This research explores the link between achievement emotions and covariational reasoning, a type of mathematical reasoning involving two variables. The study employs a case study approach, focusing on a high school calculus student named Valeria, and develops a theoretical framework based on the control-value theory and levels of covariational…

In most mathematics textbooks, each lesson is followed by a set of homework problems in one of two ways -- blocked practice and mixed practice. Additionally, most mathematics textbooks rely on a common learning strategy called overlearning, that is, mastering a skill and continuing to practice this same skill. This study investigated the effects…

Comparative judgement is a relatively new way of facilitating peer-assessment where students are shown pairs of other students' work and judge which of the two is better. Literature on example-based learning suggests that students should be able to learn from comparative judgement. We present the case of one student, Josie, whose understanding of…

Dynamic visual tools such as MATLAB have inbuilt features which are believed to be able to empower students to learn through the visualisation of three-dimensional objects. While student learning through MATLAB has been investigated regarding students in urban settings, only a handful of studies have investigated how MATLAB can assist students in…

Effectiveness of mathematical education as non-linear, composite and open system, formation and development of cognitive abilities of the trainee are wholly defined in the solution of complex tasks by means of modern achievements in science to high school practice adaptation. The possibility of complex tasks solution arises at identification of…

The calculus concepts of concavity and inflection points are often given meaning through the shape or curvature of a graph. However, there appear to be deeper core ideas for these two concepts, though the research literature has yet to give explicit attention to what these core ideas might be or what it might mean to "understand" them.…

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…

The present study investigated the object-spatial visualization and verbal cognitive styles among high school students and related differences in spatial ability, verbal-logical reasoning ability, and mathematical performance of those students. Data were collected from 348 students enrolled in Advanced Placement calculus courses at six high…

This research aims to describe students' critical thinking ability based on the level academic and gender. The populations of this study were 132 students participating in five classes of Calculus course. The research data obtained through technical tests and interview techniques. This study found that the high level of capability, both male…

In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their…

We examine how student aptitudes impact how much students learn from doing graded online and written homework in an introductory electricity and magnetism course. Our analysis examines the correlation between successful homework completion rates and exam performance as well as how changes in homework completion correlate with changes in exam…

Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…

The goal of the present study was to report an instrument designed to determine students' mathematical performances and preference for visual or analytic thinking for the calculus derivative and antiderivative tasks as well as examine the relationships among students' cognitive style, cognitive ability, and mathematical performance in calculus.…

Here we test if playing video-games require intelligence. Twenty-seven university undergraduate students were trained on three games from Big Brain Academy (Wii): Calculus, Backward Memory and Train. Participants did not have any previous experience with these games. General intelligence was measured by five ability tests before the training…

Steele and Aronson (1995) found that the performance of African-American subjects on test items portrayed as a problem-solving task, in a laboratory experiment, was adversely affected when they were asked about their ethnicity. This outcome was attributed to "stereotype threat". Performance was disrupted by the subjects' concerns about…