Characterizing middle and secondary preservice teachers' change in inferential reasoning

Title from PDF of title page (University of Missouri--Columbia, viewed on October 18, 2012).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Dr. James E. TarrVita.Ph. D. University of Missouri--Columbia 2011."May 2011"This study characterizes how a cohort of 33 middle and secondary mathematics preservice teachers' inferential reasoning changed while enrolled in a statistics course designed for future teachers. Changes in inferential reasoning from pre- to postassessments are analyzed and further elucidated by midcourse clinical interviews conducted with a stratified random sample of 12 participants. Using a modified SOLO taxonomy (Biggs & Collis, 1982, 1989), the average dominant level of inferential reasoning for the cohort shifted from Unistructural to Multistructural over the course. While 58% of all participants increased their level of inferential reasoning, growth wasmore pronounced for secondary preservice teachers. A relationship between informal and formal approaches to inferential tasks was determined as 80% of levels assigned to formal inferential task responses were concordant with the dominant informal inferential reasoning level. Classification of course tasks revealed an increased demand for adaptive reasoning with the introduction of formal inferential methods.Includes bibliographical reference

Statistics as Unbiased Estimators: Exploring the Teaching of Standard Deviation

This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator – not just a descriptive statistic for the variation (spread) in data – is related to teachers’ instruction regarding standard deviation, particularly around the issue of division by n-1. In this regard, the study contributes to our understanding about how knowledge of mathematics beyond the current instructional level, what we refer to as nonlocal mathematics, becomes important for teaching. The findings indicate that acquired knowledge of nonlocal mathematics can play a role in altering teachers’ planned instructional approaches in terms of student activity and cognitive demand in their instruction

Secondary Mathematics Teachers’ Planned Approaches For Teaching Standard Deviation

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by inservice and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master’s level students in education, as well as a tendency by in-service teachers to teach in alignment with prior learning experiences, despite professional development. Implications for teacher education and curricular development are offered

Secondary mathematics teachers\u27 planned approaches for teaching standard deviation

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by inservice and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master\u27s level students in education, as well as a tendency by in-service teachers to teach in alignment with prior learning experiences, despite professional development. Implications for teacher education and curricular development are offered