The role of sign in students' modeling of scalar equations

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.Comment: 5 pages, 1 figure, to be published in The Physics Teache

Une introduction accessible à la « Connaissance par Morceaux »

La Connaissance par Morceaux(CpM) est une perspective épistémologique qui a réussi à produire, dans le champ de la didactique des sciences, des explications significatives de phénomènes d’apprentissage, en particulier en ce qui concerne les conceptions préalables des élèves et les rôles de celles-ci dans l’émergence de la compétence. La CpM est nettement moins utilisée en mathématiques. Cependant, je fais l’hypothèse que les raisons de ce moindre usage relèvent principalement de différences historiques plutôt que d’écarts entre les processus d’apprentissage en mathématiques et en sciences expérimentales. L’objectif de cet article est de présenter la CpM d’une manière relativement accessible pour des chercheurs en didactique des mathématiques. Je présente les principes généraux et les caractéristiques essentielles de la CpM. Je m’appuie sur une variété d’exemples, y compris d’exemples en mathématiques, pour illustrer le fonctionnement de la CpM, son utilisation pratique et ce que l’on peut en attendre. J’espère ainsi encourager et accompagner une utilisation plus importante de la CpM dans la recherche en didactique des mathématiques.Knowledge in Pieces (KiP) is an epistemological perspective that has had significant success in explaining learning phenomena in science education, notably the phenomenon of students’ prior conceptions and their roles in emerging competence. KiP is much less used in mathematics. However, I conjecture that the reasons for relative disuse mostly concern historical differences in traditions rather than in-principle distinctions in the ways mathematics and science are learned.This article aims to explain KiP in a relatively non-technical way to mathematics educators. I explain the general principles and distinguishing characteristics of KiP. I use a range of examples, including from mathematics, to show how KiP works in practice and what one might expect to gain from using it. My hope is to encourage and help guide a greater use of KiP in mathematics education

Understanding and Affecting Student Reasoning About Sound Waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

Ökologische Untersuchungen zur Frühjahrsentwicklung arktischer Meereisalgengemeinschaften

This article aims to contribute to the literature on conceptual change by engaging in direct theoretical and empirical comparison of contrasting views. We take up the question of whether naïve physical ideas are coherent or fragmented, building specifically on recent work supporting claims of coherence with respect to the concept of force by Ioannides and Vosniadou [Ioannides, C., & Vosniadou, C. (2002). The changing meanings of force. Cognitive Science Quarterly 2, 5–61]. We first engage in a theoretical inquiry on the nature of coherence and fragmentation, concluding that these terms are not well-defined, and proposing a set of issues that may be better specified. The issues have to do with contextuality, which concerns the range of contexts in which a concept (meaning, model, theory) applies, and relational structure, which is how elements of a concept (meaning, model, or theory) relate to one another. We further propose an enhanced theoretical and empirical accountability for what and how much one needs to say in order to have specified a concept. Vague specification of the meaning of a concept can lead to many kinds of difficulties. Empirically, we conducted two studies. A study patterned closely on Ioannides and Vosniadou’s work (which we call a quasi-replication) failed to confirm their operationalizations of “coherent. ” A

Students’ analogical reasoning in novel situations: theory-like misconceptions or p-prims?

Over the past 50 years there has been much research in the area of students' misconceptions. Whilst this research has been useful in helping to inform the design of instructional approaches and curriculum development it has not provided much insight into how students reason when presented with a novel situation and, in particular, the knowledge they draw upon in an attempt to make predictions about that novel situation. This article reports on a study of Greek students, aged from 10 to 17 years old, who were asked to make predictions in novel situations and to then provide, without being told whether their predictions were correct or incorrect, explanations about their predictions. Indeed, their explanations in such novel situations have the potential to reveal how their ideas, as articulated as predictions, are formed as well as the sources they draw upon to make those predictions. We also consider in this article the extent to which student ideas can be seen either as theory-like misconceptions or, alternatively, as situated acts of construction involving the activation of fragmented pieces of knowledge referred to as phenomenological primitives (p-prims). Our findings suggest that in most cases students' reasoning in novel situations can be better understood in terms of their use of p-prims and that teaching might be made more effective if teachers were more aware of the p-prims that students were likely to be using when presented with new situations in physics

Transitions in Mathematics Education

Mathematics Education; Learning; Teachin

The Case for Dynamic Models of Learners' Ontologies in Physics

In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant barrier between these two ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies; but we find these ontologies are better understood as dynamic and context-dependent, rather than as static constraints. To promote one ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts.Comment: The Journal of the Learning Sciences (In Press

Improving the representational strategies of children in a music-listening and playing task: an intervention-based study.

This intervention-based study focuses on the relation between music and its graphic representation from a meta-representational point of view. It aims to determine whether middle school students show an increase in meta-representational competence (MRC) after an educational intervention. Three classes of 11 to 14-year-old students participated in the teaching experiment: one experimental class (E) and two control classes (C). An intervention on MRC was carried out on the E class during the hours that were allocated for the regular music lessons, while students from the C classes followed the regular music curriculum. E and C classes were given the same pretest and posttest, which measured students' MRC by means of six representational criteria. One month after the posttest, all classes completed a retention test. The results reveal an overall effect in favour of the E group, despite the negative results for two representational criteria. Moreover, the overall gain, to a great extent, was due to a decrease in the score of the C classes, while the gains in the E class were rather small. Theoretical, methodological and educational implications are discussed