A framework for the development and improvement of computational thinking for high school learners using a programming language and learner management system
DOI:
https://doi.org/10.17159/h1a6ee13Keywords:
APOS Theory, cognitive level of formal operations, computational thinking (CT), embodied cognition, learner management system (LMS), programming languages (PL)Abstract
Many educational departments are losing the battle against inefficient mathematics education. The Annual National Assessments (ANA) and World Economic Forum reports tell a story that performance is declining annually among learners in South Africa. The study was conducted among Grade 9 learners at a private high school in the Western Cape to establish a framework for computational thinking. The problem statement reads that it is not clear how high school learners’ computational thinking (CT) may be enhanced or improved at a cognitive level of formal operations. The research question posed is, ‘How can CT be enhanced, among high school learners, using a PL aligned to Action-Process-Object-Schema (APOS) theory?’ The research methodology was based on an interpretivist philosophy. The ontological underpinning of the study is subjective and the epistemological stance accepts opinions of learners through written, spoken and visual attributed meanings. The axiology of the researcher is that of a practising educator in programming, a teaching and learning expert and a certified Java-Alice-Greenfoot instructor through Oracle. The research strategy was based on educational design research as a validation study through interventions. Findings show that CT at a cognitive level of formal operations can be enhanced among learners through Greenfoot PL with APOS theory as lens. The support and recognition of the headmaster or line manager towards those involved in programming language (PL) and learning management system (LMS) education, determine the success of the roll-out.
References
Aho, A.V. (2012) Computation and Computational Thinking. The Computer Journal 55(7) pp.832-835.
Arnon, I., Cotrill, J., Dubinsky, E., Oktac, A., Fuentes, S.R., Trigueros, M. & Weller, K. (2014) APOS theory: A framework for research and curriculum development in mathematics education. New York: Springer-Verlag.
Bachelard, G. (1938) La Formation de l’esprit scientifique (reprinted 1983). Paris: Librairie J. Vrin.
Bannan, B. (2013) The Integrative Learning Design Framework: An illustrated example from the domain of instructional technology. In T. Plomp & N. Nieveen (Eds.) An introduction to educational design research. Enschede, the Netherlands: Netherlands Institute for Curriculum Development (SLO), pp.114-133.
Bormanaki, H.B. & Khoshhal, Y. (2017) The Role of Equilibration in Piaget’s Theory of Cognitive Development and Its Implication for Receptive Skills: A Theoretical Study. Journal of Language Teaching and Research. [Online] 8(5) pp.996-1005.
Brijlall, D. & Maharaj, A. (2014) Exploring support strategies for high school mathematics. International Journal of Science Education 7(1) pp.99-107.
Brousseau, G. (1983) Les obstacles épistémologiques et les problèmes en mathématiques. Recherches en Didactique des Mathématiques 4(2) pp.164-198.
Brousseau, G. (2002) Theory of didactical situations in Mathematics. New York: Kluwer Academic.
CDE see Centre for Development and Enterprise.
Centre for Development and Enterprise. (2014) What does research tell us about teachers, teaching and learner performance in mathematics? www.cde.org.za/what-does-research-tell-us-about-teachers-teaching-and-learner-performance-in-mathematics-2/ (Accessed 12 December 2019).
Cegielski, C. & Hall, D. (2006) What makes a good programmer? Communications of the ACM 49(10) pp.737-5.
Cetin, I. & Dubinsky, E. (2017) Reflective abstraction in computational thinking. Journal of Mathematical Behavior 47 pp.70-80, doi:10.1016/j.jmathb.2017.06.004
Chirinda, B. & Barmby, P. (2018) South African Grade 9 Mathematics Teachers’ Views on the Teaching of Problem Solving. African Journal of Research in Mathematics, Science and Technology Education. [Online] 22(1) pp.114-124.
Clark, R.E., Kirschner, P.A. & Sweller, J. (2010) Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist 41(2) pp.75-86.
