing student learning and adjusting teaching practices. Its philosophy is based on the belief that all students can learn mathematics provided they are engaged in the learning process. Keystone views classroom as a learning community where through peer-to peer interaction and cooperation, all students achieve. Contrary to other programs that put the students in competition with one another, essentially pitting them against each other for grades, our program challenges students to cooperate so that all attain the standards of excellence. Keystone is an alternative model to traditional educational practices and its basic principles should be applicable to all disciplines. ======================================================= Parmjit Singh, Nurul Akma Md Nasir & Teoh Sian Hoon The Dearth of Development in Mathematical Thinking Among High School Leavers https://doi.org/10.37626/GA9783959872188.0.093 First page: 494 Last page: 499 Abstract The prime rationale of the high school math curriculum is to develop the intellectual mind of learners who can think and apply learnt content into solving problems of different areas of learning. Thus, to assess this context, a mixedmethod approach was undertaken to assess the levels of the 640 High school leavers’ mathematical thinking acumen in the context of their preparation in facing the challenges of tertiary level. The findings depict low-level mathematical thinking attainment regarding their dearth in critical thinking and creative thinking to solve higher-order thinking tasks. They lack a heuristics repertoire to use their contextual knowledge in solving fundamental nonroutine problems. This then begs the question: how are these students to face the upcoming hurdles and challenges bound to be thrown their way at the tertiary level? Keywords: Mathematical thinking, problem solving, non-routine, heuristics ======================================================= Praneetha Singh Mathovation- Creativity and Innovation in the Mathematics Classroom https://doi.org/10.37626/GA9783959872188.0.094 First page: 500 Last page: 505 Abstract The 21st century is predicted as the century of rapid development in all aspects of life. People are creative, but the degree of creativity is different (Solso, 1995). The perspective of mathematical creative thinking expressed by experts such as Gotoh (2004) and Krulik and Rudnick (1999) refer to a combination of logical and divergent thinking, which is based on intuition but has a conscious aim and process. This thinking is based on flexibility, fluency and the uniqueness of mathematical problem solving. This paper will aim to assist the readers to find out the competencies that are required to assess the creative thinking ability and characteristic of mathematical problems that can be used in creative thinking. ======================================================= Charles Raymond Smith & Cyril Julie Towards Understanding Integrating Digital Technologies in the Mathematics Classroom https://doi.org/10.37626/GA9783959872188.0.095 First page: 506 Last page: 511 Abstract In the context of ICT integration, a presentation by a teacher during a continuing professional development session is analyzed from the instrumental orchestration as well as the Technological Pedagogical (And) Content Knowledge (TPACK) perspective. The results indicate that some of the components of instrumental orchestration were used by the teacher during the presentation. In realising these orchestrations, the teacher had to delve into the different knowledge components that constitute TPACK. It is concluded that CPD providers need to take such complexities into account when delivering training programs. Keywords: GeoGebra, ICT integration, instrumental orchestration, TPACK, mathematics teacher practices ======================================================= Panagiotis Stefanides “Generator Polyhedron”, Icosahedron Non-Regular, Discovered Invention https://doi.org/10.37626/GA9783959872188.0.096 First page: 512 Last page: 517 Abstract The Invented [2017] Polyhedron, is a Non-Regular Icosahedron, it has 12 Isosceli triangles and 8 Equilateral ones. Its Skeleton Structure consists of 3 Parallelogramme Planes Orthogonal to each other, with sides’ ratios based on the Square Root of the Golden Number [ratios of 4/π specially for π = 4/T= 3.14460551.., where T is the Square Root of the Golden Number (√Φ) equal to 1.27201965..] and related directly to the Icosahedron, whose structure is based on the Golden Number and to the Dodecahedron, whose structure is based on the Square of the Golden Number. Its geometry relates to Plato’s Timaeus “Most Beautiful Triangle”, a proposed theorization by the author [“contra” the standard usual International interpretations], presented to various national and international conferences [the Magirus/ Kepler one is a constituent part of this triangle, similar to it, but not the same with it]. ======================================================= Michelle Stephan & David Pugalee The Future of Mathematics Education in the Digital Age https://doi.org/10.37626/GA9783959872188.0.097 First page: 518 Last page: 521 Abstract How do the mathematics content and processes taught in school today need to change in order to prepare students for participation in the digital and information age? We propose to stimulate a discussion about what mathematics education should aim for in preparing students for employment and local/global citizenship in this ever-changing technological world. Our group will develop a forward-minded agenda on implementation of mathematics content and practices. This will include detailing 1) what content/practices should be kept, changed or deleted from the curriculum, 2) potential impediments to teachers implementing them and possible strategies to address these, and 3) necessary research projects to study implementations in order to make ongoing recommendations. We will aim to start with middle school (ages 12-15) with a vision to continue this working group through multiple conferences. ======================================================= Yelena Stukalin & Sigal Levy Introducing Probability Theory to Ultra-Orthodox Jewish Students by Examples from the Bible and Ancient Scripts