Many important human activities involve accomplishing goals without a script. There is no formula for true problem-solving. Heuristic, cognitive "rules of thumb" are the problem-solver's best guide. Learners should understand heuristic tools such as means-end analysis, working backwards, successive approximation, and external representation. Since…

Call for reforming mathematics teaching has been sounded loudly and strongly. Change from teaching standard algorithms to having children invent their own methods requires major pedagogical shift. Teachers must trust students' inventiveness and ability to make sense of numerical situations, be committed to thinking and reasoning as cornerstone of…