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Sweat The Small Things

“There are five birds and three worms.” That’s the set-up.

The pay-off is that Tom Hudson found significant improvement in achievement when he asked primary students, “How many birds won’t get a worm?” instead of “How many more birds than worms are there?”

Two things that probably go without saying:

  1. Your students with poor math achievement may be achieving poorly at something besides math. Like language.
  2. It’s hard not to love a job that rewards this kind of obsessive attention to detail.

23 Responses to “Sweat The Small Things”

  1. on 11 Nov 2011 at 12:09 pmScott

    I just asked my 6 year old those two questions. She did not flinch with the first but hesitated and was unsure with the second.

    As usual, thanks for sharing.

    Scott

  2. on 11 Nov 2011 at 1:11 pmGarrett

    Speaking of language problems, the only computer-based math program that has been shown to work (via controlled 3rd party trials) is ST math, which doesn’t introduce symbols or language until students get the conceptual understanding first. Reminds me of Dan’s approach.

    More info at…

    http://mindresearch.net/cont/programs/demo/tours/SolvingLinearEquations/progTour.php

  3. on 11 Nov 2011 at 2:18 pmJen

    Any teacher of elementary age kids who has been asked to give either a standardized (ie the NCLB required) test or a district designed “curriculum-based” test will recognize these issues.

    It fuels the disconnect many teachers feel between their own knowledge of a child’s strengths and weaknesses in a topic and what shows up on canned tests.

    Many of those tests, particularly at the middle school level, mix things up by asking questions in unfamiliar/odd ways. If children were all on board with “drawing it out” and really using reading comprehension strategies (and again, here I’m talking upper elementary and middle school) they would likely understand and answer correctly. BUT, those are not traits of underperforming children at this age!

    In our state tests at the middle school level, I often wondered if I should tell students to just ignore most of the introductory writing in a problem. The one I remember best was something like this:

    *large block of text* to say something like this, only more wordily: The antenna from a radio station broadcasts in a circular pattern from the antenna site to its listening area.

    Then in the middle of the question was a large line drawing of a tower with an “emanating” circle and one line drawn from the middle of the tower to the edge of the outer circle.

    Then underneath with a bit more folderol, it finally asked in the final sentence what the diameter of that circle was if that line were 20 miles long.

    Gaaaaaa. Students with difficulty reading (most of my class, more than half of whom had IEPs which included major reading issues) tuned out of that problem in the first chunk of text. Had they ONLY read the final sentence of the massive question, most would have easily gotten the problem right.

  4. on 11 Nov 2011 at 11:02 pmDavid Wees

    It certainly highlights one of the issues in math education; are we assessing our student’s understanding of math, or their understanding of cryptic instructions?

  5. on 12 Nov 2011 at 4:40 amRandom Professor

    Interesting.

    One may note that the questions don’t necessarily have the same answer though. For example, one early bird may get all three worms!

  6. on 12 Nov 2011 at 4:52 amDebbie

    My first thought was that a thrifty student might try and share out the remaining two worms between the five birds.

  7. on 12 Nov 2011 at 10:59 amlouise

    Garrett, thank you. I love the penguin. I suggested this program be used for our students from multiple different countries who are having difficulty with algebra in 9th grade. Sadly, administration thought it was too simplistic, failing to understand that the math is simple when divorced from the difficult written bits.
    Also, the program will not sell the software without expensive teacher training, so we could not adopt a pilot program which teachers could try. It was simply too expensive to give it a shot.

  8. on 12 Nov 2011 at 12:08 pmEmily

    Interesting, and not really surprising. I certainly agree that language issues can and do put up barriers between students and those who wish to assess their knowledge. It IS rewarding to discover that tiny tweak or small paraphrase that turns a dumbfounded “Huh?” into a twinkly “AH!”

    Nevertheless, I would be wary of encouraging too much ‘translation’ in our math classrooms. In this case, the students may have improved their success on this question with the change of wording, but I doubt they have increased their ability to determine “How many more…” unless of course, the new paraphrase is a lead-in to a lesson about what it means to determine just that (it may be: I have not read the study).

    The precision of mathematical language is fundamental to its effectiveness. In this example alone, the “How many more” question has just one answer, where Random Professor and Debbie have already shown substantial variance in the solution to “Will every bird get a worm?”

  9. on 12 Nov 2011 at 2:10 pmEmily

    BTW, I just reviewed a beautiful resource for primary kids that deals with this exact skill set:
    http://www.teacherspayteachers.com/Product/FREE-Monster-Problem-Solving-Math-Center

    Sure, the words pose an added challenge, but the struggle is worth it and the rewards great.

  10. on 12 Nov 2011 at 2:53 pmCarl Malartre

    Just from my small experience, language mastery seems unequal among countries. Features in math products seems different based on this.

  11. on 13 Nov 2011 at 12:40 pmSusan Meisels

    It’s hard not to love a job that rewards this kind of obsessive attention to detail.

    Yes! One of the many reasons that I love teaching.

  12. on 14 Nov 2011 at 7:19 amAndy

    I’m not sure that I understand the point (thought I didn’t read the study). The students aren’t “achieving” more because you ask one question versus the other. Assessment and achievement are joined at the hip – when you change the assessment, you’re measuring something different.