https://doi.org/10.37626/GA9783959872188.0.098 First page: 522 Last page: 525 Abstract Cultural diversity in the classroom may motivate teachers to seek examples that reflect their students’ cultural backgrounds, thus making the course material more appealing and understandable. In this context, the Holy Bible is a source of many stories and anecdotes that may be included in teaching probability theory to even ultra-Orthodox Jews. This paper aims to demonstrate the use of stories from the Bible to introduce some concepts in probability. We believe that this approach will make learning probability and statistics more understandable to the Ultra-Orthodox students and increase their motivation to engage in their studies. Keywords: cultural diversity, biblical examples, non-statisticians ======================================================= Emily K. Suh, Lisa Hoffman & Alan Zollman STEM SMART: Five Essential Life Skills Students Need for their Future https://doi.org/10.37626/GA9783959872188.0.099 First page: 526 Last page: 530 Abstract To be successful in a future STEM-focused world, students need to know more than content: students need to be STEM SMART. A STEM SMART student has the mindset of an intellectual risk taker, the tenacity to tackle tough problems while learning from mistakes, and the critical thinking skills to separate scientific information from opinions and beliefs. We use the SMART acronym (Struggle, Mistakes, All, Risk, Think) to introduce five essential life skills not obviously related to STEM (Science, Technology, Engineering, and Mathematics) disciplines but necessary for success in STEM. For each of our five essential skills, we provide an explanation of its importance, connections to relevant educational research, and real-world applications. ======================================================= Janet (Hagemeyer) Tassell, Jessica Hussung, Kylie Bray, Darby Tassell & Haley (Clayton) Carbone Elementary Pre-Service Teachers’ Beliefs about Mathematics Fluency: Transforming Through Readings & Discussions https://doi.org/10.37626/GA9783959872188.0.100 First page: 531 Last page: 536 Abstract Teacher candidates continue to enter Elementary Math Methods with the belief that mathematics fluency is synonymous to speed and rote memorization –assessed best by timed tests. In the Elementary Math Methods 2018-2021 school years, fall and spring semesters, qualitative data were gathered from pre-service elementary mathematics teachers’ pre/post-assessments of reading mathematics fluency journal articles, viewing video samples, and participating in full-class discussions. The pre- to post-assessment themes show that reading research articles may be a possible intervention to add to their clinical school observations in the K-6 setting. ======================================================= Eleni Tsami, Dimitra Kouloumpou & Andreas Rokopanos The Gender Gap in Statistics Courses: A Contemporary View on a Statistics Department https://doi.org/10.37626/GA9783959872188.0.101 First page: 537 Last page: 541 Abstract Gender equality remains a strategic objective of the EU educational system. The present paper provides a contemporary view of the gender balance in the Department of Statistics and Insurance Science at the University of Piraeus. Our results indicate that a gender gap is prevalent in this specific department, although this gap is only marginal in terms of the statistics on students. On the other hand, statistics for the academic staff reveal that the department is clearly male dominated, thus stirring the discussion of gender preferences and systemic gender bias. Our findings support the notion that the institutional change currently taking place across departments and academic communities worldwide is yet to come to fruition and considerable effort is needed in order to bridge the gender gap in science, technology, engineering and mathematics (STEM) courses. ======================================================= Ching-Yu Tseng, Paul Foster, Jake Klinkert, Elizabeth Adams, Corey Clark, Eric C. Larson & Leanne Ketterlin-Geller Using Cognitive Walkthroughs to Evaluate the Students’ Computational Thinking during Gameplay https://doi.org/10.37626/GA9783959872188.0.102 First page: 542 Last page: 547 Abstract In this paper, we describe how a team of multidisciplinary researchers, including game designers, computer scientists, and learning scientists, created a learning environment focused on computational thinking using a commercial video game Minecraft. The learning environment includes a Minecraft mod, a custom companion application, and a learning management system integration. The team designed the learning environment for students in Grades 6-8. Working with a group of educators, the researchers identified eleven high-priority Computer Science Teacher Association (CSTA) standards to guide game development. The team decomposed the standards into essential knowledge, skills, and abilities. In this study, we describe how we used a cognitive walkthrough with a middle school student to investigate: (a) the ways in which the game supports student learning (b) the barriers to learning, and (c) the necessary changes to facilitate learning. ======================================================= Ariana-Stanca Vacaretu GROWE in Math https://doi.org/10.37626/GA9783959872188.0.103 First page: 548 Last page: 553 Abstract Getting Readers on the Wavelength of Emotions (GROWE) is an Erasmus+ project initiated with the aim to develop all (including math) teachers’ competences to address students’ literacy and emotional learning needs. The GROWE classroom approach includes meaningful reading and writing learning activities and develops mastery of such strategies using diverse authentic texts (i.e. not `clean` textbook texts), while learning the discipline. Simultaneously, the students enhance their social-emotional skills by learning to recognise and manage their emotions, establish positive relationships, and make responsible decisions. This paper presents my experience in implementing the GROWE approach in my maths lessons with high-school students: the authentic texts I used and related tasks, and some implementation results. ======================================================= Shin