In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was…

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those…

The present study investigates the empirical separability of mathematical (a) content domains, (b) cognitive domains, and (c) content-specific cognitive domains. There were 122 items representing two content domains (linear equations vs. theorem of Pythagoras) combined with two cognitive domains (modeling competence vs. technical competence)…

We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students' understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit…

In a recent paper, Hu, Ericsson, Yang, and Lu (2009) found that an ability to memorize very long lists of digits is not mediated by the same mechanisms as exceptional memory for rapidly presented lists, which has been the traditional focus of laboratory research. Chao Lu is the holder of the "Guinness World Record" for reciting the most decimal…

This article reports on the results of research, the objective of which was to document and analyze the manner in which students relate different representations when solving problems. A total of 20 students attending their first year of university studies took part in the study. In order to design the problem, the underlying information in each…

Recursion is an important concept for any computer science student to master. Many first year students develop the viable "copies" mental model of recursion and can successfully trace the execution of a simple recursive function. This article discusses a study focused on determining whether the ability to successfully trace a recursive…

Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

One of most notable features of existing body of research in transition seems to be the absence of a theoretical model. The suggestion we present in this paper--to view and understand the high school to university transition in mathematics as a modern-day rite of passage--is an attempt at defining such framework. Although dominantly reflecting…

The aim of this research is to devise a cognitive tool for meeting the diverse needs of learners for comprehending new procedural knowledge. A model of affordances on teaching fraction equivalence for developing procedural knowledge for adding/subtracting fractions with unlike denominators was derived from the results of a case study of an initial…