Mathematical standards for students have increased with the development of the Common Core State Standards for Mathematics and its accompanying high stakes testing. Teachers need strong conceptual knowledge of the mathematics they teach in order to give students the opportunity to learn that math deeply. An earlier study (Ma, 1999) found that US elementary teachers lack the deep knowledge to teach math conceptually. Given the mathematics standards movements of the last two decades, it is plausible that the knowledge base of teachers has changed. Using the framework of Specialized Content Knowledge (SCK), which is the knowledge required to teach math that extends beyond the knowledge to do math, this study examines the current level of SCK held by practicing elementary teachers. It also examines themes in the explanations they give for the four topics: subtraction with regrouping; multi-digit multiplication; division with fractions; and area, perimeter, and proof.
This study used a multiple-case study design and an interview protocol with current elementary teachers (N=18). Analysis of teacher interviews indicates that elementary teacher SCK can vary with the topic being addressed, with all but two of the participants falling into different SCK levels across the mathematical content areas. This points to the need for assessments that offer topic-level data so we can determine the support individual teachers need. Most of the current teachers studied have strong Specialized Content Knowledge in areas of whole number calculation, such as subtraction with regrouping and multi-digit multiplication. In those topics they are able to create representations and justify the standard algorithms. In the areas of division with fractions and area, perimeter, and proof, however, Specialized Content Knowledge was frequently much lower, and many of the teachers struggled to create representations or explain the mathematics contained in the algorithms. This indicates a need for teacher education and professional development that extends beyond whole number operations and focuses on conceptual understanding of these challenging topics
