This paper introduces the concept of logical consistency in students' thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students' evaluation of mathematical statements and accompanying…

This phenomenology research aims to examine prospective elementary mathematics teachers' proving and proof evaluation and their thoughts on convincing according to proof type and argument type. The participants were eight prospective teachers. The data collection tools were semi-structured group interviews, interviews video recordings and the…

This article offers the construct "unitizing predicates" to name mental actions important for students' reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and…

Cognitive and behavioral studies ranging from biomechanics to motor functions and neural mirroring explorations have extensively investigated the communication of emotions in music and dance. Recognized for their ability to convey and elicit emotions, various studies aim to validate the extent to which auditory expressive cues and embodied…

As part of an investigation into the relationship between classroom dialogue and student outcome, a test of reasoning has been developed that is suitable for preadolescents (i.e. c.10-13-year-olds). Building on previous work but expanding this considerably, the test focuses upon four areas of reasoning: differentiation of facts from opinions,…

Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…

Teachers need ways to efficiently assess students' cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process…

Much recent research and theorizing in the field of reasoning has been concerned with intuitive sensitivity to logical validity, such as the logic-brightness effect, in which logically valid arguments are judged to have a "brighter" typeface than invalid arguments. We propose and test a novel signal competition account of this…

An ongoing debate in the literature on human reasoning concerns whether or not the logical status (valid vs. invalid) of an argument can be intuitively detected. The finding that conclusions of logically valid inferences are liked more compared to conclusions of logically invalid ones--called the logic-liking effect--is one of the most prominent…

Teachers have difficulty integrating proof in their mathematics instruction due to both narrow beliefs about proofs and limited understanding of proofs. Indirect proofs seem to be a particular cause for concern. In this exploratory study, we contribute to the research area by reporting on an empirical study of Norwegian pre-service teachers'…

Decades of research have established that solving geometry proof problems is a challenging endeavor for many students. Consequently, researchers have called for investigations that explore which aspects of proving in geometry are difficult and why this is the case. Here, results from a set of 20 interviews with students who were taught proof in…

Recent years have witnessed a host of innovations for conducting research with qualitative comparative analysis (QCA). Concurrently, important issues surrounding its uses have been highlighted. In this article, we seek to help users design QCA studies. We argue that establishing inference with QCA involves three intertwined design components:…

Proof by mathematical induction poses a persistent challenge for students enrolled in proofs-based mathematics courses. Prior research indicates a number of related factors that contribute to the challenge, and suggests fruitful instructional approaches to support students in meeting that challenge. In particular, researchers have suggested…

Previous evaluation studies have rarely used authentic online texts and investigated upper secondary school students' use of evaluation criteria and deep reasoning. The associations between internet-specific epistemic justifications for knowing and credibility evaluation of online texts are not yet fully understood among adolescents. This study…

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…