Opportunity-to-Learn to Solve Context-based Mathematics Tasks and Students’ Performance in Solving these Tasks – Lessons from Indonesia
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Freudenthal Institute, Faculty of Science, Utrecht University, THE NETHERLANDS
Yogyakarta State University, INDONESIA
Freudenthal Group, Faculty of Social and Behavioural Sciences, Utrecht University, THE NETHERLANDS
Nord University, NORWAY
Publish date: 2018-07-14
EURASIA J. Math., Sci Tech. Ed 2018;14(10):em1598
This study investigated whether providing opportunity-to-learn can improve Indonesian students’ performance in solving context-based mathematics tasks. On the basis of an inventory of Indonesian students’ difficulties with these tasks and an analysis of textbooks and classroom practices, an intervention program for mathematics teachers was developed. This program contained tasks with relevant and essential contexts with missing or superfluous information, but without explicitly given mathematical procedures. The program also comprised guidelines for a consultative teaching approach with metacognitive prompts and questions for discussion to promote reflection in class. A field experiment with a pretest-posttest control-group design was carried out in six junior high schools in Indonesia involving 299 eight-graders. Students in the experimental group made significantly more progress on solving context-based mathematics tasks than students in the control group. Furthermore, an analysis of students’ errors revealed that experimental students made significantly fewer task comprehension errors than control students. These results show that providing opportunity-to-learn, that is offering context-based tasks to students, which require mathematical modeling, and having teachers knowing the characteristics of such tasks and using a consultative teaching approach, can improve students’ ability in solving context-based tasks.
Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23-38. https://doi.org/10.1080/014119....
Antonius, S., Haines, C., Jensen, T. H., Niss, M., & Burkhardt, H. (2007). Classroom activities and the teacher. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (pp. 295–308). New York: Springer. https://doi.org/10.1007/978-0-....
Bernardo, A. B. I. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19(2), 149–163. https://doi.org/10.1080/014434....
Blum, W. (1993). Mathematical modelling in mathematics education and instruction In T. Breiteig, I. Huntley, & G. Kaiser-Messmer (Eds.), Teaching and learning mathematics in context (pp. 3-14). Chichester, UK: Ellis Horwood Limited.
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). New York: Springer. https://doi.org/10.1007/978-94....
Blum, W. (2015). Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do? In: S.J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education - Intellectual and Attitudinal Challenges (pp 73-96). New York: Springer.
Blum, W., & Borromeo Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects - state, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37–68. https://doi.org/10.1007/BF0030....
Boaler, J. (1994). When girls prefer football to fashion? An analysis of female under achievement in relation to realistic mathematics contexts. British Educational Research Journal, 20(5), 551–564. https://doi.org/10.1080/014119....
Borasi, R. (1986). On the nature of problems. Educational Studies in Mathematics 17(2), 125-141. https://doi.org/10.1007/BF0031....
Brewer, D. J., & Stasz, C. (1996). Enhancing opportunity to learn measures in NCES data. Santa Monica, CA: RAND.
Carroll, J. (1963). A model of school learning. Teachers College Record, 64, 723-733.
Charalambous, C. Y., Delaney, S., Hsu, H-Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117–151. https://doi.org/10.1080/109860....
Clements, M. A. (1980). Analyzing children’s errors on written mathematical task. Educational Studies in Mathematics, 11(1), 1–21. https://doi.org/10.1007/BF0036....
De Lange, J. (1987). Mathematics, Insight and Meaning. Utrecht, the Netherlands: OW&OC.
De Lange, J. (2015). There is, probably, no need for this presentation. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education – ICMI Study 22 (pp. 287-308). Cham, Heidelberg, New York, Dordrecht, London: Springer. https://doi.org/10.1007/978-3-....
Doerr, H. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 69–78). New York: Springer. https://doi.org/10.1007/978-0-....
Eurydice (2011). Mathematics education in Europe: Common challenges and national policies. Brussels: Education, Audiovisual and Culture Executive Agency.
Forman, S. L., & Steen, L. A. (2001). Why math? Applications in science, engineering, and technological programs. Research Brief, American Association of Community Colleges.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, the Netherlands: Reidel.
Goldman, S. R. (1989). Strategy instruction in mathematics. Learning Disability Quarterly, 12(1), 43–55. https://doi.org/10.2307/151025....
Graumann, G. (2011). Mathematics for problem in the everyday world. In J. Maasz & J. O’Donoghue (Eds.), Real-world problems for secondary school mathematics students: Case studies (pp. 113–122). Rotterdam: Sense Publishers. https://doi.org/10.1155/2011/5....
Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129.
Greer, B. (1997). Modeling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307. https://doi.org/10.1016/S0959-....
Grouws, D. A., & Cebulla, K. J. (2000). Improving student achievement in mathematics. Brussels: International Academy of Education.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte: Information Age Publishing.
