This dissertation reports on one effort to improve the mathematical preparation of prospective secondary mathematics teachers (PSMTs). As a design experiment, this study reports on an experimental curriculum engineered to promote specific problem solving behaviors for the purpose of enriching and unifying PSMTs' conceptual knowledge of mathematics and fostering mathematical practices that have been shown by research to be productive for mathematicians. Two case studies of PSMTs are presented, investigating their behaviors and subsequent growth as a result of their participation in the experiment. This investigation builds upon previous research into the problem solving behaviors of mathematicians, and extends this research into the arena of undergraduate teacher preparation. The Multidimensional Problem Solving Framework guided the design of tasks and activities in the instructional sequence and also provided the theoretical perspective for retrospective analyses of the data. The framework was used to identify evidence of the cycles of problem solving, use of resources, affect management, monitoring, and beliefs as PSMTs progressed through the course. Both of the students studied experienced improvement in their problem solving behavior and significant shifts in their views about mathematics. The quality of PSMTs' conceptual understanding of the mathematics at hand was revealed to greatly impact the solvers' success in constructing viable solutions. Well-connected conceptual understanding of mathematics appears to be a necessary but not sufficient condition for problem solving success.someone else would do it graphically to find the same answer, so I really liked how you could do that, so now I try to see ... In this passage, it appears that Amy recognized the shortcomings of the strictly algebraic approaches to problem solvinganbsp;...
|Title||:||Promoting and Characterizing the Problem Solving Behaviors of Prospective High School Mathematics Teachers|
|Publisher||:||ProQuest - 2008|