Procedural explanations in mathematics writing - A framework for understanding college students' effective communication practices

This study analyzes the procedural explanations written by remedial college mathematics students. Relevant literatures suggest that six communication activities might be key in effective procedural explanations in mathematics writing: (a) orienting the learner, (b) providing kernels or definitions of concepts and procedures, (c) using exemplars or worked examples, (d) providing descriptions of the process or procedure, (e) solidifying learner understanding, and (f) facilitating linguistic control of mathematical terms. Using this framework, 18 practices or types of difficulties were discovered in students' written explanations. Independent experts consistently evaluated student explanations more highly when the explanations contained arithmetic or algebraic exemplars, described specific actions and their meanings, linked new with prior knowledge, and used descriptive language; experts evaluated student explanations more negatively when students displayed difficulties reasoning with kernels, reasoning with exemplars, or with describing processes.