In everyday language, "zero" and "nothing" are generally synonyms if not interchangeable. In physics, however, these two terms are quite distinct. Zero often refers to a number and nothing often refers to the vacuum state. Furthermore, the number zero has a variety of different meanings, among which physics teachers shift…

The purpose of this paper is to propose a new ontology of reasons for inferentialism. The existing inferentialist approach to mathematics education has a methodological challenge in retrospective analysis and a noncollaborative issue stems from a narrow view of learning. The proposed ontology, built on a radical interpretation of the…

I consider three aspects of children's thinking about religious phenomena. It displays intriguing parallels with their thinking about scientific phenomena; it has an impact on their moral behavior; and it is likely to impact their religious experience. Children's gradual conceptual progress in the domain of religion resembles their conceptual…

The concept of redshift is very often used in teaching physics and astronomy, as well as in science public outreach. Redshift is an interesting topic, used to describe many physical processes such as the Doppler effect or the expansion of the universe. Nevertheless, there are unfortunately also misconceptions about redshift. When facing the…

In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: "proportional equivalence" and "unit equivalence." These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a)…

In the property listing task (PLT), participants are asked to list properties for a concept (e.g., for the concept "dog," "barks," and "is a pet" may be produced). In conceptual property norming (CPNs) studies, participants are asked to list properties for large sets of concepts. Here, we use a mathematical model of…

Exercise is essential for mastering mathematics, but it faces two major hurdles. First, students are often not motivated to do their homework. Second, checking traditional homework is a manual and labor-intensive process that becomes harder to support as the number of students increases. We argue that computer games could alleviate both problems.…

Game-based learning (GBL) has long been recognized as an effective way to engage students in learning through games, but little emphasis has been placed on scaffolding support for students, which hinders their learning. Therefore, our design of Space Adventure GBL ties games closely to scaffolds at every stage and investigates what role games and…

Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

An important topic of study in secondary mathematics is non-linear functions, including quadratic equations. In this study, findings from 25 Year 11 students indicated that difficulties with critical prerequisite concepts such as algebraic conventions impeded students' success in understanding and working with quadratics. Analysis of student…

The study aimed to analyze the content validation of the STEM-integrated on thermal and transport concept inventory instrument used to measure the problem-solving abilities of high school students. The instrument questions developed amounted to nine description questions. This type of study is development research. The steps in this research are…

Teaching music often focuses on developing musical concepts, through comparisons and discriminations. This paper contributes to the discussion on concept development in music through recognition of common elements in a situation and a shift from a local to a general level, considering theoretical approaches to mathematical generalisation. It sets…

In this article, I examine how a sample of principals in Texas and West Virginia made sense of the learning experiences of kindergarteners and how such sensemaking appeared to affect them as instructional leaders. Examining these issues creates the opportunity to consider the types of support school leaders might need to address the changing…

Redox reaction is a core chemical concept. However, its abstract nature makes it very difficult for students. Students' conceptual structure reflects their mastery of concepts, which helps teachers implement targeted educational strategies. This study aimed to explore the conceptual structures of redox reaction held by students (grades 10 to 12)…

The present study falls into the efforts to improve practices for addressing errors produced by learners in various situations involving the calculation of integrals. We attempt to clarify as precisely as possible the types of errors that secondary school students produce when using integrals in algebraic and graphical frames. Based on the…