Concrete Learners: Hands On and Real Life…Every Day

In teaching division this year, I’ve never before used so many counters for so many consecutive days in a row.  I’ve got a core group of students who feel really great about division, some of them have even been memorizing multiplication at a very fast rate, which allows them to make better sense of division.  But I also have the exact opposite end of the spectrum as well.  As soon as they see that division symbol, their eyes glaze over and they become fearful of the problem. They worry about what to do and they think they cannot divide (even through they’ve been dividing all of their lives, they just haven’t seen the number sentence for it).

To help struggling learners, I’ve been trying to make it more concrete. Our youngest learners often need to see visual representations of numbers so that the concept is not so abstract.

In this set of problems, fruit was being divided equally into bags. I decided to lay out paper bags for this student.  The problem was 14 divided by 2, and he could easily solve it. He was both proud and excited to write his answer.  Win!

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Another student though, had a little more trouble. The problem was 8 divided by 4.  Because she had done 10 divided by 2 right before this one, she forgot to put away the 2 counters to start. She hit a wall very quickly and gave up. Instantly, she had her hand up for more help.

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To help her, we re-calibrated a bit by checking the problem again.  She very quickly realized that her counters started out wrong, and she was able to fix it. That check back to the problem is what I want her to do in the first place, great mathematicians do that without any prompting.  It was clear to see that she wasn’t connecting the number sentence with the manipulatives at all. It was a quick 1 minute conference on the importance of paying attention to detail/being precise, a math practice standard that many students struggle with. I told her that the next time she should try that strategy before asking for help.

Giving these quick teaching tips while conferencing with students makes WAY more sense when those tools are right there in front of them.  I used to try to draw on student’s papers, help them extend patterns etc… but the most struggling students need those tools in their hands to actually act out and see the problem. That is when I’ve noticed teaching tips given to them have become ultra powerful!




    1. Agreed! I think I assume way too often that my third graders are ready for representation, but they are still very much concrete learners.



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