This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…

Objectives: Code style is an important aspect of text-based programming because programs written with good style are considered easier to understand and change and so improve the maintainability of the delivered software product. However teaching code style is complicated by the existence of many style guides and standards that contain…

Teacher perception is one of the most important factors determining classroom teaching practices. Multiple representations are used extensively in mathematics classrooms, especially in developing conceptual understanding. The data in this study, which aims to compare Turkish and US middle school mathematics teachers' perceptions of multiple…

A highly authentic learning setting is likely to trigger positive motivational and emotional reactions due to its emphasis on promoting the acquisition of knowledge that is connected and transferable to real-world phenomena outside the learning environment. However, a high level of authenticity is usually accompanied by a high level of complexity…

Discussions of trauma-informed practices tend to focus on student behaviors and strategies for managing those behaviors, rather than the circumstances students are experiencing. Critical educators have expressed concern that a focus on trauma-informed practices lead teachers to view students from marginalized backgrounds with a deficit lens,…

This paper is a part of a larger research study that we are conducting to develop a framework consisting of the data-driven best practices around teaching and learning algebra in K-12 classrooms. The purpose of this paper is to develop a usable definition for algebra interventions for the second stage of screening within the larger study, which…

Our study explores teaching practices that aim to promote students' learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor's guidance. During the TE, the instructor's teaching practices were…

This paper analyses a set of widely held beliefs concerning our understanding and teaching of critical thinking, a notion which is increasingly adopted by universities as their main educational goal. Existing scholarship on critical thinking throws up a vast heterogeneous collection of definitions of critical thinking. I propose a…

The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact,…

Using the tools of praxeological analysis and didactical transposition analysis, the treatments of the Fundamental Theorem of Calculus in one Norwegian, Grade 13 textbook is analysed, with a particular focus on the development of the logos block of the FTC. The terms structure, functioning and utility, first introduced by Chevallard in 2022, is…

Teachers have a key role in promoting Critical Thinking (CT). However, research on appropriate teaching methods for developing CT is scarce in primary education. This study investigated how CT can be fostered among pupils based on teachers' perceptions of the characteristics that promote CT and create obstacles in primary schools. We interviewed…

Divergence is not a new phenomenon in RE in England and Wales. A diverse range of aims and approaches have been promoted since RE provision became compulsory in 1944. Approaches include the phenomenological, interpretative, and dialogic with current debates centring around the benefits and challenges of a 'worldviews approach'. There have been a…

The "ACTFL Performance Descriptors for Language Learners" are designed to describe language performance that is the result of explicit instruction in an instructional setting. A companion to the "ACTFL Proficiency Guidelines," a document that describes broad, general language proficiency regardless of when, where or how…

The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…

Undergraduate mathematics education is essential for building a foundation for success in various scientific disciplines. Curriculum reforms in mathematics education have emphasized the need for cultivating learning skills that depend on effective student engagement (SE). Consequently, there has been growing research on the mechanisms that…