My first grade daughter and the commutative property of addition

 

Last year I wrote a lengthy review of my daughter’s kindergarten common core math workbook.  This year she has brought home the first grade edition of the Go Math! workbook, still with ‘TEST PREP’ written on most pages in case there was any doubt, and has been doing homework in it.

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Some of the things she’s being asked to do are the standard things I’d expect for first grade, like adding small numbers together.  Things like this have always been part of what’s taught to first graders, of course.  But for this book to earn the ‘common core’ stamp on the front, there must be, thrown in, a few more ‘rigorous’ questions.  Look at question 3, which is part of the ‘Spiral’ review.

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This question is, apparently, based on the standard called CC.1.OA.3.  The actual wording of this standard is:

Apply properties of operations as strategies to add and subtract.2    Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

So the commutative property of addition says that the order doesn’t matter when adding so that 2+5=5+2.  Certainly a first grader doesn’t need to know what it is called, and it doesn’t seem that this book, at least, is trying to get them to know that.  But the standard says that students should apply this property “to add and subtract” not to apply this property in such an abstract and meaningless way as this question.

Of course any four year old who knows that if you add blue to yellow you will get green, then if you add yellow to blue you will also get green.  And I do think that it is meaningful for young kids who are just learning the concept of addition to answer questions like “What is 1 plus 4?” and then “What is 4 plus 1?” to give them a chance to either make the realization that it should be the same answer, or to answer both questions and then realize that both are the same answer and to think about that for a bit.

But the way the Go Math! people wrote this question, and I have seen similarly devised questions on the state tests as well, is complete nonsense which serves no meaningful purpose.  Math is already a tough sell, sometimes, and questions like this can make young students lose interest and plant the seeds that math just isn’t for them.  Common core test writers and test prep writers are struggling to come up with questions that test the standards, particularly the new aspects of them.  So the word ‘commutative property’ came up in the first grade standards and this is the sort of question they came up with to test if the students have internalized that standard.  But in this case they have failed to come up with a meaningful question.  I’d say that a kid can very well know that the order that two numbers are added does not matter and still get this question wrong.

I came up with a somewhat better question, though still problematic, something like “If 17 plus 25 equals 42, then what is 25 plus 17?”  Again, my question is still unnecessarily forced, but it is much better than the one from this book.  Maybe there is no very good way to test this concept on a multiple choice standardized test in a meaningful way.  Some standards might lend themselves to meaningful questions, even multiple choice questions.  But ones like this that don’t should not be forced to in this contrived way.

And it’s not that this question is ‘hard’ that bothers me.  I don’t mind my child getting some challenging questions into the mix.  But I want her to have challenging questions that are meaningful, not questions that are challenging because they are confusing because test makers can’t think of a better way to test that concept.

Here’s a video of my daughter doing the math homework that had this question on it.

 

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4 Responses to My first grade daughter and the commutative property of addition

  1. Steve M says:

    I didn’t watch the video, but I’d like to ask how a 1st grader is supposed to read the assignment’s instructions? Do they expect a test proctor to read the questions out loud? If so, the word “addends” is ridiculous.

    • mpledger says:

      GR’s D read the instructions very proficiently but it was done after she couldn’t find her answer amongst the four choices based on her experience of doing similar questions.

      GR’s D knows the rules about standardised tests
      – there is only one right answer (she stopped looking at other answers once she had found one correct one in the “which one represents 6” question)
      – the test is always right (if she counts and doesn’t get an answer that’s listed than she must have counted wrong)

  2. NY Teacher says:

    Its hard to make it a meaningful test item without making it too wordy for 6 year olds:

    Jack went apple picking with his family. He picked 5 apples from the first tree, 3 apples from the second tree, and 7 apples from the third tree.

    When he added them up, Jack had 15 apples (5 + 3 + 7 = 15)

    Jack’s sister Jill picked 7 apples from the first tree, 5 apples from the second tree, and 3 apples from the third tree. Jill added up her apples too (7 + 5 + 3 = ?). How many apples did she pick?

    a) 8
    b) 10
    C) 12
    d) 15

  3. Elise says:

    I teach first grade and I totally get what you’re saying. But, I wanted to compliment on your daughter’s thinking. If I can get my students to explain their thinking like she did, I’d be so happy. Good job to her and you!

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