Teaching and assessment in math go hand in hand. What ties them together are the mathematical processes. Our job as teachers is to help students build mathematical knowledge and skills of the curriculum through the 7 mathematical processes. They include:
- problem solving
- reasoning and proving
- selecting tools and computational strategies
For instance, here are the math processes for Grade 4 from the Ontario Curriculum:
In order to begin to assess what our students have learned through the expectations and processes, we must set some learning goals to help our students learn.
A Learning Goal must:
- Have a sense of purpose
- Build on student ideas about math
- Engage students
- Help students develop mathematical ideas
- Help teachers to assess student progress
- Connect with the classroom activities
- Connect with math processes
The kinds of activities that we engage in during math class that embody math processes may include the following:
* something to ponder: can you think about what math processes can be embodied in each of the following? Are there any more we can add?
It is important to ask the right questions. The questions help us to facilitate the discussion that will follow. Questions are also used to raise issues and problems
Inquiry Based Learning.
As students solve problems, they will develop their ability to ask questions and plan investigations to answer those questions and solve related problems. The goal is to invite student entry into the math problem, and facilitate their exploration of the math.
The focus of a Gallery Walk is on the student work and interactive discussion shared around the classroom. Students have the ability to read different solutions and provide written and verbal feedback to each other, communicate, and solve problems together.
Here, the Chalkboard becomes a record of the entire lesson. This really helps us to model effective organization to our students. It also includes cooperative learning strategies including Think-Pair-Share, Think-Talk-Write & Placemat.
Here, the purpose is to support development of mathematicians in classroom learning community vs fixing mistakes in student work. We focus the whole-class discussion on 2-3 student solutions that are selected strategically by myself, the teacher. Students also share work with one another, check answers and strategies, ask questions to provoke clarification & elaboration, and defend and support mathematical thinking.
Assessments we use:
Assessments will include rubrics, performance tasks, formative and summative tasks, observations, portfolios, journals, interviews and products. Assessment will be based on Learning Goals, expectations, processes and the following Achievement Categories:
Knowledge and Understanding. Subject-specific content acquired in each grade (knowledge), and the comprehension of its meaning and significance (understanding).
Thinking. The use of critical and creative thinking skills and/or processes,3 as follows: – planning skills (e.g., understanding the problem, making a plan for solving the problem) – processing skills (e.g., carrying out a plan, looking back at the solution) – critical/creative thinking processes (e.g., inquiry, problem solving)
Communication. communicating mathematical ideas and solutions in writing, using numbers and algebraic symbols, and visually, using pictures, diagrams, charts, tables, graphs, and concrete materials).
Application. The use of knowledge and skills to make connections within and between various contexts.
All of the instructional and assessment practices can be interconnected with the Math Processes as defined in the Ontario Math Curriculum: