What is the relationship between what teachers believe about how children learn mathematics and how those teachers teach mathematics? A case study of elementary school teachers\u27 beliefs and behaviors

In a qualitative study of the beliefs and behaviors of four third and fourth grade teachers as they taught mathematics in an industrial Vermont town, teachers were found to have four fundamental common beliefs about how children learn mathematics: (a) children learn mathematical concepts by manipulating or visualizing concrete materials; (b) children learn arithmetic through specific sequenced steps; (c) children learn mathematics through practice and repetition; and (d) children learn mathematics best when they feel good about themselves and experience success in mathematics. Not all of their beliefs are in concert with the learning theories foundational to the 1989 National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Associated with each belief, the teachers had one or more factors they considered when planning mathematics lessons. They demonstrated a variety of behaviors including classroom activities and strategies concomitant with, although not necessarily congruent with each belief. There were discrepancies most commonly because of tendencies to acquiesce to the pressures of time and curricular expectations (including those expectations from the next year\u27s teachers) and to rely upon the textbook rather than build upon the strength of their convictions and beliefs about how children learn. While teachers believed that manipulating materials helps students grasp and develop concepts about the real world in mathematical terms, there was limited time devoted to the manipulation of materials. Although sequential learning was believed to be valuable, many mathematical concepts such as measurement and geometry were taught out of the context and sequence of similar concepts. Practice was typical in each classroom; repetition was prevalent in two classrooms. Many ways of boosting the confidence of students were demonstrated, although one of the teachers believed she was supportive to students when in fact supportive behaviors were not displayed. Staff development implications include recommendations for teachers to increase their knowledge of constructivism as a way that children learn and of mathematics as a field of knowledge. There are suggested actions for teacher unions, school administrations, state departments of education, post secondary schools of education, and professional organizations