On Sep 3, 2013, at 3:17 AM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
> > I have never found it necessary to discuss 'usual' content and pedagogy. What I find interesting and worthy of discussion are different approaches. I presume that the readers of this forum are more interested in those.
That "usual" content is the heart of the subject that the majority of the students fail to get. It is exactly that content, or more precisely, it is exactly that art that you are supposed to be teaching. How can that not be *the* discussion? The reason you don't get a lot of positive feedback on this stuff is that while people, including myself, are interested in different approaches, they are not interested in different approaches that avoid the content, which these activities, as you have presented, and surely as Dan has intended, clearly do.
This might be news to you. Many of us (teachers) use activities, but they are rooted with the subject we teach. We do not ask open ended (discovery) questions. We ask leading questions. We intend with all our might to teach the subject. Not just to act like we are teaching the subject. If the student does not get it, we fail, not them. We get over it, like a doctor gets over losing a patient, but still, we fail.
> >> What I see in these activities is evading "teaching the >> content". In an actual class, whether it be algebra >> or geometry after algebra, the "popcorn picker" >> problem would be nothing more than a word problem, >> maybe accompanied by a figure, and solvable by a >> student, using algebra, in a few minutes. > > I see 3 types of students in class. First there are those who didn't 'get' the content I taught. Second, there are those who can do the math but don't 'really' think that what the old guy teaches connects with the actual world outside of the classroom (more about them in a moment). Finally there are the 'Bob Hansen' students who get the math and of course see the real-world connections. Doing 'popcorn picker' - which takes 5 to 10 minutes maximum out of a class - has most of its value for type 1 and type 2 students.
Your description of the three groups is close but my version is slightly more refined. Namely, the second group isn't defined as "can do the math" because if that were true they would solve the popcorn problem with little assistance. If that were true then the TIMSS scores wouldn't be what they are today. In my definition, the second group "could have" done the math if they had put in the effort. And when they don't put in the effort it is our job as teachers to push, goad and when possible, encourage. When they do not put in the effort we have to put in the effort for them. And the first group's problem is that they shouldn't be in the class to begin with. They should be in a mathematics class, but one a couple of years prior to the one they are in. One where they have at least a chance of getting it.
It is relatively recently, the last 15 to 20 years or so, that some teachers, schools and districts started doing the absurd. They started putting the first group in classes where their chance of succeeding was less than none. And because of this, it is only recently we began to see absurdities like Dan. As I said before, you do not favor these activities because they are a ticket to teaching algebra. You favor them because it is something to do with your first group of students. I will get to the second group in the next paragraph.
> > I don't think you can appreciate the existence of type 2 students because you were a strong student. These are students who know the Pythagorean theorem and its proof and have done in-class and homework problems on them, BUT if they see a piece of graph paper with 3 dots marked at (0,0), (10,0) and (10,4) and they are asked the length of the hypotenuse they are surprised that it isn't exactly 10. > >> >> But that is not how it is presented by Dan because >> Dan clearly is not presenting this activity in the >> context of algebra. >> >> Let's recall the "acts"... >> >> http://threeacts.mrmeyer.com/popcornpicker/ >> >> 1. Which container will hold more popcorn? >> >> If this was an actual algebra class, this would have >> been the end of it. > > My students have all had algebra and have seen and used the volume and surface area formulas in my geometry classroom. The type 3 students make that connection immediately. I would estimate that less than 20% - even in honors geometry - make the connection without any prompts from me. That's one reason why I think the activity is worth some of my valuable time.
20% sounds right. But here is the catch. The next 40% of the students, that second group, would fare much better with the prompts and some freaking effort on your part to push them through the ALGEBRA than with these phony activities, that are really there for the first group. These are not the right activities for the second group and any teacher knows that. What you are doing is throwing the content up on the board, letting the third group pick it up on their own and then throwing in these activities for the first group, who should, for their own good, be in another class. The second group is not being properly taught.