Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical…

There is a clear disconnect between the linear and deductive presentation of written proofs and the non-linear and messy process of constructing one. This disconnect poses challenges for students who do not often have opportunities, or the necessary supports, to navigate the transition between the two, quite often contributing to feelings of…

Mathematics learning requires student vulnerability because students are expected to persist in making sense of complex problems despite their uncertainty. For Black students specifically, societal and educational narratives about mathematics learning and participation may implicitly communicate messages to them that they do not belong. This…

Digital multi-representation applets offer promising opportunities for promoting students' conceptual understanding by dynamically converting graphical and symbolic representations and for promoting discoveries and justifications of mathematical properties. However, learning effects of open-ended multi-representation applets seem to depend on…

In the present study, we explored whether future teachers considered spatial skills to be built up slowly and incrementally (incremental view) or considered spatial skills to be an innate, static aptitude (entity view). We also examined whether these views were associated with personal spatial skills, confidence in spatial problem-solving, or…

Background: Pedagogical content knowledge (PCK) is presumed to have a significant influence on students' academic outcomes. The theoretical underpinning of this presumption lies in the belief that teachers with high level of PCK are better equipped to deliver high-quality instruction, thereby facilitate student learning and improving their…

This study examines the implementation of environmental education in the STEAM approach for sustainability. A STEAM model for engaging students in environmental sustainability programs through problem-solving. The main focus of the study was to identify how the pre-service teacher practices the STEAM innovation in mathematics classrooms. Five…

In this paper, we examine mathematicians' views on the value of advanced mathematics for secondary mathematics teachers. The data comprise semi-structured interviews with 24 mathematicians from 10 universities. The findings indicate that the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their…

Students need to see the value in the lessons their teacher provide. As students begin to approach driving age, they may start to think about the make, model, color, and features they would want in a car; but do they think about the cost or how that cost depreciates over time? The author used these questions to develop a Desmos activity that would…

The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study…

The purpose of this study is to explore the relation between the teaching of Mathematics and the teaching of Statistics at high school level in the South African Context. The study also examines and analyses examples of statistical teaching situations from both a mathematical and a statistical perspective with view to reveal the links between the…

Exploring non-Euclidean geometries is a common way for College Geometry instructors to highlight subtleties in Euclidean geometry. The concept of congruence, going undefined or informally defined in multiple axiomatic systems, is particularly susceptible to conflation with the idea of "same measure." Taxicab geometry provides a context…

Literacy, specifically reading mathematical text, is an essential component of developing deep mathematical understanding. Given the role that textbooks play in classroom instruction around the globe, it is useful to consider how features of curriculum design might influence classroom practice related to reading. Results from studies of a…

We explore the various Mathematica functions for performing Gaussian elimination, specifically when the linear system contains input parameters. On the one hand, we want the solution, perhaps heuristically found, to be in terms of the input parameters, and as general as possible. On the other hand, we must adhere to all necessary conditions and…

Earlier approaches to sense-making in mathematics have looked at the ways students comprehend a mathematical concept. Recent research suggests that some students make sense not only of mathematical objects that have a being, but also of objects that have yet to become. In such cases, learning mathematics is not just an act of comprehending a given…