Making Math Meaningful for All

I finally got a chance to dig into my copy of Education Leadership and several articles have already grabbed my attention in a good way. I was glad to see a an article about differentiating instruction in math and some easy ways to do it.

If you’re an ASCD member you can get the article here, but I’ll try my best to summarize or feel free to borrow my copy when I’m done. I also saw one floating around in our faculty lounge.

The article is titled, Beyond One Right Answer and criticizes that math is viewed by too many students as something to answer quickly with an answer that is expected by the teacher. First of all, two widely held beliefs need to change:

  1. That all students should work on the same problem at the same time.
  2. That each math problem should have a single answer.

Two core techniques are discussed in the article. They are not new, but every teacher of math should be aware of them: using open questions, and parallel tasks.

Open Questions

The easiest way to create an open question is to provide the answer to the students and have them challenge themselves to make up the question. At first students can be uncomfortable with ambiguity, but they will warm up.

Another strategy for open questions is to ask for similarities and differences. Ask students to give two examples each of how 4 and 9 are similar and different.

Yet another strategy is to allow choice in the data provided before solving the problem.

Finally, ask students to write a sentence. Give certain vocabulary they must use, but have them design the statement.

Parallel Tasks

These are tasks that focus on the same big ideas but have different levels of difficulty. I remember that each year, we do a quilting unit and when asking kids to describe how they figured out how many quilt blocks were used, we received different suggestions from repeated addition to some kid multiplying the width by the length (we don’t teach the formula for the area of a rectangle in second grade, but it’s exciting when kids discover it on their own).

One way to create a parallel task is to let students choose between two problems. The same concepts could be covered, but one of the questions would be more difficult than the other.

A second strategy is to pose a common question like “what operation would you use to solve that problem?” or “Can you solve this in your head?”

Math is not something you train kids to do like a pet. It’s something that should be explored, discovered, played with, and made real.

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