Phoenix School Math + Exemplars = Dynamic Math Learning
This is the time of year when my students begin pestering me for “real” word problems. They love solving problems that include names of their classmates which provides a collaborative experience where they can bounce ideas off each other as they work through some pretty complex problems. My go-to resource for problems that create mathematical thinkers of my students is Exemplars.
At The Phoenix School, for many years – first in paper form, now digital – Exemplars has been a vital component of our math program. No more memorization and regurgitation that flies out of kids’ brains faster than one can imagine. Exemplars work solidifies concepts, the foundation of mathematical learning, and allows for multiple solutions and creative thinking. It has the flexibility that allows us to extend concepts on which we have been working…and it is so well organized that it is easy to determine which sets of problems we need.
Working Exemplars problems requires kids to do much more thinking than traditional mathematical formats. It teaches them to analyze information and focus on what is important in getting to the solution. An added bonus Solving Exemplars problems encourages students to use previous knowledge to work through solutions. When students discover how mathematical systems work, they can solve almost anything.
I choose a variety of math problems at all levels to begin. Varying math topics and levels helps kids learn to be flexible in their thinking and transfer learning from one topic to another with ease. Changing the names of the people in the problems to names of kids in my class creates excitement and leads to so much wonderful interaction which, in turn, leads to sharing ideas and helping each other. Each student gets a folder of problems. I put them on label paper so they can stick them in their math journals, one problem at a time. I don’t mind which order kids work the problems because math should be engaging, encouraging kids to ask questions of each other.
Some kids like to work alone, others connect to partners to work problems they have in common. Using Exemplars legitimizes working with partners. It teaches them to share strategies, talk to others, and collaborate. Traditionally teachers have considered the sharing of math work to be “cheating,” but I have found the learning is so much better for all when kids do share solutions. Math at The Phoenix School often becomes a social event as we collaborate on a particularly complex challenge, especially when we turn to using materials to represent a solution. Everyone’s ideas are considered and sometimes debated with passion.
I discuss with kids different approaches to solving problems and expect them to document work using charts/graphs/tables, words, numbers, equations, pictures/diagrams, and personal reflection. This helps students see math in multiple ways, which increases the learning. Requiring them to show visual representations helps students organize their thinking so that, as I say to my students, “Your paper talks to me. I can tell exactly what you were thinking as you worked through the problem.” I always use the more challenging form of each problem for my older students. It is easy to extend problems into algebra since so many lend themselves to finding the pattern and taking it to the algebraic equation.
From our youngest students to our oldest, we find that Exemplars problems engage, challenge, and create mathematical thinkers at every level. Our math program is truly strengthened by the Exemplars component.