Second-order covariation is a form of mathematical reasoning that needs to be characterized both concerning students' cognitive processes and the design of tasks that promote it. This contribution aims to shed light on these two issues by comparing data related to the same learning experiment performed in two different learning environments:…

Geometric habits of mind (GHoM) are the approaches that individuals use to solve geometry problems. This study aimed to determine the effect of dynamic geometry software (DGS) in activating the GHoM of pre-service mathematics teachers. The study was conducted with six teacher candidates who were enrolled in a semester-long course titled…

Prior work has established that cognitive and perceptual processes influence students' attention to notational structures in mathematical expressions, which in turn affects their problem-solving approaches and performance. Advances in educational technology provide opportunities to further investigate these processes, improve student learning, and…

This research explores two methods through which ten preservice math teachers develop an understanding of trigonometric values. Using the unit circle, preservice math teachers engage in knowledge-building activities such as paper folding and GeoGebra application. Grounded in Altman and Kidron's 2016 didactical design research, this study examines…

Traditional rote learning methods often fail to adequately develop reasoning skills in mathematics, particularly among pre-university students. This study addresses challenges in fostering mathematical reasoning abilities, as evidenced by declining TIMSS results and resistance to pedagogical innovations. My online teaching with GeoGebra (MyOT_G+)…

This study is the extension of our previous visualizing study on the commognition processes in computer-supported one-to-one tutoring. With the help of the scale of commognitive responsibility score, we found that the main triggers of the commognition process shift are the positive transfer of knowledge and cognitive conflict. On the basis of…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

A promising method to support game-based learning is to facilitate learners' externalization of cognitive and metacognitive processes. Externalizing Problem Representation (EPR) refers to a cognitive behaviour in which a learner constructs her own representations overtly. The purpose of this study is to investigate whether learning supports…

Remedial/developmental and introductory university mathematics courses have a long history of high attrition rates. Recently, university administration and mathematics departments have been considering technological solutions, and one such solution is computer-adaptive-instruction (CAI). In fact, CAI has been touted as a "silver bullet"…

Tablets have much to offer children with learning difficulties, but evidence of their effectiveness to teach academic skills is limited and cannot be easily separated from the quality of the software. This paper analyses data from 3 iterative cycles of designing an app for children with Down syndrome to support their awareness of quantity through…

An active learning environment is a technology-enriched and interactive physical space convenient for applying cooperative, active and engaged learning. It allows focus on engaging experiences for students and faculty. This study investigated pre-service teachers' perceptions and experiences in courses in an active learning environment. Eighty…

Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

In mathematic courses, construction of some concepts by the students in a meaningful way may be complicated. In such circumstances, to embody the concepts application of the required technologies may reinforce learning process. Onset of learning process over daily life events of the student's environment may lure their attention and may…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

In an attempt to study the emerging questions about design of mathematical tasks that could support the solving of challenging problems, we designed two settings of interactive diagrams that share an example represented as an animation of multi-process motion but differ in their organizational functions. The interactive settings, each comprising…