When exposed to principal components analysis for the first time, students can sometimes miss the primary purpose of the analysis. Often the focus is solely on data reduction and what to do after the dimensions of the data have been reduced is ignored. The datasets discussed here can be used as an in-class example, a homework assignment, or a…

Whether one engages in truth-seeking and whether he or she is open-minded are indicative of his or her critical behavior when responding to problems at hand. This research sought to determine the behavioural tendencies of pre-service mathematics teachers in the solution of non-routine problems based on the indicators of truth-seeking and…

This paper reports on a study aiming to develop theory and improve practice within an Engineering Education context. The focus is on the development of students' graduate-level work skills during Higher Education programmes and a specific practice example provided an ideal study opportunity. Engaged Scholarship, a research approach from Management…

The purpose of this study was to explore students' approaches to problem identification and the effects of these approaches on problem identification, problem solving, and divergent thinking. Eighth and ninth grade students (N = 90) responded to semi-structured interview prompts while completing a creative problem-solving task (i.e., Creative…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

Literature on learning trajectories is reviewed, and challenges in developing designs to support responsive instruction are highlighted. A distinctive form of design called a "multi-dimensional instructional framework" is introduced. These frameworks span key dimensions of mathematisation, such as notating and distancing the setting,…

This paper reports on an investigation of the student interaction and group development of a four-student group during collaborative mathematics problem solving. Video and written transcript of the group interaction were analysed. The group problem solving has been described by the flow of negotiative events in terms of topics discussed within the…

In this study, the middle school mathematics teachers' knowledge of division of fractions was investigated through the strategies that they proposed and the problems that they posed for division of fractions. The data was collected from 22 middle school mathematics teachers through the task and semi-structured interviews. The data of this case…

Situational complexity is the distinction between simple, technically complicated, socially complicated, and complex situations. Programs that operate in simple situations are usually able to follow a prescribed course of action, or recipe, while programs operating in more complicated or complex situations must be flexible and responsive. In this…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

Educational providers frequently respond to learning disruptions encountered by refugees, internally displaced persons, and migrant communities through online platforms. Learning modules in these digital spaces are often remotely designed, prescriptive and lack full appreciation of challenging circumstances faced by teachers and learners. To…

The increasing prevalence of online courses has highlighted the importance of digital literacy for students. This study investigates the relationship between digital literacy and academic achievement among students who participate in an online course on anatomy and physiology. The study also evaluates how different aspects of digital literacy,…

Background/purpose: This study investigated the effectiveness of Problem-Based Worksheets (PBWs) in improving conceptual understanding of logic gates. PBWs were designed with key characteristics that integrate authentic problem-solving, active student engagement, and conceptual scaffolding to support critical thinking processes. A total of 32…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

Traditional definitions and assessments of creativity often neglect to identify the complexity surrounding Black students' brilliance, leading to lack of access and funding. Further, even when recognized, Black students are often funneled into programs that do not facilitate positive development of their racial-ethnic identity. Through our…