Wednesday, February 9, 2011

Bouncing Ball Math Lab

So far, the Head of School at Natural Friends seems to have decided that what their math program really needs is better PR. To this end, he included a message from the math specialist in the school's bulletin. The math specialist has worked at Natural Friends for many years while the kids were graduating right into remedial math at their next school. She is a lot more likely to be part of the problem than part of the solution, IMHO. Here's the specialist's account of a 4th-grade "math lab":

Teacher 4 holds out a tennis ball a little above his waist height and asks his class, "Do you think you could predict how high this ball would bounce if I dropped it from 1 meter? "

Students suggest, "60 cm." "1 ½ meters.' 'To the ceiling."

"What could we do to make reasonable predictions?"

An animated discussion follows. The students know from past experience that they will have to experiment by dropping their ball a number of times from various heights to be able to make a good prediction. They decide to work in groups of three . Each group gets a ball and agrees to drop it several times from 40 cm, 60 cm and 120cm. They purposely omit dropping it from 100 cm (1 m) because they are intent on predicting the answer to Teacher 4's question before actually measuring it. From the many labs they have done in earlier grades they know that they will need to take at least three trial drops from each height and then find the average in order to get a more accurate result.

And so another Math Lab begins. By now the students are familiar with the process of planning an experiment, collecting data, graphing their data, and finally analyzing their results and testing their predictions.

These fourth graders have just learned how to calculate the mean and they will use this new skill to find the average of the three drops from each height. (In previous labs they usually took the median [the middle number of the three trials] as the average.) This lab will reinforce skills such as measuring, graphing, making 'best fit lines', and working cooperatively. It will also enable students to practice their new ability to find the mean.

There is a lively hum in the class as they students spread around the room and begin to plan their group work. They tape their meter sticks to the wall and practice dropping the ball and reading the results while the ball is in motion. Then they are ready to carry out the experiment, record the data and graph their results..

Later they find a 'best fit line' for their data points, so that they can predict how high the ball would probably bounce if it were dropped from exactly 1 meter. They then test their hypothesis by dropping the ball from 1 meter and compare this with their predictions.

This math lab is one of eight labs fourth graders will do during this academic year. For each lab, students sketch their plan, gather their materials, collect data in a data chart, then graph and analyze the data.

We have found these labs to be an excellent way for students to use and extend the mathematics that they are learning in a meaningful and highly motivated way.

and my response, sent to the Head of School and the math specialist:

I read the description of the 4th grade math lab in today's newsletter, and I have a question. When the kids take an average of three measurements, how do they perform the calculation? Do they add the numbers using the standard addition algorithm, then divide using long division? Or do they just use a calculator? If they're using calculators, they've missed an opportunity to practice their math skills. Over-reliance on calculators is one of the problems that lead to kids graduating from NF without the skills they need. (I see a calculator next to a student's elbow in one of the photos.)

If the kids use calculators for anything more challenging than 2+2, how much math is really being taught here? Kids need to achieve fluency with numbers, which comes -- wait for it -- from working with numbers. I think the calculators are a crutch used by the teacher to avoid confronting the reality of how weak the kids' math skills really are.

I didn't mention it in my e-mail, but I am also deeply skeptical of the picture painted in this description. Were the kids really engaged by the question of how high the ball would bounce? I doubt that either of my daughters would be.


  1. Man. See, that sounds to me like a SCIENCE lab - there are all kinds of scientific concepts involved there, so it could be a pretty cool lesson about physics, building hypotheses and experiments to investigate them, etc.

    But it's not a MATH lesson. It's a science lesson that (like many things in science) INVOLVES math concepts - in other words, it's building on math stuff that they have (or should have) already learned separately. This is the problem I have with a lot of the creative "math literacy" projects: It seems really unfair to expect kids to somehow intuit the underlying math skills from something much more complex that happens to involve those skills.

  2. I agree.

    The big problem with Trailblazers is that it just doesn't teach math. In fact, it hardly even mentions math.

  3. Young Curmudgeon says ...

    "If they're using calculators, they've missed an opportunity to practice their math skills." And if they weren't allowed calculators, I'd guess two out of three in most groups missed an oppurtunity to practice math as they relied on one member whose parents afterschool do the calculations.

