Balancing the Common Core Curriculum in Middle School Education: Composing Archimedes' Lever, the Equation, and the Sentence as an Interdisciplinary Unity

232 Pages·2017·3.02 MB·English

by  James H. Bunn (auth.)

BALANCING THE
COMMON CORE
CURRICULUM IN
MIDDLE SCHOOL
EDUCATION
Composing Archimedes’
Lever, the Equation,
and the Sentence as an
Interdisciplinary Unity
James H. Bunn
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
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P
reface
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 intersec-
tion: 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 con-
struction, 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 bal-
ances 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 ful-
crum 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 reori-
ent 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.
a
cknowledgments
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 pro-
vided special help with the manuscript early on.
ix
c
ontents
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
l f
ist of igures
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
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