This year, in addition to our independent study "Teaching Textbooks", our class will be learning mathematics together using a student-centered approach to learning. I call this type of learning “creative mathematics”. For many years and continuing today, mathematics has been taught using a “teaching for problem solving” approach: The teacher presents the mathematics, the students practice the skill, and finally, the students solve world problems that require using the skill. Sound familiar? Unfortunately, this “do-as-I-show-you” approach to mathematics teaching has not been successful for helping many students understand or remember mathematical concepts (Van de Walle et al., 2014).
“Teaching through problem solving” generally means students solve problems to learn new mathematics rather than just apply mathematics after it has been learned. Students learn mathematics through real contexts, problems, situations and models that allow them to build meaning for the concepts. So teaching through problem solving might be described as “upside-down” from the traditional approach of teaching for problem solving because the problem is presented at the beginning of the lesson and skills and ideas emerge from working with the problem. A problem is defined here as any task or activity for which students have no prescribed or memorized rules or methods, and for which they do not have a perception that there is a specific “correct” solution or method. In other words, the task or activity is a genuine problem that requires creativity to solve.
Here is an example of how students in our classroom, who are learning through problem solving might be introduced to proportions, allowing for creative strategies to be invented and applied before they are taught to set up proportions and solve for the unknown.
Tatyana has a coupon for 4 pizzas for $10. If the restaurant will give them the same rate for multiple pizzas, how much will 18 pizzas cost?"
The teacher, as the facilitator, will encourage the students, ask meaningful questions to deepen their understanding, and remind them that there are many correct ways to solve this problem and to try to find as many strategies as they can. In a classroom with a supportive mathematical community, it is amazing what strategies emerge! Often times, students “discover” the most common algorithms on their own, without the teacher ever having to suggest it as the easiest, most efficient method known for solving for that particular mathematical concept. And in the process, all students are empowered to create and use the strategies that work the best for them.
One of my strongest affirmations with my creative mathematics pedagogy is a quote from Bev Boss, “If it hasn’t been in the hand, the body and heart, it can’t be in the brain”. When we give the kids the freedom and the power to create their own connections to mathematics, a whole world of true understanding emerges.