Persistent difficulties in learning abstract algebraic concepts--particularly among preservice mathematics teachers--continue to hinder students' mathematical development. While prior studies have documented general misconceptions, few have grounded their analysis in comprehensive learning theories. Addressing this gap, the present study adopts…

Concurrency is often perceived as difficult by students. One reason for this may be due to the fact that abstractions used in concurrent programs leave more situations undefined compared to sequential programs (e.g., in what order statements are executed), which makes it harder to create a proper mental model of the execution environment. Students…

In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role.

Assessing students' conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by…

Biology education plays a vital role in nurturing the understanding of learners about the intricacy of life. Various efforts have emerged to strengthen learning biological concepts but there were still studies that showed that learners have low mastery in some aspects. To determine how well students understood various biological topics, including…

Background: Concept inventories (CIs) are commonly used in engineering disciplines to assess students' conceptual understanding and to evaluate instruction, but educators often use CIs without sufficient evidence that a structured approach has been applied to validate inferences about student thinking. Purpose: We propose an analytic framework for…

Concept inventories hold tremendous promise for promoting the rigorous evaluation of teaching methods that might remedy common student misconceptions and promote deep learning. The measurements from concept inventories can be trusted only if the concept inventories are evaluated both by expert feedback and statistical scrutiny (psychometric…

This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability…

Scientific and everyday knowledge domains are compared so as to reveal the distinctive differences between their goals and the cognitive processes used to attain them. The main goals, working goals, learning difficulties, knowledge structure, concept specification, knowledge organization, role of school science, program-solving instruction, formal…