Math Class for Educators
Teaching Strategies
To learn mathematics in a way that will serve them well throughout their lives, students need classroom experiences that help them develop mathematical understanding; learn important facts, skills, and procedures; develop the ability to apply the processes of mathematics; and acquire a positive attitude towards mathematics
- Ontario Mathematics Curriculum (Ontario Ministry of Education, 2005)
Below is a collection of suggested strategies for teaching mathematics, as well as links to resources where you can gather more information or view examples. These teaching strategies represent current understandings about "best practice" and they connect to research regarding what today's learners need. The intent is that these strategies can be utilized across the various strands of the curriculum.
Learning Goals & Success Criteria
Learning goals are clear statements that describe, in student-friendly language, what the focus for learning is in the classroom.
Learning goals help to give direction to the instruction that is happening. They are also actively used by teachers and students to self-assess and reflect. They should be thoroughly discussed and broken down with students. They should also be continually referred to.
The most effective learning goals reflect a cluster of curriculum expectations. In math, for example, a learning goal may include statements about the current concepts that are that are being focused on, as well as references to mathematical processes.
Success criteria are CO-CREATED gradually with students as they inquire, discover and make connections with the learning goals. They outline how students can experience success and demonstrate their thinking effectively.
Learning goals and success criteria reflect best practice in the classroom. All teachers use them differently, but they are helpful to students and thus, important to implement.
Check out these examples of learning goals and success criteria
Focus on the Processes
The mathematical processes help students learn how to "do" math-- how to think mathematically, look for solutions and share their thinking. The processes should be emphasized continually, as they are, in many ways, more important than the content itself.
Click here to learn more about each of the processes, what they mean and how you can incorporate them into the classroom.
Problem Solving
Connecting
Selecting Tools/Computational Strategies
This goal and success criteria can be applied to any problem/strand/topic and it incorporates many of the mathematical processes.
This goal is focused on using efficient and effectives strategies to solve problems quickly and accurately. It also incorporates many of the processes.
This goal and success criteria can be applied to any problem/strand/topic and it incorporates many of the mathematical processes.
Communicating
Reasoning/Proving
Representing
Reflecting
Three-Part Math Lesson
The three-part math lesson is an approach to instruction that focuses on problem-solving, application, sharing and building a collective understanding of math concepts. In a singular lesson, many of the mathematical processes can be utilized. Students are engaged in rich tasks and they are making connections.
Part 1: Minds-On/Before/Activate
Involves activating students' thinking and getting them focused on the concept(s) that will be addressed throughout the remainder of the lesson. It may involve having students work on a simple question, turn-and-talk, think-pair-share, watch a short video, listen to a book or work with manipulatives to complete a task.
Part 2: Action/During/Hands-On
Involves students actively working on applying their thinking. Often, this will entail them working on solving a problem, using various strategies, tools and manipulatives. Typically, students will work in pairs or in small groups to enable rich conversations to take place. The teacher is circulating around, assessing, facilitating talk, annotating student work, asking questions or working with a small group.
Part 3: Consolidation/After/Congress
Involves reflecting, connecting and summarizing learning. Various approaches and strategies can be utilized during this time. The ultimate goal is to look for new discoveries, key learnings, useful/efficient strategies and relevant questions that can guide the learning in subsequent lessons. Explicit teaching can occur here as well and more practice.
Check out this video describing the elements of a three-part math lesson and its benefits
Problem-Based Learning/Inquiry
"By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding. Problem solving forms the basis of effective mathematics programs and should be the mainstay of mathematical instruction".
- Ontario Mathematics Curriculum, pg. 11
Reflecting/Connecting Strategies
Bansho: "Board Writing"
Bansho is a strategy where the thinking from the beginning of the lesson to the end is recording on a board. The problem is posted, student solutions are organized according to strategy and key findings are recorded. Click here to read and see more.
A congress is a sharing strategy that encourages students to explain their reasoning. The teacher acts as a facilitator. Click here to see an example of what the process of a math congress looks like in the classroom.
Gallery walks are interactive and collaborative. Students rotate around the classroom, discuss their thinking and solutions and provide feedback for one another.
Math Congress
Gallery Walk
Check out this selection from the "Capacity Building Series" on Communication in the Classroom. It covers all three strategies discussed above.
Integrate & Relate
Math does not exist in isolation. The illustration to the right helps to highlight the value of integrated learning. It is helpful to find ways to connect math across all other subjects, as this will enable students to find real-life examples and applications. It also increases interest and engagement.
Talk About it: Number Talks & Focusing on Operations
As crucial as problem solving is, it is also necessary to focus on operations and number sense at all times.
Number Talks are great ways to encourage reasoning and mental math. Questions are presented and students work to solve them independently. Students then share their thinking and provide proof for their solutions.
Hands-On Learning: Using Manipulatives
"Using manipulatives to construct representations helps students to:
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See patterns and relationships
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Make connections between the concrete and the abstract
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Test, revise and confirm their reasoning
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Remember how they solved a problem
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Communicate their reasoning to others"
- Ontario Mathematics Curriculum, pg. 15
Click here to jump to the "Manipulatives" Page on this site for more information