Watanabe & Takako Aoki In School and Out School https://doi.org/10.37626/GA9783959872188.0.104 First page: 554 Last page: 559 Abstract Currently, learning in developed countries is centred on school education. It is not only Japanese teachers who regret that few students enjoy learning mathematics under the current school system. And in the age of 100 years of life, everyone should continue to study academics even after graduating from school. Unfortunately, learning mathematics is difficult after graduating from school. It is clear that lifelong learning has now become an important learning venue for all. I decided to call this school education “In School”, and to be released from the school system and call learning “Out School”. I will describe the richness of the future of “Out School”, which is a place for learning in the future. Out School is an important mathematical education that is an extension of In School. Key words: In School, Out School, Creativity, Mathematical Learning ======================================================= Laura Watkins, Patrick Kimani, April Ström, Bismark Akoto, Dexter Lim Representational Competence with Linear Functions: A Glimpse into the Community College Algebra Classroom https://doi.org/10.37626/GA9783959872188.0.105 First page: 560 Last page: 565 Abstract Teaching and learning strategies that encourage students to develop the ability to use mathematical representations in meaningful ways are powerful tools for building algebraic understandings of mathematics and solving problems (American Mathematical Association of Two-Year Colleges [AMATYC], 2018). The study of functions in algebra courses taught at community colleges in the United States provides students the opportunity and space to make connections between important characteristics of various families of functions. Using examples of teaching and learning linear functions from intermediate and college algebra courses in community colleges, we explore the ways instructors and students use a variety of representations (visual, symbolic, numeric, contextual, verbal, and/or physical) in teaching and learning linear functions, while connecting between and within these representations. ======================================================= Ian Willson Formative Assessment Activities for Introductory Calculus https://doi.org/10.37626/GA9783959872188.0.106 First page: 566 Last page: 568 Abstract A hands-on workshop in which participants engage as beginning learners in an extensive range of stand-alone tasks, and in which some of the tenets and guiding principles of formative assessment are used to highlight what many consider to be the best kind of teaching practice—and that which is critically important if we are to improve the quality of instruction for all. The idea is that clear articulation of just what is meant by formative assessment is provided in the actual context of ready-to-use classroom tasks. ======================================================= Kay A. Wohlhuter & Mary B. Swarthout Number Talks: Working to Deepen and Grow Number Sense Knowledge https://doi.org/10.37626/GA9783959872188.0.107 First page: 569 Last page: 573 Abstract Deep, flexible number understandings are foundational for mathematics learning. This workshop is based on two mathematics teacher educators’ journey to better understand how to facilitate future teachers’ development and use of number sense. Engaging preservice teachers in Number Talks enabled the educators to identify and to examine the strategies preservice teachers used during number talks while also providing a context for improving and expanding their own professional knowledge about number sense. Participant engagement includes experiencing Number Talks, examining preservice teachers’ work samples, and responding to the educators’ observations about number sense language (decomposition of numbers, fluency and flexibility with numbers, and mathematical properties). ======================================================= Ryan G. Zonnefeld & Valorie L. Zonnefeld Rural STEM Teachers: An Oasis in the Desert https://doi.org/10.37626/GA9783959872188.0.108 First page: 574 Last page: 579 Abstract Teacher preparation programs for STEM education should prepare teachers for all settings, including rural schools. Students across geographic locales show equal interest in STEM fields, but rural students often lack access to highly qualified STEM teachers. UNESCO (2014) notes that the disparity in education between rural and urban schools is a concern of many countries. In the United States, the National Center for Educational Statistics confirms that twenty percent of students are educated in rural schools and the STEM teachers in these schools are often the only STEM expert. These teachers become backbone teachers that set the foundation and direction of STEM education in the entire school. This paper reviews the landscape of STEM education in rural schools, explores strategies for ensuring high-quality STEM education in rural schools, and outlines early successes of a university teacher preparation program in meeting these needs. ======================================================= Valorie L. Zonnefeld Pedagogies that Foster a Growth Mindset Towards Mathematics https://doi.org/10.37626/GA9783959872188.0.109 First page: 580 Last page: 584 Abstract Research demonstrates that a student’s mindset plays an important role in achievement and that mindsets are domain specific. Carol Dweck claimed that mathematics needs a mindset makeover and has shown that teachers can foster a growth mindset through their pedagogical choices. This paper shares how one university trains preservice teachers in mathematics pedagogies that are key to fostering a growth mindset. These practices include educating students on brain function, equitable access, metacognition strategies, feedback practices, the importance of productive struggle, and learning from mistakes.
How to Write Scientific Papers - uni-freiburg.de
Paper Writing Process Searching & Structuring Literature Organizing the Paper Writing the Paper 2 1 3 ... Final paragraph is a wrap-up stressing that given the above ... Draft Write quickly, to get a draft Writing Then improve the writing iteratively

