An Investigation of Teachers' Beliefs of Students' Algebra Development

Mitchell J. Nathan, Kenneth R. Koedinger
2000 Cognition and Instruction  
Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol-precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops
more » ... em-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 teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra. The study of people engaged in cognitively demanding tasks must consider the relation between people's judgments and actions and the beliefs they hold. Several aspects of people's decision making are well established. People do not strictly follow the laws of logic and probability when weighing information or following im-
doi:10.1207/s1532690xci1802_03 fatcat:vxmtslqiijbo3b2eoi5xbpqwnq