Deepening teachers' awareness of students' mathematical reasoning through video study in an online course

This research explored the hypothesis that teachers may be able to learn how to attend to children’s productions of proof-like justifications if provided with illustrative examples of how students’ mathematical reasoning develops through engagement in problem solving with appropriate pedagogical facilitation. An experimental online course was designed and implemented to measure how studying videos from a research collection and related literature might serve to deepen teachers’ awareness of students’ mathematical reasoning. Three studies investigated teacher learning across two implementations of the course using a mixed methods approach that included analysis of a video-based pre/post assessment and discourse analysis. The assessment was administered to participants at the beginning and end of their instructional intervention. Data were collected from experimental and comparison conditions as part of a larger research project. Assessment data for various conditions were analyzed to measure change from pre to post in describing the features of mathematical arguments expressed by children in the video. Assessment data for course participants also were analyzed by individual within group for examining change in relation to what small groups discussed online in a course unit featuring different children sharing their reasoning to the same mathematical task as in the assessment video. Discourse analysis was performed on two other units with identical assignments for both implementations. Data analysis revealed evidence of learning with 91% of teachers in the course attending sufficiently well to the details of children articulating their mathematical reasoning in the assessment video for two different argument forms. This finding was supported by a higher post-assessment growth rate for these argument forms by participants in the experimental course than those in three different comparison conditions. Discourse analysis that coded for details of attending to children’s mathematical activities showed how teachers learned collaboratively by engaging in discussions online about the development of students’ mathematical reasoning in through studying and reflecting on multimedia artifacts. Findings reveal the depth and breadth of their learning about children’s reasoning about fraction ideas, how it develops, and how they view what they have learned as being highly relevant to teaching practices at elementary through secondary grades and beyond.Ed. D.Includes bibliographical referencesby Marjory Fan Paliu