COLLABORATIVE WRITING STRATEGIES - University of North …
Revise and edit together. These steps in the writing process determine what your final product will be. This makes it imperative for each group member to have an opportunity to make changes to the final draft. Read the paper out loud and discuss whether or not each idea, sentence, and paragraph connects to the ones around it.

Comparing and Contrasting - The Writing Center
critical to include in your final paper. Sometimes a particular point of comparison or contrast might be relevant but not terribly revealing or interesting. For example, if you are writing a paper about Wordsworth’s “Tintern Abbey” and Coleridge’s “Frost at Midnight,” pointing out that they both have nature as a central

Assignments 4 & 5: Researched argument rough draft and revised final paper
ENG 181: Writing about Science Fiction Literature and Film Researched Argument Assignments 4 & 5: Researched argument rough draft and revised final paper ... final paper. For your rough draft, write a 6- to 8-page essay in MLA format, double-spaced 12-point font, with 1-inch margins all around. Your essay should include an introduction that

SCIENTIFIC MANUSCRIPT WRITING GUIDE - The Writing Center
Drafting a Scientific Paper for Publication 3 Collaborative Manuscript Writing & Co-Authorship 5 Front Matter: Setting the Stage 7 ... 3 CUNY GRADUATE CENTER, THE WRITING CENTER DRAFTING A SCIENTIFIC PAPER FOR PUBLICATION Though there is no “one way” to begin the writing process, many researchers start with the Methods section of their ...

Sample APA Paper: Professional Format for Graduate/Doctoral …
18 Sep 2024 · The title of your paper goes on the top line of the first page of the body of your paper (APA, 2020, section 2.11). It should be centered, bolded, and in title case (all major words—

Understanding Writing as a Recursive Process
final draft. Writing in loops will help you create a more effective final draft. Seeing writing as a recursive process A recursive process refers to the way writers often loop back or revisit earlier work as we write. Say a writer has planned pretty carefully how a draft will be 04_ingraloop1e_25919_ch03_050_070_3pp.indd 50 13/06/19 11:16 AM

Summary: Using it Wisely - The Writing Center
The Writing Center Summary: Using it Wisely ... summary in your paper. You might use summary to provide background, set the stage, or ... Formulate an argument (including a good thesis) and be sure that your final draft is structured around it, including aspects of the plot, story, history, background, etc. only as ...

