An investigation of teachers' beliefs of students' algebra development

Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative proble m-solving difficulty. Teachers also rated their levels of agreement to a va riety of reform-based statements on teaching and learning mathematics. Anal yses suggest that teachers hold a symbol-precedence view of student mathema tical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning . High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teache rs' reform-based beliefs and their instructional decisions appears to be in fluenced by textbook organization, which institutionalizes the symbol-prece dence view. Because of their extensive content training, high school teache rs may be particularly susceptible to an expert blindspot, whereby they ove restimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.