Clark, R.E., Kirschner, P.A. & Sweller, J. (2012) Putting students on the path to learning: The case for fully guided instruction. American Educator pp.6-11.
DBE see Department of Basic Education, South Africa.
Department of Basic Education, South Africa. (2015) South African Schools Act, 1996 (Act No. 84 of 1996): Amended national norms and standards for school funding. Government Notice 17/2015. www. gov.za/sites/www.gov.za/files/38397_gon17.pdf (Accessed 16 January 2015).
Denning, P.J. (2017) Viewpoint remaining trouble spots with computational thinking. Communications of the ACM 60(6) pp.33-38.
Devlin, K. (2003) Why universities require computer science students to take math. Communications of the ACM 46(9) pp.37-39.
Dubinsky, E. (1991) Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.) Advanced mathematical thinking. Netherlands: Springer, pp.95-126.
Dubinsky, E. (2000) Mathematical literacy and abstraction in the 21st century. School Science and Mathematics 100(6) pp.289-297, doi:10.1111/j.1949-8594.2000.tb17322.x
Dubinsky, E. & Lewin, P. (1986) Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness. The Journal of Mathematical Behavior 5 pp.55-92.
Dubinsky, E. & McDonald, M. (2001) APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss & A. Schoenfeld (Eds.) The teaching and learning of mathematics at university level. Dordrecht: Springer, pp.275-282.
Grant, D. (2012) New technologies enhancing mathematics tuition in the classroom. https://www. westerncape.gov.za/news/new-technologies-enhancing-mathematics-tuition-classroom (Accessed 20 May 2012).
Hayakawa, S. (1949) Language in thought and action. New York: Harcourt Brace Jovanovich.
Hazzan, O. (1999) Reducing abstraction level when learning abstract algebra concepts. Educational Studies in Mathematics 40 pp.71-90.
Hazzan, O. (2003) How students attempt to reduce abstraction in the learning of mathematics and in the learning of computer science. Computer Science Education 13(2) pp.95-122.
Higgins, H.J. & Wiest, L.R. (2006) Individual interviews as insight into children's computational thinking. Australian Primary Mathematics Classroom 11(1) pp.25-29.
Hill, J., Houle, B., Merrit, S. & Stix, A. (2008) Applying abstraction to master complexity: The comparison of abstraction ability in computer science majors with students in other disciplines. Leipzig, Germany: s.n.
Howie, S.J. (1997) Mathematics and science performance in the middle school years in South Africa. Pretoria: Human Sciences Research Council.
Howie, S.J. (2001) Mathematics and science performance in Grade 8 in South Africa 1998/1999. Pretoria: HSRC Press.
Howie, S.J. (2004) A national assessment in mathematics within an international comparative assessment. Perspectives in Education 22(2) pp.149-162.
Howie S.J. (2013) Language and other background factors affecting secondary pupils' performance in Mathematics in South Africa. African Journal of Research in Mathematics, Science and Technology Education 7(1) pp.1-20, doi.org/10.1080/10288457.2003.10740545
Howie, S.J. & Plomp, T. (2002) Mathematical literacy of school leaving pupils in South Africa. International Journal of Educational Development 22(6) pp.603-615, doi.org/10.1016/S0738-0593(01)00030-X
Howie S.J. & Plomp, T. (2006) Contexts of learning mathematics and science: Lessons learned from TIMSS. London & New York: Routledge.
HSRC see Human Sciences Research Council.
Human Sciences Research Council. (2014) Report on the Annual National Assessments of 2014: Grades 1 to 6 & 9. www.hsrc.ac.za/en/news/view/ana-2014 (Accessed 13 August 2014).
Imenda, S. (2014) Is there a conceptual difference between theoretical and conceptual frameworks. Journal of Social Sciences 38(2) pp.185-195.