    What am I not getting?

  13. on 14 Nov 2011 at 8:29 amMichael

    What is the reason why math problems have to be worded in the most complicated manner, leaving students only to guess at what the question is really asking, rather than be straight forward and ask the intended question like “how many birds won’t get worms?”

  14. on 14 Nov 2011 at 12:35 pmAndy

    But isn’t that the point of asking the question in a particular way? One could write:

    5 – 3 =

    That, too, tests something different than “how many birds won’t get worms?” One hasn’t improved students’ understanding of math by simply changing the nature of the question.

    If a question is vague or ambiguous, that’s one thing, but there’s nothing wrong with a question that requires a little more analysis and thought. Those kinds of questions just test something different than 5 – 3 = ?.

  15. on 14 Nov 2011 at 6:59 pmJames C.

    Andy,

    I think you bring up a good point. The immediate question that comes to mind for me is why is the answer more intuitive for primary students when asked “How many birds won’t get a worm”? Is it a listening comprehension issue? When worded the second way, do the students kind of zone out mid-sentence and forget what they’re being asked? Or is there something else going on there?

  16. on 15 Nov 2011 at 6:40 amJason Dyer

    I deal with a lot of English language learners so I have to think about this sort of thing all the time.

    What is the reason why math problems have to be worded in the most complicated manner, leaving students only to guess at what the question is really asking, rather than be straight forward and ask the intended question like “how many birds won’t get worms?”

    In this case, so as to be general, so it applies to other problems where you ask “how many more X than Y?”

    In many other cases, so as to be absolutely precise. As already pointed out, even the problem above is ambiguous: what if the birds aren’t hungry? what if one bird hogs all the worms? To account for that the question would have to be reworded into something like “Given each bird attempts to get a worm and gets at most one worm, how many birds won’t get a worm?” The piling on of sub-clauses can make ghastly prose that would make my just-learned-English-last-year students have their heads explode. Hence it is worthwhile to make sacrifices for simplicity, but I have had test questions before where my attempt at linguistic simplicity backfired and I had a student interpret a problem in a different, perfectly valid way.

    A textbook author in particular can’t expect to be around to make clarifications, so they have to go for the more exact language (or more usually, resorting to mathematical vocabulary which is more exact to begin with, hence the “how many more’).

  17. on 15 Nov 2011 at 9:12 amDan Meyer
    Jason: In many other cases, so as to be absolutely precise. As already pointed out, even the problem above is ambiguous: what if the birds aren’t hungry? what if one bird hogs all the worms? To account for that the question would have to be reworded into something like “Given each bird attempts to get a worm and gets at most one worm, how many birds won’t get a worm?”

    It makes so much sense to handle those exceptions verbally, in conversation, after they’ve occurred to students, rather than in text, before anyone has thought about birds who aren’t hungry. For one, you’re helping students problematize life rather than problematizing it for them. For the other, some large fraction of your students were already assuming each bird got a worm. Those students are burdened with extra text if you lock down all the exceptions in writing.

    Jason: A textbook author in particular can’t expect to be around to make clarifications, so they have to go for the more exact language (or more usually, resorting to mathematical vocabulary which is more exact to begin with, hence the “how many more’).

    Right. The constraints on teachers and authors are so different. A lot of authors I work with would modify their own problems if they were using them live, in the classroom. I wonder how many teachers treat textbook problems with the same flexibility. Teachers’ biggest affordance is their ability to problematize material continuously, with their students, which lets them start with more ambiguous, more interesting, and less linguistically demanding material.

  18. on 15 Nov 2011 at 12:33 pmChristopher Danielson

    Dan:

    Teachers’ biggest affordance is their ability to problematize material continuously, with their students, which lets them start with more ambiguous, more interesting, and less linguistically demanding material.

    Nice pithy sentence here. Well put, my man.

    I would also add it is not only an affordance but a challenge. As one of those who both writes and teaches, I’m not sure I can recall the last time I launched a task from the book. Oh, the task is often in the book, but the book isn’t where our attention is as a class.

  19. on 15 Nov 2011 at 9:51 pmAlex Eckert

    What if two of the five birds are angry?

  20. on 16 Nov 2011 at 4:36 pmAndrewR Coulson

    This TEDx video of non-profit MIND Research Institute co-founder Dr. Matthew Peterson explains some of the thinking behind MIND’s non-verbal approach to presenting math problems: http://bit.ly/onhTBM
    (the penguin mentioned above)
    Full disclosure: I’m the President of MIND’s Education Division.

  21. […] via dy/dan » Blog Archive » Sweat The Small Things. “There are five birds and three worms.” That’s the set-up. […]

  22. […] This brings me back to the original point: attention to details—even those that most people don’t even notice (or read)—is the hallmark of a truly great professional. It’s something I want to strive for (even if that will never be evident from all the mistakes in this blog). And I’m not alone—just a few weeks ago, Dan Meyer was blogging about the difference between “how many birds won’t get a worm?” and “How many more birds than worms are t… […]

  23. […] Sweat The Small Things […]