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…

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…

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…