Jankvist, U. & Niss, M. (2018) Counteracting destructive student misconceptions of mathematics. Education Sciences 8(2) pp.1-18, doi.org/10.3390/educsci8020053
Kölling, M. (2010) Introduction to programming with Greenfoot: Object-oriented programming in Java with games and simulations. New York: Prentice Hall.
Kramer, J. (2007) Abstraction - the key to computing? Communications of the ACM 50(4) pp.36-42. April.
Kranch, D. (2010) A study of three instructional sequences for developing computer programming expertise in novice learners. Dissertation presented in partial fulfilment of the requirement for the degree Doctor of Philosophy, Capella University, Minneapolis, Minnesota, US.
Lockwood, J. & Mooney, A. (2017) Computational Thinking in Education: Where does it fit? A systematic literary review. Maynooth University, National University of Ireland, Maynooth.
Maharaj, A. (2013) An APOS analysis of natural science students’ understanding of Derivatives. South African Journal of Education 33(1) pp.1-19, doi.org/10.15700/saje.v33n1a458
Maree, K., Aldous, M., Hattingh, A., Swanepoel, A. & Van der Linde, M. (2006) Predictors of learner performance in mathematics and science according to a large-scale study in Mpumalanga. South African Journal of Education 26(2) pp.229-252.
McCarthy, J. & Oliphant, R. (2013) Mathematics outcomes in South African schools. What are the facts? What should be done? www.cde.org.za/mathematics-outcomes-in-south-african-schoolswhat-are-the-facts-what-should-be-done/ (Accessed 17 October 2013).
McGowen, M. & Tall, D. (2010) Metaphor or Met-Before? The effects of previous experience on practice and theory of learning mathematics. Journal of Mathematical Behavior 29(3) pp.169-179, doi. org/10.1016/j.jmathb.2010.08.002
McPhail, G. (2016) The fault lines of recontextualisation: The limits of constructivism in education. British Educational Research Journal 42 pp.294-313. April.
Meyer, D. (2010) A literature review of the product and process of abstraction. https://docs.google.com/document/d/1jj1FnxUz6INGajT1hXfuvMZ9sUUmLulJjT58xBqqvec/edit?pli=1 (Accessed 14 July 2010).
Moscucci, M. (2007) About Mathematical Belief Systems Awareness. CERME 5 Congress of European Society for Research in Mathematical Education Larnaca, Cyprus, 22-26 February.
Nieveen, N. (2013) Educational design research: An introduction. In T. Plomp & N. Nieveen (Eds.) An introduction to educational design research. Enschede, the Netherlands: Netherlands Institute for Curriculum Development (SLO), pp.89-101.
Papert, S. (1980) Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
Papert, S. (2005) Teaching children thinking. Contemporary Issues in Technology and Teacher Education 5(3) pp.353-365.
Pearson, K. (2008) From a usable past to collaborative future: African American culture in the age of computational thinking. Black History Bulletin 72(1) pp.41-44.
Perrenet, C. (2009) Levels of thinking in computer science: Development in bachelor students’ conceptualisation of algorithm. Education and Information Technologies 15(2) pp.87-107, doi:10.1007/s10639-009-9098-8
Philbin, C.A., Bagge, P., Darbyshire, C. & Savage, M. (2013) Exploring computational thinking. www. google.com/edu/computational-thinking/what-is-ct.html (Accessed 14 July 2013).
Piaget, J. (1965) The child’s conception of number (1941). C. Gattegno & F.M. Hodgson (Trans). New York: W.W. Norton.
Piaget, J. (1973) Comments on mathematical education. In A.G. Howson (Ed.) Developments in mathematical education. UK: Cambridge University Press, pp.79-87, doi.org/10.1017/CBO9781139013536
Plomp, T. (2013) Educational design research: An introduction. In T. Plomp & N. Nieveen (Eds.) An introduction to educational design research. Enschede, the Netherlands: Netherlands Institute for Curriculum Development (SLO), pp.9-35.
Prensky, M. (2008) Programming is the new literacy. www.edutopia.org/programming-the-new-literacy (Accessed 15 June 2008).
