The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School

Naida Bikić; Sanja M. Maričić; Milenko Pikula

doi:10.12973/eurasia.2016.02304a

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Naida Bikić ¹ ^* , Sanja M. Maričić ², Milenko Pikula ³

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¹ University of Zenica, Faculty of Philosophy Department of mathematics and computer science² University of Kragujevac, Teaching Training Fakulty in Užice³ University of East Sarajevo Faculty of Philosophy Department of mathematics and computer science^* Corresponding Author

Abstract

Background:
The aim of the study was to examine the effects of problem-based learning which was established on differentiation of content at three levels of complexity in the processing of the content of Analytical geometry in the plane.

Material and methods:
In this context, an experimental research was conducted, on a sample of secondary school students (N = 165) in order to examine whether methodical approach designed on the principles of problem-based learning based on differentiation of content gives better effects in learning compared to the traditional mode.

Results:
The results of the final measurement shown that the experimental group achieved better overall success than control group.

Conclusions:
The results suggest that the proposed methodical approach contributes to better student performance in teaching geometry and that the most significant progress is achieved in the group of students who are average in terms of success and with ones below the average.

Keywords

analytical geometry
differentiation content
geometry
mathematics
Problem-based learning

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 12, Issue 11, November 2016, 2783-2795

https://doi.org/10.12973/eurasia.2016.02304a

Publication date: 15 Aug 2016

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Article Downloads: 2557

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References

Abdullah, N., Halim, L. & Zakaria, E. (2014). VStops: A Thinking Strategy and Visual Representation Approach in Mathematical Word Problem Solving toward Enhancing STEM Literacy, Eurasia Journal of Mathematics, Science & Technology Education, 10(3), 165-174.
Akor, E.A.P. (2005). Effects of Polya’s problem-solving strategy in teaching geometry on secondary school students’ achievement and interest, Nsukka: University of Nigeria.
Achike, F.I. & Nain, N. (2005). Promoting problem-based learning in nursing education: A Malaysian experience. Nurse Education in Practice, 5, 302–311.
Ainsworth, S. & Th Loizou, A. (2003). The effects of self-explaining when learning with text or diagrams. Cognitive Science, 27, 669-681.
Alemu, B. M. (2010). Active learning approaches in mathematics education at universities in Oromia, Ethiopia, http://uir.unisa.ac.za/handle/10500/4133, (retrived May 2015)
Bulu, S. & Pedersen, S. (2010). Scaffolding middle school students’ content knowledge and illstructured problem solving in a problem-based hypermedia learning environment. Educational Technology Research & Development, 58(5), 507–529.
Bokosmaty, S., Sweller, J. & Kalyuga, S. (2015). Learning Geometry Problem Solving by Studying Worked Examples: Effects of Learner Guidance and Expertise. American Educational Research Journal, 52(2), 307–333
Darling-Hammond, L. (2005). Developing professional development schools: Early lessons, challenge, and promise. In L. Darling-Hammond (Ed.), Professional development schools: Schools for developing a profession (1-27). New York: Teachers College Press.
Deen, N. (1985): Mensen scholen mensen, Groningen: Wolters Noordhof.
Felda, D., & Cotič, M. (2012). Matematična pismenost in realistični problemi. u S. Marinković (ur): Nastava i učenje – ciljevi, standardi, ishodi (51–60). Užice: Učiteljski fakultet.
Fauzan, A. (1998). Investigating spatial perception ability of the students at grade 1 senior high school in West Sumatera. Journal of Education Forum, 23(4), 100-115.
Flores, R., Ari, F., Inan, F. A., & Arslan-Ari, I. (2012). The Impact of Adapting Content for Students with Individual Differences. Educational Technology & Society, 15 (3), 251–261.
George, D. (2005). Obrazovanje darovitih: kako identificirati i obrazovati darovite i talentirane učenike. Zagreb: Educa.
Hargreaves, A. (2003). Teaching in the Knowledge Society: education in the age of insecurity. New York: Teachers College Press.
Hattie, J. A. C. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
Hines, A. (2008). Global trends in culture, infrastructure and values. Futurist, 42(5), 18–23.
Hmelo-Silver, C.E. 2004. Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
Hong, J. Y. & Kim, M. K. (2016). Mathematical Abstraction in the Solving of Ill-Structured Problems by Elementary School Students in Korea, Eurasia Journal of Mathematics, Science & Technology Education, 12(2), 267-281.
Huang, K., Chen, C. H., Wu, W. S., & Chen, W. Y. (2015). Interactivity of Question Prompts and Feedback on Secondary Students’ Science Knowledge Acquisition and Cognitive Load. Educational Technology & Society, 18(4), 159–171.
Ilić, M.(2002). Unapređivanje, periodizacija razvoja i perspektive individualizovane nastave. Pedagogija, XL(1-2), 45-57.
Kadum, V. (2005). Učenje rješavanjem problemskih zadataka u nastavi. Pula: Igsa.
