Mass balance (MB) reasoning offers a rich topic for examination of students' scientific thinking and skills, as it requires students to account for multiple inputs and outputs within a system and apply covariational reasoning. Using previously validated constructed response prompts for MB, we examined 1,920 student-constructed responses (CRs)…

Newton's third law is one of the most important concepts learned early in introductory mechanics courses; however, ample studies have documented a wide range of students' misconceptions and fragmented understandings of this concept that are difficult to change through traditional instruction. This research develops a conceptual framework model to…

My starting point for this paper is a problem in critical thinking pedagogy--the difficult of bringing students to a point where they are able, and motivated, critically to evaluate their own deeply held beliefs. I first interrogate the very idea of a deeply held belief, drawing upon Wittgenstein's idea of a framework belief--a belief that forms…

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

Presents the results of three studies examining children's conception of the mind itself as an independent, active entity. Findings revealed a developing ability in children to interpret and produce statements personifying the mind and provided considerable evidence of children's movement toward a conception of the mind as an active agent…

This speech explores the gap between curriculum theory and curriculum practice. It begins with a discussion of Joseph Schwab's pursuit of "the practical" in curriculum theory and then searches for a basis for "the practical." Schwab's theory involves two parts: "deliberation" as the process of dealing with a problem before taking action and "the…