Math Matters @ SGDSB is Currently Under Construction to be updated yet still has many valuable resources to check out!
James Tanton is a co-founder of The Global Math Project (more info in tab on the left) and popularized "Exploding Dots" - the featured topic for Global Math Week... He is also the author the the Solve This math activities and many other authored texts...http://gdaymath.com/about/
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)
One way to visualize the interconnections among the categories of the Achievement Chart and the Mathematical Processes is shown in the gears. This diagram illustrates the viewpoint that “Skills without conceptual understanding are meaningless; conceptual understanding without skills is inefficient. Without problem-solving skills, skills and conceptual understanding have no utility.” Mathematics Program Advisory, June 1996.
Knowing facts and procedures is an important aspect of mathematics education. At each grade level students learn basic facts – mental mathematics skills and the use of standard algorithms and procedures. Conceptual understanding is another key component of mathematics education. Students with conceptual understanding see mathematics as a related whole. Applying and representing mathematical ideas in different ways for different situations, and connecting procedures and concepts are some indicators of conceptual understanding.
The mathematical processes are integral to problem solving. Students deepen their knowledge and understanding as they develop, refine, and use these processes in doing mathematics.
The seven mathematical process expectations describe the actions of doing mathematics. There are many resources available through EduGains to help teachers teach and support understanding of the mathematical processes. The following mathematical posters were provided to help students understand the Mathematical Processes.
The videos above can be found by scrolling to the bottom here.
(This document was originally shared through a virtual System Implementation Monitoring session)
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.