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 second 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 this article, the second, key phase is described, in which the teacher teaches the entire class the key skills and understandings students need in the topic being learned.

Second Phase: Whole-Class Activity

So, you’ve got your students’ attention via an innovative, impactful stimulus which has grabbed their attention and motivated them to learn more. Now it’s time to do some good, old-fashioned solid teaching.

Why “old-fashioned”? My description of this phase is partly to get your attention, and partly a commentary on what I see as a problem in much of modern pedagogy: teachers are reluctant to take over and lead their students’ learning, in the way we used to see a few generations ago.

In the “bad old days”, teachers were regarded as experts (nothing wrong with that!); more than that, they were seen as the only experts in the room (that’s the problem right there). Students were expected to sit quietly and passively to be told all they needed to know, to commit key information to mind so that they could perform in the exam that was to follow by recalling the information they had memorized.

Nowadays, educators understand that far from being some version of the “blank slate”, students are more like “thinking entities” who actively consider each piece of new information coming their way, and who attempt to fit each piece into existing mental schemas, adapting either the new piece or the prior schema so that they fit together in some form. The idea of “constructivism” has been formed to describe what is now believed to actually happen in students’ minds as they actively construct new and even unique understandings of what they are taught.

So, back to the problem, as I see it, of teachers being reluctant to take over and teach directly, in a very “didactic”, “teacher-led” or even “chalk and talk” method. Student teachers are instructed at universities that students need opportunities to think for themselves, to “own” their own learning, to engage with and process the content of each lesson. This is all true. But it is a simple step to extend from this straight-forward proposition to the idea that teachers should avoid presenting themselves as experts, and rather facilitate students’ learning “from the side”, as in “The Guide on the Side”, not the “Sage on the Stage”.

Bunkum. If we only needed teachers to step back and let students do all the thinking and deciding after presenting them with appropriate activities and resources, we wouldn’t need to keep student teachers at university for up to four or five years to earn a professional academic degree. If this were true, teacher aides could do the job of teaching, and teachers could go and find some other career that required the initiative, dedication and subject expertise they currently possess. I am sure you agree this is not true. (By the way, I am not putting down teacher aides in my last sentence; they are essential contributors to successful learning that happens in many classrooms. But they do not have the same professional training we currently require teachers to have, since the role of the teacher aide is as a support person, not the prime educator in the classroom.)

No, teachers are employed to teach. They do much more besides, including managing behavior, counseling students who are going through hard times, assessing students’ learning, negotiating and communicating with parents about their children’s education, and so on. But the job of the teacher is to so engage students in thinking about their subjects that the students learn, grow and develop in the ways that their families and their nations require. And one of the most powerful tools at a teacher’s disposal is direct, expert, didactic teaching.

In the context of the mathematics lesson, the teacher needs to very deliberately, very directly instruct students in what they need to know about the topic at hand. This will include the following:

* key terminology – eg, names of polygons
* key processes – eg, how to carry out a written algorithm
* visual models to support understanding of abstract processes – eg, bundling sticks modeling regrouping of two-digit numbers
* how to think about the topic, how to approach its typical problems – eg, the thinking that goes into solving a simple algebraic equation with a single unknown
* problem solving strategies – eg, how to use the “Guess and Check” method for the appropriate class of problems

The excellent teacher knows the value in explaining the meaning of a body of information, or how to carry out a procedure. He or she treasures the time provided by the system of schooling to impart knowledge and wisdom, to develop new ways of thinking and new skills to solve problems, in the next generation of world-changers, their students. In a math lesson, this is about helping students to build on what they already know and equipping them to go on to the next level of problem solving, possessing the knowledge and skills they will need to succeed at it.

There is a crisis in many developed countries of the world today in finding enough qualified mathematics majors to teach this beautiful, essential subject to the next generation. It is essential, in my view, that every teacher of mathematics seriously grasp the responsibility given by the system for actively educating the next generation to think mathematically and to solve everyday problems using the tools of mathematics.

Have fun! I’d love to hear how you approach your teaching of mathematics, and how your teaching is making a difference in the lives of students, in families and in the community.

Next phase: #3 Problem Solving

Photo credit: © iStockphoto.com/kristian sekulic

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