“The best way to learn is to do; the worst way to teach is to talk.” — Paul Halmos
Interesting thoughts from David Bressoud over at Launchings on being an effective teacher. He references the Academy of Inquiry-Based Learning, and I recommend you check it out. I think this approach to teaching mathematics fits very well in the context of my previous post on Math as Story.
It has been a while (at least longer than I would have liked) since I posted. I have been involved with several writing projects this summer that have taken more of my time than I initially anticipated. But the upside is that once they have been completed and publish I will be able to share the fruit of that labor here. In the meantime, back to our regularly(ish) scheduled programming.
A few weeks back I was privileged to attend CAMT 2011 (Conference for the Advancement of Mathematics Teaching). The main reasons that I made time for it on my schedule was that it was being held in my hometown of Grapevine, TX (=money saved by staying with family) and the featured speaker was Dan Meyer (=my hero in math education).
Overall it was a good experience. Not bad, not great. Good. Being a conference designed for primary and secondary teachers, I was expecting presentations that were practical for me to take back to my classroom. On the whole, I didn’t quite get what I expected. Some presentations were psychological/research driven, meaning they went along the lines of, “the numbers show that kids are failing at (blank) and possible reasons include (blank), and we can correct this by creating a culture of (blank) in education.” It was all good information, but the solution strategy seemed more speculative than practical. On the flip-side, some presentations were too practical. By that I mean that the presenter essentially gave a quasi-lesson and left me to go copy it without really fleshing out the philosophy behind why it is a good lesson, so I can then develop other lessons in a similar philosophical vein.
Of course, this could just be representative of the talks I chose to attend and not the conference as a whole.
There were of course several presentations that perfectly blended (at least for my taste) the philosophical and the practical aspects of teaching. Naturally Dan Meyer’s talks fall in this category and this why I am such a big fan of his. The main point of both his talks: a good (read engaging) math problem is like a good story. A good problem grabs your interest (usually with a powerful image), equips you to solve the problem which is different than just giving you a bunch of information, and it finally relieves the tension that was initially presented by confirming the solution (ideally with an image again, not just revealing the answer key). It also sets the stage for a sequel.
It seems so intuitive, but yet it clearly goes against the grain of how most of us were taught mathematics. It also fits into our evolving, media-saturated world better than word problems in a textbook.
The concept of a good “story” I think is also essential to our understanding of the Biblical text. As I reflect on this understanding in my own spiritual life, I see clear parallels. Narratives in Scripture often present an initial conflict that I naturally want to see resolved. This is usually followed by a coming to terms with this conflict, where characters are equipped to handle their problem (which is NOT the same as God intervening and just giving them all the answers). Then the narrative closes with an act of redemption, revealing the nature of God, and bringing satisfaction to the problem. But, just like the description of a good math story above, the Bible leaves way for a sequel. Whatever redemption we experience now, though miraculous, is temporary and incomplete. In the narrative’s attempt to resolve the conflict, to borrow a line from a song, we still haven’t found what we’re looking for.
From James Bradley, ASCI World Report:
– Mathematics helps us see the order and beauty of God’s creation and thus of God Himself. Hence, mathematics derives its purpose, meaning, and value from God. Discussion of these themes can be a legitimate and valuable part of mathematics education.
– Teachers should enjoy mathematics, receive it gladly and thankfully as God’s gift, and cultivate a classroom climate in which students enjoy it and want to do it. Educational materials should support teachers in doing this.
– Teachers need to show students explicitly how mathematics fits into our God-given stewardship of the earth and into the building of human communities. For example, teachers need to explain ways that people have used mathematics to advance principles such as justice, responsible stewardship, and community building as well as ways that people have misused mathematics.
– For much of the twentieth century, an abstract approach devoid of context dominated mathematics. By contrast, a Christian approach says that mathematics is not autonomous but rather is an aspect of an interconnected creation. Thus, teaching needs to be contextual—it needs to establish clear connections with other subjects and with the practicalities of life.
– We as Christians do not despise the physical and glorify the mental and abstract. Rather, we value our bodies as God’s creation. Thus, teachers should, as much as possible, use teaching methods that actively engage students’ minds and bodies by means such as using manipulatives and having students collect and analyze data.
– Teachers need to discuss in their classes how the surrounding cultures view mathematics and how a Christian perspective differs. For example, until fairly recently, the United States and Western Europe overemphasized human reason. Now these cultures have swung in the other direction, tending to undervalue reason and overemphasize intuition. Asian, South American, African, and Western countries tend to value mathematics solely for its economic benefits, without considering that pursuing economic gain apart from a broader framework of godly service can be harmful.
– Students often think of mathematics simply as recipes for how to do problems. Teachers need to foster an attitude of deeper reflection on what mathematics can and cannot do for human beings, on the wonder of this gift from God, and on what its order and beauty tell us about God and His creation.
Free lessons and resources for following the above in integrating Christian faith in the teaching of mathematics from the Kuyers Institute for Christian Teaching and Learning.
GOD & MATH: Thinking Christianly About Math Education 