This paper reports on themes that arose in an investigation of university lecturers' views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course?…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Building scientific arguments is a central ability for all scientists regardless of their specific domain. In organic chemistry, building arguments is a necessary skill to estimate reaction processes in consideration of the reactivities of reaction centres or the chemical and physical properties. Moreover, building arguments for multiple reaction…

Over half a century has passed since Bruner suggested his three-stage enactive-iconic-symbolic model of instruction. In more recent research, predominantly in educational psychology, Bruner's model has been reformulated into the theory of instruction known as concreteness fading (CF). In a recent constructivist teaching experiment investigating…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

In the "Republic," Plato developed an educational program through which he trained young Athenians in desiring truth, without offering them any knowledge-education. This is not because he refused to pass on knowledge but because he considered knowledge of the Good as an ongoing research program. I show this by tracing the steps of the…

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

This article investigates how social inequality is reproduced through the recontextualization of mathematics pedagogy, using Dowling's social activity method as an analytical framework. The study identifies the selection and transmission of pedagogic messages as a potential pathway. Findings indicate that teachers in upper-stream schools favour…

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is…

We developed a Quantum Mechanics Conceptual Understanding Survey (QMCUS) in this study. The survey was conducted using a quantitative methodology. A multiple-choice survey of 35 questions was administered to 338 undergraduate students. Three experienced quantum mechanics instructors examined the validity of the survey. The reliability of our…

This study aimed at identifying the level of scientific argumentation skills in chemistry subject among Omani Grade 11th students and the effects of their logical thinking skills and gender on this level. The study sample consisted of (400) male and female students selected purposely from one educational region in Oman. The study's instruments…

Supporting students in building well-grounded explanations plays a crucial role in scientific practice. Research in organic chemistry education on students' mechanistic explanations, however, has revealed various challenges. When solving mechanistic tasks, students experience difficulties when (I) deriving implicit properties from structural…

By using high-leverage models to connect student learning experiences to overarching concepts in mathematics, teachers can anchor learning in ways that allow students to make sense of content on the basis of their own prior experiences. A rectangular area model can be used as a tool for understanding problems that involve multiplicative reasoning.…

While AI has become more prevalent in our society than ever, many young learners are found holding various naive, erroneous conceptions of AI due to the influence of their technology and media environments. To address this issue, this study seeks to propose a novel pedagogical solution to improve upper-elementary school students' scientific…

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. "Concreteness fading" is a theory of instruction that offers a solution for making these connections. As originally…