Ohio Journal of School Mathematics | Issue: Issue: 1(94) Summer 2023 (2023)

Volume 94 • 2023 • Summer 2023

A few of these articles share a quiet aim: to take a topic that classrooms tend to hand students as a rule, or a warning, and put the reasoning back in. Kyle Schultz takes up the ambiguous case in trigonometry, the one where students are told to stay away from angle-side-side, and builds simple homemade manipulatives so they can see why the warning exists. Mark Hogue, Miranda Spengler, Rachel Hughes, and Caitlyn Bell do something similar with systems of equations, which often get boiled down to a sequence of steps; they introduce the solving methods through problems instead. Richard Kaufman goes after Gabriel’s Horn and its painter’s paradox, the finite volume with infinite surface area, and finds a way to make it land before a student has met calculus, by way of a melting ice cube.

The rest of the issue keeps that practical bent. Ruby Schwan and Sarah Daye count how many squares fit inside a 100 by 100 array of points and then push the problem into three dimensions. Ayse Ozturk and her co-authors read five geometry textbooks closely to see what kind of pedagogical knowledge they actually offer prospective elementary teachers. Steven Meiring argues for a standing “laboratory” place in the secondary curriculum, and Reuben Herrle with Jennifer Flory Edwards and Todd Edwards make the short case for real-world contexts that give students a reason to care.