CHAPTER 1: Elementary Mathematics is Not Trivial

The Conference Board of Mathematical Sciences (CBMS) (2012) suggests, “teachers should study the mathematics they teach in depth, and from the perspective of a teacher” (p. 23). This may be self-evident for some, but for others the statement may cause them to take pause. What about elementary teachers? The assumption might be that a university mathematics department is no place for the study of elementary topics such as counting, whole numbers, or fractions. Shouldn’t all students arrive at the university with a solid understanding of primary school mathematics? Shouldn’t they learn elementary mathematics in elementary school? However, shouldn’t they know more about elementary mathematics than what they learned in elementary school? Certainly, they have this knowledge to a degree, but is their knowledge sufficient for them to be effective mathematics teachers? The truth is that even if prospective elementary teachers arrive at the university with basic arithmetic proficiency (which is not assured) many lack depth of mathematical understanding, being unaware of fundamental concepts and relationships that trace back to elementary school mathematics content. Elementary mathematics is not trivial. We make the case here that while addressing elementary school topics, deep mathematics can be explored, to the benefit of prospective teachers.