Individual gain and engagement with mathematical understanding

TL;DR

This study investigates individual student gain in mathematics learning among preservice elementary teachers, revealing psychological differences, the impact of course goals, and challenging common beliefs about initial test scores and gains.

Contribution

It introduces a measure of individual gain in math education, linking psychological attitudes to gain levels and assessing the effect of course focus on learning outcomes.

Findings

High gain groups exhibit distinct attitudes towards learning mathematics.

Focusing on patterns and connections modestly increases average gain.

Low initial test scores do not necessarily predict higher gains.

Abstract

We examine a measure of individual student gain by preservice elementary teachers, related to Richard Hakes use of mean gain in the study of reform classes in undergraduate physics. The gain statistic assesses the amount individual students increase their test scores from initial test to final test, as a proportion of the possible increase for each student. We examine the written work in mathematics classes of preservice elementary teachers with very high gain and those with very low gain and show that these groups exhibit distinct psychological attitudes and dispositions to learning mathematics. We show a statistically significant, small, increase in average gain when course goals focus on patterns, connections, and meaning making in mathematics. A common belief is that students with low initial test scores will have higher gains, and students with high initial-test scores will have lower gains. We show that this is not correct for a cohort of preservice elementary teachers.