Interdisciplinary Perspectives on Math Cognition

✍ Scribed by Danesi, Marcel

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 343
• Series: Mathematics in Mind
• Edition: 1
• Category: Library

✦ Synopsis

This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding.

This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.

✦ Table of Contents

Front Matter ....Pages i-viii
From Biological Brain to Mathematical Mind: The Long-Term Evolution of Mathematical Thinking (David Tall)....Pages 1-28
Compression and Decompression in Mathematics1 (Mark Turner)....Pages 29-51
How Technology Has Changed What It Means to Think Mathematically (Keith Devlin)....Pages 53-78
Machine Versus Structure of Language via Statistical Universals (Kumiko Tanaka-Ishii)....Pages 79-97
Number Work: Recovering the Original Complexity of Learning Arithmetic (Brent Davis)....Pages 99-118
The Body of/in Proof: An Embodied Analysis of Mathematical Reasoning (Laurie D. Edwards)....Pages 119-139
Math Puzzles as Learning Devices (Marcel Danesi)....Pages 141-153
Diagrams in Mathematics: On Visual Experience in Peirce (Vitaly Kiryushchenko)....Pages 155-169
Laws of Form, Peirce, and Cantor (Louis H. Kauffman)....Pages 171-193
The Topology of Mathematics in the Mind and Its Interaction with Verbal and Written Language (Robert K. Logan, Izabella Pruska-Oldenhoff)....Pages 195-211
Mathematical Fiction as an Interdisciplinary Source for Mathematics Courses: Resources and Recommendations (Frank Nuessel)....Pages 213-226
Science, Magic, and the In-Between: Whence Logic (Inna Semetsky)....Pages 227-245
Geometric Cognition (Walter Whiteley)....Pages 247-263
Using Evidence to Close the Achievement Gap in Math (John Mighton)....Pages 265-276
Knowledge Building, Mathematics, and Creative Thinking: An Overview on Ontario Elementary Mathematical Teaching Beyond Twenty-First-Century Skills (Miss Stacy A. Costa)....Pages 277-286
Crypto-Mathematics in Ethnography: Estimation and Approximation via Ballparks and Eyeballing (Myrdene Anderson)....Pages 287-302
“A Mathematician, a Physicist and an Engineer”: The Meaning of “M” in STEM (Dragana Martinovic)....Pages 303-313
Why a Duck?: A Three-Part Essay on the Mathematics of Cognition (Yair Neuman)....Pages 315-320
On Mathematical Ways of Knowing: Musings of a Humanistic Mathematician (Gizem Karaali)....Pages 321-332
Epilogue: So, What Is Math Cognition? (Marcel Danesi)....Pages 333-344