Pre-service mathematics teachers (PSTs) may hold different beliefs about school mathematics and university mathematics and different beliefs about teaching mathematics between high-achieving (HA) vs. low-achieving (LA) classes. Because of the differentiation, the beliefs relationship is complex. This quantitative study administered a questionnaire…

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…

In modern information societies, evaluating information, data, or knowledge claims is crucial. As these activities are influenced by epistemological beliefs, such beliefs are a key element of education in the sense that educational institutions intend to prepare students for professional and social life. Hence, this study aims to examine the…

College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…

Teachers' and students' values influenced the teaching and learning process in the mathematics classroom. Few studies were conducted to compare teachers' and students' value in mathematics learning. This paper explores Malaysian mathematics teachers' and students' values in mathematics learning. Fifty-three mathematics teachers and 354 secondary…

The goal of the present study is to investigate the impact of procedural and conceptual teaching on students' mathematical performance over time. For this purpose, implicit differentiation and integration by parts were taught in two different ways to first-year university students of two different calculus courses: one course with Conceptual…

This research explores the use of guided notes in a post-secondary calculus course and the extent to which use enhanced students' success in a first year calculus course. Guided notes have been previously shown to be perceived as helpful to learning by students, and one study showed that the use of guided notes improved pass rates in a first year…

Capitalizing on cognitive load theory and learning by analogy, we propose two instructional methods to learn a complex linear equation (e.g. two-step equation) by building on prior knowledge of a simpler linear equation (e.g. one-step equation). We will examine the proposal theoretically in this paper. In line with the design principles of…

A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

Flipped classrooms serve as a new pedagogical approach for teaching and learning, which involves switching from the traditional teacher-centred academic agenda. Unlike the traditional classroom model, the flipped classroom enables students to understand the lesson better while learning at their own pace and enhancing their communication skills…

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians' responses, leading to four themes in expectations when…

Statistical tables associated with named probability distributions and their families, such as the standard normal, Student's t, and chi-square tables, among others, have been utilized for years and are still widely used today, especially for mathematics and statistics education. While such tables can be found in many statistics textbooks and even…

This study used a modified mathematical knowledge for teaching (MKT) framework to compare the "common content knowledge" (CCK) of two groups of purposively selected pre-service primary mathematics teachers (n = 86) in relation to spatial visualization. Specifically, thirty-five pre-service teachers (n[subscript 1] = 35) with a pure…

In this paper, we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two…

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…