Four Strategies for Teaching Math

1. Use the Concrete-Representational-Abstract approach to give students opportunities to explore concepts and make connections with prior concepts.

Concrete: Students use physical materials (real-life objects or models) to explore a concept. Using physical materials allows the students to see and touch abstract concepts such as place value. Students are able to manipulate these materials and make sense of what works and what does not work. 

Example: Students can represent 102, 120, and 201 with base 10 blocks and count each model to see the difference of the value of the digit 2 in each number.

Representational: Students use pictures, images, or virtual manipulatives to represent concrete materials and complete math tasks. Students are making connections and gaining a deeper understanding of the concept by creating or drawing representations.

Abstract: Students use numbers and symbols to represent math concepts. Students working at the abstract stage have a solid understanding of the concept.

2. Support discourse to sharpen students' higher-order thinking skills.

Allowing discourse between students – not just between the students and their teacher – establishes a classroom environment in which all contributions are respected and valued. Not only does this encourage students to advocate for themselves, to ask clarifying questions, and to assess their understanding of material, it also motivates students to actively engage in lessons by giving them agency and ownership over their knowledge. Learning becomes a collaborative effort, one in which each student can and should participate.

Discourse promotes a deeper understanding of mathematical concepts and vocabulary. It gives students the freedom to explore the "why's" and "how's" of math instead of thinking there is one right way to solve a math problem.

Example: Ask students for contributions to a list titled "What I Know About Fractions" prior to beginning the lesson. Discuss the items on the list beforehand.

3. Allow students to explore a concept before you explain it.

Situate math concepts in real-life situations and problems and use those circumstances as a context for learning. 

Examples: For a lesson in addition and subtraction, students can pretend to sell cookies in a bakery. For a lesson in fractions, students can pretend to sell slices of pizza. For a lesson in perimeter and area, students can pretend to be zookeepers, using Lego bricks to build animal enclosures and flooring.

4. Encourage students to solve problems together and to show off their work.

Have students stand up and work on math problems together, using a whiteboard wall or dry erase boards. This provides students opportunities for discussion, participation, and persistence. Students can get ideas by looking at each other's work, and teachers can see at a glance who needs help and who needs more time to work through something.