Mathematics: Problem Solving & Reasoning

This subject is not offered in 2014.

120 hours.

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Overview, Objectives, Assessment and Generic Skills sections of this entry.

It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and the Disability Liaison Unit: http://www.services.unimelb.edu.au/disability/

This subject will focus on research and issues related to the teaching and learning of mathematics in primary and secondary classrooms through the use of problem solving and reasoning. Problem solving is seen as an approach to teaching mathematics, a way of doing mathematics and mathematical content in its own right. Problem solving and reasoning focus particularly on questions related to how we think mathematically and learn more deeply in a mathematical environment that emphasises big ideas in mathematics teaching. Topics include: trends in reasoning and problem solving research; attitudes to and conceptions of problem solving and reasoning; problem solving, reasoning and working mathematically; interdisciplinarity; assessment; developing challenging tasks to increase cognitive demand; managing the problem solving/reasoning classroom; teaching students to address a challenge; raising the level of mathematical competence required for informed citizenship and lifelong learning; increasing students’ confidence in using mathematics to solve problems; the role of technology in facilitating reasoning and problem solving.

On completion of the subject students will be able to:

• Clearly Identify what defines the proficiency strands “Problem Solving” and “Reasoning” of the Australian National Curriculum;
• Devise teaching strategies that implement problem solving and reasoning in the classroom;
• Identify and demonstrate a sound understanding of educational research and practice in the area of teaching and learning mathematics through problem solving and reasoning in schools;
• Demonstrate confidence in using mathematics to solve problems.

There are three assessment tasks:

• A 1,500 word academic report exploring issues related to researching, teaching and/or learning through an approach using problem solving /or reasoning, due late semester, 30%
• A 10 minute oral presentation (equivalent 1,000 words) due late semester, 20%
• A 2,500 word research-based report, due end semester, 50%

Attendance at all classes (tutorial/seminars/practical classes/lectures/labs/online classes) is obligatory. Failure to attend 80% of classes will normally result in failure in the subject.

Blum, W., Galbraith, P., Niss, M., Henn, H.-W. (Eds.). (2007). Modelling and applications in mathematics education, New ICMI Studies Series no. 10. New York: Springer.

Clarke, D. J., Goos, M., & Morony, W. (2007). Problem solving and working mathematically: An Australian perspective. ZDM—The International Journal on Mathematical Education, 39(5-6), 475-490.

Lesh, R., & Zawojewski, J. (2007). Problem solving and modelling. In F. Lester (Ed.), Second handbook of research o mathematics teaching and learning (pp. 763-804). Charlotte, NC: IAP.

Stillman, G. A., Brown, J. P., & Galbraith, P. L. (2008). Research into the teaching and learning of applications and modelling in Australasia. In H. Forgasz, A. Barkatsas,

A. Bishop, B. Clarke, S. Keast, W-T. Seah, & P. Sullivan (Eds.), Research in mathematics education in Australasia 2004-2007 (pp. 141-164). Rotterdam, The Netherlands: Sense Publishers.

Stillman, G., Cheung, K-C., Mason, R., Sheffield, L., Sriraman, B., & Ueno, K. (2009). Challenging mathematics: Classroom practices. In E. Barbeau & P. Taylor (Eds.), Challenging mathematics in and beyond the classroom: The 16th ICMI study, New ICMI Studies Series no. 12 (pp. 243-283). New York: Springer.

This subject is not available as a breadth subject.

Students completing this subject should be able to:

• Demonstrate a superior knowledge and understanding of educational theory and practice in general and in the area of teaching and learning mathematics through problem solving and reasoning in particular;
• Express informed opinions on these issues;
• Have an understanding of the theory and practice of educational research needed to evaluate research literature and carry out appropriate research activity in this area;
• Make effective use of the findings of educational writings and research in addressing professional problems;
• Have the depth of knowledge and understanding that will enable them to be a resource for colleagues in particular professional situations;
• Demonstrate an appreciation of professional responsibilities and ethical principles which should characterise leaders in the education profession.