Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias…

Typical middle and high school math curricula are template based, meaning the use of standardized methods to solve mathematical problems as examples on which to base other problem solving. Template based math instruction may help a student to pass tests; however, it is an insufficient way to develop mathematical thinking. Mathematicians are…