Previous investigations into first year calculus students' understandings of tangent lines have revealed common misconceptions arising either from students' prior experiences with the topic or from the treatment of the subject in the calculus classroom. This study seeks to examine in-service secondary mathematics teachers' conceptions of tangent…

The multi-faceted nature of mathematics knowledge for teaching, including pedagogical content knowledge (PCK), has been studied widely in elementary classrooms, but little research has focused on senior secondary mathematics teaching. This study utilised the Knowledge Quartet (Rowland et al., "Research in Mathematics Education," 17(2),…

This paper presents a modified approach to subject-matter didactics, in which the focus is not on the content itself, but on the students' view of the content. The introduction deals with an overview of subject-matter didactics and the notion of beliefs used in this paper. The main portion of the paper deals with presenting the concepts of a book…

A recent review of literature in topic of rate of change mostly highlighted students and teachers' difficulties in handling conceptual questions. This initiated the researcher to investigate the Malaysian pre-service mathematics teacher's subject matter knowledge in rate of change through a case study design. A task-based interview was conducted…

This paper analyses how pre-service teachers approach the notion of the infinite limit of a sequence from two perspectives: Specialized Content Knowledge and Advanced Mathematical Thinking. The aim of this study is to identify the difficulties associated with this notion and to classify them. In order to achieve this, an exploratory qualitative…

We report a characterization of the reflections made by high school mathematics teachers when discussing their resolutions of three numerical tasks related to the concept of function understood as a mathematical procept. Thematic analysis was used to code and categorize the reflections. Six teachers with at least 5 years of professional experience…

Derivative concept is one of the essential studies in calculus, which is studied in teaching mathematics. Prospective mathematics teachers who have completed their studies and later become teachers will teach derivative concepts to their students at school. Therefore, knowledge of derivative concepts is vital in transforming knowledge to students.…

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…

This study aims to evaluate the university lecturers' teaching content preferences in different teaching environments at the undergraduate level of mathematics. The content that lecturers use in teaching the concept of integral is evaluated through a comparison of face-to-face and virtual classroom settings. With comparative case study being used…

This study aimed to explore the effects of an instructional intervention in which GeoGebra and the think-pair-share method were used to teach the relationship between the graph of a parametric curve and the derivatives of its component functions. The participants in the study were 19 prospective mathematics teachers. To assess the understanding of…

Research shows that teachers influence students' attitudes towards; performance in; and perceptions of a subject. Hence, the need to improve the teaching and learning of many curricular subjects has been well documented for many years. This paper focusses on efforts made to develop competence among out-of-field teachers of mathematics and…

The aim of this study was to determine the how pre-service mathematics teachers respond to unexpected questions from students about the second derivative. A qualitative research method was used for this purpose, applying a case study framed as an in-depth analysis of how pre-service mathematics teachers respond to students' ideas. The participants…

GeoGebra mathematical software is the best alternative way of teaching and learning calculus in the 21st century by exploration and visualization. This software opposes the traditional teaching and learning method, or solution only approaches and make the teaching and learning process more active in the classroom which goes with the constructive…

Quantitative analysis of the Factors Influencing College Success in Mathematics (FICSMath) Survey data indicates that high school mathematics teachers' abilities to teach for conceptual understanding is a significant and positive predictor of student performance in single- variable college calculus. To explore these findings further, we gathered…

Our investigation is concerned with new teachers developing their ability to understand student thinking. We conducted individual interviews with graduate students teaching calculus for the first time, interviewing a representative sample of graduate students before and after their first teaching assignment. The interviews were transcribed and…