Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we…

Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

The necessity for students to clarify their own cognitive structure and the amount of their knowledge mastery for self-reflection is often ignored in building the student model in the adaptive model, which makes the construction of the cognitive structure pointless. Simultaneously, knowledge forgetting causes students' knowledge level to fall…

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…

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…

Eye tracking technology enables the visualisation of a problem solver's eye movement while working on a problem. The eye movement of experts has been used to draw attention to expert problem solving processes in a bid to teach procedural skills to learners. Such affordances appear as eye movement modelling examples (EMME) in the literature. This…

Background/purpose: This study analyzes the commognition of students with low Working Memory Capacity (WMC) when solving calculus problems, particularly in integral material. Commognition, which merges cognition and communication, is explored through four indicators: keywords (stating knowns and unknowns), visual mediators (graphical…

In this exploratory work, the discourse of first-year computer engineering undergraduate students of graph theory was analyzed with the aim of improving the teaching of this branch of mathematics. The theoretical framework used is the theory of commognition, specifically, we focus on commognitive conflicts because they are learning opportunities…

Background/purpose: Academic reading presents significant challenges for English for Specific Purposes (ESP) learners, especially when processing structurally dense expository texts in STEM disciplines. This study aims to assess the impact of text-structure-aligned goals on students' reading comprehension and written summarization, while exploring…

This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…

The translation between mathematical representations was one of the indicators in understanding mathematical concepts. Understanding the things related to the process of student representation translation was very important in learning mathematics. One of the activities that plays a role in translation was unpacking the source. This study aimed to…

In this report, we present how one prospective elementary teacher (PT) engaged in the Ant Farm Task, which we designed to investigate PTs' reasoning about coordinate systems. We highlight the cognitive resources the PT drew upon in solving the task via the establishment of a Cartesian coordination and consider educational implications. [For the…

Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students' thinking on graphs as well as their potential misinterpretations and difficulties in interpreting graphs. In…

Modeling is an integral part of many computing-related disciplines and thus also represents a curricular core component in computing education in tertiary education. Competence models in which modeling is integrated at least to some extent already exist in some of these disciplines. However, for the core component of graphical modeling, a…

When comparing social science phenomena through a time perspective, absolute and relative difference (RD) are the two typical presentation formats used to communicate interpretations to the audience, while time distance (TD) is the least frequently used of such formats. This article argues that the chosen presentation format is extremely important…