My Math Makes Mind's Marvels Manifest (Mmm-mmm, good)
Problem solvers, not human calculators
Although math has classically been taught in a way that people memorize steps and formulas, in most cases, this will not lead to deep mathematical understanding and, more importantly, problem-solving application. But working from a student's level of comprehension, moving from concrete models to representation of abstract thinking, yields fine results. Rather than telling what or how to solve a problem, we bring together conditions and ask questions that support students to make their next development. Students share their strategies and thinking with peers, and critically analyze them. Through this combination of independent work and a dynamic group environment, they naturally adopt the most efficient strategy that they truly grasp.
Students are regularly involved in solving complex problems (often involving multiple steps), representing their mental strategy, explaining their thinking, and discussing and analyzing various approaches with their peers. You'd be amazed at what high-level mathematical functioning these kids are capable of!