This paper examines prospective mathematics teachers' knowledge of asymptotes and asymptotic behaviour of functions in calculus. They are university students and future facilitators of knowledge in upper secondary education. We constructed a "reference epistemological model" to describe the knowledge about asymptotes for upper secondary…

Conceptual understanding of calculus is crucial in the fields of applied sciences, business, and engineering and technology subjects. However, the current status indicates that students possess only procedural knowledge developed from rote learning of procedures in calculus without insight of core ideas. Hence, this paper aims to assess students'…

Responsive instruction--or instruction that foregrounds and takes up the disciplinary substance of student thinking--is both a hallmark of recent STEM education reforms and challenging to enact. This kind of instruction may be especially challenging in instructional contexts that mandate or rely on curriculum with set, structured learning…

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…

The purpose of this study was to investigate the misperceptions and performance of king Saud University students' about concept and finding the limit of same partial functions given in the form of both graphical and symbolic. In the collection of the data, the researcher employed the open-ended question test consisted of four items. Firstly,…

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

The purpose of this paper is to present results of a recent study in which students voted on multiple choice questions in mathematics courses of varying levels. Students used clickers to select the best answer among the choices given; in addition, they were also asked whether they were confident in their answer. In this paper we analyze data…

This paper examines the effects of policies that increase the number of students who take the first course in algebra in 8th grade, rather than waiting until 9th grade. Extending previous research that focused on the Charlotte-Mecklenburg school system, we use data for the 10 largest districts in North Carolina. We identify the effects of…

This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

The paper focuses on analysing grade 12 learner errors and the misconceptions in calculus at a secondary school in Limpopo Province, South Africa. As part of the analysis the paper outlines the nature of mathematics errors and misconceptions. Coding of learners' errors was done through the lens of a typological framework. The analysis showed that…

In this article, we demonstrate that prospective teachers' content knowledge related to defining mathematical concepts is dependent on content area. We use the example of generation (a research tool we developed in a previous study) to investigate prospective teachers' knowledge. We asked prospective secondary mathematics teachers to provide…

Seventy secondary mathematics pre-service teachers from two universities were assessed on their content knowledge, vocabulary knowledge, and their perceived confidence in teaching the content addressed on the eleventh grade state assessment. The results indicate the pre-service teachers had significant content weakness in data analysis, algebra,…

All advocates of curriculum reform talk about an increased emphasis on conceptual understanding in mathematics. In this article, the authors use many examples to address the following issues: What does conceptual understanding mean, especially in introductory courses such as college algebra, precalculus, or calculus? How do we recognize its…

We are studying two groups of preservice teachers' conceptions, progression and especially the concept of function in connection to y=x+5 when they are taking a course in algebra or one in calculus in their third and sixth term, respectively, in a teacher preparation program. There is a similar development in that they use to a higher degree a…