Howson, G. (2013). The development of mathematics textbooks: historical reflections from personal perspective. ZDM – The International Journal on Mathematics Education, 45(5), 647–658. https://doi.org/10.1007/s11858....
Husén, T. (Ed). (1967). International study of achievement in mathematics: A comparison of twelve countries (Vol. II). New York: John Wiley & Sons.
Ikeda, T. (2007). Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 457–462). New York: Springer. https://doi.org/10.1007/978-0-....
Karbalei, A., & Amoli, F. A. (2011). The effect of paraphrasing strategy training on the reading comprehension of college students at the undergraduate level. Asian EFL Journal, 13(3), 229–344.
Kletzien, S. B. (2009). Paraphrasing: An effective comprehension strategy. The Reading Teacher, 63(1), 73–77. https://doi.org/10.1598/RT.63.....
Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(1), 81–91. https://doi.org/10.1007/BF0321....
Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49(2), 225–250. https://doi.org/10.1023/A:1016....
Kunter, M., Baumert, J., Voss, T., Klusmann, U., Richter, D., & Hachfeld, A. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 105(3), 805–820. https://doi.org/10.1037/a00325....
Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174. https://doi.org/10.2307/252931....
Maass, K. (2007). Modelling tasks for low achieving students – first results of an empirical study. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education CERME 5 (pp. 2120–2129). Larnaca, Cyprus.
Maass, K. (2010). Classification scheme for modelling tasks. Journal fur Mathematik-Didaktik, 31(2), 285–311. https://doi.org/10.1007/s13138....
Mason, J., Burton, L., & Stacey, K. (1982 / 2010). Thinking mathematically. Dorchester, England: Pearson Education Limited. Second Edition.
Maulana, R., Opdenakker, MC., Den Brok, P., & Bosker, R. J. (2012). Teacher-student interpersonal behavior in secondary mathematics classes in Indonesia. International Journal of Science and Mathematics Education, 10(1), 21–47. https://doi.org/10.1007/s10763....
McDonnell, L. M. (1995). Opportunity to learn as a research concept and a policy instrument. Educational Evaluation and Policy Analysis, 17(3), 305-322. https://doi.org/10.2307/116450....
Montague, M. (2007). Self-regulation and mathematics instruction. Learning Disabilities Research and Practice, 22(1), 75–83. https://doi.org/10.1111/j.1540....
Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31(1), 37–44.
Montague, M., Warger, C., & Morgan, T. H. (2000). Solve it! Strategy instruction to improve mathematical problem solving. Learning Disabilities Research and Practices, 15(2), 110–116. https://doi.org/10.1207/SLDRP1....
NCTM (2000). Principles and Standard for School Mathematics. Reston: Author.
OECD (2003). The PISA 2003 Assessment Framework - Mathematics, Reading, Science, and Problem Solving Knowledge and Skills. Paris: Author.
OECD (2009a). Learning Mathematics for Life. A View Perspective from PISA. Paris: Author.
OECD (2009b). Take the Test. Sample Questions from OECD’s PISA Assessments. Paris: Author.
OECD (2010). PISA 2009 Results: What students know and can do. Student performance in reading, mathematics, and science (Vol. I). Paris: Author.
OECD (2013). PISA 2012 Results: What students know and can do. Student performance in mathematics, reading and science. Paris: Author.
OECD (2016). PISA 2015 Results (Volume I): Excellence and Equity in Education. PISA, OECD Publishing, Paris. https://doi.org/10.1787/978926....
Pólya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
Pusat Kurikulum (2003). Kurikulum 2004: Standar kompetensi mata pelajaran matematika Sekolah Menengah Pertama dan Madrasah Tsanawiyah. Jakarta: Departemen Pendidikan nasional.
Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many visions, many aims: A cross-national investigation of curricular intentions in school mathematics. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94....
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press Inc. https://doi.org/10.1016/B978-0....
Tomlinson, M. (2004). 14-19 Curriculum and Qualifications Reform. Final report of the Working Group on 14-19 Reform. London: Department for Education and Skills.
Tornroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stue....
Valverde. G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book. Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94....
Van den Heuvel-Panhuizen, M. (1996). Assessment and realistic mathematics education. Utrecht, the Netherlands: CD-β Press/Freudenthal Institute, Utrecht University.
Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2-9 + 23.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.
Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015a). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649....
Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015b). Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks. Mathematics Education Research Journal, 27(4), 637–662. https://doi.org/10.1007/s13394....
Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584.
World Bank (2010). Inside Indonesia’s mathematics classrooms: A TIMSS Video Study of teaching practices and student achievement. Jakarta: Author.
Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. Journal of Educational Research, 100(6), 347–359. https://doi.org/10.3200/JOER.1....