IJMECS Vol. 9, No. 1, 8 Jan. 2017

Cover page and Table of Contents: PDF (size: 775KB)

Full Text (PDF, 775KB), PP.1-14

Views: 0 Downloads: 0

ICT curriculum comparison, computing fundamentals, variable, function, math-aided ICT, transfer, computational thinking

In this article, we examine the relationship in K-12 education between Mathematics and Information and Communication Technology (ICT). The topic is reviewed from various angles, based on both a literature study and by directly contrasting the Finnish National Curriculum (FNC) of 2014 (effective since autumn 2016) with the National Curriculums of the UK (UKNC)[3] and the US (USCC)[2].

Finland has chosen a cross-curricular approach to developing the new curriculum for teaching ICT, which involves integrating it mainly with math, but also with handicraft, and various other subjects. This is in direct contrast to the UKNC, for example, which teaches ICT as its own field, to be taught through the Computing and Design/Technology syllabi. This poses a question for this research study, namely, how well do teaching math and ICT fit together? The first step towards answering this question is to establish which ICT concepts and domains are directly supported by math and which are left uncovered. As a theoretical research paper, the rationale for the inter-connectedness of math and ICT is based on the work of many researchers. To illustrate our comparison of the two subjects, in this article we concentrate on clarifying math’s and ICT’s shared concepts of variable and function.

The results of this study indicate that transfer between the subjects happens bi-directionally, which might suggest that teaching ICT in combination with particular branches of math, notably algebra would be of benefit to our students. In order to pursue this approach, extra modules for logic, basic linear algebra and set theory would also be required. The fundamentals of basic algebra, the function and the variable, and their significance as synthesizers in both algebra and ICT are highlighted. In addition, the use of calculators as function tutors is explored in an instructional classroom setting. The conclusion of this study is that although there are certain benefits to the currently chosen approach of teaching ICT in combination with mathematics, these are not enough to outweigh the advantages of adopting a more versatile dedicated ICT syllabus, such as that provided by the UKNC.

Pia S. Niemelä, Martti Helevirta,"K-12 Curriculum Research: The Chicken and the Egg of Math-aided ICT Teaching", International Journal of Modern Education and Computer Science(IJMECS), Vol.9, No.1, pp.1-14, 2017.DOI: 10.5815/ijmecs.2017.01.01

[1] Finnish National Board of Education. 2014. “Finnish national curriculum 2014”, [Online].Available: http://www.oph.fi/download/163777_perusopetuksen_opetussuunnitelman_perusteet_2014.pdf [Accessed: 01- Aug- 2016].

[2] “Mathematics Standards | Common Core State Standards Initiative”, Corestandards.org, 2016. [Online]. Available: http://www.corestandards.org/Math/. [Accessed: 02- Aug- 2016].

[3] “National Curriculum in England: Secondary Curriculum - Publications - GOV.UK”, Gov.uk, 2013. [Online]. Available: https://www.gov.uk/government/publications/national-curriculum-in-england-secondary-curriculum. [Accessed: 02- Aug- 2016].

[4] “Department for Education Computing Programmes of study: Key Stages 1 and 2”, [Online]. Available: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239033/PRIMARY_national_curriculum_-_Computing.pdf. . [Accessed: 02- Aug- 2016].

[5] “Department for Education Computing Programmes of study: Key Stages 3 and 4”. [Online]. Available: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239067/SECONDARY_national_curriculum_-_Computing.pdf. [Accessed: 02- Aug- 2016].

[6] Department for Education of the United Kingdom. 2014. “Computer science GCSE subject content”, [Online]. Available: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/397550/GCSE_subject_content_for_computer_science. pdf [Accessed: 02- Aug- 2016].

[7] Berger, T.,Frey, C. 2016. “Digitalization, Jobs, and Convergence in Europe: strategies for closing the skills gap”, [Online]. Available: http://www.oxfordmartin.ox.ac.uk/downloads/reports/SCALE_Digitalisation_Final.pdf.

[8] Blackwood, N. 2016. “Digital skills crisis: second report of Session 2016–17”, House of Commons.

[9] Billings, D. 2008. “Argument mapping”, The Journal of continuing education in nursing. 39(6), 246-247.

[10] Dijkstra, E.W. 1982. “How do we tell truths that might hurt?”, in Selected Writings on Computing: A Personal Perspective. Springer. pp. 129-131.

[11] Dijkstra, E.W. 1982. “On the role of scientific thought”, in Selected writings on computing: a personal perspective. Springer. pp. 60-66.

[12] Epp, S. 2011. “Variables in mathematics education”, in: Tools in teaching logic (ed.). Springer. pp. 54-61.

[13] Felleisen, M. & Krishnamurthi, S. 2009. “Viewpoint Why computer science doesn't matter”, Communications of the ACM 52, 7, pp. 37-40.

[14] Fluck, A., Webb, M., Cox, M., Angeli, C., Malyn-Smith, J., Voogt, J. & Zagami, J. 2016. “Arguing for computer science in the school curriculum”, Educational Technology and Society 19, 3, pp. 38-46.

[15] Frankin, J. (ed.). 2015. “OCR GCSE Computer Science 3rd Edition”, 3rd ed. Axsied.

[16] Futschek, G. 2006. “Algorithmic thinking: the key for understanding computer science”, International Conference on Informatics in Secondary Schools-Evolution and Perspectives, Springer. pp. 159-168.

[17] Gagne, R.M. 1965. The Conditions of Learning. New York: Holt, Rinehart and Winston. Inc., l970

[18] House of Commons. 2016. “Oral evidence: Digital skills gap”, [Online]. Available: http://data.parliament.uk/writtenevidence/committeeevidence.svc/evidencedocument/science-and-technology-committee/digital-skills/oral/27865.html

[19] Jarvis, S., & Pavlenko, A. 2008. Crosslinguistic influence in language and cognition. Routledge.

