## 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"):

6...
7 (holds up 1 finger)
8 (holds up 2nd finger)
9 (holds up 3rd finger)

-OR-

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:
A 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. :)

1. Wow, I didn't know there was a name for people like me who coped as best as I could while not really understanding. I hid my fingers through trig and calculus; I couldn't give up the secret that I didn't know basic math instantly. It wasn't until I homeschooled the girls that I learned how to be savvy like others.

1. I think there were a lot of us with our fingers under our desks! ;)

2. I love math visuals and manipulatives. I automatically start trying to figure out new ways to show a student how to visualize a concept when they are having a difficult time catching on. I consider it a challenge, and enjoy it when they finally get it. I rejoice with them!

1. Penney, that's beautiful! :)

3. You have helped inspire me to go get those math manipulatives out of the closet and actually USE them!!!!

1. Now THAT made me smile!!! :)

4. Math Swindler- even through my older kid's elementary education. It was not until this school year and seeing what my 2nd grader was doing per Common Core that I realized I did not have good fundamental concepts. Math always was a struggle except for Geometry. I would have benefited from math manipulatives- especially understand 10!

1. It's amazing, isn't it? I have learned so much from teaching math--including KINDERGARTEN! How can it be that I am learning fundamental concepts of math--in many ways for the first time--through this process!? :) Thanks for posting!

5. i so totally know what you're saying! my 6 year old was having the EXACT SAME PROBLEM when i was trying to teach him math... so we are backing off for a year or so on math. just not quite catching the concreteness. though he can use a number line just fine. :P

thank you for writing this!

1. Ericka, thank you so much for your comment...fascinating to hear that someone else was having the same issue. I remember the confusion so vividly. Glad you're here! :)

6. I'm so glad I'm no the only one who didn't master basic math facts until I was an adult! I was taught touch points (or touch math) and relied on that FOREVER rather than figuring out better strategies. Yikes! I'm glad to be teaching my students more efficient ways.

Thank you for leaving me a message. I love comments almost as much as I love chocolate! And I do LOVE chocolate. :)

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