Background/purpose: This research is motivated by the difficulties often experienced by students in adapting to their first year of college, especially related to learning calculus. To address these difficulties, a solution needs to be found so that these problems can be resolved. One solution that is expected to yield optimal results in…

This study aims to prepare an educational program based on integrating Science, Technology, Engineering and Mathematics (STEM) to develop students' mathematical thinking skills. It also aims to provide proposals that could have a major role in rebuilding some of the general features on which mathematics curricula can be built according to the STEM…

Theories of self-efficacy and approaches to learning are well-established in the psychology of learning. However, studies on relationships between the primary constructs on which these theories are developed are rarely reported in mathematics education research. Thus, the purpose of the current study is to provide empirical evidence for a…

Learners in the 21st century need technological support in the learning process because of the advancements made in technology for teaching and learning. A GeoGebra-oriented classroom uses one of these technologies that can be implemented in the classroom. The new developed cycle model implemented in the study and explored the effect of using…

Approaches to learning have been identified as crucial factors that influence students' mathematics performance. However, there have been mixed findings on which of the different approaches improve performance in undergraduate mathematics. Thus, this study aimed to unravel the specific effects of prior mathematics knowledge and approaches to…

This work presents an evaluation of a unified Calculus 1 course in a large Brazilian federal university. By course unification we mean having all the sections following the same weekly schedule, under the same syllabus and common assessment. We analyse two sets of data: pass rates relative to the 9 semesters prior to the unification and to the…

There is a growing interest in using comparative judgement as a peer assessment tool involving students choosing the 'better' of two pieces of work. However, it has not been shown whether peer assessment through comparative judgement is effective for students' learning. To gain a better understanding of the comparative judgement process, we…

Various studies have concluded that many students have difficulty understanding concepts related to function derivatives. One of the concepts in function derivatives is higher-order derivatives, primarily the nth derivative pattern. This study aims to: (1) identify various types of learning obstacles experienced by prospective mathematics teacher…

This paper shows the results of the epistemological and didactical analysis of the sense of variation of functions. Specifically, on the conceptions of growth and decay in a function that underlie the demonstrations of the theorem that links the sign of "f" with the sense of variation of "f". The epistemological approach…

Simon Fraser University in Vancouver, Canada offers two introductory calculus courses designed for students enrolled in science and engineering programs. Students identified as needing additional support based on their admission grades take the version of the course where students meet weekly for four hours instead of three. A new approach for the…

Netnography is a research procedure to analyse people inserted in digital communities applied, in this research, at Virtual University of the State of São Paulo, the first Brazilian public institution that offers only distance education. The aim of this paper is to know what happens in the course Calculus III, of the undergraduate in Physics, with…

In this article we present the results of a qualitative investigation into the teaching and learning of Taylor series and local approximations. In order to perform a comparative analysis, two investigations are conducted: the first is historical and epistemological, concerned with the pedagogical evolution of semantics, syntax and semiotics; the…

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

The present paper presents three deliberately chosen mathematical episodes observed in a class of engineering students taking a basic calculus course. By drawing on analyses of instrumental and relational learning strategies, the episodes are shown to illustrate instrumental approaches indicated by the students. The paper discusses positive…