Balancing the Common Core Curriculum in Middle School Education

Balancing the Common Core Curriculum in Middle School Education

James H. Bunn Balancing the Common Core Curriculum in Middle School Education Composing Archimedes Lever, the Equation, and the Sentence as an Interdisciplinary Unity

James H. Bunn Professor Emeritus Department of English University at Buffalo Williamsville, New York, USA ISBN 978-3-319-46105-2 ISBN 978-3-319-46106-9 (ebook) DOI 10.1007/978-3-319-46106-9 Library of Congress Control Number: 2016956390 The Editor(s) (if applicable) and The Author(s) 2017 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Cover Design by Fatima Jamadar Printed on acid-free paper This Palgrave Macmillan imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

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Preface Balancing the Common Core Curriculum for Middle School Students: Composing Archimedes Lever, the Equation, and the Sentence as An Interdisciplinary Unity. A good education should include a scientific and technical component, a mathematical component, a writing component, plus an aesthetic and ethical component. These kinds of inquiry are often taught separately in schools and in the Common Core Curriculum. However, in everyday use, we often bring them together. So I feature here a new three-way intersection: the basic sciences and mechanics of levering on a seesaw, the basic formulations of patterning an algebraic equation, and the basic rules for writing a sentence in English. How do they intersect? In all three forms of inquiry, balance is the mainstay. The act of balancing is central to any construction, both in the real world and in more abstract models. So I show how balancing up is a basic method of problem solving in the sciences, in math, and in the English language. Because this method of problem solving features information that balances as it combines, I use the idea of balancing feedback. I draw a few simple communication diagrams for senders and receivers that show how feedback works in these compositions. In the sender-receiver diagrams I locate a common center of information transference located at a fulcrum on a balance beam or on a lever, at an equals sign, and at a verb. What exactly brings all three of these kinds of problem solving together at a center? The fulcrum s pivot Δ, the equation s equals sign =, and the word is in a sentence, all serve similar purposes as equalizers: they vii

viii PREFACE appear at the middle of a construction, where they combine and transfer information. Each sign is a middle measure. Balancing calls for a middle measure. Aristotle s phrase lets me reorient these three forms of inquiry, in a final chapter, towards ethics and aesthetics. Chapters: Introduction, Archimedes Lever, The Equation, The Sentence, Conclusion: Seeking a Middle Measure. In each chapter I refer to pertinent sections of the Common Core Curriculum and/or Next Generation Science Standards.

Acknowledgments Hans Christian von Baeyer, Judith Bunn, Ken Christianson, Arabella Lyon, Emily Wilson, Marlon Rice, and Anthony Rozak. Special thanks go to Jim Waack who lent me his teaching manuals and lesson plans. And thanks to Mara Berkoff and Milana Vernikova, editors at Palgrave Publishers. Special thanks to Tony Rozak who redrew my drawings and who provided special help with the manuscript early on. ix

Contents 1 Introduction: Balance at the Core 1 2 Archimedes Lever 35 3 The Equation 83 4 The Sentence 119 5 Seeking a Middle Measure 161 Bibliography 209 Index 219 xi

List of Figures Fig. 1.1 Sender-Receiver diagram for exchange of information for a sentence, an equation, or a lever 8 Fig. 2.1 Plumb bob, pendulum, and tangency 41 Fig. 2.2 Hanging balance scales 45 Fig. 2.3 Hanging balance beam and lever are equivalent 47 Fig. 2.4 Body-based calipers 55 Fig. 2.5 Hinged gull wings 57 Fig. 2.6 Screw seen as an inclined plane in spiral form 66 Fig. 3.1 Squares drawn upon a Pythagorean triangle 92 Fig. 4.1 Reader-writer diagram for slots of syntax 125 Fig. 4.2 Sentence tree diagram with is at apex 136 Fig. 5.1 Bow and the Lyre 163 xiii