I'm teaching one of our math for elementary education courses and the content includes measurement and statistics. I love measurement as a context which needs statistical understanding. Measurement introduces variability, and has a strong need for producing a number to represent typical. If the question is, "How tall is the ceiling?" then 2.60, 2.7, 2.725, 2.73, 2.735, 2.735, 2.74, or 2.76 meters is not a satisfying answer.
The oreo lesson, if you are unimaginably unfamiliar with it, is the brainchild of Christopher Danielson, aka @Trianglemancsd, the purveyor of much fine snack food mathematics. (All the oreo posts; this one is sort of a wrap up.)
Previous to this lesson, we investigated measurement, did an introduction to statistical typicals, and worked on statistical displays. (Two of those covered in a previous blogpost.) On the day before oreo day, I brought three packages of oreos to class: regular, double stuf, and mega stuf. Their interest was definitely piqued; it was like they could smell the sugar. Not much mathematical interest, though. So I prompted - what might a mathematician wonder about this? They immediately jumped to the idea of is it really double, and what is mega. Then we brainstormed together - what do we need to gather data on for the next day?
Their list:
Not bad. Calorie burning turned out not to be viable with that short of a notice... but I'd like to see it! I made a data sheet, so that we'd have a whole class worth of data, and a google spreadsheet to share.OREO: data to collectweight of the whole cookieweight of white stuf in each cookie
height of each cookie (mm)diameter of each cookie
weight of cookie/black sidesheight of black cookie
height of white stufdiameter of white stuf
how many of each size fit in a specific container/height
volume by displacement
compare deliciousness of different types
nutrition informationstuffing v serving size
calorie content (burning)
The points about measuring like a scientist (half of the smallest unit) and recording to show the accuracy measured are obviously still in progress. Also the statistical thinking of gathering and using data need more development - most were happy to answer the main question with just their measurement. "It's double." "It's more than double." "It's less than double." No one used the measurements, they went entirely by weight.
That wasn't what bothered me. I expect those kind of goals to take time.
What bothered me was that they weren't into it.
They were excited about the cookies, and figuring how many each person got, and eating the cookies afterward. But they weren't into the math.
Dave Coffey sometimes recounts (or makes fun of me for) how I want to be obsolete. Sitting back and watching students direct themselves at the end of the semester. I always want to hand off to the students. Have them make it their lesson. Look, here's a pile of data! On something interesting! What can you do with it? What else could we look into? How many ways can we come at the question?
But on this day, they said no.
My personal metaphor for this is a Smothers Brothers routine. (That's how old I am.)
(The whole brilliant bit... the show was amazing. Steve Martin got his start there as a writer, for example. They used their folk singing to make the show safe for sharp political commentary. Like we use math class as a ruse to get students problem solving and thinking critically. They were cancelled and replaced with Hee Haw.)
So this lesson felt like, "Take it, class!"
"No."
My response was to ask them to make sure they got all their group's data, and to write about the measuring and their answer to the question for a standards based grading assessment. And this is a compliant class, so they did, and did a good job on it. But that's far from the peak experience for which I was hoping with this lesson.
Part of the problem, I think, was in my desire for efficiency. By introducing the problem in the previous class and then making a record sheet, I took the initiative from them. They went into fill in the blank mode, from long habit in math class. Another part of the problem was lack of a focus, in the workshop sense. I think I should have discussed statistical thinking with them, and how that's different from single measurement thinking. It's all about the data! This is very reminiscent of the Barbie Bust. It was my problem and my lesson. "My" doesn't help me be a better teacher. (Gollum.)
Reflecting afterward, I think my high expectations helped create the sense of disappointment, like an overhyped movie. And it led me to rush into a lesson instead of building suspense and anticipation. I think this kind of experience contributes to teachers who "tried that once" and that was enough to turn them off of inquiry-based learning. In the end it is the learning that needs to be the center of engagement, not the cookie.
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I went to an excellent talk by Annie Fetter of the Drexel Math Forum on Saturday. Her topic was basically how important it is for us math teachers to get students noticing things about a particular problem, and then to get them to wonder things about that problem. Very interesting talk, and she really reinforced for me how important that notice/wonder phenomenon is.
ReplyDeleteHowever.
What nags me about "notice/wonder" is exactly what you're describing in your post. I think we are jumping into "get the students to notice and wonder" without providing enough motivation. The math blogosphere has spent a ton of time and effort coming up with rich, non-pseudocontext-y problems, but I can't help thinking that the real hurdle to overcome first to getting students to that place in their heads where they feel the NEED to notice things and WANT to wonder about problems.
