It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom.…

In classical calculus textbooks, the existence of primitive functions of continuous functions is proved by using Riemann integrals. Recently, Patrik Lundström gave a proof via polynomials, based on the Weierstrass approximation theorem. In this note, it is shown that the proof will be easy by using continuous piecewise linear functions.

The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…

We conducted a systematic review to generate a comprehensive understanding of cisgendered girls' mathematical identity within the United States to better understand: (a) how mathematical identity is associated with girls' participation, engagement, and achievement in mathematics; (b) the factors related to girls' mathematical identity; and (c)…

The orthogonality of eigenfunctions in problems of unsteady heat conduction in an infinite slab with symmetric and nonsymmetric convective boundary conditions are demonstrated by performing actual integration of the products of the derived forms of eigenfunctions and by implementing the corresponding eigenvalue conditions. The analysis also…

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

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…

Many studies have investigated students' problem-posing activities. However, there has not been a strong focus on affective aspects in mathematical problem-posing. Also, students' understanding of the function concept whilst generating functions has not previously been investigated. This paper investigated students' misconceptions of the function…

This study reports on in-service mathematics teachers' views of geometry in the context of ethnomathematics. A convergent parallel mixed method design which includes both quantitative and qualitative methods was used to provide a deeper understanding of how the participants view geometry from an ethnomathematics perspective. Questionnaires and…

The present paper aims at investigating the relationship between students' attitudes toward online homework use and mathematics anxiety among secondary school students. In this study, a model has been proposed by integrating the technology acceptance model (TAM) with mathematics anxiety theory. Three hundred and forty-five secondary school…

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…

When embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our…

It is generally accepted that teachers' beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, and student beliefs together in one setting are rarely described. Based on interviews with two Abstract Algebra instructors,…

The purpose of the study was to determine ways to improve the organisation of independent work in mathematical disciplines at the university, its theoretical substantiation and the development of its methodological system. This study consisted of two parts: theoretical and practical. The theoretical part was based on the use of general theoretical…

Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes 'for each input there is one…