Deepening Mathematics Understanding of Middle School Teachers
In Year 1, raw scores for n = 66 teachers who had both pre-test and post-test scores were examined using the effect size index. The differences in means between posttest and pretest yielded an effect size of .34, which falls midway between the effect size index for "small" effects, d = 0.2, and the index for "medium" effects, d = 0.5. In Year 2, the effect size was .46, and in Year 3, the effect size was .48.
On the pre-post performance assessment, the median score increased from a 2.0 to a 4.0 on three of four rubric dimensions. The descriptors for performance at the 2.0 level included underdeveloped, sketchy, ineffective, and unclear. Descriptors for performance at the 4.0 level included complete, adequate, relevant, explained, and supporting the solution. A Wilcoxon Signed Ranks Test showed significant improvement (p. < .01) on all four dimensions from pre to post administration. Participants showed marked improvement in the areas of conceptual understanding, processes and strategies, and communication, and some improvement on accuracy, where there was little room for improvement because of the limited range of rubric levels for that dimension.
Analysis of portfolios provided further evidence that teachers had achieved a high level of mathematics performance. Results of consensus judgments among three raters of participant portfolios indicated that more than half of the sample demonstrated performance that was at or above the proficient level on each dimension of the rubric.
The behavioral checklist showed changes in teachers' behavior in group work from the beginning of the course to the end. And 99% of participants agreed or strongly agreed that the course improved their mathematical skills and understanding as well as agreed that the mathematical ideas presented in this course would be useful in their teaching.
There is preliminary evidence to suggest that changes in teacher content knowledge led to changes in classroom instruction. Further statistical analysis of classroom observations is underway to determine if indeed improvement in teacher content knowledge yielded higher RTOP scores.
