Reading comprehension is essential for both knowledge acquisition and memory reinforcement. Automated modeling of the comprehension process provides insights into the efficacy of specific texts as learning tools. This paper introduces an improved version of the Automated Model of Comprehension, version 3.0 (AMoC v3.0). AMoC v3.0 is based on two…

In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

We reflect on the limitations of our research group's prior methods for assessing covariational reasoning which primarily used graphical tasks found in extant literature. Graphical tasks dominate the literature on covariational reasoning, and through our use of these tasks we came to question the heavy reliance on them. Our concerns led us to ask…

For pre-service teachers to develop learners' number sense, they need have a broad repertoire of non-standard calculation strategies. In this paper, we present an analysis of selected research literature from 2000 to 2022 on pre-service teachers' mental mathematics published in peer-reviewed journals. The results of this brief review indicate that…

It could be argued that the main goal of the teaching process is to create accurate projections of scientific models in the minds of individuals. In this context, it could be argued that it is important to determine the change and development of the mental models that individuals create for events/phenomena and related metaphors in this process.…

The brain alone is a complex organ in which all sensory, intellectual, emotional, and intuitive perceptions take place. Today, one of the research challenges in teaching-learning science is the answer to the question of how much the application of findings from neuroscience studies on learning can be effective in improving the quality of…

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…

Reading comprehension is key to knowledge acquisition and to reinforcing memory for previous information. While reading, a mental representation is constructed in the reader's mind. The mental model comprises the words in the text, the relations between the words, and inferences linking to concepts in prior knowledge. The automated model of…

The importance of statistical and mathematical literacy has been argued for a long time from social justice and equity perspectives. In this study, the famous brain teaser in math literacy, the Monty Hall Problem is used to investigate if schema revision is possible with a minimal intervention. The participants are 55 undergraduate students. Three…

Novel forms of technology, like shared Augmented Reality (AR) holograms, can spur the discovery of new hypotheses about cognition and how it is embodied and distributed. These holograms have affordances for exploration, collaboration, and learning that have never been seen before. In the present study, we examine the multimodal ways that high…

The purpose of this paper is to investigate the relationships between adult students' mathematical micro-identities (informed by positioning theory) and their mathematics (informed by radical constructivism). I used positioning theory to conduct a detailed turn-by-turn analysis of students' micro-identities, and to inform my models of students'…

Mathematics teacher questioning plays a significant role in students' learning. Research has persisted in analyzing teacher questioning from a cognitive perspective. Considering teaching as a relational practice, we explored teacher questioning from cognitive and affective perspectives. Data comprises 14 video-audio recordings, field notes,…

Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…

"Location and Transformation" skills are critical tools for navigating the world and establishing foundational steps for geometric reasoning associated with co-ordinate grids and the Cartesian plane. The contextual nature of using local landmarks to understand students' mental representation of large-scale space has the potential to…

Learning from text is a "constructive" activity in which sentence-level information is combined by the reader to build coherent mental models. With increasingly complex texts, forming a mental model becomes challenging due to a lack of background knowledge, and limits in working memory and attention. To address this, we are taught…