Learning to memorize something without any connection seems like a near impossible feat. Memorizing a map is very difficult for me when I travel, I need it with me the whole time to connect landmarks, buildings and other streets to remember the streets I have been on.
I still haven’t figured out exactly how I ever memorized my multiplication facts as a child. It must have been a miracle, although I do remember having to actually re-LEARN my facts when I became a math teacher. I am kind of embarrassed to admit that fact, but when I sit back and think about it, should I be embarrassed about that?
I think I was made to believe that the faster I could recite those facts the smarter I was. The more I memorized in math, the better math student I was. I had no idea why I did any of the things I did and just hoped I could rely on my memory. I was one of the lucky students that was able to do this…especially in high school math.
But students who cannot easily memorize have to have something else to connect these facts to. After exploring the meaning of a fact like 5 x 7 (5 bags of 7 apples, 5 packs of 7 pieces of gum, 5 rows of 7 seats), we started to draw visuals of these things.
Drawing these visuals allowed my students to have something to connect multiplication to. Not only that, 6 x 7 is just one more group/row of 7! Eureka!
Isn’t this good for all students? Not just those who struggle? The answer is YES. With a commitment to conceptual understanding we set them up for success in higher level math courses.
Beyond Traditional Math 
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There is one area of math, namely statistics, in which visuals are very hard to come by. I am not counting the pictures and diagrams constructed with data. One of my happy realisations is that there are connections between statistical measures and mechanics which shed a lot of light on each other.
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Love this! I have been working on larger number multiplication in grade 4 over the past week. I have two young ladies in that class who struggle in math. One of them is very fluent with her multiplication facts and has all of them memorized. The other has come a long way with multiplication facts but still uses strategies for some that rely on other facts she knows. The student who has all her facts memorized is really struggling with the ideas around larger number multiplication while the student who still uses strategies is doing quite well. Interesting connection!
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When I was in elementary school, I remember having to memorize the multiplication test and taking timed tests as part of our multiplication assessment. I really enjoyed the idea of having a discussion with the student about many different ways that a multiplication problem can be represented (i.e. 5×7). It’s more efficient for students to represent multiplication with something they can relate to and understand there are multiple other strategies students can use. I am currently in a math methods class and this strategy reminded me of the number talks we have as class. Everyone is given a chance to share the strategy they used to answer the problem. Our teacher then provides a visual for the student’s thinking and we get to learn how other student’s thought about the problem and can adopt there strategy if we found that a good strategy for ourselves.
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