Kerans, D.S. (1994). Teaching geometry at primary schools in Kupang, East Nusa Tenggara. Indonesia: Surabaya State University.
Kok, B. & Davasligil, U. (2014). The Effect of Teaching Geometry Which is Differentiated Based on the Parallel Curriculum for Gifted/Talented Students on Spatial Ability, Journal for the Education of the Young Scientist and Giftedness, 2(1), 40–52
Lester, F. K. (1985). Methodological considerations in research in mathematical problem solving instruction. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (41-69). London: Erlbaum.
Leong, K.E. (2013). Factors that Influence the Understanding of Good Mathematics Teaching. Eurasia Journal of Mathematics, Science & Technology Education, 9(3), 319-328.
Mandaci, S. & Kendir, F. (2013). The effect of using metacognitive strategies for solving geometry problems on students’ achievement and attitude, Educational Research and Reviews, 8(19), 1777–1792,
Maričić, S., Špijunović, K. (2015). Aktivnost učenika i razvijanje kritičkog mišljenja u početnoj nastavi matematike. u D. Hozjan (ur.) Aktivnosti učencev v učnem procesu (281–290). Koper: Univerza na Primorskem, Pedagoška fakulteta, Univerzitetna založba Annales.
Marcucci, R. G. (1980). A meta-analysis of research on methods of teaching mathematical problem solving (Unpublished doctoral dissertation), Iowa City, IA: University of Iowa.
Mierson, S. & Parikh, A.A. (2000). Stories from the field: problem-based learning from a teacher’s and student’s perspective. Change, 32(1), 21–27.
Mwelese, J. K. & Wanjala, M. (2014). Effect of Problem Solving Strategy on Secundary School Students’ Achievement in Circle Geometry in Emuhaya District of Vihiga County. Journal of Education, Arts and Humanities, 2(2), 018–026
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Nfon, N. F. (2013). Effect of Rusbult’s Problem Solving Strategy on Secondary School Students’ Achievement in Trigonometry Classroom, Journal of Mathematics Education, 6(1), 38–55.
Paul, R.W (1992). Critical thinking: What, why, and how? New Directions for Community Colleges, 77, 3–24.
Perveen, K. (2010). Effect Of The Problem-Solving Approach On Academic Achievement Of Students In Mathematics At The Secondary Level. Contemporary Issues In Education Research, 3(3), 9–13
Peterson, T. (2004). So you’re thinking of trying problem-based learning? Three critical success factors for implementation. Journal of Management Education, 28(5), 630-647.
Raes, A., Schellens, T., Wever, B. D., & Vanderhoven, E. (2012). Scaffolding information problem solving in web-based collaborative inquiry learning. Computers and Education, 59, 82– 94.
Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., & Suydam, M. N. (2004). Helping Children Learn Mathematics (7th ed.). New York: Wiley.
Remillard, J & Kaye, P. (2002). Supporting teachers' professional learning by navigating openings in the curriculum. Journal of Mathematics Teacher Education, 5(1), 7-34.
Roeders, P. (2003). Interaktivna nastava: dinamika efikasnog učenja i nastave. Beograd, Institut za pedagogiju i andragogiju Filozofskog fakulteta.
Salman, M.F. (2005). Teachers’ identification of the difficulty levels of topics in the primary school mathematics curriculum in Kwara state abacus. The Journal of Mathematical Association of Nigeria, 30(1), 20-29.
Soedjadi. (1991). The feature of mathematics education at our primary school. Indonesia, Surabaya State University.
Trinchero, R. & Sala, G. (2016). Chess Training and Mathematical ProblemSolving: The Role of Teaching Heuristics in Transfer of Learning, Eurasia Journal of Mathematics, Science & Technology Education, 12(3), 655–668
Wilson, P.S., Cooney, T.J., & Stinson, D.W. (2005). What constitutes good mathematics teaching and how it develops: Nine high school teachers’ perspectives? Journal of Mathematics Teacher Education, 8, 83-111.
Zan, R. & Martino, P.D. (2007). Attitudes towards mathematics: Overcoming positive/negative dichotomy. The Montana mathematics enthusiasts monograph. The Montana Council of Teacher of Mathematics, 3, 157-168.

How to cite this article

APA

Bikić, N., Maričić, S. M., & Pikula, M. (2016). The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School. Eurasia Journal of Mathematics, Science and Technology Education, 12(11), 2783-2795. https://doi.org/10.12973/eurasia.2016.02304a

Vancouver

Bikić N, Maričić SM, Pikula M. The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School. EURASIA J Math Sci Tech Ed. 2016;12(11):2783-95. https://doi.org/10.12973/eurasia.2016.02304a

AMA

Bikić N, Maričić SM, Pikula M. The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School. EURASIA J Math Sci Tech Ed. 2016;12(11), 2783-2795. https://doi.org/10.12973/eurasia.2016.02304a

Chicago

Bikić, Naida, Sanja M. Maričić, and Milenko Pikula. "The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 11 (2016): 2783-2795. https://doi.org/10.12973/eurasia.2016.02304a

Harvard

Bikić, N., Maričić, S. M., and Pikula, M. (2016). The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School. Eurasia Journal of Mathematics, Science and Technology Education, 12(11), pp. 2783-2795. https://doi.org/10.12973/eurasia.2016.02304a

MLA

Bikić, Naida et al. "The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 11, 2016, pp. 2783-2795. https://doi.org/10.12973/eurasia.2016.02304a