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Two groups of mathematics faculty, one from a four-year college and one from a two-year college, redesigned their respective introductory college mathematics courses following presentation of observational data regarding how faculty had been teaching the courses. This presentation emphasised how infrequently faculty teaching introductory college mathematics employed recommended pedagogical practices. This work was part of a multi-year federal grant project designed to increase the numbers of underrepresented students majoring in STEM disciplines. While the two teams developed very different redesigned course activities, in both instances the primary motivation for initiating the work was the information provided to faculty in a professional development workshop regarding how they had previously been observed teaching the mathematics content and how infrequently they utilised the pedagogical practices recommended by STEM education experts. The paper also highlights faculty resistance to curricular reform and enumerates some ways of addressing this resistance. The paper also discusses why faculty from two-year and four-year institutions resisted working together on course redesign and provides recommendations for future efforts addressing course redesign. [ABSTRACT FROM AUTHOR]

The present study examined whether the number of manipulatives used in arithmetic strategy instruction influences learning. First graders were randomly assigned to one of the following conditions for learning a decomposition strategy to solve arithmetic problems: intervention with a single manipulative, intervention with multiple manipulatives, and a business-as-usual control condition. Both intervention conditions produced a greater increase in the use of decomposition for mental calculation than the control condition. The pattern of results across the intervention conditions varied as a function of the outcome examined. In terms of children's mastery of strategy execution with the manipulatives, there was no difference between these conditions. In terms of generalization, children whose instruction involved two complementary manipulatives tended to generalize the base-10 strategy to mental calculation to a greater extent than children whose instruction involved a single manipulative. Most noteworthy was that the findings indicated path-dependent transfer: children who mastered decomposition in the multiple-manipulatives condition were more likely to generalize this knowledge to mental calculation than those who achieved mastery via practice with a single manipulative. The implications of these findings for better understanding the conditions under which manipulatives are likely to affect learning for different outcomes is discussed. [ABSTRACT FROM AUTHOR]

By examining the effects of a national-scale teacher professional development (PD) program on instructional practices and student mathematics achievement, we contribute to calls for empirical studies investigating the impacts of such programs conducted at scale. The program corresponds well with core critical features of high-quality teacher PD and mathematics instruction identified in the literature, and the results indicate that it has had a small but statistical significant impact on teachers' instructional practices. However, no effect was found for student achievement. These results raise questions as to the importance of the critical features and how programs incorporating all of them affect instructional practices and student achievement. [ABSTRACT FROM AUTHOR]

As teachers are faced with increasing demands to meet the needs of diverse learners, such as the growing number of students with ASD, the need to accommodate each learner and provide opportunities for individualized learning becomes critical. Therefore, the aim of this A-B single-case study was to explore a variety of support strategies (e.g., video modeling, concrete manipulatives, guided practice, self-monitoring checklists, and error correction) to see which aspects of the multicomponent instruction were helpful in improving the fraction problem-solving accuracy for three students with ASD. Our analysis examined patterns in skill improvement and support levels required. All students improved their accuracy of solving fraction problems, although one student required more guidance. Using both quantitative and observational findings, we further examined each student's individual experience with the intervention and discuss future directions and implications. [ABSTRACT FROM AUTHOR]