Saturday, May 18, 2013
Visual Models Make the Math!
I remember little of early elementary school math, so I find it rather remarkable that this stands out...
My elementary school math experience was primarily composed of rules or sequential steps to memorize. One rule: add by starting with a given number rather than starting with 1. So if we had 6 and wanted to add 3, we were supposed to start with 6, rather than starting at one.
I'm not sure how I missed the instruction (I did enjoy watching Stacey, the class clown, tie Jennifer's shoelaces to her chair...recall that much better than math class), but I couldn't add by starting with a given number.
Why? Here's my 7-year-old thinking:
Should I say 6 and then count 3 more on my fingers (say "6," then "7, 8, 9"), or should the 6 count as one of the 3 numbers I'm counting? (say "6, 7, 8"):
7 (holds up 1 finger)
8 (holds up 2nd finger)
9 (holds up 3rd finger)
6 (holds up 1 finger)
7 (holds up 2nd finger)
8 (holds up 3rd finger)
Can you follow my thinking? I was so worried about the steps that I forgot to consider what I was actually being asked to do, or what it meant to add two numbers. What if someone had given me visual support?:
A number line that shows I already have 6 hops and need to add 3 more hops:
Number Rack to show that I have 6 beads and am adding 3 more:
Or Number Pieces to show that I have 6 units and add 3 more:
I don't think my teacher ever knew that I couldn't add by starting with a given number. After I missed a bunch of problems, I just gave up and put my fingers under my desk and counted, starting with 1. Because I was so busy with this inefficient addition method, I think I missed memorizing my addition facts. I don't think I mastered those until adulthood.
But I got straight-As in math through high school. I was a master math swindler.
Do you support math concepts with visual models? Do you have a story to tell about a kid like me? I'd love to read your comments. :)