Development of a framework for teaching mathematics in depth.

摘要

This study illuminates the practice of teaching mathematics in depth by developing a framework to serve practicing teachers and those who educate teachers. A thorough reading of the literature that began with all of the volumes in the decades since the publication of the Standards (1989) identified six elements that were profitable for effective instruction in mathematics. These elements formed the basis of a tentative framework for teaching mathematics in depth that was elaborated by the results of this study. The experience of a fifth-grade level team in a southeastern state as they implemented a mathematics curriculum and set of standards that demanded teaching mathematics in depth identified elements of the framework that were previously missing from the literature. The perceptions of other mathematics teacher educators from the university and the school district were also incorporated into the framework.;Two findings emerged from the study with implication for teaching mathematics in elementary school. The first is that the conceptualization of teaching mathematics in depth is strongly influenced by the teacher's orientation toward a learning perspective. The teachers use those practices which they believe will contribute most to an increase in student understanding of a particular topic. The second finding to emerge is that the actualization of teaching mathematics in depth is contingent upon balancing the dual forces of the pacing guide (an external scheduling mechanism) and the teachers' desire to teach for mastery. Teachers create their instructional plans according to their assessment of existing student comprehension and understanding. They are seeking mastery of the topic, but the school administration's pacing guide pressures the tempo of their plans.;This manuscript reveals that each of these findings holds practical implication for improvement of instruction of mathematics in elementary school---addressing pacing, the definition and timing of mastery, learning theory, and assessment efficiency. Each contributes to mitigating gaps in the research literature, and each contributes to the development of the framework. Moreover, there are implications for research due to the significant overlap of this study with the recent adoption of Common Core State Standards (CCSS) and plans for national assessment instruments.