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…

Three proofs for the problem show there exist irrational numbers a and b such that a to the b power is rational'' are presented and discussed. (DT)

An activity which involves the drawing of geometric designs on familiar number arrangements (such as the addition and multiplication tables and the hundred chart) is used to help students discover patterns and at the same time maintain computation skills. (DT)

Two enrichment articles are presented; one dealing with finding partial fractions and reducing to polynomials; the other, with finding the heaviest object from eleven others of equal weight where all twelve are identical in appearance. (JG)

A rational presentation of the so-called long division method for extracting the square root of a number. Diagrams are used to show relationship of this technique to the binomial theorem. Presentation exposes student to many facets of mathematics in addition to the mechanics of funding square root and cube root. Geometry, algebraic statements,…

A method is described for finding the two numbers which will form a linear combination with two given numbers a and b yielding the greatest common divisor of a and b. (DT)