We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…

3D geometry is an essential concept in mathematics because it relates to real-world experiences and numerous mathematical topics. However, some students still have difficulty understanding this geometry. Therefore, this study aims to identify and describe students' epistemological obstacles to the dimensions of representation, spatial structure,…

This article proposes an interconnected framework, "Ways of thinking in STEM-based Problem Solving," which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry,…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

In the first main section of this thesis, I investigate superirreducible polynomials over fields of positive characteristic and also over [set of rational numbers] and [set of integers]. An n-superirreducible polynomial f(x) is an irreducible polynomial that remains irreducible under substitutions f(g(x)) for g of degree at most n. I find…

The notion or expectation of simplifying final mathematical results remains problematic in that it is ill-defined, tied more closely to algorithmic versus conceptual understanding, and decontextualized from the content, purpose, and application of the mathematics in question. In this article, the authors advocate for a tool-focused view of…

Background/purpose: Although mathematical representation ability is a significant ability and an interesting topic to study, quite a few researchers have studied this ability, and even fewer have examined it through the implementation of epistemic learning patterns based on problem-solving. In fact, this learning pattern is epistemic and makes…

This paper investigates the connection between the spiral teaching method and mathematical rigor in K-12 education. Defining rigor as a balanced integration of conceptual understanding, application, and procedural fluency (contrasting it with rote learning), the paper posits that the spiral approach cultivates this rigor. By revisiting…

The study aimed to determine the mistakes of students in operations with algebraic expressions, and their misconceptions that may lead to errors. The study adopted case study method, one of the qualitative research models. The participants were composed of 48 (24 boys, 24 girls) randomly selected among 8th grade students in three different classes…

It is common for students to make mistakes while solving mathematical problems. Some of these mistakes might be caused by the false ideas, or misconceptions, that students developed during their learning or from their practice. Calculus courses at the undergraduate level are mandatory for several majors. The introductory course of…

ChatGPT, an artificial intelligence-supported chatbot, has become a resource in the field of education for students across various disciplines. The conversation that unfolds based on the user-generated questions and ChatGPT's responses implies the emergence of an argumentation between the student and ChatGPT. In this study, the argumentation…

The aim of this study is to determine the distribution of the questions in an 8th grade mathematics textbook in terms of the categories (mathematical content, mathematical literacy contexts, mathematical processes, PISA mathematics proficiency scale levels, and item types) within the PISA mathematics literacy framework. Investigation of the…

The aim of this study was to examine the proportional reasoning skills of seventh-grade students before and after the implementation of STEM activities involving proportional and non-proportional relationships. Case study, one of the qualitative study methods, was used in the research. The data for the study was obtained from eight students. Seven…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students'…