Colloquium September 18

Date: Friday, September 18

Time: 16:00 to 17:00

Place: 455 McBryde (Commons Room)

Speaker: Signe Kastberg of IUPUI School of Education

Title: Factors influencing the application of mathematical knowledge in teaching situations

Abstract: Mathematical understanding has long been viewed as essential in the development of an effective mathematics teaching practice. Researchers have identified various sorts of mathematical knowledge, including knowledge of an "applied mathematics teachers may need to teach children" (Hill & Lubienski, 2007, p. 751), that impact student performance in mathematics. Yet how do prospective teachers develop this applied knowledge, and what factors might influence the application of this mathematical knowledge? Ball, Lubienski, & Mewborn (2001) suggest that an examination of the mathematical knowledge used by teachers, as they build models of children's mathematics and design tasks for children, may unearth evidence of the applied mathematics needed for teaching. D'Ambrosio (2004) and others have suggested that listening orientations may influence the application of mathematical knowledge in practice. To explore the application of mathematics knowledge in practice and factors that influence application, models of prospective teachers' understandings of number were developed. These models were part of cases that also included the following: teachers' levels of comfort and perceived success with mathematics, their listening orientations, their models of a child's mathematics, and tasks designed for the child. The case studies were used to test the following hypothesis:

Prospective teachers' understanding of number, level of comfort and perceived success with mathematics, and listening orientation account for variation in their models of a child's understanding of number and tasks proposed for the child.

Factors that accounted for variation in teachers' models and the tasks teachers' designed include elements of their mathematical knowledge and orientations toward listening. Case studies and implications for curriculum in mathematics content courses for prospective teachers will be shared.

References:
Ball, D., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433-456). New York: Macmillan.
D'Ambrosio, B. (2004). Preparing teachers to teach mathematics within a constructivist framework: The importance of listening to children. In T. Watanabe & D. Thompson (Eds.), The work of mathematics teacher educators: Exchanging ideas for effective practice (Vol. 1, pp. 135-150). San Diego, CA: Association of Mathematics Teacher Educators.
Hill, H., & Lubienski, S. (2007). Teachers' mathematics knowledge for teaching and school context: A study of California teachers. Educational Policy, 21, 747-768.

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