This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

Theoretical frameworks for mathematics teaching and learning technology-supported provide a systematic structure in examining the contribution of the tool to conceptual development. This study examines the processes for the use of spreadsheets and the mathematical development of the participants in the tasks for performing the conversions between…

The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is…

In 1981 Dixon introduced a clever idea for factoring large numbers. This idea has become the basis for many current factoring techniques. In this paper, we show how to implement the idea on the computer in the classroom. Additionally, pseudocode is given for finding examples suitable for demonstrating Dixon factorization.

During the last decade, many governments and ed-tech companies have demonstrated an increased interest in digital personalised learning, which resulted in a variety of often game-like adaptive learning environments. However, there has been limited attention for the impact of these personalised learning technologies on children's learning…

Numbers and variables often follow the same principles of arithmetic operations, yet numbers can be computed to a value whereas variables cannot. We examined the effect of symbols--numbers versus variables--on middle school students' problem-solving behaviors in a dynamic algebra notation system by presenting problems in numbers (e.g., 3+5-3) or…

To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and 3 in 3 + 5 - 3). We examined how symbols--specifically variables versus numbers--and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

Mathematics education is important for students with developmental disabilities. Additional research is needed that examines interventions to teach grade-level mathematics content to these students. In this single-case multiple probe across participants study, researchers explored the functional relation for four middle school students with…

In this article, we explore Whitehead's claim that experience is fundamentally affective. We do so in the context of an Italian primary school classroom featuring the use of the multitouch application "TouchCounts." We study the way in which the children and the iPad take each other up and the meanings of number and arithmetic that…

National assessments suggest that many students do not display proficiency with fractions. Considering that time and materials are precious resources, many educators are looking to use technology to provide supplemental instruction with low demand on the instructor. The current study utilized a multiple-baseline design to examine the effects of…

Connecting theory and practice in teaching is sometimes difficult, as it requires expensive or delicate equipment, thus limiting the teacher to giving demonstrations in which students are passive participants. Numerical mathematics, as an applied discipline, should be taught on real world examples. By using inexpensive Arduino hardware, we can…

The purpose of this study is to examine the effects of concrete and technology-assisted learning tools on developing the conception of place value, mathematical achievement and arithmetical performance of primary school 4th graders. The study group was comprised of three different primary schools. There were no group differences prior to…

It is hard to imagine that, eight hundred years on, the study of Fibonacci could affect the lives of teenagers in Australia. Or is it? A mathematics class of more able Year 9 students in a regional city of Western Australia feels that it has happened to them. Thirty-two students submitted a Fibonacci task as a mathematics assessment, with many of…

The rapid growth of the offer of available educational resources raises the issue of their appropriation by teachers. Although the term appropriation is widely used in mathematics education research, there is no clear conceptualization allowing researchers to understand the processes involved. In this paper, we attempt to fill this gap by…