MODELING MATH THROUGH PROBLEM SOLVING to strengthen strategic competence
The third way we discussed modeling mathematics ideas was through problem solving and task selection. The teachers engaged the challenge and struggle of selecting appropriate tasks. They tried out several problems before settling on the best task for research lessons for their group of students. By selecting a rich task and maintaining its cognitive demand during implementation, teachers provided their students with the opportunity learn more rigorous mathematics (Stein et al., 2007). Students modeled mathematics by wrestling with the selected task and working with their group to find solutions and presented their ideas to the class.
When teachers taught the lesson in their respective classrooms, Alice provided guidance by building on the “dialogue occurring in small groups and students questioning of each other’s strategies as well as their own” to help students work together to “develop a final product that made sense to each one of them and had a strong central idea.” Giving her students the opportunity to struggle enabled them to be “confident of their final solutions.” Tina, another teacher, encouraged her students by letting them know that there was more than one way to solve the problem. Mary maintained a high level of cognitive demand throughout the task saying that she “had the patience and confidence to listen to the students speak and not have my own assumptions.”