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…

Using a logarithmic looking glass, multiplication is reduced" to addition. (MM)

The author shows that the set of all sequences in which each term is the sum of the two previous terms forms a vector space of dimension two. He uses this result to obtain the formula for the Fibonacci sequence and applies the same technique to other linear recursive relations. (MM)

Illustrations are provided which show how some algebraic manipulations done prior to doing calculations can eliminate unnecessary storage of data, reduce the total number of needed steps, and avoid overflow. (MN)

This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)

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

Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

Two methods are considered for finding the logarithm of a number using elementary arithmetic. (DT)