Decimals and the related areas of ratio and proportion are recognised as one of the most challenging and complex areas of mathematics for young children to learn. In this study, four dynamic digital representations were used by Year 4 (9-10 years old) students in a set of video-recorded, individual task-based interviews to explore key concepts of…

Digital technology is indispensable for doing and learning statistics. When technology is used in mathematics education, the learning of concepts and the development of techniques for using a digital tool are known to intertwine. So far, this intertwinement of techniques and conceptual understanding, known as instrumental genesis, has received…

The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the…

Taking as its point of departure, situations arising in classrooms exposed to a heavy use of CAS, exemplified by the Danish upper secondary school mathematics program, the paper discusses the use of "old" cognitive frameworks of mathematics education as an alternative to more recent theoretical developments in the field. The paper draws…

We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative…

This paper discusses the conception of an online formative assessment tool in the field of functional thinking and focuses on the first cycle of a design-based research project. This tool is based on a preceding qualitative research project in an Austrian grade 7 class for examining students' conceptions as well as possible influences of designed…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

The authors provide a dynamic Ferris wheel computer activity that teachers can use as an instructional tool to help students investigate functions. They use a student's work to illustrate how students can use relationships between quantities to further their thinking about functions.

In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…

In this paper, we explore the relationship between scaffolding, dialogue, and conceptual breakthroughs, using data from a design-based research study that focuses on the development of understanding of probability in 10-12 year old students. The aim of the study is to gain insight into how the combination of scaffolding for content using…

The subject of the article is usage of modern computer technologies through the example of interactive geometry environment Geogebra as an innovative technology of representing and studying of geometrical material which involves such didactical opportunities as vizualisation, simulation and dynamics. There is shown a classification of geometric…

The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

This article explicates the development of top-view numeric coding of 3-D cube structures within a design research project focused on 3-D visualization skills for elementary grades children. It describes children's conceptual development of 3-D cube structures using concrete models, conventional 2-D pictures and abstract top-view numeric…

This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a…