Number and numeration gone wrong

This came from a workbook bought by the kids’ grandparents.

Can someone please explain the purpose of the jars of bugs here?



17 responses to “Number and numeration gone wrong

  1. Ok, so we’re talking quantity and composition/decomposition here. Which is great, until you try to make sense of quantity with the physical objects presented as “helpful(?).” I’m going to use pseudo-engagement here, as I think there is a real difference between that and pseudo-context, but that discussion is for a different day. The visuals add nothing, and probably only add to confusion and misconception. Well maybe that’s a little harsh, as at least there is more black bugs than red bugs. One last thought: I wonder about the purpose of the four lid holes of the ones jar compared to the five lid holes of the tens jar.

  2. thats really great. I think we could start a blog just on math visuals gone wrong. Unless the publisher wanted random pictures of bugs that have no relevance to the problem whatsoever.

    Have you seen this one?

    I am curious what other gems you can find in this book.

  3. Michael Paul Goldenberg

    Sure. To make the grandparents feel good and make the kids completely confused about how place value works. Which leaves the math educator dad on the verge of a cardiac infarction.

  4. Chris (@absvalteaching)

    On second look, the directions say it all: “Look at the numerals and words on the jar.” Which obviously means don’t look at the actual jar and its contents. A behavioral curricular approach?

  5. Agree with Chris … this is an exercise in following directions and learning not to look for meaning. It is, after all, an arithmetic workbook.

  6. Pingback: Distraction in action | Resource Room Dot Net Blog

  7. I am thinking that this arbitrary sprinkling of distracting graphics may be rather common — inspired my latest blogpost…

  8. Shouldn’t we see the same kind of bugs in both jars?

    • Michael Paul Goldenberg

      Only if you want things to make sense. Same kind, same (relative) number for each kind of jar. You know: mathematically sensible. Apparently, that was a secondary consideration here. Or not even that high on the list.

  9. There is no (visually apparent) difference between the number of bugs in the “1 ten” jar and the “9 tens” jar. Worse, there is no difference between “8 ones” and “0 ones” jars! The bugs *could* be helpful if there was a direct correspondence between the *number of bugs* and the *numbers being added.*

  10. Yes, that’s what I find most appalling about the attempts to make things visual. It’s worse than nothing; if a student *does* try to glean information from it, it will be wrong. The abstract-thinking person sticking the book out is thinking, “yea, tens have more, so I’ll have more stuff in there” — smaller, of course, further confounding the concept as well as the big idea that you’re supposed to add the same kinds of things to each other — and checking that off the “done!” list and moving on. Meanwhile, the student is learning “WTF?” or, at best, “Ignore everything but the numbers. Copy them. Right answer.” YOu know, math !

  11. Thanks for the support here, folks. We seem to be in agreement that the visuals are useless at best, and most likely counterproductive—possibly in several ways. The difference between pictures that have a mathematical structure and pictures that serve to make things look nice is what I try to capture with the language of diagrams (former) and decorations (latter, and what is clearly present here). See here for more.

    In the spirit of productive positivity, I am doing some thinking about what would be a better version of this page. Let me know what you find/create.

  12. Well, the bugs don’t *really* line up nicely on those strips of sticky paper used to catch flies, but… each strip could have ten flies, and then the uncaught flies could be the ones. If you insist on ‘bundles of bugs’, that is…

  13. Is this one of those mega skill workbooks? If so, I don’t think they put a lot of thought into the graphics they used, with the possible exception that they at least considered the “tens” bottles should contain more bugs than the “ones” bottles. Likely they cared more about pumping out a book with maximum content for minimal cost. It’s a book you buy to keep your kid busy on a long car trip, and you have the hope that they will learn something as they work through it, or at least maintain their skills and avoid the dreaded summer slide.

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