Bambang Riyanto, Zulkardi Zulkardi, Ratu Ilma Indra Putri, Darmawijoyo Darmawijoyo


By modeling learning students enjoy learning and doing mathematics in new ways. This study aimed firsly to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for valid mathematical learning; secondly, to produce senior high school mathematics modeling, lesson plan, and student worksheet for practical mathematics learning; lastly, to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for potentially effective mathematics learning. This study used method of development research that consisting of 3 steps, i.e., analysis, design, and evaluation. In the analysis stage, researcher did student analysis, curriculum, and mathematical modeling. Second stage are to design and product. Finally, researchers applied a design of formative evaluation consists of self-evaluation, one-to-one, experts review, small group, and field test. Based on experts review, one-to-one, small groups, and field test were obtained valid, practical, and potentially effective, i.e. mathematical modeling tasks, lesson plan, student worksheet to teach mathematical modeling in senior high school and Mathematical modeling tasks and student worksheets to learn mathematical modeling in senior high school.


learning, senior high school mathematics, modeling approach

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Ahamad, S.N.S.H., Li, H.C., Shahrill, M., & Prahmana, R.C.I. (2018). Implementation of problem-based learning in geometry lessons. Journal of Physics: Conference Series, 943(1), 012008.

Akker, J., Bannan, B., Kelly, A.E., Nieveen, N., & Plomp, T. (2006). Educational Design Research. Enschede: SLO

Anderson, J. (2010). Collaborative problem solving as modelling in the primary years of schooling. In: Kaur, B., & Dindyal, J., (Eds.). Mathematical Applications and Modelling. Singapore: World Scientific Publishing Co. Pte. Ltd.

Anthony, G., & Hunter, R. (2010). Communities of mathematical inquiry to support engagement in rich tasks. In: Kaur, B., & Dindyal, J., (Eds.). Mathematical Applications and Modelling. Singapore: World Scientific Publishing Co. Pte. Ltd.

Arseven, A. (2015). Mathematical modelling approach in mathematics education. Universal Journal of Educational Research, 3(12), 973-980.

Balakrishnan, G., Peng, Y.Y., & Eng, E.G.L. (2010). Mathematical modelling in the Singapore secondary school mathematics curriculum. In: Kaur, B., & Dindyal, J., (Eds.). Mathematical Applications and Modelling. Singapore: World Scientific Publishing Co. Pte. Ltd.

Ball, D.L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In: Biddle, B., Good, T., & Goodson, I., (Eds.). International Handbook on Teachers and Teaching 2. Dordrect: Kluwer Press.

Ball, D.L., & Cohen, D.K. (1999). Developing practice, developing practioners: Toward a practice-based theory of professional education. In: Sykes, G., & Darling-Hammond, L., (Eds.). Teaching as Learning Profession: Handbook of Policy and Practice. San Fransisco: Jossey Bass.

Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What make it special? Journal of Teacher Education, 59(5), 389-407.

Biccard, P. (2010). An investigation into the development of mathematical modelling competencies of grade 7 learners. Unpublish Doctoral Dissertation. Stellenbosch: University of Stellenbosch.

Bliss, K., Libertini, J., Levy, R., Zbiek, R.M., Galluzzo, B., Long, M., Teague, D., Godbold, L., Malkevitch, J., Kooij, H.V.D., Giardano, F., Fowler, K., Pollak, H., Gould, H., Montgomery, M., & Garfunkel, S. (2016). GAIMME: Guidelines for Assessment & Instruction in Mathematical Modelling Education. Philadelphia: COMAP & SIAM.

Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education discussion document. Educational Studies in Mathematics, 51(2), 149-171.

Blum, W., Artigue, M., Mariotti, M.A., Sträßer, R., & Heuvel-Panhuizen, M.V.D. (2019). European didactic traditionsin mathematics: Introduction and overview. In: Blum, W., Artigue, M., Mariotti, M. A., Sträßer, R., & Heuvel-Panhuizen, M.V.D. European Traditions in Didactics of Mathematics. Switzerland: Springer.