Adults with learning disabilities (ALD) - RCSLT
subsequent consultations on the draft. The paper was developed and written by the ALD Position Paper Steering Group, which comprised of Viki Baker, Louise Oldnall, Elenor Birkett, Geraldine McCluskey and Jo Morris. ... with the profession for the purposes of writing this paper is the overwhelming passion, energy and commitment for people with ...

CHECKING YOUR DRAFT EHC PLAN - Together Trust
Your final EHCP is a legally binding document and the provision in section F MUST be provided. Your Draft EHCP should not have a school placement named in Section I. Section I will be finalised when the school consultation period has been completed, once the draft EHCP is agreed. BEFORE YOU START PLEASE ENSURE YOU HAVE A COPY OF THE DRAFT …

THE DOCUMENTED ESSAY General Guidelines - Hunter College
writing and revising the final paper. GETTING STARTED. The first step in writing a research paper is to ask a meaningful question about a subject. A meaningful question is one which deals with an important aspect of a subject and which can be answered, at least tentatively, with available information. If your professor assigns a topic or a

ENGLISH HOME LANGUAGE PAPER 3 RESOURCE PACK - Roodie
Learners need to be taught the writing process from drafting, editing through to the final product. In addition, learners need to be given constructive feedback from the educators in order to assist them to improve their writing skills. Paper 3 is weighted more heavily than Paper 1 and Paper 2, which is out of 70 and 80 marks

APA 7th ed. (Student version) Sample Paper (Final)
Instead, the paper’s title should be used. It is assumed that the paper begins with an introduction. The entire paper is to be double-spaced throughout. According to the 7th edition of the . Publication Manual of the American Psychological Association, the font should be accessible (i.e., easy to read) and consistent throughout the draft.

Sample Paper for Regular Liberty University Class
Sample Class Paper with Non-Structured Abstract: Final 2 Abstract Provide a concise overview (with about 200-250 words), of the main points of your paper.You may organize the abstract in a ...

Process Robustness White Paper - PQRI
The objective of this paper is to unify understanding of the current concepts of process robustness and how they apply to pharmaceutical manufacturing. The paper also provides recommendations on development and maintenance of a robust process. The concepts presented here are general in nature and can apply to many manufacturing situations; however,

How to Write Your First Research Paper - Poorvu Center for …
draft. This paper presents guidelines on how to initiate the writing process and draft each section of a research manuscript. The paper discusses seven rules that allow the writer to prepare a well-structured and comprehensive manuscript for a publication submission. in ad - dition, the author lists different strategies for successful revision.

A Guide to Writing an Academic Paper - HfWU
1 About these Guidelines and Academic Research and Writing 2 and decorated. The following figure 2 depicts the sequence of writing an academic paper. Figure 2: Writing an Academic Paper is Like Constructing a House Source: Own image If you were to get a topic for your assignment and started writing straight away, this

Sample Paper for Liberty University Practicum Class
Sample Class Paper with Structured Abstract: Final 1 Liberty University Master of Public Health ... Final Draft Claudia S. Sample ID: L123456789 December 28, 2020 Words: 1624 .

Process Approach to Teaching Writing Applied
essence, process approach to teaching writing focuses on the writing process rather than the final product. II. Process Approach Versus Product Approach ... Give out a pile of about 10 to 15 slips of paper. Tell the students to write a question about the story on each slip of paper ... produces a final draft. Tip: ...

EXAMINATION TIMETABLE FOR U.C.E (NEW LOWER SECONDARY CURRICULUM) FINAL ...
TIME ALLOWED FOR THE QUESTION PAPER: The time allowed for each paper is shown against the name of the paper and NO EXTRA TIME IS TO BE ALLOWED. In case of any discrepancy, the time stated on the question paper must be taken as correct. Any time allocated for reading through questions, studying maps, etc. is included in the total time

A guide to technical report writing - Institution of Engineering …
A guide to technical report writing – What makes a good technical report? 03 10 laws of good report writing 1. produce the report for your reader(s) 2. keep the report as short as possible 3. organise information for the convenience of the reader 4. include accurate references 5. ensure your writing is accurate, concise and straightforward

DNP Final Project Handbook - Radford University
Radford University DNP Final Project Handbook 4 Choosing a DNP Project Scope of DNP Project Each DNP Project will: • Focus on a change that impacts healthcare outcomes either through direct or indirect care. • Have systems (micro-, meso-, or macro- level) or population/aggregate focus. • Demonstrate implementation in the appropriate arena or area of practice.

