It is widely acknowledged that communicating mathematical thinking is complex, difficult, and often messy. In this article, the authors explore how mathematical thinking is communicated, providing examples of strategies for teachers and students to use in the mathematics classroom.

Over a sixteen-week term, the study dove into how chess could enhance math skills for eleventh graders at three public schools in Cartagena, Colombia. It assumed that chess would sharpen their minds and problem-solving prowess. Seventy-one pupils took part, trying out a chess-centric way of learning. Researchers used multiple statistical…

As a group of middle school mathematics teachers and teacher educators, the authors have focused their attention on using innovative practices coupled with high cognitive demand tasks to engage students, pique their interest in mathematics, and promote conceptual understanding. This article explores their three-act task design. In act 1, students…

To assist second language learners in becoming effective, aware, and reflective participants in higher education, support can be provided by integrating structured awareness raising approaches in the language curriculum. Drawing on self-regulation principles, such a structured awareness raising curriculum is most notably sustained by reflective…

A renewed emphasis was placed on ratio and proportional reasoning in the middle grades in the Common Core State Standards for Mathematics (CCSSM). The expectation for students includes the ability to not only compute and then compare and interpret the results of computations in context but also interpret ratios and proportions as they are…

This paper shows some research which analysed the didactic functionality of Personal Learning Environments (PLEs) and Open Educational Resources (OERs). They were created by students from the Master's Degree in Information and Communication Technologies applied to language teaching and processing, at Universidad Nacional de Educación a Distancia…

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features…

As a college biology instructor, I often see graphs in lab reports that do not meet my expectations. I also observe that many college students do not always adequately differentiate between good and poor (or misleading) graphs. The activity described in this paper is the result of my work with students to improve their graphing literacy. The…

These proceedings contain the papers and posters of the International Conference on e-Learning (EL) 2019, which was organised by the International Association for Development of the Information Society and co-organised by the Instituto Superior de Engenharia do Porto, in Porto, Portugal, July 17-19, 2019. The EL 2019 conference aims to address the…

This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…

The purpose of this study was to investigate undergraduate students' performance while exposed to complementary computational modelling activities to improve physics learning, using the software "Modellus." Interpretation of kinematics graphs was the physics topic chosen for investigation. The theoretical framework adopted was based on Halloun's…

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5…

Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…