This paper discusses the ways in which digitally enabled transformation in mathematics education could envisage a role for rationality in post-normal science and wicked problems. The scene is set firstly by reviewing the ways in which digital media have been designed and used in transformative mathematics education as a rationale for thinking about such media for wicked problem education. The problem is set in epistemological terms: can normal science approaches contribute to post-normal science? By considering the basic arguments regarding wicked problem education, I focus on the discussion of a specific constructionist digital tool called 'ChoiCo: Choices with Consequences', designed to embed mathematical ideas and facilitate mathematical reasoning, yet be about grappling with wicked problems. The final section discusses student discourse to set the scene for what such reasoning might look like in the context of grappling with wicked problems.

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 (Using, Discriminating, Generalizing, Synthesizing) model, introduced by Hoyles and Noss in 1987, in order to frame and analyze students’ mathematical meaning-making process involving setting out goals; posing conjectures; using mathematical ideas to test them; and exploring, generalizing, and expanding these ideas. This dynamic process was contextualized and connected to a flow of two different types of transitions: (1) transitions within the different representations of MaLT2 and (2) transitions beyond MaLT2, among the representational contexts of the digital microworld, artistic ideas, and abstract mathematics. In our analysis, we use this theoretical concept to trace the kind of mathematical meanings connected to multidisciplinary notions embedded in dance and music, such as synchronicity, symmetry, periodicity, and harmony, emerging from this learning context. We also look into the way these mathematical meanings were gradually evolved from being implicitly integrated in digital and artistic ideas to being reflected on and generalized.

Drawing upon constructionism and neo-materialist approaches on the role of physical activity and the human body in teaching and learning mathematics, this paper investigates the meanings constructed by students while collaboratively carrying out tasks focusing on the dynamic aspects of the concept of angle in the educational context of a 6(th) grade class of a public primary school in Greece. Paying particular attention to the specific material configurations at play, we try to analyse the construction processes through which angle was used both as a measure represented by a number and as a directed turn in the simulated 3D space of a digital tool that combines 3D Turtle Geometry and dynamic manipulation. Following a design-based research method, mathematical meanings are analysed as contingent assemblages involving gestures, embodied metaphors, navigation in virtual spaces, viewpoints, figural representations of 2D and 3D geometrical objects and ways of verbal and symbolic expression.

Could computational thinking be a strong tool for children to understand complex 21st-century issues? Our knowledge is limited since most designs focus on sequential programming and on the cognitive aspects of computational thinking. This paper discusses a design that integrates ill-structured socio-scientific issues with programming and other computational concepts, in a playful and meaningful context. The design, called ChoiCo (Choices with Consequences), builds on the idea of "integrated affordances"that enables layered computational access, allowing children to be players and designers of choice-driven simulation games. We elaborate on a design-based research that studied children’s activity, who progressively played, modified and co-created games that simulated real-world issues. We describe four strategies developed by the children to make sense of the simulated problems through a systems thinking approach. We also discuss how they formulated these strategies by utilizing the affordances of map design, data manipulation and coding. © 2021 ACM.

In this paper, we discuss the need for new approaches to research regarding coding to support students in developing practices in computational thinking, such as abstraction and decomposition, in multidisciplinary contexts. We explore students' activities with a tool integrating constructionist textual programming activity with game-based learning and specifically game modding. In this context, we designed a programmable 'design-to-play' game developed with the computational environment MaLT2. MaLT2 offers the affordances of textual programming, dynamic manipulation, and 3D navigation for the design of 3D animated models aiming to give children access to, otherwise, complex, computational and mathematical ideas. To develop an understanding of children's learning activity regarding computational practices, we organised an empirical study with middle-school students, who played a game called 'Code-the-Mime'. It is a charades-based game in which the players manipulate, programme, and modify a digital human model to describe a word to their teammates. The preliminary findings indicate that the affordances of MaLT2 in conjunction with the game context enabled students to express and develop key computational practices, including decomposition, pattern recognition, analysis and abstraction, in a meaningful and multidisciplinary context. Practitioner notes What is already known about this topic Computational Thinking is considered a key 21(st)-century skill in preparing the young to become digital citizens. It involves concepts and practices that can be used to solve problems computationally across multiple fields. However, there is still limited knowledge of how students develop computational practices, such as abstraction, pattern recognition, decomposition, and how they may express and apply them in diverse contexts. Students' engagement with computational practices is unlikely to be supported either by closed, simplified coding tasks or higher-level advanced programming exercises. There is a need to clarify the manifestation of these practices and how they can be realised and expressed and used by learners in meaningful and transdisciplinary contexts. What this paper adds It suggests the design of constructionist computational games that integrate design and programming into the gameplay, aiming to engage students with computational practices in a multidisciplinary, authentic context. It provides an example of a 'design-to-play' charades-like game, developed in a 3D modelling programming environment, that embeds real-life representations into computational design, to enable 'syntonic learning' of computational practices. Furthermore, it analyses student learning activity to elaborate on arguments and issues related to this approach. Implications for practice and/or policy There is added value in disconnecting computational thinking from positivist diagnostic approaches related to respective concepts and studying it in ways more related to realistic problem-solving situations and multidisciplinary contexts. The study contributes to the scientific clarification of computational practices concerning how they are being realised and expressed by the students in different contexts through an original example of educational practice. The discussed approach and tools can contribute to the design and development of innovative digital media, embedding affordances for concepts and practices while maintaining relevance and interest for their users.

This entry explores computer-based learning (CBL) designs that are informed by the learning theory of constructionism. First, it discusses different definitions and types of CBL and explores the pedagogical approaches that underpin CBL designs through a brief history of CBL in education. Next, it elaborates on the role of the constructionist paradigm in CBL and presents different CBL designs that are based on constructionism. Then it focuses especially on the use of constructionist CBL approaches for supporting students to cultivate their computational thinking. The final part discusses the educational challenges and the near future of constructionist CBL.

Buteau, Sacristin and Muller's target article raises the pertinent issue of how to describe a sustained undergraduate course on computational thinking and programming for mathematical learning. There is so little work on this issue that it is worthwhile to reflect on this study and to raise questions regarding the options and tools available or needed to understand sustained constructionist activity. Here, I focus on questions regarding how to understand the instructor's craft knowledge in practice and what constructionist mathematical learning may look like when programming is at the service of engagement with mathematical concepts.