Do the Representations Help or Hinder?

In this video, I encourage you to take a look at the representations you/the curriculum are using to help kids learn their facts.  Do they help or hinder their ability to develop strategies beyond counting?


  1. Shawna Goodwin

    I love this concept. I have a first grader who is amazingly artistic. He struggles with certain concepts of math, but I’m sure he would catch on quicker if I utilized models FOR thinking because of the visual for patterns and relationships. Thanks!


    I especially love the way the unifix cubes were used. It will help them to understand the concept of partitioning, aswell.

  3. Fawn Chan

    Excellent. The focus should be on using models to develop relationships (& thinking strategies) which then becomes models for thinking. A math model/representation that focuses only on getting an answer is a model of thinking and not a model for thinking.

  4. Delinda Wall

    Love the hole punch idea. We have done this with just dots on a folded page, but this is easier and more fun. Thanks!

  5. AudreyHW

    What an enlightening video! I hadn’t really distinguished between modeling FOR and OF but this makes so much sense, especially when it’s paired with the number relationships. I will be more conscious of my thinking now as well as my students’
    Thanks, Christina!

  6. Holly Knox

    So as I look at the array activity it shows the array 5×2 as five columns times 2 rows. Everything we teach, including our Investigations work describes this the opposite way. The first number in the expression, the five, would represent how many rows you have in your array and the two would represent how many columns. This may seem trivial but I think kids need to know this and have an understanding as we teach the distributive property. Does anyone else see this?

  7. Christina Tondevold Post author

    Holly, I know some people get worked up about the “correct way” to talk about area models. To me there is no correct way. Do you say length x width always? Or do we do width x length? Yes some curriculums have kids always say rows first, then columns…which equates to length x width when they move into area model. Commutative property is really what I want to develop to help them understand that it doesn’t matter, they are both the same. However, in real-world scenarios it does matter and in a lot of them it’s always width x length.

    My husband is a contractor and if someone tells him they want a 5-0, 3-0 (5’0″ by 3’0″) window that window is very different than a 3-0, 5-0 window. In construction the first measurement is always the width. So, yes I want kids to understand that with arrays & area models it doesn’t matter which number is which because we will get the same product. But when it comes to actually using those ideas in real scenarios, the measurements will matter…and may be different than what the textbook teaches.

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