This paper reports the results of three questionnaires applied to sixty-seven students preparing to become university-level mathematics teachers; the questionnaires were focused on knowing their conceptions and their mastery of the representations of functions in the development of power series. The theoretical and methodological background rests…

This study aimed to better understand the effect that the flipped method of instruction has on students' learning approaches using interactive math lecture videos in a second-year vector calculus course. Three hypotheses were tested to determine if students' perceptions of their level of active engagement, the number of interactive lecture videos…

Research across five countries has identified inability to pay attention to mathematical detail -- the discipline of noticing -- is an issue in senior secondary school mathematics teachers. The test and questionnaire completed by an Australian cohort further identifies a reluctance to employ non-routine questions in assessments, with teachers…

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

Improving students' performance in Calculus is a challenge for many colleges and universities. One way of improving students' performance as well as their metacognition and study skills is to provide opportunities for them to receive support outside of the lecture. A modified version of the Motivated Strategies for Learning Questionnaire (MSLQ)…

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

Many factors play a role in a students' learning experience, but students' course interaction behaviors are particularly important toward fostering success. Instructors build learning tools (such as videos, online quizzes, etc.) that provide students with the opportunity to extend their learning outside the classroom. These tools require students…

As part of a large-scale survey of over 4000 undergraduates at British universities, 238 economics students reported on their experiences of studying post-compulsory secondary mathematics qualifications (A-levels) and the preparation they provided for their degrees. Participants were positive about their experience of post-compulsory mathematics…

Graphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers' perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted…

Improved access to technology has led to an increase in the number of online courses and degree programs in higher education. Despite continuous progress, little attention is paid to "understanding" students prior to implementation of learning and teaching processes. Being a valuable input for design of online learning environments and…

Calculus courses often present a large number of difficulties to undergraduate students of scientific studies, especially in engineering degrees. These difficulties are sometimes related to teaching and assessment strategies. In this paper, a teaching innovation experience is presented within the framework of the Universitat Oberta de Catalunya.…

In this research, I provide an overview of potentially selected interactive mathematical instructions that help learners-educators identifying the most effective practices for teaching a course on differential equations. Based on my practical experience, positive and negative aspects of the used techniques are discussed. Immediate reactions on the…

This article is the result of research aims to describe the patterns and characteristics of the process of metacognition student of mathematics in solving calculus problems. Description was done by looking at changes in "awareness," "evaluation," and "regulation" as components of metacognition. The changes in…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

This study is part of a more extensive research project that addresses the understanding of the derivative concept in university students with prior instruction in differential calculus. In particular, we focus on the analysis of students' responses to a sequence of tasks that require a high level of understanding of the concept, and complement…