This study analysed first-year preservice teachers' understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design…

Africanised play is a pedagogical transformation that stresses integrating play pedagogies, African culture and digital learning within the mathematical curriculum. This transformation contributes to learners developing problem-solving, mathematical, digital skills and appreciating culture. Given that, there still needs to be more knowledge on the…

This study aimed at developing an imagineering learning process model with logical solutions by using documentary research and relevant experts' viewpoints with regard to the process of Imagineering Learning--problem-based learning (PBL) involving logical and computational thinking. The data were then synthesized in order to find the relationship…

In mathematics, problem-solving can be considered to be one of the most important skills students need to develop, because it allows them to deal with increasingly intricate mathematical and real-life issues. Often, teachers attempt to try to link a problem with a drawn diagram or picture. Despite these diagrams, whether given or constructed, the…

As computational thinking (CT) gains more attention in K-16 education, problem-solving has been more emphasized as a core competency that can be found across various domains. To develop an evaluation framework that reveals students' problem-solving competency, this study examined solutions for the Bebras Computing Challenge which requires students…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

The ideas of computational thinking (CT) and computer science (CS) are increasingly being integrated into K-12 education. Yet, insufficient attention exists regarding access and exposure of CT and CS for students with disabilities. In this Technology in Action, the authors sought to present an argument--as well as actual activities--for teachers…

Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed…

In order to teach Computational Thinking (CT) skills to young students, Block-Based Programming Environments (BBPEs) are integrated into secondary school computer science (CS) education curricula. As a CT skill, abstraction is one of the prominent skills, which is difficult to enhance and measure. Researchers developed some scales for measuring…

In this case study, we investigate one teacher's implementation of DNR-based combinatorics curriculum in their high school discrete mathematics class. By examining the teacher's practices in whole-class discussions of two counting problems, we study how they advanced a variety of ways of thinking to support the development of a set-oriented way of…

Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we introduce…

A well known physics problem is to calculate the friction forces required to support a ladder against a wall. A more tractable problem is to calculate the friction forces needed to support an inclined beam on a ball or a cylinder. In the latter case there are three rather than two points of sliding support. Measurements and calculations are…

We investigated whether three interventions -- studying incorrect worked examples, studying correct worked examples, or receiving feedback -- improved children's 0-1,000 (Experiment 1) and adults' 1 thousand--1 billion (Experiment 2) number-line estimation precision relative to a no intervention control group. At pretest, participants estimated…

A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks--tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students'…

Objective: Explicit instructions to students to use the index finger to trace out specified elements of mathematics worked examples have been shown to improve mathematics learning outcomes; however, there is limited research on whether the magnitude of tracing actions impacts these outcomes. Method: Using an experimental design, 34 adults were…