This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

The purpose of this study was to investigate how the 8th graders interpreted the equal sign in the pan balance activities they created on Scratch. Five eighth graders (4 girls and 1 boy) in Turkey participated in this study. Case study was employed as a qualitative research method. Data was gathered through the Scratch files created by the…

The goal of this paper is to explore dynamic geometry environments (DGE) as a type of computer programming language. Using projects created by secondary students in one particular DGE, we analyse the extent to which the various aspects of computational thinking--including both ways of doing things and particular concepts--were evident in their…

This study examined the effects of students' construction of computer-based educational games, using Scratch, on their mathematical equation-solving performance and their attitudes towards learning mathematics with the assistance of technology. A one-group, pretest-posttest quasi-experimental study design, was adopted. A total of 89 seventh grade…

This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received…

This paper describes a 54-hour summer institute for grades 6-12 mathematics and science teachers (N = 19) with a comprehensive approach to preparing teachers to use computational thinking (CT) in their classrooms, including training in Python computer programming with Lego® Mindstorms® robotics, mathematics content sessions, and opportunities to…

With an increased push to integrate coding and computational literacy in K-12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to…

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

In this paper, we describe the design and implementation of computer programming activities aimed at introducing young students (9-13 years old) to the idea of infinity, and in particular, to the cardinality of infinite sets. This research was part of the "WebLabs" project where students from several European countries explored topics in…

Recursion is an important concept for any computer science student to master. Many first year students develop the viable "copies" mental model of recursion and can successfully trace the execution of a simple recursive function. This article discusses a study focused on determining whether the ability to successfully trace a recursive…

Recreational Programming (RecPro) is the discipline that encourages the study of computer programming through ludic problems. Problems that are typically studied within this discipline are similar to those of Recreational Mathematics (RecMat), which sometimes leads to the confusion of these two disciplines. The objective for RecPro is to write…

One of the biggest problems in teaching Mathematics is the motivation of students (Kloosterman, 1997; Lambic, 2008). The core of this problem is insufficient comprehension of reasons by students, why they want to learn Mathematics and in which way they could apply acquired knowledge of Mathematics (Southwell, 1994; Musto, 2008). Since programming…

From the point of view of functional programming, a computational process to solve a problem is described as a mathematical function taking some arguments (corresponding to the data of the problem) and returning as a result its solution. Turtle Graphics can be used to describe the movements of a virtual turtle, which leaves a trail along his path…