Recently, the community of mathematics educators recognized the importance in elementary grades to think algebraically. Researchers found that students throughout elementary school have the ability of understanding powerful unifying mathematical concepts that are the keystone of both arithmetic and algebra. Students learning and articulating these concepts increase their understanding of arithmetic and provide them with a solid foundation for extending their knowledge of arithmetic to learn algebra.

The purpose of this research was to examine mathematics teachers' beliefs about students' cognition from arithmetic to algebraic concepts and to understand whether these teachers believe the above are related to students' beliefs and to the level of difficulty of both arithmetic and algebraic word problems versus symbolic problems. The study also examined teachers' beliefs about mathematic learning and instruction and teachers' beliefs about algebraic problem solving. In short, this study examined teachers' beliefs about students' competencies on acquiring mathematical content. The reason for this study was to expand the literature on the nature of mathematics teacher's beliefs, their authority, and their inconsistency across grade levels.

This study included mathematics teachers from Kindergarten through Grade 12 from a single school district in a rural mid-Atlantic state. All participants were either mathematics teachers (middle school and high school grades) or elementary school teachers who teach all of the major content areas, including mathematics. The sample consisted of 128 mathematics teachers. Data were obtained using a 3-part survey developed by Nathan and Koedinger (2000a). From the 128 teachers that received the survey link via email, 41 elementary mathematics teachers and middle mathematics teachers participated in this study.

As a result of this study, K-8 mathematics teachers believe complex algebra story problems are difficult for students to solve. Teachers believe that students should know how to solve symbolic algebraic equations before solving matching complex algebraic story problems.