Title: The Effects of Mastery of Editing Peers’ Written Math Algorithms on Producing Effective Problem Solving Algorithms
Description: In 2 experiments, I tested the effects of a treatment package for teaching 4th graders to edit peers’ written algorithms for solving math problems such that an adult naïve reader could solve the problem. In Experiment 1, the editors were the target participants and the writers were the confederates. Participants were placed in a dyad that consisted of a writer and an editor. The writer and editor repeatedly interacted in writing until the writers produced an algorithm that resulted in adult naïve readers solving the problem. The editor was supplied with a checklist as a prompt for the editing process. Each dyad competed against a second pair of students, using a peer-yoked contingency game board as a motivating operation. Experiment 1 demonstrated that the treatment package increased participants’ accuracy of writing math algorithms, so that a naïve reader could solve the math problems. The target participants acquired the verbally governed responses through peer editing alone, and as a result the participants produced written math algorithms.

Experiment 2 measured the behaviors of the editor and writer using a multiple probe design across participants with two groups of 4 writers and 4 editors. The dependent variables were: 1) production of previously mastered math problems, such that a naïve reader could read and solve the math problem without ever seeing the problem, 2) the emergence of explanations of “why” (function) from learning “how” to solve a multi-step math problem, 3) production of novel written math algorithms (i.e., find the perimeter and extended multiplication), and 4) cumulative number of untaught math problems attempted. The independent variable was the same as Experiment 1 except a) the editors did not have access to a checklist and b) the peer-yoked contingency game board was removed. The results demonstrated that all participants produced written math algorithms such that both the writers and editors affected the behavior of naïve readers. I discuss the emergence of explanations of the function (“why”) of math that occurred as a result of being able to explain “how” to solve problems.

Moreover, the participants attempted more untaught math problems, demonstrating the resistance to extinction for attempting untaught math problems. Findings suggest that as a function of the intervention, reinforcement for solving math problems was enhanced.