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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.

This study investigated sixth-grade students' development of multidisciplinary models involving the integration of mathematics, science, and statistics, together with shared STEM practices. Mathematics and science featured a reciprocal relationship within the real-world context of tsunami inundation. Experimenting with water tubs comprising "landmasses" and "shore slopes" of varying angles, students explored how varying the slope of the shoreline affects the inundation distance. Given that organising and structuring data are essential to the creation of models as systems of representation, students' modelling revealed a basic understanding of key statistical concepts and processes, including variation and covariation, and an ability to identify trends both within and across data sets. Students were able to apply their learning in recommending ways of minimising the impact of a real-world tsunami, demonstrating how such an investigation can facilitate understanding of natural phenomena. The overall findings indicate how elementary-grade students can successfully engage in independent multidisciplinary modelling within integrated STEM investigations and develop important conceptual understandings in the process.

How might fourth graders address the problem of measuring the size of a leaf? And why might their classroom teachers choose such a shape to measure? One group of fourth-grade students in an urban Australian school were interested in knowing the sizes of leaves on a passionfruit vine growing at their school. The children were excited after a visit from an agricultural scientist, who shared his knowledge about photosynthesis. This article presents mathematical modeling explored in their classroom, as students explored ways to predict the surface area of a leaf (leaf size), within an agricultural science context involving fruit production. The first author and her co-teacher, who regularly shared teaching responsibilities, worked with an agricultural scientist in designing the inquiry for their fourth-grade class.

This article reports on a study in which third-grade students (8-9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained the outcomes, quantified their chances of colour selections, and created two representations displaying the probabilities. Children displayed awareness of randomness and variation, together with proportional reasoning, as evident in their identification of one or more colours as having a greater chance of being selected, or equal chances when proportions of colours were equal. Evidence of children's metarepresentational competence appeared in their creation of two representations to display their probabilistic outcomes, with bar and circle graphs, as well as stacked bars, created. The inclusion of their own forms of inscription revealed a range of probability and statistics understandings. In selecting and justifying their preferred representations for conveying their outcomes, students favoured both bar and circle graphs, with a focus on how accurately, effectively, and efficiently their representation displayed the data, with the importance of the inscriptions highlighted.

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.

Computational thinking is widely recognized as important, not only to those interested in computer science and mathematics but also to every student in the twenty-first century. However, the concept of computational thinking is arguably complex; the term itself can easily lead to direct connection with "computing" or "computer" in a restricted sense. In this editorial, we build on existing research about computational thinking to discuss it as a multi-faceted theoretical nature. We further present computational thinking, as a model of thinking, that is important not only in computer science and mathematics, but also in other disciplines of STEM and integrated STEM education broadly.

An Australian longitudinal study of 319 Kindergartners developed, implemented and evaluated an intervention, the Pattern and Structure Mathematics Awareness Program (PASMAP). It comprised of repetitions and growing patterns, structured counting and grouping, grids and shapes, partitioning, additive and multiplicative structures, measurement and data, and transformations. Each component was implemented, evaluated and refined as a cyclic process in collaboration with co-operating teachers, replacing and extending the regular mathematics program. An innovative pedagogical approach was effective in engaging students in modelling and representing, visualising and generalising, and sustaining their learning. On an interview-based measure of mathematics achievement pre- and post-intervention, there were significant differences found between the intervention and comparison groups at the end of the intervention year (p < 0.026) and highly significant differences found at the follow-up assessment (p < 0.002) ten months later. A descriptive analysis showed students' progress through five levels of structural development where most students advanced through one or more levels as they progressed through the program. The upper third of students demonstrated emergent generalisations at the structural and advanced structural level which supported early algebraic thinking. Less-able students also showed impressive growth--half of these students moved from pre-structural to at least emergent level over the duration of the program. Students' growth in structural development is exemplified at five points during the intervention through fine-grained analyses of mathematical representations and explanations. The study demonstrates that Kindergartners are capable of developing mathematical patterns and structural relationships well beyond curriculum expectations.

