"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

Identifying students' difficulties in understanding Gauss's and Ampere's laws is important for developing educational strategies that promote an expertlike understanding of the field concept and Maxwell's equations of electromagnetic phenomena. This study aims to analyze and compare students' understanding of symmetry when applying Gauss's and…

Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers' perceptions of inductive…

Frequently, the shadow of financial insolvency is present in economies, whether between countries, companies or the general population (people) who contract the obligation of a loan, credit or other debt. Debt restructuring is one of the most effective financial tools to face this. Through mathematical modeling with algorithms designed for the…

It is imperative that a profound transformation be carried out in the traditional way in which we teach science subjects, so it is necessary that the role of student change from being a mere recipient of information to being the main player in the construction of his knowledge. One of the strategies to achieve this is to make use of ICT, within…

The purposes of calculus courses are often the acquisition of knowledge itself, the development of skills and the understanding of important concepts, such as functions, derivatives, the chain rule, integrals and the fundamental theorem of calculus. However, full conceptual understanding is frequently not achieved. In this article, we examine the…

Measuring the distance between countries and the goal of equality of opportunity in education has been the focus of recent contributions in the economic literature, which have concentrated either on intergroup gaps in access to a given level of studies or on intergroup gaps in educational achievement. We argue that both aspects are important and…

The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

Solving the position of a simple pendulum at any time is apparently one of the most simple and basic problems to solve in high school and college physics courses. However, because of this apparent simplicity, teachers and physics texts often assume that the solution is immediate without pausing to reflect on the problem formulation or verifying…

In this paper we analyze and discuss students' performance in a CAS environment related to the simplification of rational expressions. Results indicate that if students have more initial paper-and-pencil techniques, the CAS environment spurs them to deeper theoretical reflections than for students who have fewer techniques. [For the complete…

This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms,…

We deal with the study of the senses and the meanings generated in the representation of the unknowns in the resolution of word problems involving two unknown quantities. The discussed cases show the difficulties that the students beginning the algebra learning have to deal with when using the equality between "unknown things". For them,…

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…