One Should Separate Related Topics!

This is part of a multifaceted strategy to teach heterogeneous classes.
Read about it in this article: Reaching the Full Range.

In a previous post, I discussed the benefits of “lagging homework“.  These included extending student exposure to new ideas, which benefits everyone: stronger students get the forward motion they want and need, and students who need more time to absorb the concept get more time.

In this brief post, I will present another way to extend exposure, which yield the same benefits for the same reason: separating related topics.

Most of us teach related topics consecutively, hoping that if the previous topic is still fresh in the student’s mind, it will make the next one easier to grasp. Examples are teaching factoring right after teaching the distributive rule, or teaching sine, cosine and tangent in one fell swoop, series after sequences, and so on.

Well, most of us are wrong. It is far more effective to separate related topics. Here are some examples:

• factoring using manipulatives, then some time later, the distributive law
• the tangent ratio, based on slope and the 10-cm circle, then some time later, sine and cosine
• quadratic functions, using graphing technology, then some time later, quadratic equations
• sequences, based on iterating linear functions, then some time later, series
• exponential functions, starting with ten-sided dice, then some time later, logs

If you separate related topics, when you get to the second topic, you have a built-in review of the first one. And thus you’ve created forward motion (moving on to something else after introducing the first topic), and extended exposure (revisiting the first topic when working on the second.) Another advantage of this approach is that it communicates to the student that they are learning for the long run: any important topic may and will come back.

The gap can be anything from a few weeks to a whole semester.

Even though it is not widely known, this is a powerful idea, and it is not too difficult to implement.

–Henri

[More on extending exposure]