Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving…

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…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

This paper focuses on students' mathematical discourse emerging from interactions in the digital environment GeoGebra, in which one can construct virtual objects that realize mathematical signifiers and then interact with them. These virtual object realizations can become "dynamic interactive mediators" (DIMs) that influence the…

Inspired by the entering of computer algebra systems (CAS) in the Danish upper secondary school mathematics program, this article addresses, from a theoretical stance, what may happen when traditional procedures are outsourced to CAS. Looking at the commands "solve" and "desolve," it is asked what happens when such CAS…

This paper develops an understanding of the issues, interests and concerns within the mathematics education community related to the use of computers and other digital technologies in the teaching and learning of mathematics. It begins by arguing for the importance of understanding this landscape of interests and concerns, and then turns to the…

This paper describes a task-based dynamic geometry platform that is able to record student responses in a collective fashion to pre-designed dragging tasks. The platform provides a new type of data and opens up a quantitative dimension to interpret students' geometrical perception in dynamic geometry environments. The platform is capable of…

The symbolic manipulation capabilities of computer algebra systems, which we refer to as CAS-S, are now becoming instantiated within secondary mathematics textbooks in the United States for the first time. While a number of research studies have examined how teachers use this technology in their classrooms, one of the most important factors in how…

In this study, we examined special education students' use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8- to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems.…

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These "design principles" focus on the evolution of digital representations since the early 1990s, and we attempt to take forward our collective understanding of the cognitive and cultural…

We examine teachers' classroom activities with the spreadsheet, focusing especially on episodes marked by improvisation and uncertainty. The framework is based on Saxe's cultural approach to cognitive development. The study considers two teachers, one positively disposed towards classroom use of technology, and the other not, both of them…

The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new…

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his "big ideas" as he lived through the most amazing innovations in technology that have changed our lives…

We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

Wireless networks are fast becoming ubiquitous in all aspects of society and the world economy. We describe a method for studying the impacts of combining such technology with dynamic, representationally-rich mathematics software, particularly on participation, expression and projection of identity from a local to a public, shared workspace. We…