Narrative Writing Self-Assessment Checklist Grade 6
6 Aug 2016 · writing to life. I used complete sentences. I varied my sentences to make my writing interesting. Punctuation (L.6.2) Before I wrote my final draft I checked to make sure I used punctuation correctly (commas, quotations, parentheses, dashes, etc.). Spelling (L.6.2) Before I wrote my final draft I checked to make sure all

YOUR SCREENPLAY WITH FINAL DRAFT 12
FINAL DAFT 12 Final Draft makes going from idea to outline as easy as 1-2-3 Final Draft 12 makes going from idea to outline even easier with the Final Draft 1-2-3 workflow. Using the 1-2-3 workflow, you can brainstorm a story on the Beat Board™, drag the Beats to the Outline

Patent Writing: From Basic Till Filing - IIT Guwahati
Patent Writing: From Basic Till Filing IIT Guwahati 15/19. About Gandhian Young Technological Innovation awards 2018 More than 3000 + projects were submitted. 23 projects were selected for BIRAC-GYTI and GYTI awards 2018 and presented by president of India in Rastrapati Bhavan Cultural Center.

Writing a Short Story - teachgrowsow.com
written for them on the line below. Some students may need to copy their final draft onto a draft page first, instead of copying it directly onto their nice paper, if seeing red marks causes confusion or frustration. 5. Give students nice paper (or use the one provided) for creating a final draft, including the corrections made during proofreading.

Developing Detailed Rubrics for Assessing Critique Writing: …
the critique. After distributing and discussing the final draft of the rubrics in class, we spent several class sessions discussing articles related to the theme of legacy admissions, chosen for the purpose of critique writing in the three sections; looking at sample model critiques; and writing practice critiques in class. As additional

How to write a review paper - ACSESS
10 Jan 2019 · these papers. More detailed review-writing instructions that walk a prospective author through each component of the paper (title, abstract, introduction, etc.) can be found in Mayer (2009). Steps for Writing a Review Paper. Before You Begin to Search or Write . 1. Clearly define the topic. Typically, a review writer works in the related field ...

The Writing Process - University of Washington Tacoma
, also called pre-writing or brainstorming, is the foundation of a successful paper—without it, you’ll have nothing to draft, revise, edit, or submit to your professor. Here are some different ways to invent or begin the writing process. • Note-taking — This can be …

Tips for Organizing Your Essay - Harvard College Writing Center
of the paper, including “introduction,” “methods,” and “discussion.” Even when you are not required to use subheadings, it can be helpful to put them into an early draft to help you see what you’re written and to begin to think about how your ideas fit together. You can do this by typing subheadings above the sections of your draft.

Revising Your Draft - California State University, East Bay
finished a draft before looking at it again, maybe a day or at least a few hours. When you return to the draft, be honest with yourself and ask yourself what you really think about the paper. *This obviously won’t work if you wait until the last minute to start your paper, so managing your time really begins when you first receive the assignment.

Informative/Explanatory Writing Checklist: Grade 4
4 Aug 2016 · Grammar I used strong words and phrases correctly to bring my writing to life. Punctuation Before I wrote my final draft I checked to make sure I used punctuation correctly (capitalization, commas, quotations, etc.) Spelling Before I wrote my final draft I checked to make sure all my words were spelled

INTRODUCTION - Cambridge University Press & Assessment
Final Draft is a four-level academic writing series for high beginning / low intermediate- to high advanced-level students of North American English. The series prepares students to write in a college or university setting by focusing on the topics, rhetorical modes, skills, vocabulary,

Academic Essay Writing for Postgraduates - The University of …
Unit 2 Writing the introduction 9 Unit 3 Acknowledging your sources ... draft and revise the assignments you will be doing for your Master’s degree at Edinburgh. We focus on ... paper for use in this course. (Full details of all cited sources are given in the .

Tuck Everlasting Writing Assignment - norwellschools.org
Tuck Everlasting Writing Assignment Directions: We will be writing an essay on Tuck Everlasting in class. We will begin by writing your draft the old-fashioned way—on paper…yes, that thin, white object with lines on it. Your final draft will be typed in class with the aide of a keyboard. More specifics about the final draft will come later.

