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…

Young children can generalize from known to novel, but the underlying mechanism is still debated. Some argue that from an early age generalization is category-based and undergoes little development, while others believe that early generalization is similarity-based, and the use of categories emerges over time. The current research brings new…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…

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…

Mechanical reasoning is crucial for many engineering fields, yet undergraduate engineering students struggle to understand discipline-specific formalisms from their courses that model mechanical concepts. The current investigation observed undergraduate engineering students' speech during mechanical reasoning and the benefits of attending to…

There is emerging recognition that mechanistic reasoning about scientific phenomena as well as developing an interdisciplinary understanding of science are valuable for student success. Our team of chemistry, biology, and teacher education researchers strives to support students in their interdisciplinary learning and engage them in causal…

As students gain more experience with design concepts, they should progress from novice to expert design thinkers. The purpose of this research was to identify the constructs of growth in design thinking (DT) over short- (one weekend) and long-term (10 weeks) design challenges. A DT mindset questionnaire was completed by students in a third-year…

The global climate emergency raises important questions for the future of fieldtrips in geographical education. Building on a longer history of these debates in the discipline, geography educators are paying increased attention to the environmental impacts of field-based education, as demonstrated by the Royal Geographical Society-Institute of…

The samples of evidence we use to make inferences in everyday and formal settings are often subject to selection biases. Two property induction experiments examined group and individual sensitivity to one type of selection bias: sampling frames - causal constraints that only allow certain types of instances to be sampled. Group data from both…

It is widely assumed within developmental psychology that spontaneously-arising conceptualizations of natural number--those that develop without explicit mathematics instruction--match the formal characterization of natural number given in the Dedekind-Peano Axioms (e.g., Carey, 2004; Leslie et al., 2008; Rips et al., 2008). Specifically,…

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…

This study compared the analogical reasoning of three groups that differed in their creative expertise: professional actors, undergraduate acting majors, and nonactors. Using an Analogy Finding Task, in which participants identified valid and nonvalid verbal analogies, three aspects of participants' analogical reasoning were measured: the number…

Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…

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…

Lockwood has argued that taking a set-oriented perspective is critical for successful combinatorial enumeration. To date, however, the research literature has not yet captured the cognitive processes involved in taking such a perspective. In this theoretical paper, we elaborate the constructs of spatial structuring and spatial-numerical linked…