Reddy V. (2014) 20 years of TIMSS in South Africa: Building our analyses for in-country use. Presentation to IEA, General Assembly Vienna, October. Pretoria: HSRC.
Reddy V., Kanjee, A., Diedericks, G. & Winnaar, L. (2006) Mathematics and science achievement at South African Schools in TIMSS 2003. Pretoria: HSRC Press.
Reddy, V., Van der Berg, S., Janse van Rensburg, D. & Taylor, S. (2012) Educational outcomes: Pathways and performance in South African high schools. South African Journal of Science 108(3-4), doi:10.4102/sajs.v108i3/4.620
Reddy, V., Zuze, T.L., Visser, M., Winnaar, L., Juan, A., Prinsloo, C.H., Arends, F. & Rogers, S. (2015) Beyond benchmarks: What twenty years of TIMSS data tell us about South African education. Pretoria: HSRC Press.
Selby, C. & Woollard, J. (2014) Refining an understanding of computational thinking. University of Southampton. https://eprints.soton.ac.uk/372410/ (Accessed 2 March 2020).
Sfard, A. (1991) On the dual nature of mathematical conceptions: Reflections on processes and objects on different sides of the same coin. Educational Studies in Mathematics 22 pp.1-36.
South African Mathematics Foundation. (2018) Grade 12 maths results: Addressing the challenges. www. samf.ac.za/(S(00ea3k45cr1w5b23q35jwb55)X(1)A(-xxZtnTc0QEkAAAAZjEwYWFkZDgtMjA3YS00M zIxLWFmNDAtZWIyMDFlYmYwMmIwjeuWmoqZ4U3np7BTcgH0CGECS0A1))/grade-12-maths-results-addressing-the -challenges (Accessed 30 January 2018).
Spaull, N. (2013) South Africa’s education crisis: The quality of education in South Africa 1994–2011. Report Commissioned by CDE. Johannesburg, South Africa.
Tall, D.O. (2004) Thinking through three worlds of mathematics. In Proceedings of the 28th International Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway, 14-18 July, pp.281-288.
Tall, D.O. (2008) The transition to formal thinking in mathematics. Mathematics Education Research Journal 20(2) pp.5-24, doi.org/10.1007/BF03217474
Truran, J. (1992) Integers as jelly beans. Australian Mathematics Teacher 48(2) p.25.
Van den Akker, J. (1999) Principles and methods of development research. In J. Van den Akker, R.M. Branch, K. Gustafson, N. Nieveen & T. Plomp (Eds.) Design approaches and tools in education and training. Boston: Kluwer Academic, pp.1-14.
Van den Akker, J. (2003) Curriculum perspectives: An introduction. In J. Van den Akker, W. Kuiper & U Hameyer (Eds.) Curriculum landscapes and trends. Dordrecht: Kluwer Academic, pp.1-10.
Voogt, J., Fisser, P., Good, J., Mishra, P. & Yadav, A. (2015) CT in compulsory education: Towards an agenda for research and practice. Education and Information Technologies 20(4) pp.715-728.
Wademan, M.R. (2005) Utilising development research to guide people-capability maturity model adoption considerations. Doctoral dissertation, Syracuse University. Dissertation Abstracts International, 67–01A. UMI: 3205587.
Weber, S. (2010) Design science research: Paradigm or approach? In Proceedings of the 16th Americas Conference on Information Systems, Lima, Peru, 12-15 August p.214. http://aisel.aisnet.org/amcis2010/214 (Accessed 02 March 2020).
Wilensky, U. (1991) Abstract meditations on the concrete and concrete implications for mathematics education. In I. Harel & S. Papert (Eds.) Constructionism. Norwood N.J.: Ablex.
Wing, J. M. (2006) Computational thinking. Communications of the ACM 49(3) pp.33-35.
Wing, J.M. (2008) Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society A 366 pp.3717-3725, doi:10.1098/rsta.2008.0118
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