As STEM education becomes more prominent at the school level, many possibilities could be suggested for beginning experiences to create a foundation for young students as they begin their journeys with respect to STEM learning. The research reported here is based on the premise that building statistical understanding will enhance young students' learning as they engage with STEM learning experiences. This paper hence reports on an activity created to introduce students in Year 3 to the concept of statistical variation with data in a STEM-related context where variation occurs in an easily measured and realistic fashion. Students' capabilities to appreciate the fundamental nature of statistical variation and use it for comparison in a STEM context were assessed through responses in student workbooks, to questions on an end-of-year survey, and in individual interviews. The results illustrate the beginning stages of student thinking about variation and the use of data when learning is embedded within a STEM context. They show that students can take on the idea of variation and use it in explaining their experiences with the hands-on activity, which involved comparisons of a hand-made and machine-made product.

This article reports on a 4th-grade problem activity implemented as part of a 4-year longitudinal, design research study across grades 3-6. The activity integrated the four STEM disciplines through a focus on design. Following investigations of their feet measurements and shoes, two classes of 9-year-olds explored the roles of designers and engineers in shoe manufacture, experimented with materials, and then designed and constructed their own pairs of shoes. A conceptual framework, "towards informed design" (adapted from Crismond and Adams in J Eng Educ 101(4):738-797, 2012), is advanced for exploring students' learning while designing. Drawing on this framework, consideration is given to students' use of design strategies, including posing their own problems and design aims, sketching their shoe designs, testing and reflecting on their products, and redesigning and reconstructing. Although more students expressed a desired shoe than a design problem to be solved, they nevertheless were able to develop their own design aims and constraints. Designing a functional and aesthetically pleasing shoe was most common, together with comfort. Material properties typically less accessible to young students (water repellent, durable, insulated) were also considered in their designs. Students' attention to detail in their design sketches (e.g., style features, 2-D and 3-D perspectives, measurements, materials) suggested they had progressed beyond beginning designers. Likewise, students' increased satisfaction with their redesigns, displaying knowledge of material properties, measurement and spatial skills, and design processes indicated progress towards informed design.

Science, technology, engineering, and mathematics (STEM) education is an emerging initiative in Australia, particularly in primary schools. This qualitative research aimed to understand Year 4 students' involvement in an integrated STEM education unit that focused on science concepts (e.g., states of matter, testing properties of materials) and mathematics concepts (e.g., 3D shapes and metric measurements) for designing, making and testing a strong and safe medical kit to insulate medicines (ice cubes) at desirable temperatures. Data collection tools included student work samples, photographs, written responses from students and the teacher, and researcher notes. In a post-hoc analysis, a pedagogical knowledge practice framework (i.e., planning, timetabling, preparation, teaching strategies, content knowledge, problem solving, classroom management, questioning, implementation, assessment, and viewpoints) was used to explain links to student outcomes in STEM education. The study showed how pedagogical knowledge practices may be linked to student outcomes (knowledge, understanding, skill development, and values and attitudes) for a STEM education activity.

In this article, we report on sixth-grade students' responses to a set of problem activities that required the application of mathematics, science, and engineering knowledge in designing and constructing a paper bridge that could withstand an optimal load. Increasing students' application and awareness of their disciplinary learning and how they are applying this in an integrated STEM activity remains a challenge for educators. In addressing this issue, we included a focus on knowledge reflection and knowledge scaffolding through thought-provoking student workbooks. Among the findings are students' capabilities in planning, designing, reflecting, constructing, and redesigning. Students' planning indicated that they could justify their proposed bridge type/s, which often included a combination of types, by referring to their STEM understandings. At the same time, students remained cognizant of the problem boundaries. Students' design sketches indicated an awareness of the problem constraints, an understanding of basic engineering principles, and an application of mathematics and science knowledge. Students' reflections on their actions helped them to improve their bridge constructions. Suggestions are presented for knowledge scaffolding to facilitate the flexible and innovative application of STEM learning to new problem situations.