What could they possibly be thinking!?! : understanding your college math students

✍ Scribed by David T. Kung; Natasha M. Speer

• Publisher: The Mathematical Association of America
• Year: 2020
• Tongue: English
• Leaves: 143
• Series: MAA notes
• Category: Library

✦ Synopsis

We’ve all been there. You’re grading a problem and just can’t understand why a student wrote what they did. “What could they possibly be thinking!?!” Over years, good teachers understand their students’ thinking more and more, developing an encyclopedia of the ways students (mis)understand—and the best teachers draw on that knowledge every day as they:

anticipate common ways of thinking as well as difficulties and plan instruction accordingly,
recognize a variety of ways students approach particular problems and correctly diagnose the source of student difficulties,
write engaging activities that leverage likely ways students will think and then help students learn challenging ideas.
This volume will help you build your encyclopedia of student thinking more quickly. Organized by course, it takes you on a tour of common student errors—adapted from the mathematics education literature—and dives into how students understand (both productively and unproductively) the mathematics we love.

As our community transitions from passive lectures to more interactive (and more effective) methods, knowledge of student thinking becomes more important. Modern teaching requires us to anticipate and be able to understand what students do and say while working on problems or engaging in some inquiry-oriented assignment. We need to correctly diagnose student difficulties and, instead of just telling them ``the right way'' to think, respond in ways that will help students see their errors and then refine their reasoning.

✦ Table of Contents

What Could They Possibly Be Thinking!?!
Preface
0 Foundational Ideas
1 Limits
2 Derivatives
3 Integration and the Fundamental Theorem of Calculus
4 Sequences and Series
5 Proof Writing
6 Linear Algebra
7 Differential Equations
8 Analysis
9 Abstract Algebra