Sunday, November 25, 2012

When does a rock stop being a rock?

When does a pebble stop being a pebble and become a stone?
When does a stone stop being a stone and become a rock?
When does a rock stop being a rock and become a boulder?

I ask my wife these three questions too frequently. She's had enough of my philosophizing. So maybe you can help me out here? Are the answers too subjective? Is there an objective, definitive, agreed upon set of answers to these questions? Are the answers determined by weight? size? volume? mass? density? ootsies? (a la Christopher Danielson)

I'm thinking bigger picture here: How do we bring this type of thinking or wondering to our students more often? When dealing with measurement, how do we get our kids to know the correct (or most logical) way to measure quantifiable items without telling them? Would asking these types of questions help encourage our students to be better problem solvers or be better at applying the right terminology?

So many questions... here's more:
Living in the USA, our customary units system of measurements seems counterproductive with inches, feet, yards, fathoms, miles, ounces, cups, pints, quarts, gallons, barrels, etc. Terminology can be difficult enough for students and to throw all these different measurements at kids (nay, humans) can only seem daunting. When should we use feet to measure something instead of inches or yards? I envy the metric system and, well, let's leave it at that. These measurement questions become even more relevant as I dive into estimation with my students and as I update each week.

I haven't posted in a while and feel like I need to ease back into my blogosophy (blogging philosophy?). I'm not sure I just eased back into it. What do you think here?



  1. This comment has been removed by the author.

  2. I get your message loud and clear. Learning (and teaching) math requires common terminology and rules. Through questioning we can help reinforce the language of math and refine the nuances of the rules.
    Right now my 10th graders here in Canada are being introduced to imperial units in their measurement unit. I agree that it (imperial) is much less user-friendly than the metric system.
    For me, the engagement needs to be there in order for the questioning to develop naturally. I think too often we are dealing with topics (eg factoring polynomials) that are not innately engaging. The challenge is to create these engaging tasks to practice the questioning and apply the math processes. This is where i appreciate your efforts along with Dan to create such tasks.
    Sorry for rambling,
    P.S. I hope you can get back on the blogging horse as I find your thinking helpful.

  3. Try throwing a pebble/stone/rock at someone and he'll for sure be able tell you the distinct differences among them. It's equal to the size of the lawsuit. Boulder is a really pretty town in Colorado.

    If you ask @MrAntiSEC (aka David), he'll tell you that SEC teams should measure their runs in inches or feet because... well, you know, them boys are just really slow.

  4. I think you have stumbled onto Sorites' Paradox. I have always thought there has got to be some fantastic way to present this in a three act problem. I tried to encourage debate, but students liked gut judgement, also it may have been above grade eights.

  5. @Blaise
    Good luck with imperial. I'm thinking of some ideas to create some worthwhile tasks on measuring... and I see the key focus as something where students are given objects or objects and they need to explore what units of measurements would make most sense to them. Of course, they'd have to provide justification.
    Yes, Timon I have stumbled onto something like Sorites' Paradox. Right now, I'm owning this thought of relating measurement to a better understanding (or misunderstanding) of number sense and more importantly how my students can be aware of these happenings in their lives. Yes, toss this one up on that bulletin board of 3Acts.
    Thanks guys for the feedback!

  6. Love the visuals! Must agree with Fawn...depends on the "ouch" factor!

  7. You don't care about the rock/pebble thing in particular, right? It seems to me that you are interested in something having to do with mathematical definition, and its purpose. In recent weeks, these questions have come up in my College Algebra class:
    (1) "Is a linear function a polynomial?" (i.e. when is a polynomial no longer a polynomial?)
    (2) "Can a sequence be both arithmetic and geometric?" (i.e. is it possible to be both a rock AND a pebble?)

    One mode of mathematics instruction devalues these questions. We go to the definition and get on with our lives. A different mode values these questions highly. In this mode, we ask what seems *right*. SHOULD a linear function count as a polynomial? This gives us something to argue about. Then we consult the definition-not because we couldn't make a decision on our own, but so that we know how everyone else talks about these things.

    I find that sorting tasks are good for getting these discussions going. No need for three acts, I don't think. Just a bunch of carefully chosen examples and a room full of students with incomplete knowledge.

    Thanks for spreading the good word of Ootsies.