Effective math instruction requires knowing what important mathematical skills students need to acquire, and being aware of which instructional practices best foster these skills. The following is a list of 15 components of effective math instruction, and tips on how to use educational technology, like your smart board, to integrate these ideas into your lessons.

Knowing What to Teach

When deciding where the instructional emphasis should be for the grade level you teach, consider NCTM’s Curriculum Focal Points. NCTM has identified three central mathematical topics for each grade level, with work in the higher grades building on what was learned in earlier grades.

Approaches to Teaching Mathematics

Like their counterparts in literacy, math teachers have a debate about which philosophical approach to teaching mathematics is best. The two important factions are skills-based instruction, with an emphasis on computational skills and recall of facts, and problem solving, where students must communicate about how they solved a problem and should contemplate alternate solutions. Ideally, teachers should strive for a balance between the two approaches.

Skills-Based Instruction

There’s no denying that students need to develop fluency with facts and recall of information. Go to sites like Gynzy to download fun, interactive tools and games to help students develop fluency and automaticity.

Problem Driven Instruction

Accept different ideas about how a problem should be solved, and give students opportunities to use higher order thinking skills to communicate their ideas about different ways to apply skills to solve problems.

Connect to People in the Real World

Connect what you’re teaching to real world applications. Inspire your students with a video or a podcast about how engineers and scientists apply mathematical concepts to design earthquake resistant buildings or to compensate for the decay of the elliptical orbit of a satellite. Then let them work collaboratively on solving a problem based on their interests.

Have a Positive Attitude

Project an optimistic attitude about mathematics, and communicate your confidence in your students’ ability to succeed in math.


You can demonstrate an enthusiasm for the content and a belief that all of your students can learn the material by differentiating your instruction to appeal to their different learning styles, readiness levels and interests. Download tools for skills practice from a site like Gynzy, and integrate them into tiered assignments designed to focus on your students’ individual needs.

Actively Engage the Students

Your students cannot be passive recipients of information, and they shouldn’t be sitting back and watching their classmates solve problems. Use software for your smart board to design interactive, problem-solving activities so that all of your students can work collaboratively and build on each other’s strengths.

Use Challenging Problems

Give your students challenging problems to solve. Don’t have them calculate when that train is going to arrive at its destination. Mathematics is much more stimulating than that, and students should be exposed to the exciting challenges of real-world problems whenever possible.

Use Interdisciplinary Connections

Connect what you’re teaching to other things your students are learning. Use literature, art, or a pivotal event in history to introduce an investigation of an authentic problem. Integrate video, images, music or other multimedia content into your lesson. Support your students’ ability to solve problems by connecting ideas and language to numerical representations.

Allow Students to Work Collaboratively

Appeal to their social nature and increase student achievement by having them work in pairs or small groups to share their ideas and solve problems.

Give Students Opportunities to Communicate Mathematically

How are you letting your students process their thinking and communicate their understanding? Give them lots of opportunities to do this, and allow them to do it in different ways that appeal to different learning styles. They may draw a picture, write in a journal, or participate in whole group discussions.

Formative Assessments

Gain insight into your students’ understanding of basic concepts by engaging them in whole-class discussions where they will answer open-ended questions. Have them complete graphic organizers at the smart board to help you see how they’re organizing information.

Students Should Use Manipulatives and Other Tools

Teaching with manipulatives increases student achievement and improves students’ attitudes towards math. Visit Gynzy to download virtual manipulatives and tools for use on your smart board.

Make the Abstract Concrete

You can find animations of complex, abstract concepts like formula derivations, and integrate them into your direct instruction presentations. Being able to visualize complex ideas will help students to understand, remember and apply these concepts to solve problems.

These are my ideas for 15 important components of a good math lessons. What would you include?