Page 19 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Presented at the start of every course in this curriculum document are seven mathematical process expectations that describe a set of skills that support lifelong learning in mathe- matics and that students need to develop on an ongoing basis, as they work to achieve the expectations outlined within each course. In the 2000 mathematics curriculum, expec- tations that addressed the mathematical processes were present within individual strands to varying degrees. Here, the mathematical processes are highlighted in each course to ensure that students are actively engaged in developing their skills to apply them throughout the course, rather than only in specific strands.
The mathematical processes are as follows: problem solving
reasoning and proving
reflecting
selecting tools and computational strategies connecting
representing
communicating
Each course presents students with rich problem-solving experiences through a variety of approaches, including investigation. These experiences provide students with opportuni- ties to develop and apply the mathematical processes.
The mathematical processes are interconnected. Problem solving and communicating have strong links to all the other processes. The problem-solving process can be thought of as the motor that drives the development of the other processes. It allows students to make conjectures and to reason as they pursue a solution or a new understanding. Problem solving provides students with the opportunity to make connections to their prior learning and to make decisions about the representations, tools, and computational strategies needed to solve the problem. Teachers should encourage students to justify their solutions, communicate them orally and in writing, and reflect on alternative solutions. 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 accurate as possible.
THE MATHEMATICAL PROCESSES