Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

In this study, we have explored the effectiveness of two instructional approaches in the context of the motion of objects falling at terminal speed in the presence of air resistance. We ground these instructional approaches in dual-process theories of reasoning, which assert that human cognition relies on two thinking processes. Dual-process…

Problem-solving is the essence of mathematics and is the main goal in learning mathematics. Many students did not have good problem-solving skills based on the field observations. The problems grew up because the students were not used to solving the problems and the problem-solving stages. They did not include issues with high complexity, such as…

Sequence stratigraphic and Wheeler diagram interpretations require a strong combination of conceptual understanding and diagram reasoning skills. Students are generally exposed to the foundational concepts within sequence stratigraphy (relative sea level, eustasy, base level, and accommodation) in a variety of courses along their degree path,…

The ability to identify errors by sight and sound--commonly referred to as "error detection"--is a musical ability needed in a variety of music professions. Instructors of undergraduate aural-skills courses often agree that strong error-detection skills are an essential outcome of these courses; however, error-detection activities are…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

The research aimed to analyze the students' abilities in solving realistic mathematics problems using "What-If"-Ethnomathematics Instruments with content focused on plane and space materials. The "What-If"-Ethnomathematics instruments are instruments that enable educators to analyze various errors and obstacles experienced by…

Children need support in the early elementary grades to construct a deep, formal understanding of foundational prealgebraic concepts. In this article, the authors share recommendations for teaching one such foundational concept--mathematical equivalence. First, they define mathematical equivalence and discuss research supporting the benefits of…

Thinking is a tool to construct knowledge in learning mathematics. However, some college students have not been fully aware of the importance of constructing their knowledge. Therefore, this study aims to explore students' thinking processes in completing mathematical proofs through assimilation and accommodation schemes. This research was…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…

The logos of many atomic energy regulatory bodies present a paradox in that the depictions of atomic structure that they portray tend to be 'wrong' in relation to the rules that govern pictorial representations of atomic structure that we teach. These logos present chemistry educators with excellent classroom resources to enhance critical thinking…

In this work, we examined mathematical knowledge mobilised by mathematics teachers while interpreting students' answers, which we denote as Interpretative Knowledge (IK). In particular, we analysed the IK of prospective mathematics teachers (PTs), who were students of a Mathematics Education course for the Master's Degree in Mathematics. In order…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

This research is driven due to significant role of textbooks possessed in a country. The purpose of this study is to analyse the Malaysian Form Two Science textbook as this learning tool may acts as one of the reason that affects national Science education. The textbook was analysed based on content element adapted from Florida University…

The central dogma of molecular biology, a model that has remained intact for decades, describes the transfer of genetic information from DNA to protein though an RNA intermediate. While recent work has illustrated many exceptions to the central dogma, it is still a common model used to describe and study the relationship between genes and protein…