Teaching Number Sense

The last 2 chapters give the essential number relations that students need to explore in order to strengthen number sense.

Number Sense is a collection of conceptual ways of looking at problems. Discussion, introspection and deliberate practice would be essential for learning them.

In this chapter we will explore different teaching strategies that can be employed for learning the above.

1. Avoid Timed tests

Speed is the enemy of deep thinking. The focus should be on different ways of thinking about a problem.

Speed should be encouraged only after complete understanding of the concepts involved and many similar problems have been practiced.

2. Problems with Multiple Solutions

Posing problems with multiple solutions provides plenty of opportunities for students to reason numerically. It’s a chance to explore numbers and reasoning perhaps more creatively than if there was “one right answer.”

3. Discussions in the classroom

The most effective strategy is to encourage students to discuss the issues at hand. These will encourage students to listen carefully to other ideas & arguments, evaluate them, critique them, crystallize their own ideas, present their own suggestions and be ready for support or rebuttals.

Students should also be asked to explain the mental process by which they arrived at the solution.

The teacher should also ensure that she does not react with words or gestures when a student is explaining. This will ensure that all kinds of solutions would be shared without restraint. Let other students respond.

Such discussions are also valuable Formative Assessment opportunities to check strengths, weaknesses, understandings and misconceptions of individual students.

Such class discussions are preparations for students in group-decision making in real life situations.

4. Math Chats/ Talks

Math Chats are very similar to class discussions. They have been developed formally into a well-defined strategy by some math educators for probing the thinking processes of students.

They are extended discussions, about a problem, with individual or small group of students. The intention is to probe deep into the thinking processes of the student and identifying wrong understandings.

5. Encourage Mental Calculations

Mental calculations force students to think flexibly about numbers & number relationships. They also improve memory ability to hold numbers & procedures in their "short term" memory areas.

6. Encourage Estimations

Most of the math problems we encounter in daily life need estimations and mental math, not accurate answers. Estimations can also provide a hint as to the reasonableness of the answer and ways to solve a problem.

7. Model different methods for computing the same problem

Encourage students to present alternate views of looking at problems and solving them.

8. Use Happy Drills

Development of number sense needs a lot of practice which should be doe with interest and pleasure.

If drills are boring then learning would not happen. PKS used to say that "drilling" without "thinking" produces only "holes" of "non-understanding".

Happy drills are explorations which reveal surprising patterns either in the process or in the solution. They have been explained in Chapter 13.3. Many of the activities in Section 34 on Recreational Math would be ideal candidates for happy drills.