Connecting, Reasoning and Proving, Problem solving, 

Reflecting, Representing

Communicating, Selecting Tools and Computational Technologies)
5. Math Curriculum Grades 1-8 Mathematics Curriculum - Ontario

Effective Mathematics Instruction is happening in our classroom to support student learning when:

Ongoing Assessment for Learning is provided for your child: questions are posed that evoke student thinking; differentiated instruction is used; assessment for learning information is recorded; instructional plans may be changed based on comments students make. 

We utilize many approaches: open or parallel questions are often asked; students are encouraged to self-scaffold and teacher scaffolds by leading rather than telling students; alternative methods are regularly offered when students struggle. (EduGAINS, Assessment For and As Learning with Mathematical Processes)

Math lesson emphasizing the math processes looks like this: see Representing math lesson sample.

Mathematical thinking is communicated orally, visually, kinaesthetically, and in writing in every day math class. 

Life-long learners of mathematics build new knowledge and skills in prior knowledge using the mathematical processes. The interrelated aspects of Problem Solving include: 

Representing, Reflecting, Connecting, Reasoning and Proving, Selecting Tools and Computational Strategies.

(EduGains) 

Examples of assessment for and as Learning with Mathematical Processes are as follows when a student sees himself doing...
1. Problem solving:  I know I am doing problem solving when I select, sequence and apply processes appropriate to the task; use critical thinking skills to solve a problem.
2. Reasoning and Proving: 

I know I am reasoning and proving when I hypothesize and make conjectures; decide how to test my hypothesis; test my conjecture; infer, justify, and conclude. 

3. Reflecting: I know I am reflecting when I think about reasonableness; consider the implications of data collected; self-monitor my progress.
4. Selecting tools and computational strategies: I know I am selecting tools and computational strategies when I use manipulatives and/or technology to understand new concepts, to communicate, or to perform tasks; consider the question before I choose my computational strategy.
5. Connecting: I know I am connecting when I see how new concepts and skills build on old ones; apply mathematics to solve problems inside and outside of mathematical class.
6. Representing: I know I am representing when I mathematize a situation using concrete materials, pictures, diagram, graphs, tables, numbers, words or symbols.
7. Communicating:  I know I am communicating when I use clear language to make presentations, and to explain and justify solutions when reporting for various purposes and different audiences; use mathematical symbols, labels, units and conventions correctly; use mathematical vocabulary appropriately. (Growing Success, 2010)

Understanding of mathematical concepts. 

• Thinking: It is the use of critical and creative thinking skills and/or processes: there are 3 skills: 1. planning skills (e.g., understanding the problem, making a plan for solving the problem), 2. processing skills (e.g., carrying out a plan, looking back at the solution), 3. critical/creative thinking processes (e.g., inquiry, problem solving).
• Communication: It is the conveying of meaning through various forms (e.g., providing explanations of reasoning or justification of result orally or in writing; communicating mathematical ideas and solutions in writing, using number and algebraic symbols, pictures, diagrams, chars, tables, and concrete materials).
• Application: It is how to use of knowledge and skills and make connections within and between
various contexts such as, 1. transfer of knowledge and skills to new context, 2. making connections within and between various contexts (e.g., connections between concepts; connections involving use of prior knowledge and experience; connections between mathematics, other disciplines, and the real world).

The development of learning skills and work habits is an integral part of a student’s learning. Teacher will work with your child to help him or her develop the learning Skills and work habits and become effective learners. The learning skills and work habits are: Responsibility, Organization, Independent Work, Collaboration, Initiative, Self-regulation. 

The reason is as Harlen (2006) explains, “Using the terms ‘formative assessment’ and ‘summative assessment’ can give the impression that these are different kinds of assessment. What matters is how the information is used." In todays' assessment, students are an active participant of assessment processes by assessing their work and peers. 
Please see the video below to understand how the assessment is being used to improve student learning.