September 18, 2012

What would you do?

I work at a small, independent and expensive school. We work in a (international) community that does not have many other educational options for students. So here's my dilemma...

In one of my math classes I have 7 of the 8 seniors and there is some very difficult classroom dynamics and chemistry that comes with such a small group that also lacks academic leaders. At this point I see 3 students that are sources of great distraction or negativity. They seem almost proud of their dysfunction. I also see 3-4 students who are quieter, more introspective and who are ready to learn and succeed, but struggle to overcome the distractions of the other 3. I have had individual conversations with this second group and they have expressed great frustration with their classmates (in all classes).  These 3 distracting students are, in the words of a grade 12 student, “hindering our education.”

For me that is a big fat line in the sand that you don't cross. To mix, confuse and create my own metaphor... You can lead a horse to water and maybe you can't make the horse drink, but you sure as hell better not let one horse stop the rest of the herd from getting a drink.

This is not a new problem, but with IB exams coming all too soon there is a sense of urgency I feel more each time I wake up. The school has failed to solve the problem and many teachers seem content to simply chuckle and shake their heads.

So. What would you do?

September 14, 2012

What Got Me Thinking - Sept 14

Whiteboarding Mistake Game: A Guide - A great addition to whiteboarding in class. A long post, but worth the read.

Clever Hans - A story of a clever horse that "could do math" and a reflection on how it could and should change what we do as (math) teachers.

"The Exeter (Math) Series" - A series of posts on Exeter Math. Includes many resources, discussions of pedagogy and much more. A must read for those interested in Exeter Math.

The World of Mathematical Reality - via Keith Devlin

September 06, 2012

Robots & Calculus - Part 1

As part of SL Math I have to teach Kinematics, last year I sort of rushed through it. I was too easily convinced by the smiles and nods that learning was happening. In calculus, I've never felt like my students accomplished much more than simply learning a series of steps to get the right answer. Sure they can solve the problems and most of my kids got very good IB scores last year. But! I wanted more.

Too often in SL Math kinematics is window dressing and an excuse for context on a calculus problem and rarely more than that. As a physics guy I see kinematics as the driving motivation behind differential calculus. So this year I swore I'd actually walk the talk. In come the robots!

My school, like any other, has its problems, but we are blessed with dreamers and an administration that are willingly to fund those dreams. 4000 euros later we have lego robots coming out our ears. Our school already supports two FTC teams, one middle and one high school team, so it wasn't a stretch to find more funding for robots.

The students were given about 40 minutes to create their "car" with the two stipulations that it had one motor and allowed for easy removal of the NXT brick (so other classes could use the brick).

And now for the calculus...

Part 1 - Constant Velocity

I pre-programmed 7 functions for the students. The first 3 are constant velocity functions. Student's used Logger Pro's video capture and analysis features to create position and velocity graphs and equations for each function.

Students wrote each set of equations on the board so as a class we had more data from which to make conclusions. I proceeded  to math-teacher-ninja them to see that the slope of the velocity equations was virtually zero when compared to the other parameters. Then the jump to see the similarity in the slope of the position and the constant value of the velocity was quick and easy. Leaving the students to conclude (written in my 2-grade hand writing):

If s(t) is linear then v(t) is constant.  Velocity is the slope of position.
If s(t) is linear then v(t) is constant.  Velocity is the slope of position. 

What more could a teacher ask for?

After these conclusions the students worked some very simple problems. Working with equations, graphs and most importantly writing rules to go from linear position to constant velocity and vice versa. I dangled the idea of the integration constant in front of them, not looking for full understanding, but trying to raise awareness that information was lost or is missing when moving back and forth between position and velocity.

Next up: Linearly increasing velocity in Part 2. Coming soon...