How One Comes to Know: Models and Theories of the Learning of Mathematics

This cartoon humorously reflects the following facts: (1) Schools have been created by social groups to prepare their young for membership in society; (2) to this end, every society has determined what knowledge it expects its young to acquire (e.g., wanting Stripe to whistle); and (3) each society has made provisions for how students are to acquire that knowledge (i.e., by the curriculum advocated, teaching standards, etc.). Unfortunately, establishing such goals and procedures is no guarantee that learning will occur. Assessment of student performance (e.g., finding out whether Stripe can whistle) is the only way one can determine whether students have acquired the intended knowledge. Given this perspective, there are two fundamental epistemological questions that must be asked and answered.