It is through The Mathematical Processes that we can promote THINKING

Critical thinking plays a significant role in mathematics. When faced with problems to solve mathematicians routinely make reasoned judgments about what, and how to think. While thinking about mathematical concepts, procedures, strategies, tools, representations, and models, decisions are made through the use of criteria and appropriate evidence. To think like a mathematician is to think critically through the mathematical processes. By promoting, teaching and assessing critical thinking through the processes, teachers not only help students to learn to think like a mathematician, they ensure students think to learn about mathematics. By placing the quality of thinking at the core of learning mathematics teachers can make learning meaningful and engaging for both students and teachers.

"The mathematical processes can be seen as the processes through which students acquire and apply mathematical knowledge and skills. These 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 reflect on their own thinking (a process known as “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 cannot be separated from the knowledge and skills that students acquire throughout the year. Students must problem solve, communicate, reason, reflect, and so on, as they develop the knowledge, the understanding of concepts, and the skills required in all the strands in every grade."(The Ontario Curriculum Grades 1-8 Mathematics, page 11)

Reasoning and Proving Communicating Representing Connecting

Representing Selecting Tools & Computational Strategies Problem Solving

Connecting Mathematical Processes with the Achievement Chart

Mathematical Processes - Resources

"The mathematical processes can be seen as the processes through which students acquire and apply mathematical knowledge and skills. These processes are interconnected (The Ontario Curriculum Grades 1-8 Mathematics, page 11)". These processes are developed along a continuum, across the grades. Click on the links below to access the K-12 Math Process Expectation Continuum.

K-12 Mathematical Process Expectation Continuum - Google DOC

(This document was originally shared through a virtual System Implementation Monitoring session)

Assessing the Processes

Assessment For and As Learning with the Mathematical Processes: This one page document includes learning goals and success criteria with sample questions and feedback for five of the mathematical processes.

Generic Rubric for the Seven Mathematical Processes: This rubric shows possible connections between the mathematical processes and the achievement chart categories.

Assessing Mathematical Processes - A Complex Process by Dr. Chris Suurtamm:

Mathematics is more than content. Doing mathematics is a complex process and proficiency in mathematics means a certain level of expertise, competence, knowledge, and facility in mathematics. This article discusses the importance of recognizing mathematical processes and the challenge of examining mathematical processes in the assessment process.

How do students communicate their understanding of mathematics? By incorporating visible thinking strategies into daily lessons, teachers will observe changes in student learning. Those changes will make a difference in closing the achievement gap in mathematics.” (Visible Thinking in the K-8 Mathematics Classroom, Page 148)