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…

The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to…

Traditionally, the difficulties associated with mathematics were largely seen as coming from the cognitive demands of mathematics itself. It is now accepted that language and mathematics are connected in mathematics learning and teaching, and, the potential challenges of language in mathematics have been investigated by a number of researchers.…

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…

Many students experience considerable difficulties when they learn and then attempt to construct and communicate proofs of conjectures using the principle of mathematical induction. Although research on the pedagogy of mathematical induction has gained only occasional attention since the 1970s, there has been an increasing interest in this field…

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…

Outlines the application of relational logic to data retrieval, describes how the discipline relates to modern data base technology, and discusses some of the key issues involved. Some examples illustrate the use of relational concepts in automated question-answering systems. Notes and references are provided. (Author/JD)

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…