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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**