Session Information
24 SES 07, Mathematics Teachers' Training (Part 1)
Paper Session to be continued in 24 SES 08 A
Contribution
The concept of Mathematical Knowledge for Teaching (MKT) refers to the mathematical knowledge required for teaching mathematics: see (Ball, Thames and Phelps 2008) for a detailed characterisation. MKT expands upon and refines, in the case of mathematics teaching, the earlier concept of Pedagogical Content Knowledge (PCK) (Shulman 1986). This paper reports on an intervention to develop the MKT of Mathematics and Science Education undergraduates in an Irish University by focussing on the design of formative and summative assessment tasks for use in second level classrooms. MKT incorporates both subject matter knowledge and pedagogical content knowledge and relates to the specialised knowledge a teacher must possess in order to carry out the mathematical tasks of teaching (like explaining or choosing an appropriate example). This research will concentrate on the aspects of MKT needed for good assessment practice such as asking productive mathematical questions, designing or modifying tasks, and critically evaluating textbook materials. The design of such elements of teacher education programmes is a live issue in the mathematics teacher education community. In 2009, Superfine and Wagreich have noted that “[t]he field of mathematics education currently lacks models for the design and implementation of content courses aimed at developing pre-service teachers’ mathematics knowledge for teaching” (2009, p.25).
The research project will involve a series of workshops. The series will begin by introducing students to carefully chosen frameworks for classifying the cognitive demand of tasks (Smith and Stein 1998), the type of reasoning required by tasks (Lithner 2008), aspects of problem-solving involved in tasks (O’Sullivan 2014), and design of tasks (Swan 2008). Students will then use the frameworks to evaluate textbook and examination exercises and to design their own tasks. In addition, students will be introduced to techniques to improve their in-class questioning skills. This workshop will use the work of Watson and Mason (1998) to develop strategies to help with higher-order questioning skills and the encouragement of mathematical discussion in class. During the series of workshops the students will create a portfolio of their own tasks and questioning techniques, and reflections on their design. Boston (2013) asserts that improving students’ opportunities to learn mathematics with understanding requires mathematics teachers to select and implement high-level tasks in ways that maintain students’ engagement in thinking and reasoning throughout an instructional episode (p.14). Therefore these skills of recognising, selecting and developing high-level tasks are essential to develop during initial teacher education programmes.
The workshops will be designed and delivered by Majella Dempsey and Ann O’Shea and will be complemented by a guest workshop by Professor Malcolm Swan (an international expert on task design).
The research questions are:
Can students’ skills in critical evaluation of assessment tasks be developed using a focused intervention?
Can students’ skills in the design of assessment tasks be improved using a focused intervention?
What is the role of MKT in the development of assessment tasks?
Method
Expected Outcomes
References
Boston, M.D. (2013). Connecting changes in secondary mathematics teachers’ knowledge to their experiences in a professional development workshop. Journal of Mathematics Teacher Education. 16 (1):7–31 Lithner, J. (2008). A research framework for creative and imitative reasoning. Educ Stud Math 67:255–276 Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(4): 268-275 Superfine, A.C. and Wagreich, P. (2009). Developing mathematics knowledge for teaching in a content course: a “design experiment” involving mathematics educators and mathematicians. In Mewborn, D.S. & Lee, H.S. (Eds), Scholarly Practices and Inquiry in the Preparation of Mathematics Teachers. San Diego: AMTE Swan, M. (2014). Design Research in Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. Swan, M. (2008). Designing a Multiple Representation Learning Experience in Secondary Algebra. MARS/Shell Centre, University of Nottingham: England Watson, A. & Mason, J. (1998). Questions and Prompts for Mathematical Thinking. Derby: Association of Teachers of Mathematics.
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