Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

Multiple representations can enhance students' understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students' "learning" with multiple representations, little is known about supportive "teaching"…

An important topic of study in secondary mathematics is non-linear functions, including quadratic equations. In this study, findings from 25 Year 11 students indicated that difficulties with critical prerequisite concepts such as algebraic conventions impeded students' success in understanding and working with quadratics. Analysis of student…

The current study is part of a comprehensive research on linking visualization, students' construction of geometrical concepts and their definitions, and students' ability to prove. The aim of the current study is to investigate the effect of learners' understanding of definitions of geometrical concepts on their understanding of the essence of…

The current study attempts to investigate whether using multiple diagrams attached to a geometry task could reduce difficulties in the proving process regarding concepts in three-dimensional geometry. Ninety 12th-grade students participated in the study. The research included the use of a questionnaire whose items invited open-ended responses…

Worldwide, there has been an increased emphasis on enabling students to recognise the real-world significance of mathematics. Mathematical literacy is a notion used to define the competencies required to meet the demands of life in modern society. In this article, students' encounters with mathematical literacy are investigated. The data comprises…

It is well established that spatial reasoning skills (i) support mathematics achievement, (ii) are malleable, and (iii) can be improved through training. More recently, there has been interest in using spatial training to causally support corresponding improvements in mathematics achievement; however, findings so far appear to be mixed. The…

Studies in mathematics education have shown interactions between a variety of emotions and the quality of learning. Research has found that positive emotions are among the main factors that engender a sense of well-being. In the current study, we focused on emotions that may be aroused while coping with mathematical challenges, and sought to…

The aim of this research was to explore the mathematical connections that pre-university students make when they sketch the graph of a derivative function and an antiderivative function. Also, we tried to explain the origin of the mathematical connections identified. We assume mathematical connections as a cognitive process through which a person…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

Teaching senior secondary mathematics presents a number of challenges, such as provision of a prescribed curriculum, homework expectations and preparing students for externally imposed high-stakes assessment tasks. In order to address these challenges, an increasing number of senior secondary mathematics teachers are incorporating a flipped…

This study investigated the effects of students' constructions of geometrical concepts related to the circle on their construction and validation of proofs. The participants were 110 high school students. A questionnaire was administered; both qualitative and quantitative methods were used to analyze the results. Afterwards, in-depth interviews…

In Australia, many Year 10 students choose not to enrol in Year 11 and 12 intermediate and advanced mathematics courses, despite having the ability to complete these courses successfully. Girls, in particular, remain significantly underrepresented in such courses. In this study, Year 10 students identified by their teachers as capable of…

Given the important role played by students' spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes…

School leaders employ various school-based actions to influence students' subject enrolments at senior secondary levels (Years 11 and 12), which in turn affect students' entrance into tertiary courses and career choices. In the context of reported declines in the proportion of students opting to study higher-level mathematics, this qualitative…