Matt — I’m going to “Plan B” the rest of my work on this unit because I’m doing a presentation on using Web 2.0 tools in math and I want a spectacular example of inquiry based learning and how these tools can enable us to do things we have not found easy up to this point. I’m thinking about an application of Twitter in math class that I hope will overcome some of the old co-op model issues we’ve been discussing and will foster students’ ability to frame their problems, questions, and responses. The notions of (i) having only 140 characters and (ii) there being a larger audience able to see and respond are intriguing. I also think that the traditional KWL activity could be rewritten to help students frame better questions about what in math is giving them difficulty. The idea of investigable vs. non-investigable questioning seems also to apply to students’ being able to better articulate their difficulties with their work.
If my grant application is successful and I and move forward the Australia plan, I’ll definitely be in touch for feedback as I develop my initial idea of basing that pro-d on inquiry based learning. Meanwhile, creating an example of a manageable way to infuse inquiry into math class in order to support what Dan Meyer calls “math reasoning and patient problem solving” has the potential to become a money-maker for me (now on a fixed income!). Western Canadian teachers are in the process of rolling out a new math curriculum, and there is a great thirst for ‘stuff’ that is well-conceived and gives high school teachers a handle on how to engage students by letting “math serve the conversation” (Meyer, 2010).
Finally, my uploaded assignment cannot really be considered a paper in a formal sense. I decided to create a working document that would show you the process I went to through in order to create a collection of questions that I think change a typical ‘transmission’ taught lesson (Tall, p. 357) into an inquiry based learning activity.
Let me start with the video that inspired me to change directions this week.
I’ve tackled the problem of improving the effectiveness of teaching in math in a number of courses during the IM program, but I haven’t been entirely happy with what I’ve come up with to date. I keep returning to the Pythagoras theorem partly because it’s covered in two grade levels (8 and non-academic 10) in BC and partly because it’s one of those topics that’s easy to remember and use without having any real understanding of what it means, why it works, or how it can be useful.
Let’s take each of these in turn.
- What it means
Most teachers show and tell the Pythagoras theorem rather than letting the students figure out the relationship themselves. Or … if they put scissors and graph paper into the kids’ hands, they’re still using the illustration to back up the theorem rather than as a way to invite the students into asking: “What matters here?” (Meyer, 2010). Commonly the result is that theorem is memorized and the example is forgotten. Then when difficulties arise in subsequent grades, the theorem rather than its underpinning of understanding is reactivated in an attempt to efficiently move students into more complex applications in trigonometry. This is when math becomes like a house of cards. If the bottom floor is poorly remembered, the superstructure becomes very fragile and can fall apart when something new and different is introduced on the top.
- Why it works
This gets at the use of ‘proofs’ and pushing even students who will find these hard to follow to the edge of their understanding. Proofs have all but disappeared as a part of a the high school math curriculum, and yet figuring out why something works in math is when the the most powerful fusion of concepts and skills occurs. The Pythagoras proof is not complicated for high school students to follow (although I think the algebra goes by a little fast in this video), and adding it back into the course can develop students’ grasp of how the skills they are learning are tools with which to build more complex and meaningful mathematical thought ‘structures’.
- How it can be useful
This is less of an issue with concepts such as the Pythagoras theorem than it is in algebra. However, although the traditional textbook problems of trees and fences and walls and laddersmake reference to actual objects, they seem contrived and disconnected from the students’ real lives. You can tell kids that the concept is fundamental to construction (getting corners square without a protractor) but this is just more show and tell. Dan Meyer’s approach is to get them to buy into the problem solving process by engaging their emotions. He calls it “baiting the hook.”
So this week, I’m keeping this conversation between ‘dydan’ (Dan Meyer) and ‘Independent George’ ( a blog respondent) in mind as I work my way into ‘mathland’ again.
George: The Pythagorean theorem was my first encounter with proofs …, and I remember not being able to really grasp it at first, but nevertheless being aware that we were on the cusp of something huge.
Dan: George, I feel like every math class from Algebra through Precalculus exists (in part) to set up this awareness that we’re “on the cusp of something huge,” that some wisp of this concept transfers over to that one, that this can all be predicted somehow…”
That’s the exact feeling I want to go for with my Australian teachers if I get there and as well as with my math audience at ISTE in June if I can. I’ll appreciate any and all feedback you can give me on this week’s assignment.
Meyer, D. (2007, March 22). Geometry – day65 – Pythagorean theorem. [Web log]. Retrieved from June 4, 2010, from http://blog.mrmeyer.com/?p=177
Pythagoras’ Theorem. (2008, January). Created by Digitalmud.org. Retrieved from June 4, 2010, from Metcalfe at http://www.metacafe.com/watch/1056183/pythagoras_theorem/#
Tall, D. (2008). How humans learn to think mathematically. Unpublished manuscript, University of Warwick. Retrieved December 4, 2009, from http://www.davidtall.com/book.pdf
TEDxNYED presents Dan Meyer. (2010, March). Retrieved from June 4, 2010, from YouTube athttp://www.youtube.com/watch?v=BlvKWEvKSi8
Water-proof of Pythagoras’ theorem. (2006, December). Retrieved March 17, 2010, from YouTube: http://www.youtube.com/watch?v=hbhh-9edn3c