A Note for Teachers

The material on this site is designed for students to use on their own. But that doesn't mean teachers can't use the material in their classrooms. In fact, I encourage teachers to use the investigative approach in their classrooms.

I used the investigative/discovery/project-based method in my classroom for years. I won't claim that the method resulted in better student outcomes because "student outcomes" is an ill-defined term, so it doesn't mean anything. (What "student outcome" are you looking for? Test scores?? Is that what you want kids to get out of their educations, better test scores??? But I digress.)

For me, the "student outcome" I was looking for was real engagement, a curiosity about the world, an enthusiasm for learning in general, if not the specific subject matter itself. This is not something that be measured in test scores.

I thought then and continue to think now that the investigative method is better for students for a number of reasons.

• Investigation (and it's off-shoot, trial and error) a more natural way of learning. You don't become a better driver, for example, by reading a book or listening to someone talk about driving.

• Investigating (and finding and fixing mistakes) is more interesting and important than memorization and regurgitation. Face it, most of the math skills we are supposed to learn in high school math are virtually worthless in "real life". In my years after school (before I became a teacher), I never once "simplified" a radical or some algebraic expression. Further, if you are trying to get the students to engage in critical thinking (which most schools would say is one of their goals), then lecture and examples is a very poor way of getting there.

• Investigation (and finding and fixing mistakes) is more relevant for life after-school. For most jobs or careers, students are not going to have some "teacher" lecturing them on how to do something. Rather, they will be presented with a task to do and some tools to work with, and they will have to figure out how to get the job done.

• A proper project will engage the student much more than traditional assessments. A "proper project" is both individualized and relevant or "authentic" to the student. It is something that sparks the student's interest. Not every project in these courses is "proper", but that was the goal. A test is never relevant or authentic to students; it is something to be endured to get a grade.

I also think that the investigative approach made me a better a teacher.

• The investigative approach allows teachers to differentiate instruction. It is a basic truism of teaching that some students don't need much help to learn; others need more help. The investigative approach, properly implemented, allows the teach to focus his/her attention on those who need it most. Traditional instruction is, essentially, one size fits all.

• The investigation approach focuses on asking questions rather than receiving answers. Nothing spurs curiosity and engagement more than the ability of students to ask questions. Traditional teaching is very "closed"; students may be reluctant to interfere with the teacher's flow to ask questions. And, from my experience, many teachers are not receptive to students asking questions.

• Project-based assessment is far superior for assessing students' progress in understanding concepts and applications. Quizzes and tests are far superior to assess students' skills. But education that focuses on skills is outdated in our modern world.

In the next section (coming soon), I will describe how I implemented this, but I have to say that this method is not for the faint-hearted. To implement this method, a teacher must be willing to buck the traditional methods of math teaching and established procedure. That is not encouraged by many school systems. Facing a room full of kids, the teacher must be willing to cede some control over the classroom (which is frightening to some), be willing to move away from quizzes and tests as assessments (which is heresy to established thinking). For a bunch of reasons (which I won't go into here), I was ok with all that.

That said, I found that I enjoyed teaching this way so much more than the traditional style. Sitting down a talking with a group of students as they went through the investigations gave me greater insight into how they thought. And (I know this sounds cliche-ish), the students often taught me a great deal. Teaching in this way was never boring.

If you are a teacher looking to break free of traditional math teaching, I would love for you to give this method a try. I am not saying it is THE solution to everything. (I am arrogant, but not THAT arrogant anymore.) But at least it is different, at least you are trying something. That's a start if nothing else.