Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

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…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

Four experiments examined the claims that people can intuitively assess the logical validity of arguments, and that qualitatively different reasoning processes drive intuitive and explicit validity assessments. In each study participants evaluated arguments varying in validity and believability using either deductive criteria (logic task) or via…

Mathematical proof is a logically formed argument based on students' thinking process. A mathematical proof is a formal process which needs the ability of analytical thinking to solve. However, researchers still find students who complete the mathematical proof process through intuitive thinking. Students who have studied mathematical proof in the…

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…

When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

In this study, teacher education students' concerns, sense of efficacy, and anxiety related to the future use of data to drive educational decision-making were explored. In alignment with prior research with practicing teachers, this sample of pre-service teachers reported concerns (thoughts, preoccupations, and feelings) that indicate they are…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

The research is a study of the Husserlian approach to intuition, informed by Merleau-Ponty's theory of perception, in the case of a prospective teacher of mathematics. It explores the two major stages-categories of intuition, the essential relations between them, and their vital role in the emergence of empirical and abstract mathematical…

The emergence of a proof image is often an important stage in a learner's construction of a proof. In this paper, we introduce, characterize, and exemplify the notion of proof image. We also investigate how proof images emerge. Our approach starts from the learner's efforts to construct a justification without (or before) attempting any…

A model is proposed to assess the effect of different content representation design principles on learners' intuitive beliefs about using e-learning. We hypothesized that the impact of the representation of course contents is mediated by the design principles of alignment, quantity, clarity, simplicity, and affordance, which influence the…

When people evaluate syllogisms, their judgments of validity are often biased by the believability of the conclusions of the problems. Thus, it has been suggested that syllogistic reasoning performance is based on an interplay between a conscious and effortful evaluation of logicality and an intuitive appreciation of the believability of the…