How do we humans react to confusion and difficulty?
- Amelia claims grumpily “I don’t get the multiply and divide by 10 thing.” She tends to get grumpy when confused.
- Tomas minimizes his struggles. “I’m fine now. I was just confused on yesterday’s quiz. I’m good now.”
- Nicole writes notes to us on her quiz. “I need more instruction in this concept. It makes no sense at all.”
- Michael withdraws into silence. “Shall we get the blocks for this, Michael?” Silence. “Which part is confusing?” Silence. Sigh.
Welcome to what might be the hardest job in the world to do well.
Sometimes, we can get parents to bring a student in before school. Kathleen was working with Amelia before school; we wanted to clear up the multiplying and dividing by 10s ‘thing’.
Kathleen put down a block in the ones place on a place value chart, then picked up her knitting (to indicate that Amelia is on her own now). “Amelia, can you show what happens when you multiply that block by 10?” (knit, knit, knit) Amelia picks it up, counts out 9 more, and puts them back in the ones column. She tilts her head, picks them up again, and exchanges them for a 10s rod. She’s about to put it in the ones place but then slides it to the 10s column. Kathleen smiles, clears the mat and puts down two blocks in the ones place, returns to knitting. Amelia picks up one, counts out 9 more, exchanges them for a rod, puts it in the 10s column, and repeats that for the other block. (Kathleen is knitting furiously, trying not to look, not to show ANY impatience.) Kathleen puts down a 10s rod and asks Amelia to multiply it by 10. Amelia counts out 9 more rods, looks at the 10 rods, exchanges them for a 100 flat, and puts it in the 100s column. This continues for a LONG time. Kathleen knitting, Amelia exchanging. We move to 2 blocks, 3 blocks (“What’s 21 times 10?”). After 9 or 10 problems, Kathleen asks Amelia to write down her answers. “32 x 10 = 320”… “Why, Amelia?” “Because you can see the exchanges.” Okay.
On the 14th problem, Amelia brightens. “Hey, you’ve been trying to trick me! It’s easy. You just move each block one column bigger!”
It only takes her 3 more problems to figure out how to multiply by 100. And 5 problems to understand division by 10. She offers division by 100 unprompted. Decimals? No problem. Soon she’s moving digit cards (instead of blocks) left and right across the place value chart.
Twenty-five minutes. That’s what it took. Nineteen of those minutes purely visual; it took that long for a pattern to establish itself in Amelia’s brain.
And in Kathleen’s knitting.
You see, this is how children learn.
Children are not adults. Adults can look at a pattern like multiplication by 10 and make sense of it.
Many, many children cannot. What they need is T-I-M-E.
What we need as adults is the patience to W-A-I-T while the child repeats a visual procedure a dozen times, when the adult would see the pattern after one or two examples.
The payoff: We never have to reteach this concept. We’ve been teaching like this for years, and see students retaining this hard-earned conceptual understanding permanently.
Visual understanding is MUCH more robust than abstract, memorized learning.
Moral of this story:
Bring your knitting 🙂
Oh, and some gummi bears for good work. Learning is its own reward (on some planets), but we’re not proud — whatever works.