Assessing EC-4 preservice teachers' mathematics knowledge for teaching fractions concepts

Recognizing the need for U.S. students' mathematics learning to be built on a solid foundation of conceptual understanding, professional organizations such as the National Council of Teachers of Mathematics (2000) and the Conference Board of the Mathematical Sciences (2001) have called for an increased focus on building conceptual understanding in elementary mathematics in several domains. This study focuses on an exploration of two aspects of Hill, Schilling, and Ball's (2004) mathematics knowledge for teaching: specialized content knowledge (SCK) and knowledge of content and students (KCS) related to fractions concepts, an area that is particularly challenging at the elementary level and builds the foundation for understanding more complex rational number concepts in the middle grades. Eight grades early childhood through four preservice teachers enrolled in a mathematics methods course were asked to create concept maps to describe their knowledge of fractions and interpret student work with fractions. Results showed the preservice teachers to be most familiar with the part-whole representation of fractions. Study participants were least familiar with other fraction representations, including fractions as a ratio, as an operator, as a point on a number line, and as a form of division. The ratio interpretation of a fraction presented the greatest difficulty for study participants when asked to describe student misconceptions and create instructional representations to change students' thinking.