Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

This study examines the behavior of individuals when two intuitive rules in their minds lead to two different outcomes concerning a problem. In the absence of the formal knowledge, intuitive rules can affect the mathematical thinking. Hence, studies have usually compared the correct answer of the related formal knowledge with the incorrect one…

There is mixed evidence as to whether concrete manipulatives (e.g., toy animals) are better than abstract manipulatives (e.g., counters) for teaching mathematical concepts to children. Concreteness is defined as the amount of extraneous information a manipulative provides, and in this study we aimed to unpick which dimensions of concreteness…

This study aims to test the effectiveness of GeoGebra Augmented Reality in improving students' mathematical problem-solving skills. The method used is a quasi-experiment with a posttest-only control group design. The research population is students of the Mathematics Education Study Program at a private university in Indonesia, with a sample of 32…

Flipped learning has been recognized as a promising pedagogical model for methodological progress in educational environments. Studies have shown the effectiveness of flipped learning when used with appropriate educational technologies and learning strategies. On the other hand, comprehensive guidance is required to combine this pedagogical model…

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…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…

The question is whether or not we or any student are allowed to define a measure of variability in some other way that is not written in textbooks and officially approved. We compare the sum of squares of all deviations against the usual sum of squares of deviations from the mean.

Through instructional tasks, teachers can present content in ways that require students to apply critical thinking, problem-solving, and other cognitive skills. The purpose of this mixed methods collective case study was to determine how teacher-assigned instructional tasks in mathematics impact students' learning of mathematical concepts. In this…

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240…

Playing mathematical games helps many senior secondary school students--especially girls--acquire basic mathematical skills, but it can be difficult. Thus, this study examined how gender-related mathematical gameplay affects secondary school students' performance. The design of the study was quasi-experimental. Purposively, a sample of fifty…

Coordinate geometry is an important part of mathematics. It helps students develop thinking, logic, and problem-solving skills. This study was conducted to test the effectiveness of the CORE learning model in promoting students' mathematical problem-solving skills when they learn the method of coordinates in a plane. Consequently, this study used…