I was recently working with teachers to analyze their students’ work. Students had to find the difference for 72-35. After they reviewed the work, I asked them to share the strengths they noted in the student work. One teacher mentioned that students were using strategies. I asked for an example, to which she said “More on the floor, go next door”. I am not sure if I was more depressed about the comment or that the teacher saw it as a strength! Is that a strategy? Or is it a memorized line to nudge students to perform a memorized process.
Why do we consistently want to tell students tricks for doing mathematics, rather than helping them think mathematically? Do students know what “More on the floor, go next door” means? I can hear the classroom talk:
Why is it a problem when the number at the bottom has a greater value? (no comment)
What does it mean to “go next door”? (look at the other number)
Why do you change the number? (no answer)
How do you change the number? (make the 7 a 6 and make the 2 a 12)
Why did you do that? (there was more on the floor)
And around we go…
Why are we teaching this? Is the goal simply to get a correct answer? Our students struggle with understanding place value and tricks like this play a role in their struggles. Why not ask questions that focus on understanding place value?
Tell me about 72 using your understanding of tens and ones. (7 tens and 2 ones)
What is confusing about this subtraction problem? (we don’t have enough ones to subtract)
Is there another way to think about 72 that would allow us to subtract? (6 tens and 12 ones)
Do 6 tens and 12 ones have the same value as 7 tens and 2 ones? How do you know?
How might thinking about 72 in that way help us subtract?
A deep understanding of place value supports our students’ abilities to perform multi-digit computations. Let’s stop the tricks and help our students understand place value!