Having been fortunate to observe a variety of math classrooms (check out our work at the number lab), especially within the independent school sector, we’ve come to learn a great deal about what makes a math classroom effective, which we will write about across several blog posts. Today we are focused on the lack of metacognitive instruction and coaching within many math classrooms.
Metacognition research has assisted educators in changing the way we view learning. We know high achieving students usually apply metacognitive processes in their learning and problem solving. And students who apply metacognitive processes tend to be higher achievers. Recent studies have shown that even young children can apply metacognitive processes when the tasks fit their interests and capabilities. And any age-related development may likely be due to lack of appropriate exposure in school.
Also key is the finding that metacognition is domain-specific, and thus learning environments must cultivate the domain-specific metacognitive tools kids need in order to achieve at high levels within the domain.
Looking specifically at mathematics, kids need classrooms in which high level cognitive processes are expected of them and work with CUN problems (complex, unfamiliar, and non-routine) is the core practice. They need classrooms in which mathematics is presented as a coherent set of ideas, not disparate “units” or skills that present a fragmented discipline. Kids need teachers who will coach, model, and name strategies that will assist students with their metacognitive development. And they need daily opportunities to attempt to do this difficult work of metacognition within the domain of mathematics.
Based on our experience, this rarely happens, even in the many expensive and well-resourced independent school classrooms.
The only way to teach the type of mathematics problem-solving appropriate for innovation-driven societies is by giving kids the opportunity to learn complex mathematics daily, starting at the beginning of their mathematics career. In many, many classrooms kids are spending most of their precious academic minutes on low-level tasks such as repeatedly applying a procedure, memorizing a rule, or trying to mimic the teacher’s method of solving a problem. Any metacognitive coaching is reduced to acronyms the child can use to memorize a rule (ex. FOIL), choral recitation, or very brief bouts of metacognitive coaching within tasks that already just require low cognitive demand. Rarely are classrooms providing the rich mathematics instruction that is the territory for practicing metacognitive skills and rarely are teachers providing children with the support they need to struggle to understand the metacognitive skills and processes suitable for solving the math expected in innovation-driven societies.
Not at Long-View. Our two-hour math blocks in which the kids are working on whiteboards support thoughtful metacognitive instruction and coaching.