To Örebro University

This dissertation aims to contribute to theoretical development and deepen the understanding of the role of programming in mathematic seducation. It explores the opportunities that visual programming offers young students to engage in mathematizing. The study approaches this from two complementary perspectives: programming as a goal of mathematics education and programming as a means for supporting mathematical development. Through iterative classroom interventions, the mathematizing of first-grade students’ programming was closely observed, providing detailed insights and enabling fine-grained analysis.

The theoretical contribution presents mathematizing as a framing concept for understanding students’ programming within mathematics education. Viewing programming through this lens clarifies its relevance to mathematics education. This is significant for researchers and teachers, helping them understand how to integrate programming into their teaching. By applying horizontal and vertical mathematization, the distinction between programming as a goal and as a means is elaborated.

The findings show how students demonstrate skills in problem formulation, complex problem-solving, and connecting multiple mathematical concepts into meaningful structures. However, the results also highlight challenges and limitations: using a programming environmental one does not guarantee engagement in problem-solving, and the choice of programming environment shapes the opportunities students have to explore mathematical concepts. These findings stem from positioning students at the center, and they carry significant implications for teaching practice.

Visual programming has become a popular way to provide young students with the opportunity to engage in complex problem-solving, often referred to as computational thinking. Most frameworks for computational thinking are comprehensive yet lack a fine-grained perspective on young students' engagement in programming. Therefore, this paper aims to unpack young students’ enacted problem-solving as they engage in open-ended programming in a visual programming environment (VPE). Through the lens of abstracting and decomposing, we contribute with a close-up understanding of how young students tackle complex problems in a VPE. Data generated in a Swedish first-grade classroom consisted of screen recordings and plans from 13 student pairs, working during four lessons to produce animated stories in ScratchJr. Through the analysis, six enactment patterns were constructed, showing that students as young as seven to eight years old can solve problems involving multiple components, arranging them into cohesive solutions. There were major differences in the problem-solving process involving whether or not the students followed their plans, captured in plan-driven and in-the-moment enactment patterns. Plan-driven enactment patterns elicited shifts within abstracting and decomposing practices, which we consider essential for programming since such enactment patterns more often elicit complex problem-solving. The results suggest that young students should be encouraged to use plans extensively when working in a VPE.

A growing body of research concerned with computational thinking (CT) has emerged the last couple of years, but there is still a lack of consensus about the definition of CT. There are also gaps in the understanding of how young children manifest CT. With this paper, we contribute to the field by taking an action perspective with the CT of K-3 students. The analysis focus on iterative acts of abstraction and decomposition as a core process that elicits development of CT. We call these iterative acts the Abstraction/Decomposition spiral (AD spiral). By illustrating the AD spiral through the actions of two first grade students, the analysis shows how visual representation of an emerging solution, and the development of a plan are two important elements when young students solve problems in a coding context, developing their CT.

There is a lack of knowledge in research about the intersection between programming and mathematics in an educational context relevant to young students. This paper aims to contribute to the research field with a theoretical framework that captures this intersection. The intersection is explored by interpreting open programming tasks in a visual programming environment through the lens of Bishop’s six mathematical activities, resulting in a framework that shows how mathematical activities intersect with either a context-independent programming process or context-dependent programming processes.

This study examines how a tinkering task in visual programming environments can provide opportunities for developing problem solving skills. We pursue this by analyzing eleven students in year 8 working with a tinkering task in a visual programming environment during a mathematics class. They were asked to create repeating patterns. Their work and discussions were analyzed through a lens of abstraction and decomposition, two elements of computational thinking. The analysis reveals how some students became thoroughly engaged in problem solving while others had a shallower experience of randomly manipulating the pre-made code. Since it was not the difficulty of the task but rather the random outcome of their manipulation of the code that determined whether they became engaged or not suggests that there is a need for support structures to fully tap into the potential of tinkering tasks to elicit problem solving.