Page 13 - Math 9-10 (2009)

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The Mathematical Processes
Presented at the start of every course in this curriculum document is a set of seven expecta- tions that describe the mathematical processes students need to learn and apply as they work to achieve the expectations outlined within the strands of the course. In the 1999 mathematics curriculum, expectations relating to the mathematical processes were embedded within indi- vidual strands. The need to highlight these process expectations arose from the recognition that students should be actively engaged in applying these processes throughout the course, rather than in connection with particular strands.
The mathematical processes that support effective learning in mathematics are as follows: • problem solving
• reasoning and proving
• reflecting
• selecting tools and computational strategies • connecting
• representing
• communicating
The mathematical processes are interconnected. Problem solving and communicating have strong links to all the other processes. A problem-solving approach encourages students to reason their way to a solution or a new understanding. As students engage in reasoning, teachers further encourage them to make conjectures and justify solutions, orally and in writing. The communication and reflection that occur during and after the process of problem solving help students not only to articulate and refine their thinking but also to see the problem they are solving from different perspectives. This opens the door to recognizing the range of strategies that can be used to arrive at a solution. By seeing how others solve a problem, students can begin to think about their own thinking (metacognition) and the thinking of others, and to consciously adjust their own strategies in order to make their solutions as efficient and accu- rate as possible.
The mathematical processes cannot be separated from the knowledge and skills that students acquire throughout the course. Students must problem solve, communicate, reason, reflect, and so on, as they develop the knowledge, the understanding of concepts, and the skills required in the course.
Problem Solving
Problem solving is central to learning mathematics. It forms the basis of effective mathematics programs and should be the mainstay of mathematical instruction. It is considered an essential process through which students are able to achieve the expectations in mathematics, and is an