The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

Purpose -- This article comprehensively examines the existing body of literature about the assessment tools employed for evaluating higher-order thinking skills (HOTS) in mathematics within the last five years. The study endeavors to offer a comprehensive overview of measuring instruments for HOTS in mathematics, utilizing precise and up-to-date…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

We review literature relevant to using technology in the teaching/learning of mathematics to highlight four roles of effective technology use: (a) promoting cycles of proof; (b) presenting and connecting multiple representations; (c) supporting case-based reasoning; and (d) serving as a tutee. We then discuss how they intersect with good…

Current international curriculum frameworks and research advocate for K-12 mathematics to emphasize proof and argumentation. This review synthesizes literature related to conceptions, content, and supportive actions for proof and argumentation across four grade-level bands: K-2, 3-5, 6-8, and 9-12. Our systematic search and subsequent screening…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…

Quantitative literacy has been recognized as an important skill in the higher education and workforce communities, focusing on problem solving, reasoning, and real-world application. As a result, there is a need by various stakeholders in higher education and workforce communities to evaluate whether college students receive sufficient training on…

Background: There is increasing interest in applying neuroscience findings to topics in education. Purpose: This application requires a proper conceptualization of the relation between cognition and brain function. This paper considers two such conceptualizations. The area focus understands each cognitive competency as the product of one (and only…

In assessing the quality of science teaching for an effort such as the National Assessment of Educational Progress (NAEP), it is important to understand what is meant by scientific thinking--the search for explanations. Instruction should involve higher-order cognitive skill development, but it is difficult to measure reasoning and understanding…

This book presents 24 papers dealing with learning theory and its application at the postsecondary level, many stemming from the ideas of Robert Sternberg and Howard Gardner. Articles include: (1) "Introduction" (Richard Kelder); (2) "Teaching Variability in Problem Solving" (Patricia D. Stokes); (3) "Cognitive Theory and…