[20] Kleiner, I. 1989. “Evolution of the function concept: A brief survey”, The College Mathematics Journal 20, 4, pp. 282-300.

[21] Köhler, W. 1970. Gestalt psychology: An introduction to new concepts in modern psychology. WW Norton & Company.

[22] Lee, I., Martin, F., Denner, J., Coulter, B., Allan, W., Erickson, J., Malyn-Smith, J. & Werner, L. 2011. “Computational thinking for youth in practice”. ACM Inroads 2, 1, pp. 32-37.

[23] Lee, R. 2013. “Teaching Algebra through Functional Programming: An Analysis of the Bootstrap Curriculum”.

[24] Levy, D. 2013. “Racket Fun-fictional Programming to Elementary Mathematic Teachers”.

[25] Lonka, K. & Cho, V. (ed.). 2015. Report for EU Parliament 2015: Innovative Schools: Teaching & Learning in the Digital Era: Workshop Documentation.

[26] Menger, K. 1954. “On variables in mathematics and in natural science”, The British Journal for the Philosophy of Science 5, 18, pp. 134-142.

[27] Milne, I. & Rowe, G. 2002. “Difficulties in learning and teaching programming—views of students and tutors”, Education and Information technologies 7, 1, pp. 55-66.

[28] Organisation for Economic Co-operation and Development. 2016. “Skills for a Digital World”.

[29] Parnas, D.L. 1972. “On the criteria to be used in decomposing systems into modules”, Communications of the ACM 15, 12, pp. 1053-1058.

[30] Perkins, D. & Salomon, G. 1988. “Teaching for transfer”, Educational leadership 46, 1, pp. 22-32.

[31] Piaget, J. & Duckworth, E. 1970. Genetic epistemology. American Behavioral Scientist 13, 3, pp. 459-480.

[32] Portugal, C. 2014. “Hypermedia E-book as a Pedagogical Tool in a Graduation Course”, International Journal of Modern Education and Computer Science, Vol. 6(9), pp. 8.

[33] Rakes, C.R., Valentine, J.C., McGatha, M.B. & Ronau, R.N. 2010. “Methods of Instructional Improvement in Algebra A Systematic Review and Meta-Analysis”, Review of Educational Research 80, 3, pp. 372-400.

[34] Resnick, M., Maloney, J., Monroy-Hernández, A., Rusk, N., Eastmond, E., Brennan, K., Millner, A., Rosenbaum, E., Silver, J. & Silverman, B. 2009. “Scratch: programming for all”, Communications of the ACM 52, 11, pp. 60-67.

[35] Rich, P.J., Leatham, K.R. & Wright, G.A. 2013. “Convergent cognition”, Instructional Science 41, 2, pp. 431-453.

[36] Schanzer, E.T. 2015. “Algebraic Functions, Computer Programming, and the Challenge of Transfer”.

[37] STEM education coalition One-Pager. 2016. “STEM Education, Good Jobs, and U.S. Competitiveness”, [Online]. Available: http://www.stemedcoalition.org/wp-content/uploads/2016/01/STEM-Factsheet-Updated2.pdf.

[38] Syslo, M.M. & Kwiatkowska, A.B. 2006. “Contribution of informatics education to mathematics education in schools”, International Conference on Informatics in Secondary Schools-Evolution and Perspectives, Springer. pp. 209-219.

[39] Tarski, A. 1994. Introduction to Logic and to the Methodology of the Deductive Sciences. Oxford university press.

[40] Usiskin, Z. 1988. “Conceptions of school algebra and uses of variables”, The ideas of algebra, K-12 8, pp. 19.

[41] Ursini, S. & Trigueros, M. 2001. “A model for the uses of variable in elementary algebra”, PME CONFERENCE, pp. 4-327.

[42] Van Roy, P., Armstrong, J., Flatt, M. & Magnusson, B. (2003). “The Role of Language Paradigms in Teaching Programming”, Proceedings of the 34th SIGCSE Technical Symposium on Computer Science Education, ACM, New York, NY, USA, pp. 269-270.

[43] Vygotskij, L.S. 1978. Mind in society the development of higher psychological processes. Cambridge, Harvard University Press.

[44] Wilkie, K.J. & Clarke, D.M. 2016. “Developing students’ functional thinking in algebra through different visualizations of a growing pattern’s structure”, Mathematics Education Research Journal 28, 2, pp. 223-243.

[45] Wilkie, K.J. 2016. “Learning to teach upper primary school algebra: changes to teachers’ mathematical knowledge for teaching functional thinking”, Mathematics Education Research Journal 28, 2, pp. 245-275.

[46] Wilkie, K.J. 2016. “Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school”, Educational Studies in Mathematics pp. 1-29.

[47] Willcutt, E.G., Petrill, S.A., Wu, S., Boada, R., Defries, J.C., Olson, R.K. & Pennington, B.F. 2013. “Comorbidity between reading disability and math disability: concurrent psychopathology, functional impairment, and neuropsychological functioning”, Journal of learning disabilities 46, 6, pp. 500-516.

[48] Wing, J.M. 2006. Computational thinking. Communications of the ACM 49, 3, pp. 33-35

[49] Ylioppilastutkintolautakunta, ”SÄHKÖINEN YLIOPPILASTUTKINTO – MATEMATIIKKA”, [Online]. Available: https://www.ylioppilastutkinto.fi/images/sivuston_tiedostot/Sahkoinen_tutkinto/fi_sahkoinen_matematiikka.pdf