A Beginner's Guide to Teaching Mathematics in the Undergraduate Classroom PDF
Preview A Beginner's Guide to Teaching Mathematics in the Undergraduate Classroom
A Beginner’s Guide to Teaching Mathematics in the Undergraduate Classroom This practical, engaging book explores the fundamentals of pedagogy and the unique challenges of teaching undergraduate mathematics not com- monly addressed in most education literature. Professor and mathematician, Suzanne Kelton offers a straightforward framework for new faculty and graduate students to establish their individual preferences for course policy and content exposition, while alerting them to potential pitfalls. The book discusses the running of day-to-day class meetings and offers specific strategies to improve learning and retention, as well as con- crete examples and effective tools for class discussion that draw from a variety of commonly taught undergraduate mathematics courses. Kelton also offers readers a structured approach to evaluating and honing their own teaching skills, as well as utilizing peer and student evaluations. Offering an engaging and clearly written approach designed specifically for mathematicians, A Beginner’s Guide to Teaching Mathematics in the Undergradu- ate Classroom offers an artful introduction to teaching undergraduate math- ematics in universities and community colleges. This text will be useful for new instructors, faculty, and graduate teaching assistants alike. Suzanne Kelton is Associate Professor of Mathematics at Assumption Uni- versity in Worcester, MA. She received her Ph.D. in Mathematics at the Uni- versity of Virginia and has taught mathematics to learners across a range of universities and colleges. A Beginner’s Guide to Teaching Mathematics in the Undergraduate Classroom SUZANNE KELTON First published 2021 by Routledge 52 Vanderbilt Avenue, New York, NY 10017 and by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2021 Taylor & Francis The right of Suzanne Kelton to be identified as author of this work has been asserted by her in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Names: Kelton, Suzanne, author. Title: A beginner’s guide to teaching mathematics in the undergraduate classroom / Suzanne Kelton. Description: New York : Routledge, 2021. | Includes bibliographical references and index. Identifiers: LCCN 2020029011 | ISBN 9780367429010 (hardback) | ISBN 9780367429027 (paperback) | ISBN 9781003000044 (ebook) Subjects: LCSH: Mathematics–Study and teaching (Higher) | Mathematics. Classification: LCC QA11.2 .K46 2021 | DDC 510.71/1–dc23 LC record available at https://lccn.loc.gov/2020029011 ISBN: 978-0-367-42901-0 (hbk) ISBN: 978-0-367-42902-7 (pbk) ISBN: 978-1-003-00004-4 (ebk) Typeset in Avenir and Dante by KnowledgeWorks Global Ltd. Access the Support Material: www.routledge.com/9780367429027 To my husband, for his steadfast love and support. To my son, for his positive outlook and unrelenting belief in me. To my daughter, for never letting me forget what is truly important. To Timothy, Alexander, & Rosabel ∼ my rock, my light, & my love ∼ Contents Acknowledgements ix Introduction 1 Course Overview One 6 A Note on Terminology 7 Determining Desired Learning Outcomes 7 Assessment 13 Determining a Beginning Classroom Strategy 15 Backward Design 15 s t n Quick Glance: Terminology Overview 16 e t n o Course Policies, Philosophies, and Syllabi Two 17 C Course Policies 18 vii Syllabi 36 The Basics of the Classroom Three 47 The First Day of Class 47 Preparing for Class 53 During Class and Office Hours 63 After Class 85 Assessment Four 87 Fostering Academic Honesty with Assessment 88 Homework 90 Quizzes 90 Preparing Students to Take an Exam 92 Writing an Exam 97 The Exam Was Too Long! 100 Grading an Exam 102 Addressing Instances of Academic Dishonesty 106 Course Grades 107 Challenges and Opportunities within Commonly Taught Courses Five 111 Discussion Sections 111 Algebra – Is It Too Late?! 113 Precalculus 115 Calculus I: Differential Calculus 126 Calculus II: Integral Calculus 134 Sophomore Calculus 150 Elementary Linear Algebra 152 Proof Courses 156 Upper-Level Courses 159 Growth through Evaluation and Education Six 161 Self-Evaluation 163 Peer Evaluations and Collaborations 170 Student Evaluations 173 s nt Pedagogical Professional Development 178 e t n Co Going beyond Traditional Lecture Seven 179 viii Preparing to Try Something New 179 Active Learning 181 Course Designs for Active Learning 188 Online Courses 194 A Final Note on Innovation 197 Conclusion 199 References 200 Index 205 Acknowledgements This book would not exist if not for the support of my colleague, James M. Lang. He saw potential in a scrappy little manuscript and offered the encour- agement, advice, and guidance necessary to create the book before you. Thank you, Jim, for helping me make this book a reality. My colleague, Charles Brusard, was the one of first to read the early manu- script and he urged me to pursue its publication. His ardent support was the s t driving force to begin the long journey towards the current book. n e I extend my gratitude to Edward G. Dunne, who was Senior Editor of the m e American Mathematical Society (AMS) Book Program when I approached g d e him in 2010 regarding the original manuscript. He generously pursued its wl posting on the AMS website, which has been a great honor. o n k Assumption University (then Assumption College) provided the sabbatical c A required to significantly expand and update the manuscript. Thank you to x the staff at the Assumption University library for their efforts in retrieving i research articles on my behalf. I offer my sincere appreciation to those who provided essential feedback and invaluable suggestions for improvement through formal or informal reviews, especially Rachel Arnold, Jessica A. de la Cruz, Eric M. Howe, Steven Klee, and Fatemeh Mohammadi. Special thanks to Tim Woodcock for reading countless revisions and providing assurances throughout this lengthy project.
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