# STEM education in the primary years to support mathematical thinking: using coding to identify mathematical structures and patterns

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## Abstract

Cross-curricula opportunities afforded by STEM education (Science, Technology, Engineering and Mathematics education), supports an environment where students can develop twenty-first century competencies. One approach to addressing cross-curricula opportunities in STEM education is the introduction of computer science (computer programming—coding) as a basic skill/literacy for all students. Coding (computer programming) is a language that draws on a set of syntax rules (or blocks for primary school students) that informs a computer program to execute a series of functions. While there is evidence that computational thinking (the thinking used for coding/computer programming) and conceptual development in mathematics are connected, there is limited research related to how such a confluence applies to primary school students. The aim of this article is to provide insight into how mathematical knowledge and thinking, specifically the identification of mathematical patterns and structures, can be promoted through engagement with coding activities. The data for this article is drawn from year 2 students (n = 135) in two Australian primary schools. A teaching experiment approach was adopted for the study with a small intervention group (n = 40) undertaking coding lessons for 6 weeks. Data collection comprised of pre-test and post-tests with a focus on patterning and coding in conjunction with video-recorded lessons. The study provides evidence that the learning that takes place through coding instruction can lead to higher levels of students’ mathematical thinking in relation to identifying mathematical patterns and structures that can lead to generalisations.

## Keywords

Mathematical thinking Primary Patterning Coding## Notes

### Acknowledgements

I would like to thank Emeritus Professor Elizabeth Warren for her continued mentorship and feedback for this study. I would also like to acknowledge Angela Hennessey for her work as the research assistant on this project, as well as the schools and students who have participated in the study. This research first appears in a MERGA conference paper (Miller and Larkin 2017).

