Hong Qian, PhD StudentPeter Youngs, Associate Professor

Michigan State University

Presentation to Global Education GroupFebruary 16, 2011

The Influence of University Courses and Field Experiences on Elementary Teaching Candidates’

Mathematical Knowledge for Teaching: New Evidence from Four Universities in China

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

An example of MKT measures

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?

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

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

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

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.

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.

Methods and Data SourcesPrograms 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)

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 ________?

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

Data Analysis

MKTPFA j : DV (MKT PFA score for teaching candidate j )

z j : IVs (e.g. math courses, field experience)

x j : control variables (e.g. math score in College Entrance Examinations)

MKTPFA j = βz j +θx j + e j

MKTNO i = βz i +θx i + e i

FindingsNumber 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)

FindingsNumber 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)

FindingsNumber 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)

FindingsNumber 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)

FindingsExposure to Representations of Practice

0.404 (N&O) -0.127 (PFA)

Exposure to Decompositions of Practice

1.509* (N&O) 1.268* (PFA)

FindingsOpportunities to Engage in Approximations of Practice

2.007* (N&O) 1.300 (PFA)

Discussion Importance of topics addressed in math

methods courses Testing the theory: decompositions and

approximations Value of student teaching with full

responsibility

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

More InformationContactHong Qian Peter YoungsPh.D. Student Associate ProfessorDept. of Teacher Education Dept. of Teacher EducationMichigan State University Michigan State Universityqianhon1@msu.edu pyoungs@msu.edu