These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place…

President Garfield's life is reviewed, and his proof of the Pythagorean theorem is presented. (DT)

Six short articles concerned with mathematics education are included. (FL)

Complex numbers and trigonometry are used to prove that a given constructed line is equal to the length of one side of a regular pentagon inscribed in a unit circle. (MP)

Six conjectures are established concerning a rectangular solid with the lengths of all its face diagonals and the lengths of all its edges being positive integers. (MP)

The fundamental role of the theorems of Pappus and Desargues in the construction of nomograms is explained. (DT)

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

In this article, a continuation of SE 513 148, the author presents seven additional applications of group theory to high school mathematics. These applications can be used, not only to illustrate the group concept, but also to extend the development of ideas in the high school curriculum. (SD)

This is part two of a two-part SMSG elementary school text for third-grade students. The development of mathematical ideas in the text is grounded in appropriate experiences with things from the physical world and the immediate environment. Chapter topics include: (1) addition and subtraction; (2) length and area; (3) multiplication; (4)…

An approach close to the original Greek geometric point of view regarding the question and proof of the irrationality of the square root of two is given. (MN)

Topics discussed include: maximizing the volume of a box, finding different size squares on a geoboard, the angles formed by the hands of a clock, and questions related to three consecutive integers. (MP)

Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

This paper discusses the process of investigating a mathematical situation, making conjectures, formulating an equation, then using mathematical induction to show the result is valid. Several examples appropriate for secondary school level are given. (DT)

A case is made for a comprehensive curriculum that includes strong competencies with not only number ideas and computation, but also with other mathematical topics such as geometry, statistics, probability, and estimation. (MP)