Hong Qian, PhD Student Peter Youngs, Associate Professor Michigan State University Presentation to Global Education Grou

1. The Influence of University Courses and Field Experiences on Elementary Teaching Candidates’ Mathematical Knowledge for Teaching: New Evidence from Four Universities in China Hong Qian, PhD Student Peter Youngs, Associate Professor Michigan State University Presentation to Global Education Group February 16, 2011

2. Overview of Presentation • Research Questions • Literature Review • China Context • Theoretical Framework, Hypotheses • Methods and Data Sources • Measures • Findings

3. An example of MKT measures

4. Research Questions • What are the associations between the number and nature of university-level math courses taken and MKT in a) number and operations (N&O), and b) patterns, functions, and algebra (PFA)? • What are the associations between experiences in math methods courses and MKT in a) N&O, and b) PFA? • What are the associations between engagement in student teaching with/without full responsibility for instruction and MKT in a) N&O, and b) PFA?

5. Literature Review • Research on teacher characteristics (e.g., Clotfelter et al., 2007; Croninger et al., 2007) • Effects of teacher preparation components on student learning (Boyd et al., 2008; Constantine et al., 2009); results point to need to study nature of learning activities/experiences • Research on mathematical knowledge for teaching (MKT) (Hill et al., 2008; Hill, Rowan, & Ball, 2005; Rockoff et al., 2009) • Comparative studies of Chinese and U.S. teachers (Ma, 1999; An, Hulm, & Wu, 2004) • Little research on how teaching candidates’ experiences in teacher preparation affect their MKT

6. China Context • Chinese teachers’ strong math content knowledge and MKT (Ma, 1999; An, Hulm, & Wu, 2004) • Recent changes in teacher education policy and practice in China -Through 1990s, most elementary teachers had completed only secondary education -Two educational reforms in 1999 called for upgrading qualifications for elementary teachers -Rapid changes in 2000s to implement new mandate

7. China Context • Despite policy changes, wide variation in teacher education reform • Differences across three main regions (Paine & Fang, 2007) -More developed coastal areas in East and South -Fairly well-developed inland areas -Least developed, remote areas • Variations across three main regions • Variation within more developed regions -Administration, coursework, degree of selectivity, relative emphasis on single-subject vs. multiple-subject preparation

8. Theoretical Framework, Hypotheses • Theory of teacher learning informed by work of Grossman and Ball • Theory: Enacting MKT is a complex activity requiring content knowledge, teaching-specific knowledge, ability to enact instructional activities and assess student learning, and knowledge of when to enact certain activities/assessments (Grossman et al., 2009; Ball & Forzani, 2009) • For most competent adults, enacting many aspects of MKT is unfamiliar or even unnatural • Thus, according to this theory, teaching candidates must have structured opportunities to acquire MKT and learn to enact key practices successfully • Hypothesis 1A: The number of the university-level mathematics content courses taken by a teaching candidate will be directly related to their level of mathematical knowledge for teaching (MKT). • Hypothesis 1B: The nature of the university-level mathematics content courses taken by a teaching candidate will be directly related to their level of MKT.

9. Theoretical Framework, Hypotheses • Hypothesis 2A: The extent to which a teaching candidate is exposed to representations of practice during courses will be directly related to their level of MKT. • Hypothesis 2B: The extent to which a teaching candidate is exposed to decompositions of practice during courses will be directly related to their level of MKT. • Hypothesis 2C: The extent to which a teaching candidate has opportunities to engage in approximations of practice in courses and field experiences will be directly related to their level of MKT. • Hypothesis 3A: The extent to which a teaching candidate engages in student teaching with full responsibility for instruction will be directly related to their level of MKT. • Hypothesis 3B: The extent to which a teaching candidate engages in student teaching (including student teaching when they do not have full responsibility for instruction) will not be related to their level of MKT.

10. Methods and Data Sources Programs • 4 teacher preparation programs Zhejiang, China; 3 teacher preparation programs in Michigan, U.S. (data not included in paper) • Each Chinese program prepared elementary teachers to teach either multiple subjects or only elementary math • The Chinese programs varied with regard to program administration, selectivity, size, and single-subject vs. multiple-subject focus Teaching Candidates • Elementary teaching candidates in final year of their preparation programs (n=8, 15, 32, 45 candidates from the Chinese programs; n=100 total) • Teaching candidate surveys with items about coursework, field experiences, opportunity-to-learn • Mathematical knowledge for teaching surveys (N&O and PFA)

11. Inside Baseball: What happened re: data collection in the US vs. data collection in China? 3 US Programs • 2 told us that they (not us) would send an e-mail to possible participants; we ended up with 15 participants from these programs combined • 1 provided us with the names and contact info for about 60-65 teaching candidates; we ended up with 35 participants • Some initial participants only completed one survey • $20 gift card for each survey completed; did not use $2 bills (value of providing initial incentive; based on social exchange theory) • Lesson: Negotiate access to teaching candidates at outset 4 Chinese programs • We had a colleague on the ground in China • Able to get direct access to 25 teaching candidates at each program during class; all participants completed both surveys • $10 gift card for completing both surveys ($10 is of great value in China) • Lesson: Pay attention to ________?

12. Measures • MKT N&O/PFA score • Number and nature of mathematics content courses • Topics addressed in general pedagogy and math methods courses • Length of student teaching • Representations of practice • Decomposition of practice • Approximations of practice

13. Data Analysis MKTPFA j = βz j +θx j + e j • MKTPFA j : DV (MKT PFA score for teaching candidate j) • zj: IVs (e.g. math courses, field experience) • x j: control variables (e.g. math score in College Entrance Examinations) MKTNO i = βz i +θx i + e i

14. Findings Number of Math Content Courses Taken 0.318 (N&O) 0.298 (PFA) Nature of Math Content Courses Taken number theory (N&O) mathematical reasoning (N&O)

15. Findings Number of Topics Addressed in general pedagogical Courses 1.332** (N&O) 0.787* (PFA) Nature of Topics Addressed in general pedagogical Courses Classroom Management (N&O) Student Collaborative Learning (N&O and PFA)

16. Findings Number of Topics Addressed in Math Methods Courses 0.686* (N&O) 0.982*** (PFA) Nature of Topics Addressed in Math Methods Courses Math Curricula in Schools (PFA) Methods of Teaching Math (N&O and PFA) Methods for Solving School Math Problems (PFA) Psychology of Math (PFA)

17. Findings Number of Weeks of Student Teaching with Full Responsibility for Instruction 0.531* (N&O) 0.170 (PFA) Number of Weeks of Student Teaching (including student teaching without full responsibility for instruction) 0.170 (N&O) -0.202 (PFA)

18. Findings Exposure to Representations of Practice 0.404 (N&O) -0.127 (PFA) Exposure to Decompositions of Practice 1.509* (N&O) 1.268* (PFA)

19. Findings Opportunities to Engage in Approximations of Practice 2.007* (N&O) 1.300 (PFA)

20. Discussion • Importance of topics addressed in math methods courses • Testing the theory: decompositions and approximations • Value of student teaching with full responsibility

21. Limitations and future research • Use of MKT measures in Chinese context • Need for longitudinal research that examines effects on math instruction • Role of interview data in explaining processes by which teacher preparation affects MKT

22. More Information Contact Hong Qian Peter Youngs Ph.D. Student Associate Professor Dept. of Teacher Education Dept. of Teacher Education Michigan State University Michigan State University qianhon1@msu.edupyoungs@msu.edu