Generative AI tools (GenAI) are increasingly used for academic tasks, including qualitative data analysis for the Scholarship of Teaching and Learning (SoTL). In our practice as academic developers, we are frequently asked for advice on whether this use for GenAI is reliable, valid, and ethical. Since this is a new field, we have not been able to…

Answers and examples are given to sixteen questions related to traditional ways of performing the operations of arithmetic. (MP)

Early calculating methods and devices are discussed. These include finger products, the abacus, ancient multiplication algorithms, Napier's bones, and monograms. (MP)

A few examples are discussed of situations where some solution to writing a computer program for an algorithmic problem is immediately evident, but the best solution is some distance away. (MP)

This investigation concerns the repeated application of the rule "take the sum of the squares of the digits." (MP)

An alternate method for factoring quadratic equations is presented as being quicker and easier to use than the trial-and-error method. (MP)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (MP)

The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

A computer program in BASIC is presented, with the underlying algorithm explained, for multiplying any two multi-digit numbers and obtaining an exact answer. (MP)

A class's struggle with the computer solution of a nontrivial problem is related. The use of algorithms allowed a trial-and-error approach.

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)

Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)

A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)

A classroom photography activity is outlined that motivates learning of mathematical topics such as estimation, geometry, ratio, measurement, and algorithms. (MP)