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Engaging activities for teaching linear algebra

Shintaro Fushida-Hardy, Pranav Nuti, Megan Selbach-Allen

Abstract

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some questions instructors can ask themselves to design novel and engaging activities when constrained to teaching from a particular curriculum.

Engaging activities for teaching linear algebra

Abstract

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some questions instructors can ask themselves to design novel and engaging activities when constrained to teaching from a particular curriculum.
Paper Structure (25 sections, 6 figures)

This paper contains 25 sections, 6 figures.

Table of Contents

  1. INTRODUCTION
  2. GOALS AND CONSTRAINTS
  3. Goals
  4. EXPL
  5. LINK
  6. Constraints
  7. ACTIVITY DESIGN
  8. RELA
  9. CURR
  10. SAMPLE ACTIVITIES
  11. Maps and Distances
  12. COLL, RELA
  13. LINK
  14. EXPL
  15. Perpendicularity and Approximations
  16. ...and 10 more sections

Figures (6)

  • Figure 1: Maps and Distances example.
  • Figure 2: Two problems from Perpendicularity and Approximations. Students approximate the vector $w$ as a linear combination of $u$ and $v$.
  • Figure 3: Problem 1 of Various Sneaky Mathematicians.
  • Figure 4: Problem 2 of Various Sneaky Mathematicians.
  • Figure 5: Problem 4 of Various Sneaky Mathematicians.
  • ...and 1 more figures