The Most Valuable Lesson I've Learned in 10 Years of Teaching

When I began teaching I knew something was wrong with how I had been taught and how I was currently teaching. I did what I could to adjust my style, but the change was slow. I couldn't put my finger on the problem - so I couldn't really solve the problem. Each year I'd try something new... then in my 5th year of teaching I took over a math position from a friend and former colleague. She gave me some of her math materials to give me a head start. I took her materials and (with minor adjustments) just ran with them. In the process I discovered or at least was able to verbalize what had been missing for me all these years. The simple "Joy of Discovery. "

During that year; I watched kids get excited about making connections. They cheered when they began seeing patterns. My math classes in school were never like this... I wasn't using flashy multimedia, or a modern textbook, kids were simply working together, making observations and drawing conclusions. Magic.

Why are people willing to spend hours working out Sudoku puzzles? Why are kids excited to spend hours with a video game? Why do mathematicians and scientist devote their lives to research?

There is inherent joy in the act of discovery. As a species that evolved intelligence at the cost of physical strength it shouldn't surprise us that we have a built in reward system for learning and discovery.

It seems to me that modern math education is not in need of more technology or new standards. Rather as math educators we need to focus our energy on returning the joy of discovery to our math classes. Isn't that what is so good about Dan Meyer's 3 Act approach and so wrong with the Khan Academy approach?

This topic came up again as I was describing the Exeter Math program to an administrator  I found that I was using language very similar to as if I was teaching a textbook driven course - which was a bit troubling. Yet there is a key difference. While Exeter is paper based and not all the problems are amazing - it forces the joy of discovery back into the classroom. The burden to discover is on the students. It is a problem first solution second approach. The complete opposite of most (math) classrooms.

If I reflect on all the PD, all the TED talks, all the blog posts, all the books and all the long conversations over a beer or two three the most valuable lesson I have learned in 10 years of teaching has be the recognition of the value, the motivation, and the sheer joy of discovery.

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?

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

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. 

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...

The Class I Always Wanted

In high school and college, being the nerd that I am, I always dreamed of a fantastic course where I and other students simply got to ask cool questions and where we were given the time, resources and space to find the answers. I dreamed of learning to program something that I wanted create - not being told what to create. I dreamed of building a robot or a contraption that did nothing useful but was fun and challenging. I dreamed of a true nerd elective where problems came first and solutions came second, where problems came from creativity and solutions came from a desire to learn and not from a lecture.

Next year I get to create that course. I get to teach a Nerd Elective! The course was created on the premise that many students at my school were not being challenged with the current math and science structure. We have the beginnings of a robotics program and the resources to support it. The stage is set. Now all I have to put the structure together and create the environment for the students to thrive in...

The Plan So Far...

• I will give a brief intro to some ideas: Lego robots, iPad app development, Flash programming, Kodu Game Lab (maybe) and anything else I can find in the next 5 weeks. 
• Students will create their own question or project including time frames with goals, deadlines and expected challenges. 
• Students will work alone or hopefully in groups of 2. 
• Final choice of projects and deadlines will be supervised and negotiated. 
• Projects MUST be interesting to the STUDENT. 
• Student will create a record (blog?) of there work including discoveries, progress and challenges.  

What I need...

• Framework to foster creativity and maintain accountability. 
• Rubrics to grade student work?
• Reasonable expectations for students. 
• More project platform ideas. 
• General advice. What am I not thinking about? 

Piece-wise Function

My IB students are working on a portfolio project that will requires some piece-wise functions to model. I used the function below as a tongue-in-cheek example of a piece-wise function. Including the idea that changes in function type ideally have a contextual reason or event that changed the system or scenario being modeled.

Oddly enough they all understood what I was talking about...

What Got Me Thinking - June 1st

Mindset - Carol Dweck's book discussing the ideas of "closed vs. growth" mindsets. A very good (and easy) read. If you haven't read it you need to. It was the summer read at my previous school and for my current school.

Grit - Character is a better measure of student success than most anything else. Similar idea but maybe with more resolution than Mindset.

Our Buggy Moral Code - Dan Ariely's TED talk. Not really math/physics related, but pretty interesting research on irrational behavior. He touches on the ideas of pain but mainly focuses on cheating and what influences when and how much we cheat.

Flipped Classroom? - An article on the ever more talked about "flipped classroom." Why does a video lecture seem so much better than asking the kids to go home and read a chapter? I can't help but think that a flipped classroom is just passing the buck...

Building a New Culture of Teaching and Learning - Great commentary on schools and learning. Worth the time investment to listen.

People Stuck on an Escalator - Was used by a former head of math to set the stage for an all faculty discussion on Mindset. He also used it to start his classes each year.