Developing teachers’ mathematics knowledge for teaching

1. Developing teachers’ mathematics knowledge for teaching Challenges in the implementation and sustainability of a new MSP Dr. Tara Stevens Department of Educational Psychology and Leadership Dr. Gary Harris Department of Mathematics Dr. Zenaida Aguirre-Munoz Department of Curriculum and Instruction

2. Support provided by the National Science Foundation Math Science Partnerships Program under Award No. 0831420. The opinions expressed in this presentation are those of the WTMSMP personnel and associates and do not necessarily reflect those of NSF.

3. West Texas Middle School Math Partnership • Four institutions of higher education. • Spread over 84,000 square miles of West Texas. • Graduate level mathematics course taught at each institution. • Emphasis on developing mathematics self-efficacy and cultural sensitivity

4. Context of the WTMSMP • Mathematical knowledge for teaching • Hill et al. (2008); Hill, Rowan, & Ball (2005) • Deep understanding of mathematical concepts to allow explanations of why specific mathematical procedures work, descriptions of mathematical terms in language understood across the developmental levels of students, and explanations of students errors. • Sowder, Philipp, Armstrong, & Schappelle (1998) • Middle school math teachers “are not familiar with the content except at a rather superficial, disconnected, and symbolic level” (p. 31).

5. Context of the WTMSMP • Texas Assessment of Knowledge and Skills • State adopted textbooks • Bromley & Apple (1992) • Prescribed delivery • Darling-Hammond & McLauglin (1995); Porter & Brophy (1988) • Teacher training emphasis on memorizing facts

7. WTMSMP • Graduate level course with emphasis on deep conceptual understanding of the algebraic structure of the rational number field. • Time spent teaching about the importance of mathematics self-efficacy for teachers and students. • Stevens et al. (2004); Stevens et al. (2006); Anderson et al. (1988); Midgley et al. (1989)

8. Research and Evaluation • Participation in WTMSMP activities will be associated with increases in teachers’ deep conceptual knowledge of elementary mathematics, teachers’ mathematics, and teaching self-efficacy. • Within subjects (initial), between subjects (in progress) • Participation in WTMSMP activities will be associated with higher levels of mathematics achievement in public school students. • Between subjects (year three)

9. WTMSMP Initial Findings Quantitative Qualitative When initially asked “What knowledge and skills should highly qualified middle school math teachers possess,” teachers sited more pedagogical skills than content. After the intensive course, the majority (70%) shifted priorities to content based responses. • Overall, participants performed slightly better on the number concepts and algebra MKT tests (not statistically significant). • Evidence was present for the significant growth in only the Sul Ross participants on one measure, the MKT Algebra test (t(6)= -2.54, p = .04).

10. WTMSMP Initial Findings Quantitative Qualitative Participants’ initial reports of self-efficacy were high when addressing the open-ended questions, “Suppose your school adopted a new math program and it required that you begin to teach some topics you have never taught before. What initial action would you take? Would this affect your beliefs about your ability to teach effectively?” About 30% indicated they felt less confident after taking the course because they realized they needed to know more about the mathematics content they teach. • Overall, pre- and post-test comparisons on self-efficacy measures indicated statistically significant growth in all areas with the exception of self-efficacy for classroom management. • Although the same pattern of growth was observed for both TTU and ASU participants, SRS participants did not report statistically significant increases in their overall sense of teaching self-efficacy. The UTPB group reported significant increases in only their instructional self-efficacy.

11. Although all participants reported gaining knowledge from the WTMSMP course and quantitative results indicated an overall increase in self-efficacy, about half the respondents still had fears about future intensive math courses. Of these, 68% provided content-based fears.

12. Variations across Locations • The participants did not significantly differ by location on any of the pretest variables (i.e., conceptual knowledge, self-efficacy) and did not significantly differ on the number of hours of mathematics taken in college, years teaching mathematics, or prior hours of inservice training. • Differences in participant number across locations. • Differences in teaching context (e.g., rural versus urban). • Differences in

13. Interpretations • Many participants entered the WTMSMP expecting a focus on pedagogy and had to adjust to the mathematics focus. • Although participants left with a high degree of mathematics self-efficacy, they will need mastery experiences with the new content to develop the same degree of self-efficacy for courses II and III. • Adjustments are necessary to address variations in outcomes across locations.