Bonotto, C. (2007). How to replace word problems with activities of realistic mathematical modelling. In: Blum, W., Galbraith, P., Henn, H.W., & Niss, M. (Eds.). Modelling and Applications in Mathematics Education: The 14th Icmi Study. New York: Springer.

Cobb, P., Wood, E., Yackel, E., & Mcneal, B. (1992). Characteristics of classroom mathematics traditions: an interactional analysis. American Educational Research Journal, 29(3), 573-604.

Doerr, M.H. (2006). Examining the tasks of teaching when using student’s mathematical thinking. Educational Studies in Mathematics, 62(1), 3-24.

Eric, C.C.M. (2010). Tracing primary 6 students’ model development within the mathematical modelling process. Journal of Mathematical Modelling and Application, 1(3), 40-47.

Eric, C.C.M. (2013). Students’ designing an ideal tourism route as mathematical modelling. In: Stillman, G. A., Kaiser, G., Blum, W., & Brown, J.P. Teaching Mathematical Modelling: Connecting to Research and Practice. Brazil: Springer.

Even, R., & Tirosh, D. (1995). Subject-matter knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1-20.

Ferri, R.B. (2018). Learning How to Teach Mathematical Modeling in School and Teacher Education. Kassel: Springer International Publishing.

Frejd, P. (2012). Teachers’ conceptions of mathematical modelling at Swedish upper secondary school. Journal of Mathematical Modelling and Application, 1(5), 17-40.

Garofalo, J., & Lester, F. (1985). Metakognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163-176.

Haines, C., & Crouch, R. (2010). Remarks on a modelling cycle and interpretation of behaviours. In: Lesh, R., Galbraith, P.L., Haines, C.R., & Hurford, A. (Eds.). Modeling Students’ Mathematical Modeling Competencies. New York: Springer.

Hendroanto, A., van Galen, F., van Eerde, D., Prahmana, R.C.I., Setyawan, F., & Istiandaru, A. (2018). Photography activities for developing students’ spatial orientation and spatial visualization. Journal of Physics: Conference Series, 943(1), 012029.

Hill, H.C., Ball, D.L., & Schilling, S.G. (2008). Unpacking pedagogical content knowledge: conceptualizing and measuring teachers’ topic-spesific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.

Hino, K. (2007). Toward the problem-center classroom: Trends in mathematical problem solving in Japan. ZDM Mathematics Education, 39(5-6), 503-514.

Kantowski, M.G. (1981). Problem solving. In: Fenemma, E. (Ed.) Mathematics Education Research: Implication for the 80’s. Reston, VA: National Council for the Teaching of Mathematics (NCTM).

Kawasaki, T. (2012). The problems of mathematical modelling introduction on mathematics education in Japanese school. Journal of Mathematical Modelling and Application, 1(5), 50-58.

Kilbane, C.R., & Milman, N.B. (2014). Teaching Models Designing Instruction For 21st Century Learners. New York: Pearson.

Knott, A. (2014). The Process of Mathematisation in Mathematical Modelling of Number Patterns in Secondary School Mathematics. Unpublish Dissertation. Stellenbosch: Stellenbosch University.

Lingefjard, T. (2006). Faces of mathematical modeling. Zentralblatt Fur Didaktik Der Mathematik, 38(1), 96-112.

Maa?, J., O’meara, J., & Patrick, O. (2018). Mathematical Modelling for Teacher: A Practical Guided to Applicable Mathematics Education. Switzerland: Springer.

Martinez-Luaces, V.E. (2005). Engaging secondary school and university teachers in modelling: Some experiences in South American countries. International Journal of Mathematical Education in Science and Technology, 36(2), 193–205.

Mousoulides, N. (2007). The Modeling Perspective in the Teaching and Learning of Mathematical Problem Solving. Unpublish Dissertation. Cyprus: University of Cyprus.

