Skip to main content
\(\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Section4.1Project Overview

A major theme of this course is the discovery of “familiar” arithmetic and algebra in unfamiliar places. These explorations are meant to illuminate that algebra is far more than a set of procedures suitable for simplifying and solving equations involving numbers; algebra is a name for fundamental structures and ways of reasoning that can be found in places where numbers aren't even present.

This, principally, highlights both a connection and a distinction between quantitative reasoning, which emphasizes concrete, contextual, and critical uses of number skills, and mathematical reasoning, which exposes the abstract, fundamental, and logical principles of which the former is one special case. Quantitative reasoning makes these skills practical; mathematical reasoning makes them durable.

Our semester project will be to design and deliver a professional development workshop for elementary and secondary math educators, designed to help them (and by extension their students) discover what algebraic thinking is, through activities using tangles, knots, links, and/or braids. The materials developed for this project will be shared here, and after testing them, I hope we can share them more widely through professional development networks for math educators.


  1. Understand algebraic thinking by identifying it in a wide variety of contexts.
  2. Contrast several models of teacher professional development, including the Math Teachers Circle model.
  3. Design resources for, and facilitate, a workshop for in-service teachers on knot theory and algebraic thinking.