Ohio Journal of School Mathematics | Issue: Issue: 1(80) Fall 2018 (2018)

Volume 80 • 2018 • Fall 2018

A surprising amount of this issue argues that you can show a mathematical idea before you can say it. Wasim Akram Mandal proves the arithmetic mean–geometric mean inequality almost without words, and Greg Orosi does the same for the sum of the first n integers with nothing but a symmetry argument. Julie Nurnberger-Haag turns to children’s picture books and asks which ones actually draw shapes correctly, and Lara Dick and Rebecca Ogle have students write fractions in hieroglyphs and reason like Ancient Egyptians. Todd Moyer even runs the van Hiele levels of geometric thought through clips from Monty Python and the Holy Grail.

The flip side is getting students to say what they see. Karl Kosko and Elizabeth Guilford track how elementary children move from tacit to explicit argument, and hand teachers a tool for reading that growth in K–5 writing and talk. Michael Waters takes ordinary exercises and shows what it takes to turn them into problems worth thinking about. Taylor Wood and Jenna Odom follow prime factorizations into the question of when a hypotenuse length gives more than one primitive Pythagorean triangle, and Michael Flick and Debbie Kuchey report from the 2018 State Tournament of Mathematics.