In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area…

This is a position paper in the field of Engineering Education, which is at the very beginning in Europe. It relates challenges in the new field to the emerging technology of (Computer) Theorem Proving (TP). Experience shows, that "teaching" abstract models, for instance the wave equation in mechanical engineering and in electrical…

We examined subjects' ability to judge the soundness of informal arguments. The argument claims matched or did not match subject beliefs. In all experiments subjects indicated beliefs about spanking and television violence in a prescreening. Subjects read one-sentence arguments consisting of a claim followed by a reason and then judged the…

This concluding commentary takes the perspective of research on practicing scientists and engineers to consider what open areas and future directions on relational thinking and learning should be considered beyond the impressive research presented in the special issue. Areas for more work include (a) a need to examine educational applications of…

In this article we present the results of a study focused on engaging students in argumentation to support their growth as mathematical learners, which in turn strengthens their science learning experiences. We identify five argumentation categories that promote the learning of argumentation skills and enrich mathematical reasoning at the…

If an organic chemistry student explains that she represents a mechanistic step because ''it's a productive part of the mechanism,'' what meaning could the professor teaching the class attribute to this statement, what is actually communicated, and what does it mean for the student? The professor might think that the explanation is based on…

This case study demonstrates the ability of high school chemistry students, with varying levels of math preparation, to experience learning-gains on state and district assessments as it relates to chemical reactions, thermodynamics, and kinetics. These advances were predicated on the use of a teaching style rooted in abstract reasoning. The…

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects…

The language-based analogical reasoning abilities of Deaf children are a controversial topic. Researchers lack agreement about whether Deaf children possess the ability to reason using language-based analogies, or whether this ability is limited by a lack of access to vocabulary, both written and signed. This dissertation examines factors that…

Students often struggle with solving mechanism problems in organic chemistry courses. They frequently focus on surface features, have difficulty attributing meaning to symbols, and do not recognize tasks that are different from the exact tasks practiced. To be more successful, students need to be able to extract salient features, map similarities…

This study explores first-year university students' reasoning as they learn to draw Lewis structures. We also present a theoretical account of the formal procedure commonly taught for drawing these structures. Students' discussions during problem-solving activities were video recorded and detailed analyses of the discussions were made through the…

The aim of this investigation is to explore the preservice teachers' reasoning about variation (variability or spread) when they analyze data in situations that involve risk. In particular, in this communication the responses to two problems of a questionnaire administered to 96 preservice teachers are reported. The problems are of comparing…

This is a conceptual paper aimed at chemistry educators. The purpose of this paper is to illustrate the use of the semantic code of Legitimation Code Theory in chemistry teaching. Chemistry is an abstract subject which many students struggle to grasp. Legitimation Code Theory provides a way of separating out abstraction from complexity both of…

We present a multiple-choice test, the Montana State University Formal Reasoning Test (FORT), to assess college students' scientific reasoning ability. The test defines scientific reasoning to be equivalent to formal operational reasoning. It contains 20 questions divided evenly among five types of problems: control of variables, hypothesis…

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of…