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This article proposes an interconnected framework, Ways of thinking in STEM-based Problem Solving , which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry, systems thinking, and design-based thinking, which collectively contribute to adaptive and innovative thinking. It is argued that the pinnacle of this framework is learning innovation, involving the generation of powerful disciplinary knowledge and thinking processes that can be applied to subsequent problem challenges. Consideration is first given to STEM-based problem solving with a focus on mathematics. Mathematical and STEM-based problems are viewed here as goal-directed, multifaceted experiences that (1) demand core, facilitative ways of thinking, (2) require the development of productive and adaptive ways to navigate complexity, (3) enable multiple approaches and practices, (4) recruit interdisciplinary solution processes, and (5) facilitate the growth of learning innovation. The nature, role, and contributions of each way of thinking in STEM-based problem solving and learning are then explored, with their interactions highlighted. Examples from classroom-based research are presented, together with teaching implications., Competing Interests: Conflict of interestThere are no financial or non-financial interests that are directly or indirectly related to this submission., (© The Author(s) 2023.)

Much of the mathematics that children experience in school neglect the skills increasingly needed for citizenship, particularly the power of complex data to investigate and make sense of the world. We draw on the relatively new field of data science as a multi-disciplinary approach to investigate problems through analysis of massive, non-standard, incongruous and/or messy data. Our exploratory qualitative study had as its research question: What can children learn about citizenship when they engage with data science? The case study in this paper illustrated ways that children's learning about citizenship were enriched through an age-appropriate data science investigation. The study analysed classroom video from a Year 4 classroom (aged 9-10) over six lessons that integrated curricula in digital technologies, health, and mathematics. In these lessons, the children generated and analysed non-standard data and debated social, well-being and privacy issues as they considered their activities in cyberspace. The video data were analysed using a framework based on critical citizenship education literature that examined dimensions of power, collective engagement, individual responsibility and action. Three key findings emerged. First, the case study highlighted skills in citizenship education developed through data science, positioning children as agents and advocates. Second, the study showed how a complex data investigation in citizenship education was achievable with primary children through meaningful curriculum integration. This is important given that problems that citizens address are typically interdisciplinary. Finally, the findings revealed a gap between data science skills and those developed in the mathematics curriculum, and recommend ways that the maths curriculum could be updated., (© FIZ Karlsruhe 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.)