To Örebro University

This study contributes to the call for influencing practice by increasing attention to how learning environments can be designed to support learning in statistical inference. We report on a design experiment in secondary school (students 14–16 years old), that resulted in a set of lessons with the learning goal of teaching students how to apply concepts and principles of hypothesis testing for making an inference as to whether or not students in secondary school can taste the difference between two brands of cola soda. The design experiment resulted in four design principles for a simulation-based approach for learning hypothesis testing in secondary school. The design principles highlight the combination of practical and digital simulations of samplings. They stress the need for using random generators that allow for high reliability in collecting sample data and introduce a simulation-based method for determining p-values, i.e. to quantify how likely or surprising a sample result, or a result more extreme, is under a null hypothesis.

In this handbook chapter, we suggest that in designing resources for mathematics education, it is important that the designers explicitly contemplate whether and how the resources contribute to teaching. We guide the readers in considering how instructional design practices and the resulting resources always convey a specific positioning of the teacher within the educational process and expectations of teaching as a profession at large. We draw on conceptualizations of teaching as a complex endeavor in proposing that designing for supporting mathematical learning directly is insufficient. We then discuss two design research examples in which designing for teaching was overtly taken as a goal, and where digital resources played a role. We use these examples to derive three types of design tasks that, we propose, characterize designing for teaching: designing for resource relevance and clarity to the teacher and for resource viability in the teacher’s classroom. We comment on contributions of digital resources to these tasks.

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.

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.

The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment tha taddressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in lower-secondary school (students 14–16 years old) and consisted of three lessons on pattern generalization. Each lesson was tested and refined twice by the research team. The design experiment resulted in the emergence of the FlexTech orchestration, which provided teachers and students with opportunities to utilize the flexibility to construct, switch and mark in the orchestration of an instrumental math-GoGAR.

This literature review looks into the roles that programming and mathematics can take in relation to each other in an educational environment. This is done by retrieving papers from Web of Science and MathEduc on mathematics and programming in education, prior to university level, and analysing their tasks through a lens of Instrumental Orchestration. The four different exploitation modes identified are manipulating a physical entity, manipulating a virtual entity, creating own interactive environment and creating, testing and refining mathematical algorithms. Depending on how mathematics and programming are positioned in the four modes, the emphasis on mathematics and programming varies, resulting in different outcomes of the lessons.

Mathematics education is still behind in the implementation of digital technology. Digital technology can support classroom talk, but this potential needs to be further explored. This study reports on a project that develops and explores task design principles, through a series of interventions, that are intended to utilize digital technology to enrich mathematics lessons. The results consist of three design principles together with their theoretical and empirical arguments from analysis of a lesson series about pattern generalization. The three principles exploit opportunities provided by technology to make reasoning available for examination to all students, and to focus students’ attention between different aspects of mathematical reasoning.

Implementing research results to school practice with a high level of fidelity is a big challenge for the research community in mathematics education. Technology induced teaching of mathematics adds further challenges to such issues since it is an area where many teachers are unexperienced. In this paper, we report on a literature review based on papers published in SERJ and which reports on studies involving the investigation of a technology induced intervention. The review is guided by a newly developed framework, which provides dimensions for analyzing issues argued to be crucial in implementing research results. Based on results of the literature review I discuss themes for developing research on technology induced teaching of statistics to face challenges in the implementation of the research results in the practice.