Three-Component Mathematics Education

There is a long-standing debate about how mathematics education should be designed and implemented for students, with two alternatives, situational and symbolic mathematics, featuring prominently in the debate. Brain research can shed some light on how to resolve this debate. The existence of situational, verbalized, and visuospatial brain networks, and the connectivities between these networks, suggests that representations of mathematical knowledge should also be situational, verbalized, and symbolic and, moreover, should be mutually transformative and interrelated. Previous research has demonstrated the importance of situational and verbalized mathematics, but they are often viewed as a preliminary and complementary introduction to formal symbolic mathematics. Each of the three mathematics types and their transformations should be core learning objectives in mathematics education.