Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

In this report, we present cases where students constructed new quantities through operating on quantities that does not fit the definitions of existing theories on quantitative operations. As a result, we identified five quantitative operators--operators that can be used on single qualities in order to transform the quantity to a new…

This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…

One of the most difficult types of arithmetic word problems in primary school is compare problems. Among these problems, the most problematic are those in which the relational term is not consistent with the arithmetic operation required for the solution. This study investigates how 10-11-year-old primary school pupils' read and interpret compare…

The use of online learning objects in teaching algebra is examined in this research, emphasizing its benefits, such as accessibility, flexibility, interactive involvement, differentiated instruction, quick feedback, and links to real-world situations. Strategies include conceptual comprehension, interactive practice, individualized learning,…

Feedback is a powerful instructional tool. However, even after decades of thorough studies, some questions regarding feedback remain unanswered. In particular, it is yet to be determined whether feedback elaboration is indeed helpful to students. In the study presented here, we take a learning analytics approach to investigate the effect of…

As an interdisciplinary and multicultural educational framework takes the centrality of the delivery of 21st-century education across all levels, this study attempts to address the competencies that prospective and neophyte teachers need to possess to effectively design contextualized education. Through stepwise multiple regression analysis,…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

Repeating patterning proficiency predicts students' later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in…

In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

Teacher perception is one of the most important factors determining classroom teaching practices. Multiple representations are used extensively in mathematics classrooms, especially in developing conceptual understanding. The data in this study, which aims to compare Turkish and US middle school mathematics teachers' perceptions of multiple…

This article examines the cognitive structures of secondary school mathematics pre-service teachers (PSTs) in Mayotte regarding fundamental mathematical concepts such as theorem and proof. A deep understanding of these concepts is essential for effective teaching practice. To explore this, we employed the free word association test, a…

In this paper, we report the analysis of thought processes used by Pre-Service Teachers' (PSTs') through clinical interviews as they solved an algebra task involving a linear pattern. The PST's were asked about a mathematical model they had constructed to describe a pattern problem. Our analysis suggests that conflict factors arise due to…