In Teaching Math, What's the Right Mix of Content and Context?

“Polynomial functions!”

“Trig identities!”

“How about the properties? Commutative, associative, distributive.”

So unfolded a laundry list of what a group of math teachers considered the more painful and less necessary concepts covered in the average high school math curriculum.

The laments, aired at EduCon 2.5 in Philadelphia at Science Leadership Academy last weekend, were part of a discussion around how to rebuild math instruction under the radically different—and admittedly unlikely—parameters posed by moderator Mike Thayer, a math teacher at Summit Public Schools in New Jersey.

Thayer, who also has a background teaching high school physics, proposed a scenario in which high school freshmen would take a one-year course (or a one-semester course in a block scheduling system) that covered the essentials of Algebra 1 and 2, Geometry, and possibly parts of Trigonometry. Any additional math concepts might be learned in a cross-disciplinary fashion through other courses. For example, chemistry teachers would be responsible for teaching

students the basics of logarithms while covering the pH scale. Biology teachers would explain concepts of exponential growth to their students when discussing species population and reproduction.

The rationale of such a course, Thayer said, would be to create a version of math instruction that more fully lives with the inquiry-based learning approach embraced by the Science Leadership Academy, the public magnet high school where the conference took place. His vision—which hinges on what he concedes is a large assumption that students would enter high school competent in basic computational thinking—is for a course that would both streamline a high school student’s general math experience, and empower and encourage them to learn additional math skills to solve real-world problems of their own interest.

As one teacher at the discussion put it: “I'd like to delete polynomial functions, but I’d like my students to see a roller coaster and think, ‘There must be math involved in that,’ and to go online and try and figure that out.”

Thayer asked the teachers to consider four questions as they imagined the hypothetical course:

1. WHAT STAYS AND WHAT GOES? Consider both what concepts would get more or less emphasis, as well as what method of learning (lectures, work sheets, group work, collaborative projects, etc.) would work best.
2. NEXT STEP FOR STUDENTS? Options could include more advanced mathematics courses, independent mathematics projects, courses in other subjects that included applicable advanced math concepts, or some combination.
3. HOW WOULD TEACHING CHANGE? Choose which lessons you'd save and which lessons you'd skip. Envision whether you'd use the same kinds of exercises to develop students skills, and whether you'd structure class time in the same manner, or perhaps utilize it differently.
4. WHAT WOULD YOU ASSESS? Tests should reflect the purpose of the course, to develop students' understanding of the theoretical and practical purposes of math.

Most of the discussion during the 90-minute talk focused on the first two points, and the group generally agreed the course would need to focus on changing student thought processes.

“What I am hearing is that if we would like to really make math meaningful for our students, we need to do things to create the ability for them to be truly mathematical thinkers,” Thayer said at one point after hearing a few responses.

There were, however, disagreements over the relative importance of concepts. And a couple of teachers even asked whether geometry would fit within the parameters of such a course.

The group also questioned whether a focus on real-world math applications would be the most likely way to spur students into independent investigation, and whether that focus could create an unintended bias in the kind of material covered. As an example, teachers noted that using tools like 101 Questions, a website that asks users to think of a question related to a displayed image, could result in an excessive focus on proportionality.

Thayer encouraged such discourse, suggesting it would be essential in his new model.

“I think the first thing for us, in order to be masters in context as well as content, is to recognize our strengths and weaknesses,” he said. “I would love for somebody else to be able to come into my classroom and explain why [a concept] is important.”

In a speech at EduCon earlier that morning, Philadelphia public schools Superintendent William Hite stressed the need for teachers to move from content to context expertise. And in a later discussion, Science Leadership Academy founding Principal Chris Lehmann conceded such an approach could be more difficult in a math classroom, but not impossible.

Thayer, meanwhile, warned that if math teachers didn’t find a way to make that difficult shift, they could be marginalized.

“Most of the stuff we teach” in traditional courses, he said, “the Khan Academy does it for free.”