Great Math Lesson Series:

Phase I Phase II Phase III Phase IV Phase V
Introduce Stimulus Whole-class Activity Problem Solving Synthesis & Reinforcement Revision & Recap

This is the final of a five-part series of articles on how to teach a great mathematics lesson, using a simple, purposeful template that can be adapted for any math topic and any age level. In the fifth phase, the teacher provides students with their ‘take-away’ for the lesson – the key points to be remembered and carried forward to the next lesson, and to future times when the learning is needed.

Fifth Phase: Revision & Recap

As short as the fourth phase of a math lesson might be, the final phase is even shorter. However, the time needed should be guarded so that the benefits from the final summing up statements are not lost to students. The teacher’s intention at this time is to:

  • reiterate key concepts and skills one last time
  • connect the lesson which is just concluding with future experiences
  • ‘carry forward’ the learning in students’ thinking so that it is not lost as they walk out the door
  • set up future learning experiences which will connect with this lesson
  • assign assessment or practice exercises, such as homework, to require future revision of the lesson not long in the future

Teacher Asks a Question

One challenge for every teacher, which is particularly acute for teachers of mathematics, is to find ways for students to retain what they have learned after they have left the immediate environment of the classroom and that particular lesson. Why is this especially difficult for math teachers? I believe for the following two reasons:

  • many students do not enjoy mathematics, and so are likely to be quick to forget what they have learned, even intentionally (‘thank goodness math is over for another day, and I don’t have to think about it again until the next math class’)
  • to a far greater extent than other disciplines, mathematics deals with abstract entities which have no physical form; the numbers themselves. For this reason, connecting the thinking and the processes of doing math to the ‘real world’ outside the classroom may take some deliberate effort which students may be reluctant to do.

Having said this, we do our students a disservice if we fail to help them to make the connections which we know exist between a math lesson and other, out-of-class experiences. The teacher who loves math needs to ‘evangelize’ his or her students to see the beauty, facility and functional usefulness of the math that is learned in the classroom. For some students, it may be just one teacher who has this sort of passion who can ‘light the fire’ under the students’ thinking, to encourage them to see the applications for math that are all around them.


Some suggestions for strategies to help students carry their learning forward both to future math classes and to other situations in which the mathematics is useful:

  • Ask quick ‘pop quiz’ questions that require what was covered in the lesson
  • Set homework tasks that repeat key processes which students engaged in during the lesson
  • Ask students to explain what they have learned to another person, such as a parent
  • Preview the next math class with a ‘mini-ad’ for the class – what exciting things are planned for tomorrow?
  • Describe a common everyday experience to which the material learned in this lesson can be applied
  • Tell a story about your own experiences of using the math which was the subject of the lesson

How Can We Motivate Students to Love Math?

A Great Math Lesson will capture students attention; explain key concepts and skills; give students opportunities to grapple with mathematical problems using their own thinking capacities; include expert reiteration of key content to consolidate learning; and connect the lesson to future experiences. This five-phase template for any math lesson is designed to maximize student engagement, focus on key mathematical truths and help students to connect those truths to their lives outside the math classroom. In so doing it is hoped to help students connect math to the rest of their lives, to help them to understand the material and ultimately to enjoy the experience of learning mathematics.

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Photo credit: © Gordon