We consider designs for conceptual learning where students first engage in pre-symbolic problem solving and then articulate their solutions formally. An enduring problem in these designs has been to support students in accessing their pre-conceptual situated process, so that they can reflect on it and couch it in mathematical form. Contemplative…

We need to know what it means to be an expert in working life today. Universities are often accused of neglecting the basic idea that higher education should be relevant to working life, and research on the subject of expertise in today's workplace is lacking. Thirteen experts from different fields were interviewed and the obtained data were…

Education research has established that teachers' beliefs matter because they can affect classroom practices and student outcomes, and beliefs are viewed as an important construct within statistics education. However, relatively little research about the beliefs of in-service statistics teachers has been conducted. Additionally, little research…

This study combined virtual reality (VR) technology, the 6E (Engage, Explore, Explain, Engineer, Enrich, and Evaluate) model, and STEM (Science, Technology, Engineering, and Mathematics) education to develop a hands-on activity aimed at helping students to achieve "learning by doing." The participants were 162 tenth-grade students,…

The purpose of this study was to gain insight into how employing Case-based (CB) and Non-case-based (NCB) discussions facilitate high-level learning, and whether or not there is a relationship between students' learning outcomes. Findings revealed that students' perceived cognitive presence, learning and satisfaction were significantly higher in…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

It is difficult to inculcate the knowledge, skills, competence, quality and values that students need to gain through traditional approaches of teaching. Therefore, approaches of teaching which make students active in learning, which lead them to solve daily life problems and thus inculcate in them the upper order thinking skills need to be used…

In this report, we discuss background research on the development of student understanding of quadratic functions and present a provisional learning progression for quadratic functions and quadratic equations. We also describe task shells that are linked to the learning progression. The learning progression and task shells can be used as a…

Design thinking is a collaborative problem solving and human-centric approach that fosters innovation by elevating participants' creative thinking abilities. Design thinking techniques and practices have been implemented into different curricula in secondary and post-secondary education to address the need for new skills to be learned for the…

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

Arguably, constructive alignment has been the major challenge for assessment in the context of problem-based learning (PBL). PBL focuses on promoting abilities such as clinical reasoning, team skills and metacognition. PBL also aims to foster self-directed learning and deep learning as opposed to rote learning. This has incentivized researchers in…

The choice of instructional strategies, methods and techniques used by teachers is important in terms of establishing an effective learning environment. The purpose of this study is to examine the most common methods teachers use in their lessons and the factors that influence their choice of methods by using game theory. Game theory has different…

This study aimed to combine the use of electronic technology and dynamic testing to overcome the limitations of conventional static testing, and adapt more closely to children's individual needs. We investigated the effects of a newly developed computerized series completion test using a dynamic testing approach and its relation to school…

Because of the lack of tools available to assess problem-solving skills, teachers often revert to more traditional instructional approaches (e.g. lecture-based, memorization) that fail to prepare learners for the complexity of dynamic work environments. To overcome this challenge, technology solutions are needed that accurately and efficiently…