Previous research has suggested that when feature inferences have to be made about an instance whose category membership is uncertain, feature-based inductive reasoning is used to the exclusion of category-based induction. These results contrast with the observation that people can and do use category-based induction when category membership is…

This article describes the authors' use of three game shows--"Survivor," "The Biggest Loser," and "Deal or No Deal?"--to determine to what degree students engaged in mathematical thinking: specializing, conjecturing, generalizing, and convincing (Burton, 1984). Student responses to the task of creating winning strategies to these shows were…

Conditional reasoning consists in combining a conditional premise with a categorical premise and inferring a conclusion from them. Two well-known conditional arguments are Modus Ponens (MP: "If P then Q; P//"therefore Q), which is logically valid and Affirmation of the Consequent (AC: "If P then Q; Q//"therefore "P"), which is not. The latter is…

Building a Universe populated by stars identical to our Sun and taking into consideration the wave-particle duality of light, the biological limits of the human eye, the finite size of stars and the finiteness of our Universe, we conclude that the sky could very well be dark at night. Besides the human eye, the dominant parameter is the finite…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

Purpose: The purpose of this paper is to investigate leadership curricula in UAE business and education management programmes and examine the extent to which they are derived from and linked to students' cultural and Islamic values using Habermas' critical theory. Design/methodology/approach: The study employs a mixed methods approach that takes…

Basic courses on logic are common in most computer science curricula. Students often have difficulties in handling formalisms and getting familiar with them. Educational software helps to motivate and improve the teaching-learning processes. Therefore, incorporating these kinds of tools becomes important, because they contribute to gaining…

Dominant educational approaches in chemistry focus on the learning of somewhat isolated concepts and ideas about chemical substances and reactions. Reform efforts often seek to engage students in the generation of knowledge through the investigation of chemical phenomena, with emphasis on the development and application of models to build causal…

Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts-in-action and theorems-in-action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric…

This literature review explores visualisation within the context of learning in design, engineering and technology education. The investigation first defines visualisation, providing examples of activities that utilise visualisation skills within an applied field. Then exploration of the mental mechanisms of visualisation used to engage with those…

This article investigates some of the specific features involved in accommodating the idea of actual infinity as it appears in set theory. It focuses on the conceptions of two individuals with sophisticated mathematics background, as manifested in their engagement with variations of a well-known paradox: the ping-pong ball conundrum. The APOS…

Use of self-generated analogies has been proposed as a method for students to learn about a new subject by reference to what they previously know, in line with a constructivist perspective on learning and a resource perspective on conceptual change. We report on a group exercise on using completion problems in combination with self-generated…

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as…

Life scientists increasingly use visual analytics to explore large data sets and generate hypotheses. Undergraduate biology majors should be learning these same methods. Yet visual analytics is one of the most underdeveloped areas of undergraduate biology education. This study sought to determine the feasibility of undergraduate biology majors…

The purpose of this study was to detail teachers' proving activity and contribute to a framework of Mathematical Knowledge for Teaching Proof (MKT for Proof). While working to justify claims about sums of consecutive numbers, teachers searched for key ideas and productively used examples to make, test and refine conjectures. Analysis of teachers'…