This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We…

The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities…

Hinterecker, Knauff, and Johnson-Laird (2016) compared the adequacy of the probabilistic new paradigm in reasoning with the recent revision of mental models theory (MMT) for explaining a novel class of inferences containing the modal term "possibly." For example, "the door is closed or the window is open or both," therefore,…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

The aims of the study were (1) to develop a domain-general computer-based assessment tool for inductive reasoning and to empirically test the theoretical models of Klauer and Christou and Papageorgiou; and (2) to develop an online game to foster inductive reasoning through mathematical content and to investigate its effectiveness. The sample was…

When asked to determine whether a syllogistic argument is deductively valid, people are influenced by their prior beliefs about the believability of the conclusion. Recently, two competing explanations for this belief bias effect have been proposed, each based on signal detection theory (SDT). Under a response bias explanation, people set more…

Scientific reasoning ability (SRA) is widely recognized as an essential goal for science education. There is much discussion on the design and development of assessment frameworks as viable tools to foster SRA. However, established assessments mostly focus on the level of students reasoning attainment. Student ability to use evidence to support…

We report 3 experiments investigating novel sorts of inference, such as: A or B or both. Therefore, possibly (A and B). Where the contents were sensible assertions, for example, "Space tourism will achieve widespread popularity in the next 50 years or advances in material science will lead to the development of antigravity materials in the…

Research in attribution theory has shown that students' causal thinking profoundly affects their learning and motivational outcomes. Very few studies, however, have explored how students' attribution-related beliefs influence the causal thought process. The present study used the perceived control of the attribution process (PCAP) model to examine…

Weber and Alcock's (2004, 2009) syntactic/semantic framework provides a useful means of delineating two basic categories of proof-oriented activity. They define their dichotomy using Goldin's (1998) theory of representation systems. In this paper, I intend to clarify the framework by providing criteria for classifying student reasoning into…

This paper offers a typology of forms and uses of abduction that can be exploited to better analyze abduction in proving processes. Based on the work of Peirce and Eco, we describe different kinds of abductions that occur in students' mathematical activity and extend Toulmin's model of an argument as a methodological tool to describe students'…

In "Assessing the Belief Bias Effect With ROCs: It's a Response Bias Effect," Dube, Rotello, and Heit (2010) examined the form of receiver operating characteristic (ROC) curves for reasoning and the effects of belief bias on measurement indices that differ in whether they imply a curved or linear ROC function. We concluded that the ROC…

One of the most important open questions in reasoning research is how inductive reasoning and deductive reasoning are related. In an effort to address this question, we applied methods and concepts from memory research. We used 2 experiments to examine the effects of logical validity and premise-conclusion similarity on evaluation of arguments.…

A Chemistry Concept Reasoning Test was created and validated providing an easy-to-use tool for measuring conceptual understanding and critical scientific thinking of general chemistry models and theories. The test is designed to measure concept understanding comparable to that found in free-response questions requiring explanations over…