Page 25 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

of problem solving support students as they work to articulate and refine their thinking and to examine 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 understanding how others solve a problem, students can begin to reflect on their own thinking (a process known as “metacognition”) and the thinking of others, as well as their own language use (a process known as “metalinguistic awareness”), and to consciously adjust their own strategies in order to make their solutions as efficient and accurate as possible.
The mathematical processes cannot be separated from the knowledge, concepts, and skills that students acquire throughout the course. All students problem solve, communicate, reason, reflect, and so on, as they develop the knowledge, the understanding of mathematical concepts, and the skills required in all strands.
Problem Solving
Problem solving is central to doing mathematics. By learning to solve problems and by
learning through problem solving, students are given, and create, numerous opportunities to connect mathematical ideas and to develop conceptual understanding. Problem solving forms the basis of effective mathematics programs that place all students’ experiences and queries at the centre of mathematical learning. Therefore, problem solving should be the foundation of mathematical instruction. It is considered an essential process through which all students are able to achieve the expectations in mathematics and is an integral part of the Ontario mathematics curriculum.
Problem solving:
• increases opportunities for the use of critical thinking skills (e.g., selecting appropriate tools and strategies, estimating, evaluating, classifying, assuming, recognizing relationships, conjecturing, posing questions, offering opinions with reasons, making judgements) to develop mathematical reasoning;
• supports all students in developing their own mathematical identity;
• allows all students to use the varied mathematical knowledge and experiences they bring to
school;
• supports all students in making connections among mathematical knowledge, concepts, and
skills, and between situations inside and outside the classroom;
• has the potential to promote the collaborative sharing of ideas and strategies, and promotes
talking about and interacting with mathematics;
• empowers students to use mathematics to address issues relevant to their lived realities;
• facilitates the use of creative-thinking skills when developing solutions and approaches;
• supports students in finding enjoyment in mathematics and becoming more confident in their
ability to do mathematics.
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