The Foundation for a Meaningful Life
Kindergarten - Grade 9 in Southborough, MA

Problem-Based Learning in Math

Seventh-grade students in Craig Ferraro’s pre-algebra class have been stretching their math muscles through problem-based learning this fall. Drawn from the Harkness Method, a discussion-based teaching and learning approach, problem-based learning in math class allows students to unravel and tackle complex problems as a group project. The short-term goal is that students are able to handle more difficult problems because they are working in an environment where they learn from each and where not knowing the answer is okay. The larger long-term goal is that students build greater confidence in their abilities to face challenges and deal with complexity head-on.
Craig first started to explore problem-based learning in 2016 at a conference on the Harkness Method at Phillips Exeter Academy. He tried it with his pre-algebra advanced class during the winter term last year and this year Upper School math teachers Joe Buteau and math department chair Cassandra Papalilo are using the methodology in their classes as well. He describes the biggest difference as a shift in mindset for students to “being okay with not knowing.” Students are told that its okay if they didn’t understand every problem on the homework as they’ll spend the next class working through the problems together. Students work with partners up at the board presenting problems to the class and, they ask questions of one another and discuss every piece of the problem. The problems are designed to be daunting in scale. Here is an example from a recent class:

The human population of Earth is roughly 7,000,000,000, which is usually expressed in scientific notation as 7 x 10 to the ninth power. The average number of hairs on a human head is 5 x 10 to the fifth power. Use scientific notation to estimate the total number of human head hairs on earth.

Many of the problems, like the one above, have real-world applications that students can identify with, understand, and enjoy wrestling with. “Students recognize that the work is challenging but they enjoy discussing the problems and thinking about them,” says Craig. He also believes that the learning methodology is yielding results. “I did a lot of this style of work with my pre-algebra students last year and their end of year assessments were some of the best I have seen,” he says. “I believe that being exposed to this type of work helps students do well in situations where they might otherwise be stressed.”