The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

Many areas of mathematics naturally lend themselves to machine-based computing environments, which suggests that computational environments may serve as useful mediating tools for the teaching and learning of mathematical content. While some mathematics classes are leveraging the use of computational tools, the implementation of computer…

In this article, we seek to understand how university students learn to use programming as an instrument for 'authentic' mathematical investigations. We use the instrumental approach as a framework, focusing on how the transformation of the programming language into an instrument requires that the user develops or mobilizes multiple schemes at…

This article reports on an exploration of how second-graders can learn mathematics through programming. We started from the theory that a suitably designed programming language can serve children as a language for expressing and experimenting with mathematical ideas and processes in order to do mathematics and thereby, with appropriate tasks and…

This study aims to investigate students' computational thinking (CT) through mathematical tasks integrated with programming in Scratch. Participants completed four tasks that required students to solve coding problems, which were focused on prime numbers and the prime factorization algorithm. The study was designed as a case study and the unit of…

In this research, we explore the potential for computational thinking (CT) to benefit the spatial reasoning abilities of thirty-three middle-school students (aged 11-13) in grades 6 and 7. There is an increasing focus on the explicit development of spatial reasoning throughout the mathematics curriculum, such as geometry, as students' success in…

We investigate three 8th-grade students' mathematical meanings developed in the context of using linked representations to generate animations of figural models tuned in musical rhythm in "MaLT2," a programmable Turtle Geometry in 3D resource affording dynamic manipulation of variable values. We adopted a modified version of the UDGS…

We present here the lessons learned by iteratively designing a tutorial for first-year university students using computer programming to work with mathematical models. Alternating between design and implementation, we used video-taped task interviews and classroom observations to ensure that the design promoted student understanding. The final…

While programming was introduced to mathematics classrooms in the 1980s, emerging robotic technologies have encouraged more widespread integration of these technologies to support the development of K-12 students' mathematical reasoning. The recent emphasis of programming and computational thinking in K-12 education has highlighted the need to…