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April 2012 Vol. 19. No. 5 Focus on Engaging Curriculum

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Math = Problem-solving

Brad Latimer: Mathematics, Science Leadership Academy

By by Connie Langland on Mar 30, 2012 03:34 PM
Photo: Harvey Finkle

Mathematics teacher Brad Latimer has a raft of strategies to help his students learn challenging algebra and calculus.

On a recent day, he started with a “warmup” question, challenging his senior calculus students to create a formula for calculating the area of a trapezoid. “It’s perfectly possible,” Latimer assured them.

Then came the topic of the day, estimating the area under a curve. It’s a concept hard to visualize, so Latimer sat down at his laptop, and soon the whiteboard that dominates the front wall lit up with a dramatic upward curve on a graph. For the next 10 minutes, teacher and students played with the curve, cutting it vertically into progressively smaller slices. The smaller the slice, the more accurate the calculation, they all agreed.

A teacher for seven years, the last four at the Science Leadership Academy (SLA ) in Center City, Latimer teaches using a mix of instruction, small-group work, and individual problem-solving. This is standard stuff, typical of most good math classrooms.

What may be less common is the way Latimer and other SLA teachers approach tests and quizzes. SLA, affiliated with the Franklin Institute, is built around project-based learning.

“We use projects to both show us where students are in terms of certain skills and to show us that they not only understand the content but can apply it to a larger problem,” Latimer said.

The second-quarter project in calculus focused on derivatives and required creating a website that included citations. Some projects involved financial analysis, others population trends.

“Every project was so different. You could see students going in areas that interested them,” said Latimer. At first, he said, students hated the idea. “It’s a lot easier when step 1 is this, step 2 is this, step 3 is this, and here’s the answer. It’s much harder to tell them, ‘You know the concept, figure it out for yourself.’ By the end they were really proud of what they had done.”

Even Latimer’s quizzes are new wave, so to speak. SLA teachers break down their courses into learning blocks called standards, and every standard is assessed through the year.

“The thing that’s different – students essentially have an unlimited number of opportunities to raise their grade. They can retake the test, but not the whole test, just the standard they missed,” Latimer said.

“The one thing I want students to realize is that mathematics in its most boiled-down form is problem-solving,” Latimer said. “They will need to know how to wrestle with a problem, how to collaborate with their peers, how to engage in the inquiry process. Some of them will need the specific content, but math is problem-solving.”

Comments (4)

Submitted by Brian Cohen (not verified) on April 10, 2012 12:07 pm

The one major thing that I focus on in this article is the brief mention of standards-based grading. I have been using standards-based grading at the Academy at Palumbo for the past 7 months with great success. Students are allowed to come and re-test with the same content on different problems to show their mastery. This week I have a lot of students asking to show me what they learned. This has changed the dialog in my class from "can I re-take that test" to "can you show me how to do ___ so I can retake the standard." I wonderful shift.

For more info, check out this:

Submitted by Anonymous (not verified) on April 12, 2012 12:28 pm

Yes, but when students are re-testing the same content with a different problem haven't they just memorized the technique at that point? How does that show mastery?

Submitted by Anonymous (not verified) on April 11, 2012 6:34 pm

I teach math in a Philly high school and I'm intrigued by standards based grading. I'm hoping that other high school math teachers who use this method can point me to some resources and/or give some advice.

My main hesitation and concern with this approach is the added demands on my time as a teacher, not only with grading re-takes, but also with writing different tests and just keeping track of who has passed what and who hasn't. With 170 students, I don't know if I could keep it all together.

Additionally, how do you create a sense of urgency in the classroom if students know that they have multiple chances to take a test on the same material?

Finally, what about the students who do pass the standards? Do you move on with instructing the class in new material, and hope the students who haven't passed yet get tutoring or figure things out on their own?

I know that these issues can be overcome, but I'm not sure how. Thank you in advance for your responses!

Submitted by Teacher Action Group (not verified) on April 16, 2012 9:27 pm

For anybody intrigued by this article -- and wanting to learn more from Brad Latimer -- he will be presenting at this year's Curriculum Fair and Citywide Summit, sponsored by Teacher Action Group.

The event is Saturday, April 28th and registration is free.

Learn more here:

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