    And what Becs says above. Seems like lots of science going on there.

    I haven't purchased Aharoni's book yet, but it is definitly on the list.

  4. Young Curmudgeon, good point.

    It's possible that only one kid per group even pushed buttons on the calculator! In that case, 2 out of 3 kids lacked even minimal exposure to taking an average.

    This might be why Trailblazers assigns homework. Classwork is done in groups, so homework is the only way to make each individual kid do something. Bah humbug, I say. Teach the kids during their time at school, and leave their home life alone.

    And if you spend math time teaching science, when do you teach math?

  5. I just came back from a PTA meeting at which our elementary school principal discussed our school's aggregate scores on the Iowa Test of Basic Skills. In general, the scores were quite high -- up in the 90th percentile range. That was true even of the scores on "math concepts," "problem solving and estimation." The one score that stood out, though -- it was more in the 60th or 70th percentile range -- was computation. Our school uses Everyday Math.

    Even though the computation scores stood out as relatively low, the principal assured us that they were a big improvement over four years ago, before we started using Everyday Math. I asked what math curriculum we used back then. Turns out it was Investigations.

    As you know, I have no use for the national obsession with standardized test scores, and no strong opinions about the right way to teach math. But I just thought you'd get a kick out of that story.

  6. Chris, I'm not a huge fan of standardized tests myself. But if any subject is testable, it's basic math, which has clearly defined right and wrong answers.

    Investigations is possibly even weaker than Everyday Math. It's all bad.

  7. PsychMom asks:

    John Mighton..does anyone know what kind of math he encourages/teaches?

  8. Was I the only kid who HATED this kind of thing? Not only would I have not cared about how high the ball would bounce, but I hated group work. Just teach me the concept and give me 20 math problems and let me work through them in peace.

    I cannot imagine that the kids were as excited about this as the description implies. I really don't believe that they decided themselves to work in groups of three and try dropping it from different heights but not one meter. I mean, can you really picture some 4-grade kid saying "gee, guys, there's only one way we're going to figure this out! Let's work together in groups of three!" Sounds like something that'd happen maybe in an educational cartoon shown in science class, but not in real life.

  9. Megan, I'm with you. I would have hated it too.

    Faux-progressive projects can be very coercive. Here's a situation where the teacher asks the class a question ("How high will the ball bounce?") but the answer I would have genuinely had as a child ("I don't know and I don't care") is clearly disallowed.

    There's enormous social demands being made on the kids, beginning with the demand to fake interest in the question. The social curriculum is more difficult than the mathematical one.

    It's misleading the way this thing is described, as if the kids spontaneously decided not to directly measure what the teacher asked. It's actually right out of the Trailblazers textbook. The kids were walked through a pre-ordained script, which is never alluded to in the write-up.

  10. PsychMom: John Mighton encourages what he calls "guided discovery," which is a compromise between the "constructivist" pedagogy pushed by most ministries of education, and traditional approaches to math. He is opposed to pure "discovery" methods of teaching math because he believes that the lack of incrementalism inherent in these methods confuses kids needlessly and turns a lot of them off math. He believes that every kid should be able to understand and enjoy math, and he has had quite a bit of success with his methods (and with his workbooks), though he has met with resistance as well.

    You might want to check out his books, The Myth of Ability and The End of Ignorance.

  11. Remembering math class from my childhood, I think the only problem I would have with this project would be, I'd feel anxious about my classmates seeing my ineptitude at it. But what if I were to discover, I wasn't so lousy at it after all?
    I do know working long division problems were drudgery. We did a lot of them. Even though I gained competency at them, they remained pure drudgery, done in isolation, without any apparent meaning; sometimes finding patterns, shortcuts, different ways of looking at the numbers but no one ever talked about it so neither did I. I just dutifully worked the algorithm, like everyone else, I guess.

  12. SCF, the traditional method can be done badly too. They call it drill-and-kill for a reason.

    The best method would give enough practice so that kids could achieve mastery, but not so much that it would just be a chore. Also, there should be plenty of theory and challenges for the bright kids to think about.

  13. To NorthTOMom...thanks from PsychMom.

    He just held a workshop in Hamilton that our teacher went to this past weekend.

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