Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three…

This article describes the initial implementation of an innovative program for elementary-age children involving origami and pop-up paper engineering to promote visuospatial thinking. While spatial ability measures correlate with science, technology, engineering, and math (STEM) success, a focus on spatial thinking is all but missing in elementary…

This study examines epistemic thinking in action in order to shed light on the relation between students' personal epistemologies and their online learning practices. The study is based on observations of the learning behaviors of 6th-grade students (n = 38) during two online inquiry tasks. Data were collected through think-aloud protocols and…

This article aims to account for students' assessments of the plausibility and applicability of analogical explanations, and individual differences in these assessments, by analyzing properties of students' underlying knowledge systems. We developed a model of explanation and change in explanation focusing on knowledge elements that provide a…

In an 8-month teaching experiment, I investigated how 4 sixth-grade students reasoned with reversible multiplicative relationships. One type of problem involved a known quantity that was a whole number multiple of an unknown quantity, and students were asked to determine the value of the unknown quantity. To solve these problems, students needed…

This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

The examination of alternative hypotheses can initiate students into scientific practices and equip them with scientific literacy skills that will help them participate in ongoing debates involving complex socio-scientific problems. Hypothesis testing, in which the examination of alternative hypotheses is situated, has received much attention in…

Looking away from an interlocutor's face during demanding cognitive activity can help adults and children answer challenging mental arithmetic and verbal-reasoning questions (Glenberg, Schroeder, & Robertson, 1998; Phelps, Doherty-Sneddon, & Warnock, 2006). While such "gaze aversion" (GA) is used far less by 5-year-old school children, its use…

This article reports on a case study from a design-based research project that investigated how students make sense of the disciplinary tools they are taught to use, and specifically, what personal, interpersonal, and material resources support this process. The probability topic of binomial distribution was selected due to robust documentation of…

This study investigates how collaborative knowledge construction within an inquiry learning environment can be assisted with scaffolds that aim to support students' hypothesis generation process. Sixty-six students on a university preparatory track worked collaboratively on a kinematics task. The instructional goal was to develop students'…

Using the perspective of instructional conversation, we investigated how one teacher regulated student participation and conceptual reasoning in the middle-school mathematics classroom. We examined the elicitations--questions and provocative statements--made by the teacher over a four-day algebra lesson. Analyses showed how the teacher…

Learning science includes learning to argue with "inscriptions": images used to symbolize information persuasively. This study examined sixth-graders learning to invest inscriptions with representational status, in a geographic information system (GIS)-based science investigation. Learning to reason with inscriptions was studied in emergent…

Promoting the ability to reason generatively about novel phenomena and problems students may encounter in their everyday lives is a major goal of science education. This goal proves to be a formidable challenge in domains, such as molecular genetics, for which the accumulated scientific understandings are daunting in both amount and complexity. To…

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns,…