Difficulties in mathematics are argued to stem from impairments of a specialized system of numerical magnitude representation. This study investigates whether different measures of numerical magnitude understanding in kindergarten uniquely predict mathematical achievement concurrently and 6 months later, and also examines the relative explanatory…

This study investigated the introduction of the second law of thermodynamics using the Legitimation Code Theory (LCT) (semantic waves) among first year chemistry students. The aim of the study was to investigate the extent LTC (semantic waves) reduce the entropy concept's complexity and abstractness when introducing the second law of…

The proper and thorough functioning of the education process is based on the cooperation of the elements in education. Among the elements that should cooperate and act in harmony are teachers, school administrators and experts in educational management and supervision. Further, a curriculum is needed for the education process to proceed in a…

In high school, students extend understanding of linear and exponential functions and explore trigonometric functions. This includes using the unit circle to connect trigonometric functions to their geometric foundation, modeling periodic phenomena, and applying (and proving) trigonometric identities. These ideas are fundamental for trigonometric…

To shed light on the value of the area model as a tool to elicit pre-service teachers' (PSTs') understanding of fractions and area, we explored their understanding of the fractional knowledge and geometric measurement knowledge incorporated in the area model by providing PSTs area models in an "atypical" way. We administered a written…

This paper aims to show how the Logic of Game Theory can facilitate the structuring of games for the learning of mathematical concepts, in a way which is cognitively resonant with students' attitudes and epistemologically sound from the mathematical standpoint. We propose a kind of game, based on an inquiry approach to mathematics, called Digital…

The 2019 published report of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem (IPBES) reveals that the decline in species and habitats induced by human activities is continuing. School students still have difficulties to understand the meaning of biodiversity and the consequences of its loss. The underlying assumption of…

The aim of this research is to reveal the understanding of dimensions and sub-dimensions of the place value in natural numbers of gifted and non-gifted students attending fourth grade. A mixed approach was adopted in the research. The research is quantitative in terms of revealing the levels of place value, counting, representing, naming,…

We investigate the level of understanding of probability as related to games and gambling, and the concept of independence of events using a convenience sample of college undergraduates taking an introductory course in applied business statistics. We examined the students' perception of the role of skill in winning at four different games through…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

The present study takes a novel quantitative approach to examine whether the change mechanisms hypothesized by conceptual change theories are involved in reconceptualizing teaching from a teacher-centred to a student-centred approach. We assessed changes in approaches to teaching, measured with the Approaches to Teaching Inventory-Revised (ATI-R),…

The paper addresses concept formation processes of a student in the field of geometry. More precisely, the paper deals with the question of how to assist a student in a mathematical concept formation process -- in the context of area calculations in triangles -- with a specially designed learning environment based on the usage of 3D printed…

Proof plays many important roles in mathematics. Proofs should do more than simply verify that a statement is true; instead, a proof should also explain why a statement is true and enrich both the author's and the readers' understanding of the statement and important mathematical ideas within it. Common practice in high school geometry classrooms…

This paper explores the effect teachers' participation in a targeted inquiry-based/nature of science (NoS) continuing professional development programme had on Irish primary children's experiences of scientific inquiry and developing conceptions of NoS. Data were gathered from 459 children from 10 Dublin schools. The findings revealed that their…