My colleague Mercedes McGowen and I examined a measure of individual student gain by pre-service elementary teachers, remedy related to Richard Hake’s 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, and as a proportion of the possible increase for each student.

We examined the written work in mathematics classes of pre-service elementary teachers with very high gain and those with very low gain and showed that these groups exhibit distinct psychological attitudes and dispositions to learning mathematics.

We showed 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 showed that this is not correct for a cohort of pre-service elementary teachers.

**McGowen_Davis_gain_paper**

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