If you spend a day visiting the math classes in Lower School, you will see a variety of rich learning experiences and engagement. While you will, no doubt, notice differences from classroom to classroom, you will also notice common threads carefully woven throughout our program and practice. One of the most important threads you will see is an emphasis on open-ended problem-solving.
When many of us think back to our math education in elementary school, we likely remember lots of practice. After being taught how to solve a particular problem, we practiced and practiced the procedure. However, with so much emphasis on practice and calculation, the ‘why’ of math could be easily lost on students, leaving many to simply memorize procedures, or worse, to think that there is only one way to solve a given problem. Today, math education and programming have seen a shift towards an emphasis on critical thinking and reasoning rather than rote memorization.
In the Lower School, students experience math through a balance of practice and problem-solving. Of course, a practice still serves an important purpose, and students do need to be able to calculate efficiently. However, we want students to recognize themselves as powerful problem solvers and not just powerful calculators. When students are given open-ended problems to solve, they have the opportunity to reason, talk about their thinking, notice patterns and make connections. These behaviors help students understand concepts more deeply and generalize their skills. Problem solving also allows students to think more flexibly, notice multiple solution paths and find value in another person’s path even when it looks different than their own path.
When presented with the following scenario, a group of third-grade students worked collaboratively and showed their true problem-solving power!
The problem read…
A car has 3 girls inside. Each girl has 3 boxes. Each box has 3 big cats. There are 3 small cats for each big cat. How many legs are in the car?
The discussion began with one student proudly announcing, “We need to multiply”. That comment was followed by another student, who responded, “Multiply what? There are so many options”. The students quickly realized that there were many different paths they could take to begin the problem, and they were off to the races! Throughout the class, the children excitedly worked together to find strategies for coming up with the total number of legs. One group of students decided to begin by focusing on the number of legs in each box. Another group began working on one group of “legs” at a time, girls, big cats, little cats, etc. Yet another group decided to start by figuring out the number of legs for one girl and her three boxes of cats. As various solutions began to emerge, the children were encouraged to find the discrepancies and explain their rationale to others. After much debate and discussion, the children convinced each other that there was in fact only one correct total but that there were numerous correct solution paths.
When we emphasize open-ended problem solving, students, like these third graders, have many more opportunities to stretch themselves beyond procedures and algorithms and find their power as mathematicians!
