I teach math and programming classes at the Kirby School in Santa Cruz, CA, a private school for grades six through twelve.
Although I teach math, the central principle of my work is that whatever I teach must serve all my students. Though it is important that each student gain a solid grounding in arithmetic, statistics, geometry, and basic algebra, we mathematics teachers often mislead ourselves about the direct applicability of our course content to students’ daily life.
For example: How many quadratic equations have you had to solve in the past week? Unless you are a math teacher, or are working in one of a few specific math-intensive fields, probably not many. Yet we make quadratic equations a centerpiece of our traditional Algebra I curriculum, and spend a great deal of time trying to teach ninth-graders to factor quadratic polynomials. This isn’t to say that there’s no value in studying quadratic equations (or any other math content); the point is that when we read math content standards, it’s easy to get bogged down in tiny chunks of measurable skill and lose sight of the bigger picture.
So, my intention is to teach students a way of thinking, and let the skill development follow. Starting from well-chosen problems — true problems, not exercises (though those have their place) — we can have fruitful discussions about how we think and what makes a solution good and where insight comes from. Using real problems also allows us to talk about the real transferable skills that will make a student successful in any future career:
- perseverating and observing patiently in the face of confusion
- asking probing questions
- attending to detail
- communicating accurately and clearly
- defining problems and solutions
- estimating numeric answers
- checking answers against reality (and not just the back of the book)
At more than ten years into my teaching career, this is far and away the most effective approach I’ve found for motivating students and getting them to solve tough problems. It’s also the most fun I’ve had as an educator.
Serve the students’ learning. That’s why I do this.