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:
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!

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

  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.


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