摘要：The study of mathematics exemplifies the intellectual quest for comprehensive
and consistent thinking. Today this quest, as bequeathed to us by the Greeks, has
been abandoned in mathematics education in favor of relatively mundane tasks of
calculating with formal algorithms and applying those calculations in supposedly
more meaningful “real world” contexts. An excuse in forsaking this intellectual
quest, especially in the early grades, is that young children are incapable of
understanding the conceptual nature of mathematics. This “incapability thesis,”
which absolves teachers in the early grades themselves from developing a
conceptual understanding of mathematics, is called into question. An alternative
philosophy of mathematics education for teaching the conceptual nature of
mathematics dating back to Parmenides and Plato is presented and illustrated in
ways that may well be within the reach of young children. Some problems and
potential implications for mathematics teacher education are considered.