Lyceum of the Philippines University
%PDF-1.7 %âãÏÓ 1480 0 obj > endobj 1487 0 obj >/Filter/FlateDecode/ID[6D8A7ADA53FD9B43AD3F6B99DE51B1EC>9BCEAD21FD23E642B2CD50B48CE1C1A1>]/Index[1480 15 1497 1 ...

A Brief Guide to Writing the Philosophy Paper - Harvard University
Jen decided before she began writing her paper that Smith’s argument ultimately fails because it trades on an ambiguity. Accordingly, she began her paper with the following sentence: In this paper, I will refute Smith’s argument against the existence …

Writing your essay – an overview - University of Southampton
Now you can write your first draft. Finally you will need to edit your essay, to produce a final polished draft. The number of drafts needed will vary. At all stages of the essay writing process, you will need to have the title firmly in mind. It is a good idea to write the title on a separate piece of paper or index card and have it in front of

A Brief Guide to Writing the Psychology Paper
WrITINg CeNTer BrIeF gUIde SerIeS A Brief Guide to Writing the Psychology Paper The Challenges of Writing in Psychology Psychology writing, like writing in the other sciences, is meant to inform the reader about a new idea, theory or experiment. Toward this end, academic psychologists emphasize the importance of clarity and brevity in writing

SENIOR PHASE GRADE 9 NOVEMBER 2017 ENGLISH FIRST …
5. Show all the aspects of the writing process until the final draft : planning, writing , proofreading and editing. 6. All planning must be indicated as such. It is advisable to draw a line through all planning. 7. Pay attention to spelling, vocabulary and sentence construction. 8.

Rough Drafts without Tears: A Guide to a Manageable Procedure …
Improving Student Writing JEFFREY K. MCDONOUGH Syracuse University In facing their writing assignments, students in my introductory phi-losophy courses confront two primary obstacles. First, they often don’t have a feel for what sort of paper they are expected to write. They easily mistake an extended expression of opinion, or a replaying of

HOW TO WRITE AN EFFECTIVE PEER REVIEW REPORT - SAGE …
whether a paper: a. falls within the scope of the journal b. is novel and/or significant enough in content to be published, and c. is clear and consistent enough in its presentation to be understood. 2. If edits are necessary before the paper is …

Writing Philosophy Papers: A Student Guide - Oregon State …
handbook is that writing is a process, not a product. A paper is a long-term project, not a last minute grind. The success of your writing requires that you spend time throughout the term on the writing process -- pre-writing, scheduling, researching, preparing a draft, reviewing and revising, and polishing your paper. This section of the

Thesis Statements - The Writing Center
paper. What is a thesis statement? A thesis statement: tells the reader how you will interpret the significance of the subject matter under discussion. is a road map for the paper; in other words, it tells the reader what to expect from the rest of the paper. directly answers the question asked of you. A thesis is an interpretation of a question or

The Basic Outline of a Paper - Academics
End with a strong clincher statement: an appropriate, meaningful final sentence that ties the whole point of the paper together (may refer back to the attention grabber) Additional Tips Decide on the thesis and main points first You do not need to start writing your paper with the introduction

final draft instructions - University of Chicago
General Instructions for Final Draft of Short Paper (18.310) Your first draft was in every case reasonably well written, but I want you to make an attempt to make your final draft look professional. To this end, I want you to look at what professional journal papers look like, and try to emulate them. This involves: 1.

Prospectus - Harvard University
writing. Write a draft part or section when you feel the inner pressure and excitement to do so. Don’t delay. This is your thesis, and it belongs to you. You become the authority. You will learn to trust your own judgment and take charge of the writing process, even while listening to …

What is Process Writing? - sites.tufts.edu
thoughts on paper. If it’s hard for them, you become their scribe. They talk and you ... rather than on the final result. Editing After writing several drafts, it is time to proofread, check grammar, spelling and punctuation. ... When you type up their writing, type exactly what they leave in their final draft EXCEPT the remaining spelling ...

10 Things To Do Before You Submit Your Essay - University of York
Writing Resources Final Draft Checklist 2. Check your references are accurate and correct. You have finished your essay and you think it is ready for submission. Now go through the checklist below, as it should help you spot possible flaws in your essay be-fore submitting it. You are also strongly advised to have