Direct Instruction…Do We Need It?

I thought that would get your attention! Now just hear me out. I want you to consider that there is really very little in math that students must learn through direct instruction, that is explicit instruction from a teacher. Let me give two examples, and then I’m sure you can think of others.

Take, for example, expanded notation [eg., 234 = (2 x 100) + (3 x 10) + (4 x 1)]. Yes, students need to be directly taught the conventions for writing a number in expanded notation. They would have no way of knowing that we put parenthesis around each multiplication expression, nor could they discover it through exploration. But they can construct their own learning about what expanded notation is (describing the value of each digit using a multiplication expression) through exploration with base-ten blocks and careful questioning by the teacher. Be sure to check out this blog post for more on that.

Another great example is decimal equivalencies. Say, for example, you are trying to teach the concept that 0.4 and 0.40 are equivalent. That is a very abstract concept for students to grasp through direct teaching. Instead, have students use base-ten blocks to build 0.4 and 0.40. Note that when using base-ten blocks for decimal values, we typically use the flat to represent ones, the rod for tenths, and the unit for hundredths. If they build those two numbers, how could the not see the equivalence? Have them build a few more similar pairs (0.7 and 0.70, etc.) and then have them explain why the two numbers in each pair are equivalent.

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