This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

Despite the proliferation of video-based instruction and its benefits--such as promoting student autonomy and self-paced learning--the complexities of online teaching remain a challenge. To be effective, educators require extensive training in digital teaching methodologies. As such, there's a pressing need to examine and comprehend the…

The National Council of Teachers of Mathematics (NCTM) has been emphasizing the importance of teachers' pedagogical communication as part of mathematical teaching and learning for decades. Specifically, NCTM has provided guidance on how teachers can foster mathematical communication that positively impacts student learning. A teacher may have…

I present my perspective on the design process in this article, arguing for a focus on student learning and "slow design" that stems from knowledge of mathematics and their support system in the learning process. I have a question about the design process academization and task design research direction. Numerous examples from my work at…

In this study, we evaluate the impact of rehearsing teaching skills in a mixed-reality classroom simulator on graduate teaching assistants' (GTAs) instructional practices as well as undergraduate student learning outcomes. The simulator training is intended to provide GTAs opportunities to deliberately practice essential pedagogical skills that…

This pilot study explores the effectiveness of a strategy for overcoming post-primary students' misconceptions within the topic of algebra. Although central to the study of mathematics, algebra can be an area of difficulty for many students. A misconception is typically classified as flawed understanding of a concept causing repeated errors, and…

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence--namely, in Toulmin's sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument…

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…

Purpose: The purpose of this scientific monograph is to show new and creative approaches to different school subjects in primary and secondary level. Methodology: Interdisciplinary and international comparative approaches were used. Now according to the 7th Framework Program, the preferred form of Science Education (www.scientix.eu) is preferred…

The 9th International Conference on Educational Data Mining (EDM 2016) is held under the auspices of the International Educational Data Mining Society at the Sheraton Raleigh Hotel, in downtown Raleigh, North Carolina, in the USA. The conference, held June 29-July 2, 2016, follows the eight previous editions (Madrid 2015, London 2014, Memphis…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…