In summary, the study results indicate that after two years of implementation, the PD program did not have a statistically significant impact on teacher knowledge or on student achievement in rational numbers. These second-year results are consistent with the results at the end of the first year. At the end of the first year, the PD program did not have a significant impact on teacher knowledge or student achievement. Observations of teachers were conducted only in the first year. In the first year, the PD program had a statistically significant impact on one measure of instructional practice (the Teacher elicits student thinking Scale), a nearly significant impact on a second (the Teacher uses representations Scale, p = .054), but no significant impact on the third measure of instructional practice used in the study (the Teacher focuses on mathematical reasoning Scale).
Exploratory analyses based on a pooled sample, which combined data from the first and second years of the study to maximize the precision of the estimated effects, suggest that on average, each year of the PD had a statistically significant positive effect on SK, one of the two dimensions of teacher knowledge measured by the study. There was no effect on CK, the other dimension of teacher knowledge. Other exploratory analyses suggest that there was no significant differential effect of the PD for teachers who differed in baseline knowledge or prior experience, or for students who differed in baseline achievement. Exploratory analyses also suggest that students taught by teachers with higher knowledge scores exhibited significantly higher achievement, after controlling for prior achievement and other student background characteristics.
Although teachers' mathematical knowledge may be associated with student achievement gains, and thus may be a useful focus for PD, the PD tested did not have an effect on teacher knowledge of a magnitude that translated into an impact on student achievement. The results suggest that teachers' SK may have improved with each year of study PD. However, it is unclear whether multiple years of PD would produce larger gains in SK, especially without configuring the PD to take into account teacher mobility. Within a given year, our impact results suggest that, in order to affect achievement outcomes, the PD would have to be more efficient than the PD tested here in improving SK on an annual basis. Finally, while our evidence and evidence from other studies indicates that there is an association between teacher knowledge and student achievement, we do not know the relative importance of SK and CK. The study PD was primarily focused on SK and was not as directly focused on CK. Providing PD that places more direct emphasis on CK is another potential avenue for future study.