The Mathematical Processes
The mathematical processes are the processes through which students acquire and apply mathematical knowledge and skills. These processes are interconnected. Students should be actively engaged in applying the below seven processes throughout their mathematical program in all five strands, 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 • representing • communicating
Teaching through Problem Solving
Problem solving is central to learning mathematics. By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding. Problem solving forms the basis of effective mathematics programs and should be the mainstay of mathematical instruction.
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 range of strategies that can be used to arrive at a solution. By seeing how others solve a problem, students can begin to reflect on their own thinking, and the thinking of others, and to consciously adjust their own strategies in order to make their solutions as efficient and accurate as possible.
“Teaching through problem solving as described in the Ontario Curriculum and the Guide to Effective Instruction is not a weekly event (e.g., problem of the week or problem solving lesson of the week), it is a mode of effective instruction to develop conceptual understanding, reasoning and proving, in fact all of the process expectations.
The 3 part lesson is a structure for daily implementation with a 50 min to 60 min numeracy block, as all 3 expert panel reports suggest that mathematics be taught in 60 minute blocks.” (Kathy Kubota-Zarivnij LNS 2009)
The Ontario Curriculum Grades 1 – 8 Revised Mathematics 2005

Math Unit One

Patterning

Multiples: