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…

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…

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…

In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative…

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

There is considerable interest in the cultivation of student graphic literacy among educators and researchers, especially in the sciences. Previous research, however, has shown that many students manifest difficulties in using diagrammatic representations. One explanation that has been proposed to account for these difficulties is that certain…

The use of external representations has a potential to facilitate inquiry learning, especially in hypothesis generation and scientific reasoning, which are typical difficulties encountered by students. This study proposes and investigates the effects of a three-dimensional thinking graph (3DTG) that allows learners to combine in a single image,…

Gesturally controlled information and communication technologies, such as tablet devices, are becoming increasingly popular tools for teaching and learning. Based on the theoretical frameworks of cognitive load and embodied cognition, this study investigated the impact of explicit instructions to trace out elements of tablet-based worked examples…

A growing body of literature has identified quantitative and covariational reasoning as critical for secondary and undergraduate student learning, particularly for topics that require students to make sense of relationships between quantities. The present study extends this body of literature by characterizing an undergraduate precalculus…

In third grade the focus on math word problems becomes prominent. In the limited third grade research, teacher-mediated explicit instruction with multiple exemplars, teaching students to use visual representations, and the incorporation of self-strategies, have proven effective. For these practices to reach their full potential though, their…

With the advances in mobile network technology, the use of portable devices and mobile networks for learning is not limited by time and space. Such use, in combination with appropriate learning strategies, can achieve a better effect. Despite the effectiveness of mobile learning, students' learning direction, progress, and achievement may differ.…

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…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

The authors explore the role of comparison in improving graph fluency. The ability to use graphs fluently is crucial for STEM achievement, but graphs are challenging to interpret and produce because they often involve integration of multiple variables, continuous change in variables over time, and omission of certain details in order to highlight…

One measure of the impact of a new idea in geography education is how well it is incorporated into teachers' everyday practice. "Spatial thinking" is not really a new idea in geography education; spatial analysis has long been one of its core traditions, but the use of the term is novel and only beginning to be widely used. By spatial thinking the…