This article describes an experiment with LogEx, an e-learning environment that supports students in learning how to prove the equivalence between two logical formulae, using standard equivalences such as DeMorgan. In the experiment, we compare two groups of students. The first group uses the complete learning environment, including hints, next…

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,…

After targeted instruction designed to improve student conceptual understanding of physics, a significant fraction of students are not able to answer many questions in a consistent manner. Prior research suggests that even those students who demonstrate that they acquired the relevant knowledge and skills (i.e., possess the requisite…

The aim of this study was to investigate how students interpret the verbal definitions given for quadrilaterals in parallelogram family and reasoning in this interpretation process. It was also aimed to reveal the easiest definitions for students to understand, and to determine which mathematical terms they do not understand in given definitions.…

Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our approach incorporates…

One pedagogical approach to challenge a persistent misconception is to get students to test a conjecture whereby they are confronted with the misconception. A common misconception about a 'direct linear relationship' between area and perimeter is well-documented. In this study, Year 4-6 students were presented with a conjecture that a rectangle…

In this article, the authors describe their experiences with planning, implementing, and revising a lesson for which the goal is for students to consider the mathematical and pragmatic issues that are related to a task of maximizing the area for a fixed perimeter. The authors also wanted students to engage in the Standards for Mathematical…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

The belief that we are living in a post-truth age raises a number of complex, paradoxical questions. Does it suggest, for example, that truth no longer matters? Or, that the idea of truth no longer exists? The university, of course, has long been associated with the interests of truth -- not only in searching for truth, but in telling the truth.…

Tinkering is often viewed as arbitrary practice that should be avoided. However, tinkering can be performed as part of a sound reasoning process. In this ethnomethodological study, we investigated tinkering as a reasoning process that construes logical inferences. This is a new asset-based approach that can be applied in computer science…

This study was aimed to develop a general argumentation framework for evaluating the quality of causal arguments across scientific and social contexts. We designed a computer-delivered assessment that contains four scenario-based argumentation tasks. Each task asks students to identify relevant evidence from provided data sources and use the…

Two studies examined factors that predicted children's tendencies to match objects versus relations across scenes when no instruction was given. Study 1 examined a) age and b) nationality as a proxy for cultural differences in experiences with relations. The results showed that Chinese and U.S. children across ages all showed an initial bias to…

In this study, Turkish pre-service science teachers' moral reasoning patterns and the factors which influence their decisions while discussing genetics-related socio-scientific issues (SSI) were investigated. A basic qualitative approach was adopted for this purpose. Seven third-grade pre-service science teachers enrolled in the study.…

Previous studies have shown that students who have completed differential and integral calculus often accept and employ empirical arguments as proofs, but this is not the case for students who have had at least one upper-level proof course; these students tend toward the use of deductive proofs. This paper finds that a majority of the students…

Students of introductory economics are often able to predict changes in equilibrium price correctly on standardized assessments, but make consistent errors in predicting changes in equilibrium quantity. To examine the reasons for this pattern, the authors collected open-ended explanations written by students and categorized their reasoning using a…