Ohio Journal of School Mathematics | Issue: Issue: 1(87) Spring 2021 (2021)

Volume 87 • 2021 • Spring 2021

A few of these pieces keep circling back to the thing students see first. Foley and Wachira want a different gateway course, making the case for Quantitative Reasoning as the math that carries students from high school into college, and pointing to Ohio’s growing set of QR courses on both sides of that line. Hawthorne, Michael, and Miley look at the other end of the pipe. Standardized tests have started replacing symbols with concrete diagrams, and the authors find that a fraction diagram measures almost nothing about whether a fifth-grader understands fractions or the picture itself. Most students answered with symbolic shortcuts or surface cues. Pressed to explain, though, the same students showed real thinking, which is why the authors would rather use these items as formative tasks than as test questions.

The rest of the issue puts its own first representations in front of students. Dales walks through the 2021 Mathical Book Prize winners and argues for children’s books as a way into the subject. Wheeler and Hogan teach volume to middle-graders with homemade slime. And Meiring takes the old puzzle of weighing objects on a two-pan balance and follows it to a surprise, that the weights have to be powers of three and the bookkeeping needs a base-three system with a negative digit.