some things to know
Back in 1908 Felix Klein did a series of lectures targeted at school teachers with a focus on “elementary mathematics from an advanced standpoint“. Even 100 years ago there was an acknowledged gap between school maths and research maths. The Klein Project is named after Felix and shares his goals of bridging this gap.
goals of the project, as I understand them
How many of us stay in tune with the maths we did in college? My own background is mostly theory. I have pretty distinct memories of taking writtens and orals my senior year, proving most of the underpinnings of calculus in Real Analysis and studying groups and rings in Abstract Algebra. Number Theory along with Combinatorics/Graph Theory were some of my favorite classes. I have forgotten more mathematics than the majority of people will ever know and I suspect a lot of teachers are like that.
I used to spend hours every day reading/practicing/explaining math. Unless I am willing to do that again I doubt I will get back to being as in touch with higher level maths as I was back in college. On the other hand, I’m amazing at just about all aspect of precalculus. I can glance at student work and spot the problems with minimal effort. I know how to question kids to make them think and prod them to a point that they crave understanding and not just answers. It’s a trade off that I’m just fine with as a math teacher, but that doesn’t mean that I don’t miss the higher level stuff.
The Klein Project is trying to help high school teachers stay connected with research-level maths. I am not going to take the time to wind back up to my senior math major glory days, but I will totally sit down and read a short paper explaining tandem rigging for crew. These papers, or vignettes as they are being called, are meant to be 4ish pages taking a view of a specific topic with a message about the math. A vignette is meant to be read seriously–have out a pencil, paper, maybe even geogebra, and be ready to dig into the topic. While working through Bill McCallum’s paper I chose to prove a few of the equations to myself and it was rather satisfying. I also mocked up a few of the ideas in Geogebra. Outside of PCMI, I don’t often get that feeling of satisfaction with my mathematics anymore. My teaching, sure, but not my math ability.
A goal with these vignettes is to show teachers something beyond what they know. The math detailed in a vignette should be explicit. It should be modern (okay, last hundred years may not sound modern, but for math is totally is). It should have the reader convinced of the importance of the math. Now, that’s not to say that everyone will find every topic riveting or personally important to them–Graeme’s paper on rowing configurations is probably not something I will ever use (more of a single-person kayaker, myself), but that doesn’t mean it isn’t a great read about the mathematics.
One part of the project that I really appreciate as a teacher is that these vignettes are not curriculum. They are not telling me what or how to teach to my kiddos. They are for me as a professional mathematics educator. I love to be treated like a competent professional. I feel like these vignettes will be for me what modern medical journals are for doctors–a way to keep up with the mathematical world. I have things like Mathematics Teacher (which I would like, but NCTM seems to be offline right now), but this is something different that satisfies the mathematician in me.
events from the week and a call to arms. or pens. or tablets.
For five days at the American Institute of Mathematics in Palo Alto, CA, a group of about 30 math researchers, teachers of teachers, and high school teachers worked together to bring the Klein Project out of the planning stages and into the writing/publishing vignette stage. A lot of the talk centered around the content of vignettes; their size, their message, their accompanying materials. The organizers put on a good conference and I think steps were made that will keep the project moving forward. I also think there is a long way to go in regards to how the Klein Project will be brought to the attention of teachers, but it’s all a work in progress.
At this point I feel able to help write a vignette, but I don’t feel that I could do it by my lonesome. Pair me with someone that really knows a topic, and then I could probably make something happen. I actually have an email in my inbox from another participant that’s a partial vignette that I’ve only had a chance to skim and I cannot wait to have a free hour to sit down and really dig into to offer quality feedback. As I stated earlier, I’ve been out of the pure math game for a while, but given some time and direction I could bone up on a subject and help produce something awesome and readable about it.
So here is my question for you, fair folk of the edublogosphere, does the ideas of getting the chance to reconnect with research level maths light your fire? I know that some of us out here have master’s and PhD’s in maths and could probably write some awesome vignettes relating that learning to high school teachers. I’m looking pointedly at the Math Munch folk, as I feel they would enjoy reading the vignettes, suggesting topics for some, or possibly even writing a few themselves. Also, if you’re not subscribing to Math Munch, you should be. It’s like Sunday morning comics for math teachers!
interested in the klein project and the vignettes?
Check out the official wikispace. Yes, I know there’s a lot of german, but if you click on ‘Klein Vignettes‘, you’ll end up in the right spot for reading the preliminary vignettes. I told you this was an international venture. All sorts of awesome people are working in.
Currently in the works is a blog where the vignettes, along with accompanying applets, links, etc, will be posted weekly. As the vignette writing has just started, it will be a bit until the blog goes live but something like that in my reader would make for a nice weekly dose of mathematics. I’ll keep you posted.
forward thoughts and worries
The following is a collection of thoughts I had throughout the conference related to how it will move forward and how other teachers will react to it. This section is more for me as I ruminate best on things I’ve written out, so feel free to skip unless you enjoy thinking about logistics.
-How do we get teachers to understand that such vignettes are as worthy of their time as other PD? That by learning more about the connections between the maths they teach, the maths they learned in college, and the maths in research they will be able to build stronger lessons with deeper connections across topics which in turn will benefit their students’ understanding.
-Many of the vignettes are going to make teacher uncomfortable/embarrassed about their own knowledge, so it will need to be very clear that the vignettes are supposed to push the boundaries of their knowledge. That, yes, the writers know you may not have ever seen this topic, but give it a chance! Think about it! You will understand but you have to try! Hard work is the best work. Vignettes are hard work.
-There will be teachers who do not care and see no relevance to the vignettes to what they do in the classroom. Do we worry about those teachers? Do we try to reach them? Or do we write them off (at least until buy in from interested teachers has been achieved)?
-I think if teachers are willing to go through with the uncomfortable aspects of reading the vignettes (not understanding items at first, realizing extra studying/paper & pencil work may be involved to understand, etc), the power they will get from figuring out the maths will be extremely beneficial. I’ve always had the sense that a lot of the teachers that do math like the order of it all, but were never that into higher level math (especially math education majors who spent college more focused on the teaching aspects). How much power could such teachers, who clearly have a solid grasp of the fundamentals of high school maths, derive from working through the vignettes? That “wow, I’m awesome” feeling of figuring out a challenge that isn’t about an administration problem or students. Those things are part of being a teacher, but so is remembering what it’s like to accomplish hard math–something the kids go through all the time.
-My favorite quote from the whole week was “you don’t have to be sick to get better”. I want that embossed and printed on something that I see everyday.
Many of the ideas in this post were taken from the various talks given at the Klein Project meeting. I took a lot of notes, as I am wont to do, and I would like to acknowledge the following people whose wonderful ideas I am riffing off of in this post: Bill Barton, Bill McCallum, Yuriko Baldin, Christiane Rousseau, and Graeme Cohen