That's a lot more difficult issue than simply coming up with rich math tasks, I suspect. I also have a strong suspicion that developing those habits has got to start early in kids' lives - maybe even before they arrive in school.
This sounds like a great problem to do with students, and I think I also would have been disappointed by the class reaction. I do like, however, that you began by asking students what they wondered about the three packages of cookies. I am surprised that by engaging them in this question that they were not more motivated to find the answers.
ReplyDeleteWhat a quality reflection! The students came up with so many great questions when you introduced the task it is really a shame that it turned into a dud. Perhaps with more ownership and less teacher involvement they would have been more into it. I agree with Carrie that we need to promote good questioning skills and intrinsic motivation from an early age. However, since I don't see them until they are in high school, I start as soon as I can, on the first day of school. I try to encourage questions and mistakes!
ReplyDeleteI can sense the enthusiasm in your post... right up to "What bothered me was that they weren't into it." Makes me think about Dave's post "Whose problem is it?" http://deltascape.blogspot.com/2012/01/whose-problem-is-it.html
ReplyDeleteDo you think any of this is related to what they think 221 should be about? Two possibilities: Misconception #1: 221 "is supposed to be" a method course. I had one who expressed a concern like that in my office, saying she wasn't learning how to teach, and when I explained it was a math course with education focus rather than a course in math pedagogy, she seemed pretty surprised (my bad, I suppose!). Misconception #2: What you are asking them to do isn't math. You know what I mean re: math practices vs. rote, so I won't elaborate. Do you think either of those might partly explain the flop?
I do think the "whose problem is it" issue is the most compelling explanation here. But then what are we to do with the "great" tasks we've discovered over the years? Offer choices, perhaps?
Thanks for sharing this, John. It will be in the back of my mind for a long time.
ReplyDeleteI could really relate to this experience, John. It happened almost exactly this same way for me with one of my two 8th grade Algebra classes last year. Nothing like that sorry, wet-soudning plop of a beloved lesson idea hitting the floor. Ugh.
ReplyDeleteThe launch of the idea is so important, but sometimes it's not the only thing that matters. Some lesson ideas require me to "develop their dissatisfaction" because they need to buy in over a little time before students have enough intellectual need to power them into or through the next step.
In major account sales (like selling a site license for your software to a school district), there's a model for developing dissatisfaction and intellectual need called SPIN - Situation Problem Implications Need-Payoff - that I sometimes still draw from when setting this kind of thing up with students. The idea is that for big problems of intellectual need, people don't all arrive at that moment of need at the same time. Or they don't all understand it as a need. Or they don't understand the implications of that need enough to care (yet).
The fact is that readiness for intellectual need is a great gift, but it can't be forced or rushed.
When coaching young new major account sales people, I often found that I needed to get them to understand this point – namely, that cultivating readiness is never time that is wasted.
I use this so much in the classroom every day it is outrageous.
Sometimes my students' skills are still so weak or tenuous they cannot appreciate the scale of the problem or intellectual need they really have.
This is something I find Henri Picciotto to be completely brilliant at. I have never seen anybody so thoroughly and joyfully scaffold student inquiry to set them up to become massively and acutely aware of their intellectual need and dissatisfaction. He would have them chase down data, fill in tables, measure their steps or throws or whatever, to the point at which students could see that, Man, this is a giant PITA! I really wish there were a way I could ______ (fill in your golden payoff here).
I too had this insight when I did the Oreos lesson last year. The kids didn't get the motivation.
This year, because 8th graders can always be provoked about matters of "fairness" and are always on the lookout for ways they are being cheated, I plan to have them do some heavy-duty mathematical inquiry into these questions (probably as consumers) before I introduce the question of whether Double Stuf Oreos are truly double.
They need to build up a good head of steam (and adolescent outrage) to propel them up the mountain of mathematical investigation they'll have to do to make it a worthwhile and triumphant arrival at the top.
Some people might say this is artificial and manipulative, but I would argue that leveraging situational motivation is one of the most powerful tools we teachers have in our toolboxes. Sufficient "intellectual need" for the learning is crucial, but I find it to be self-defeating magical thinking whenever I try to believe that this intellectual need will arise on its own whenever I need it.
Thanks for this thoughtful post.
- Elizabeth (@cheesemonkeysf)