Muhtadi, D., Sukirwan, Warsito, & Prahmana, R.C.I. (2017). Sundanese ethnomathematics: mathematical activities in estimating, measuring, and making patterns. Journal on Mathematics Education, 8(2), 185-198.

Mumu, J., Prahmana, R.C.I., & Tanujaya, B. (2018). Construction and reconstruction concept in mathematics instruction. Journal of Physics: Conference Series, 943(1), 012011.

Nuari, L.F., Prahmana, R.C.I., & Fatmawati, I. (2019). Learning of division operation for mental retardations' student through Math GASING. Journal on Mathematics Education, 10(1), 127-142.

Riyanto, B., Zulkardi, Putri, R.I.I., & Darmawijoyo. (2017). Mathematical modeling in realistic mathematics education. Journal of Physics: Conference Series, 943(1), 012049.

Riyanto, B., Zulkardi, Putri, R.I.I., & Darmawijoyo. (2018). Mathematical learning through modeling task in senior high school: Using nutrition context. Journal Physics: Conference Series, 1097(1), 012102.

Riyanto, B., Zulkardi, Putri, R.I.I., & Darmawijoyo. (2019). Learning mathematics through modeling tasks in elementary school: Using growth of population context. Journal of Physics: Conference Series, 1166(1), 012033.

Robinson, K. (1999). Creativity, Culture and Education. Report. London: National Advisory Commitee on Creative and Cultural Education.

Saleh, M., Prahmana, R.C.I., Isa, M., & Murni. (2018). Improving the reasoning ability of elementary school student through the Indonesian Realistic Mathematics Education. Journal on Mathematics Education, 9(1), 41-54.

Saxena, R., Shrivastava, K., & Bhardwaj, R. (2016). Teaching Mathematical Modeling in Mathematics Education. Journal of Education and Practice, 7(11), 34-44.

Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In: Grouws, D. (Ed.) Handbook of Research on Mathematics Teaching and Learning. New York: Mcmillan.

Stillman, G., & Brown, J.P. (2014). Evidence of implemented anticipation in mathematising by beginning modellers. Mathematics Education Research Journal, 26(4), 763-789.

Stillman, G., Brown, J., & Galbraith, P. (2010). Researching application and mathematical modelling in mathematics learning and teaching. Mathematics Education Research Journal, 22(2), 1-6.

Sullivan, P., Knott, L., & Yang, Y. (2015). The relationships between tasks design, anticipated pedagogies, and student learning. In: Watson, A., Ohtani, M. Task Design in Mathematics Education: an ICMI Study 22. New York: Springer.

Tessmer, M. (1993). Planning and Conducting Formative Evaluation. Philadelphia: Kogan Page.

Wessels, H. (2014). Levels of mathematical creativity in model-eliciting activity. Journal of Mathematical Modelling and Application, 1(9), 22-40.

Wong, K.Y. (2008). An extended Singapore mathematics curriculum framework. Maths Buzz, 9(1), 2-3.

Yanagimoto, T. (2005). Teaching modelling as an alternative approach to school mathematics. Teaching Mathematics and its Applications, 24(1), 1-13.

Zulkardi & Putri, R.I.I. (2019). New school mathematics curricula, PISA, and PMRI in Indonesia. In: Vistro-Yu, C.P., & Toh, T.L. (eds.). School Mathematics Curricula, Mathematics Education – An Asian Perspective. Singapore: Springer.

Zulkardi. (2002). Developing a Learning Environment on Realistic Mathematics Education for Indonesian Student Teachers. Unpublished Dissertation. Enschede: University of Twente.

Zulkardi. (2006). Formative Evaluation: What, Why, When, and How. Retrieved Juni 2019. from

Zulkardi. (2017). Pembelajaran pemodelan matematika. Seminar Nasional Matematika dan Pendidikan Matematika (SNMPM). Palembang: Universitas Sriwijaya.



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Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
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Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.

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