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…

This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students' responses on a task regarding the…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

The importance of mathematical connections in teaching mathematics is broadly acknowledged in the literature. Nevertheless, more research is needed to clarify how different types of mathematical connections manifest in classroom interactions and how they can support student learning. This article uses the commognitive framework to analyse 15…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

This study aims to evaluate cognitive conflict in constructing mathematical concepts, based on thinking errors. The data were collected through observations of words or sentences, leading to the derivation of qualitative outputs. Furthermore, the results showed that the two selected subjects experienced cognitive conflicts regarding thinking…

This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

Mathematical tools allow us to clearly explain the phenomenon studied in administrative science. Various studies have shown that linear function is a concept, widely used in administration, as well as in other kinds of science, but difficult for students to grasp and assimilate as a tool in their studies. That is the reason that the objective of…

The goal of this design-based research study was the creation and evaluation of a mini-unit intended to foster perceptually grounded understandings of the concept of slope in middle-school students. Central to this unit was an innovative device designed to create a productive pedagogical space between student intuition for steepness and formal…

Conceptual understanding of calculus is crucial in the fields of applied sciences, business, and engineering and technology subjects. However, the current status indicates that students possess only procedural knowledge developed from rote learning of procedures in calculus without insight of core ideas. Hence, this paper aims to assess students'…

The transition from arithmetic to algebra is a well-known difficulty in school mathematics. In order to succeed, learners require inter alia a better understanding of algebraic symbols, equality, equations and working with negatives/subtraction. This article reports on a response pattern analysis (RPA) of learners' responses to six test items…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…