Teaching Calculus

In response to a blog I wrote about Jaime Escalante, Philip at Tampa/Paris blog asked me about our school's A.P. Calculus course. I got answers from the teacher, Chris Dupuis. Q: How far behind are the kids when they start? A: The 12th grade kids are solid with basic algebra, and then each has somewhat "random" holes in their math knowledge beyond that. (The kids arrive to our 9th grade with very low skills. Can't add 1/2 plus 1/4. Failed MCAS. But we fix that fairly well).

We do significant review of algebraic and trig topics in September and slowly scaffold calc tools and skills along the way. The rigor gets harder each month. So it's different from a suburban AP course.

Confidence is a key theme. (Remember, most AP Calc courses are for the top math kids in the school. They're very confident. Not in our school. Almost everyone takes Calc. We have a number of kids taking [and passing] AP Calc who are below the 50th percentile on math SAT).

When you operate outside of our students' confidence zone it's very easy for them to give up. They might still do work for you if have a personal relationship with them. But they will give up on believing they could actually succeed in the course.

Of course, they have to master to the hard material that to pass the AP test. But if you do it too soon, and outside their confidence zone, student buy-in plummets. It's a delicate balance.

I believe the genius of what Jaime Escalante did had less to do with his calculus teaching but more to do with desire to go back and help middle schools build math curriculum so it pointed to better supporting AP Calc. He realized kids needed extra time so had them coming in before and after school. At MATCH, the culture helps make each minute go farther. At my old school (in New Hampshire), maybe 30 minutes of an hour are hard academic work. Here, a 56 min period is really 52-56 minutes of academics.

We're much better now in vertically aligning the courses of Grade 9, 10, 11 to set the table for calc.

Q: Are kids just learning to do a bunch of discrete skills or are they learning to think Calculus? A: I don't think it's possible to pass AP Calc without some reasonable "understanding" of Calc. There's no way to memorize to do enough problems on the exam, especially on the free-response section, to pass. (Of course not all our kids pass).

But we still have kids whose basic skills are not strong. Therefore they struggle to, say, find a derivative without making mistakes. We need to ratchet up those skills. That way they can stick with the whole class, and I can push them to a higher level of understanding. I suppose the answer is probably somewhere "in between" what you'd likely consider discrete skills and really "thinking" Calc.