## References

- Ackerman, E. (2001). Piaget's constructivism, Papert's constructionism: What's the difference? http://learning.media.mit.edu/content/publications/EA.Piaget%20_%20Papert.pdf. Retrevied October 24, 2018.
- Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2018).
*The Australian curriculum.*https://www.australiancurriculum.edu.au/. Retrieved May 16, 2018. - Benton, L., Hoyles, C., Kalas, I., & Noss, R. (2017). Bridging primary programming and mathematics: Some findings of design research in England.
*Digital Experiences in Mathematics Education,**3*(2), 115–138.CrossRefGoogle Scholar - Blanton, M., & Kaput, J. (2011). Functional thinking as a route into algebra in the elementary grades. In J. Cai & E. Knuth (Eds.),
*Early algebraization: A global dialogue from multiple perspectives*(pp. 5–23). Berlin: Springer.CrossRefGoogle Scholar - Clark-Wilson, A., & Hoyles, C. (2017).
*Dynamic digital technologies for dynamic mathematics*. https://www.nuffieldfoundation.org/sites/default/files/files/Hoyles%2041909%20-%20Executive%20Summary.pdf. Retrieved January 12, 2018. - Clements, D. H., Battista, M. T., & Sarama, J. (2001). Logo and geometry.
*Journal for Research in Mathematics Education, Monograph,**10,*i-177.CrossRefGoogle Scholar - Cohen, J. W. (1988).
*Statistical power analysis for the behavioural sciences*. Hillsdale: Lawrence Erlbaum Associates.Google Scholar - Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. In A. Kelly & R. A. Lesh (Eds.),
*Handbook of research design in mathematics and science education*(pp. 231–265). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Cooper, T., & Warren, E. (2008). The effect of different representations on years 3 to 5 students’ ability to generalise.
*ZDM Mathematics Education,**40*(1), 23–37.CrossRefGoogle Scholar - Cooper, T. J., & Warren, E. (2011). Years 2 to 6 students’ ability to generalise. In J. Cai & E. Knuth (Eds.),
*Early algebraization*(pp. 187–214). Berlin: Springer.CrossRefGoogle Scholar - Creswell, J. (2008).
*Research design: Qualitative, quantitative, and mixed methods approaches*(3rd ed.). Thousand Oaks, CA: SAGE Publications.Google Scholar - English, L. D. (2016). STEM education K-12: Perspectives on integration.
*International Journal of STEM Education,**3*(1), 1–8.CrossRefGoogle Scholar - García-Peñalvo, F. J., Reimann, D., Tuul, M., Rees, A., & Jormanainen, I. (2016).
*An overview of the most relevant literature on coding and computational thinking with emphasis on the relevant issues for teachers*. Belgium: TACCLE 3 Consortium.Google Scholar - Han, S., & Bhattacharya, K. (2001). Constructionism, learning by design, and project based learning. In M. Orey (ed)
*Emerging perspectives on learning, teaching, and technology*. http://pirun.ku.ac.th/~btun/papert/design.pdf. Accessed 10 Sep 2019. - Hattie, J. A. C. (2009).
*Visible learning: A synthesis of over 800 meta-analyses relating to achievement*. London: Routledge.Google Scholar - Highfield, K. (2015). Stepping into STEM with young children: Simple robotics and programming as catalysts for early learning. In C. Donahue (Ed.),
*Technology and digital media in the early years*(pp. 150–161). New York: Taylor & Francis.Google Scholar - Hoyles, C. (1985). Developing a context for LOGO in school mathematics.
*The Journal of Mathematical Behavior*,*4*(3), 237–256.Google Scholar - Hoyles, C., & Noss, R. (1992). A pedagogy for mathematical microworlds.
*Educational studies in Mathematics,**23*(1), 31–57.CrossRefGoogle Scholar - Lesh, R., & Lehrer, R. (2000). Iterative refinement cycles for videotape analyses of conceptual change. In R. Lesh & A. Kelly (Eds.),
*Research design in mathematics and science education*(pp. 665–708). Hillsdale, NJ: Erlbaum.Google Scholar - Lewis, C. M., & Shah, N. (2012). Building upon and enriching grade four mathematics standards with programming curriculum. In
*Proceedings of the 43rd ACM technical symposium on computer science education*(pp. 57–62). ACM.Google Scholar - Lüken, M. M. (2018). Repeating pattern competencies in three-to five-year old kindergartners: A closer look at strategies. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.),
*Contemporary research and perspectives on early childhood mathematics education*(pp. 35–53). Cham: Springer.CrossRefGoogle Scholar - Meng, C., Idris, N., Leong, K. E., & Daud, M. (2013). Secondary school assessment practices in science, technology and mathematics (STEM) related subjects.
*Journal of Mathematics Education,**6*(2), 58–69.Google Scholar - Miller, J., & Larkin, K. (2017). Using coding to promote mathematical thinking with year 2 students: Alignment with the Australian curriculum. In A. Downton, S. Livy, & J. Hall (Eds.), 40 years on: We are still learning! (Proceedings of the 40th annual conference of the mathematics education research group of Australasia, (pp. 469–476). Melbourne: MERGA.Google Scholar
- Miller, J., & Warren, E. (2012). An exploration into growing patterns with young Australian Indigenous students. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia) (pp. 505–512). Singapore: MERGA.Google Scholar
- Moore, T. J., Stohlmann, M. S., Wang, H., Tank, K. M., Glancy, A. W., & Roehrig, G. H. (2014). Implementation and integration of engineering in K-12 STEM education. In S. Purzer, J. Strobel, & M. Cardella (Eds.),
*Engineering in pre-college settings: Research into practice*(pp. 35–60). West Lafayette, IN: Purdue University Press.CrossRefGoogle Scholar - Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development.
*Mathematics Education Research Journal,**21*(2), 33–49.CrossRefGoogle Scholar - Noss, R. (1986). Constructing a conceptual framework for elementary algebra through Logo programming.
*Educational Studies in Mathematics,**17*(4), 335–357.CrossRefGoogle Scholar - Papert, S. (1980).
*Mindstorms: Children, computers, and powerful ideas*. New York: Basic Books Inc.Google Scholar - Papert, S., & Harel, I. (1991).
*Constructionism*. New York: Ablex Publishing Corporation.Google Scholar - Papic, M. (2007).
*Mathematical patterning in early childhood: An intervention study*. Unpublished PhD thesis, Macquarie University.Google Scholar - Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning.
*Journal for Research in Mathematics Education,**42*(3), 237–268.CrossRefGoogle Scholar - Partnership for 21st Century Skills (P21) (2019).
*Framework for 21st century learning*. http://www.battelleforkids.org/networks/p21. Retrieved June 30, 2019. - Prensky, M. (2008).
*Programming is the new literacy*. http://www.edutopia.org/literacy-computer-programming. Retrieved February 12, 2018. - Prinsley, R., & Johnston, E. (2015).
*Transforming STEM teaching in Australian primary schools: everybody’s business*. Australian Government: Office of the Chief Scientist.Google Scholar - Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds.
*Journal of Cognition and Development,**14*(3), 376–396.CrossRefGoogle Scholar - Savard, A., & Highfield, K. (2015). Teachers’ talk about robotics: Where is the mathematics? In M. Marshman, V. Geiger, & A. Bennison (Eds.),
*Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia*(pp. 540–546). Sunshine Coast: MERGA.Google Scholar - Stahl, B.C. (2003).
*How we invent what we measure: A constructionist critique on empiricist bias in research.*Paper presented at the 9th Americas conference on Information Systems, Florida.Google Scholar - Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.),
*Handbook of research design in mathematics and science education*(pp. 267–306). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar - Sullivan, P. (2011).
*Teaching mathematics: Using research-informed strategies*. Camberwell: ACER.Google Scholar - Threlfall, J. (1999). Repeating patterns in the early primary years. In A. Orton (Ed.),
*Pattern in the teaching and learning of mathematics*(pp. 18–30). London: Continuum.Google Scholar - Vasquez, J., Sneider, C., & Comer, M. (2013).
*STEM lesson essentials, grades 3–8: integrating science, technology, engineering, and mathematics*. Portsmouth, NH: Heinemann.Google Scholar - Voogt, J., & Roblin, N. P. (2012). A comparative analysis of international frameworks for 21st century competences: Implications for national curriculum policies.
*Journal of curriculum studies,**44*(3), 299–321.CrossRefGoogle Scholar - Warren, E., & Cooper, T. (2007). Repeating patterns and multiplicative thinking: Analysis of classroom interactions with 9-year-old students that support the transition from the known to the novel.
*The Journal of Classroom Interaction,**2*(1), 7–17.Google Scholar - Warren, E., & Miller, J. (2013). Young Australian Indigenous students’ effective engagement in mathematics: The role of language, patterns, and structure.
*Mathematics Education Research Journal,**25*(1), 151–171.CrossRefGoogle Scholar - Warren, E., Miller, J., & Cooper, T. (2012). Repeating patterns: Strategies to assist young students to generalise the mathematical structure.
*Australasian Journal of Early Childhood,**37*(3), 111–120.CrossRefGoogle Scholar - Wing, J. M. (2006). Computational thinking.
*Communications of the ACM,**49*(3), 33–35.CrossRefGoogle Scholar - Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: the tension between algebraic thinking and algebraic notation.
*Educational Studies in Mathematics,**49,*379–402.CrossRefGoogle Scholar