• https://theoejwilson.com/
  • santuy4d
  • mariatogel
  • santuy4d
  • garuda slot
  • garudaslot
  • https://edujournals.net/
  • nadimtogel
  • https://mitrasehatjurnal.com/
  • slot gacor hari ini
  • g200m
  • 55kbet
  • slot gacor
  • garudaslot
  • link slot gacor
  • https://perpustakaan.stpreinha.ac.id/mahasiswa/
  • https://www.lml.stpreinha.ac.id/lab/
  • https://cursosvirtuales.icip.edu.pe/nice/
    • PROSPECTIVE MATHEMATICS TEACHERS’ COGNITIVE COMPETENCIES ON REALISTIC MATHEMATICS EDUCATION | Yilmaz | Journal on Mathematics Education

    PROSPECTIVE MATHEMATICS TEACHERS’ COGNITIVE COMPETENCIES ON REALISTIC MATHEMATICS EDUCATION

    Rezan Yilmaz

    Abstract


    Realistic Mathematics Education (RME) is based on the idea that mathematics is a human activity; and its main principle is to ensure the transition from informal knowledge to formal knowledge through contextual problems. This study aims at revealing how RME is configured in the minds of prospective mathematics teachers and their cognitive competency in that sense. For that purpose, at the end of the process, in which the approaches used in mathematical education including RME are examined and interpreted, 32 prospective teachers were asked various open-ended questions. Moreover, they were expected to pose contextual problems that could be used in RME. After analysing the obtained data via qualitative research techniques, it is seen that the majority of the prospective teachers possesses theoretical knowledge on RME. However, it is also observed that their ability to present its differences and similarities with other approaches and to pose contextual problems suitable to RME has been decreased.

    Keywords


    Realistic Mathematics Education; Prospective Mathematics Teacher; Cognitive Competency; Contextual Problem

    Full Text:

    PDF

    References


    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/10.1080/01411920500401971.

    Alfieri, L., Brooks, P.J., Aldrich, N.J., & Tenenbaum, H.R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1-18. https://doi.org/10.1037/a0021017.

    Altun, M. (2011). E?itim fakülteleri ve matematik ö?retmenleri için liselerde matematik ö?retimi (Mathematics Education in High Schools). Bursa: Alfa Akademi.

    Anderson, L.W., & Krathwohl, D.R. (2001). (Eds.) Taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Needham Heights, MA: Allyn & Bacon.

    Anderson, J., White, P., & Wong, M. (2012). Mathematics curriculum in the schooling years. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Research in mathematics education in Australasia 2008–2011 (pp. 219–244). Rotterdam: Sense Publishers.

    Aubrey, K., & Riley, A. (2016). Understanding and using educational theories. London: Sage.

    Ausubel, D.P. (1963). The psychology of meaningful verbal learning. New York: Gruene and Stratton.

    Ayer, A.J. (1936). Language, truth and logic. Oxford: Oxford University Press.

    Barell, J. (2010). Problem-based learning: The foundation of 21st century skills. In J. Bellance & R. Brandt R (Eds.), 21 st century skills (pp. 174-199). Bloomington: Solution Tree Press.

    Barnes, H. (2004). Realistic mathematics education: Eliciting alternative mathematical conceptions of learners. African Journal of Research in Mathematics, Science and Technology Education, 8(1), 53-64. https://doi.org/10.1080/10288457.2004.10740560.

    Barrett, T.C. (1976). Taxonomy of reading comprehension. In R. Smith & T. C. Barrett (Eds.). Teaching reading in the middle grades. Reading, MA: Addison-Wesley Publishing Co.

    Barrows, H.S. (1986). A taxonomy of problem?based learning methods. Medical Education, 20(6), 481-486. https://doi.org/10.1111/j.1365-2923.1986.tb01386.x.

    Battista, M.T. (1994). Teacher beliefs and the reform movement in mathematics education. The Phi Delta Kappan, 75(6), 462-470.

    Baumert, J., & Kunter, M. (2013). The effect of content knowledge and pedagogical content knowledge on instructional quality and student achievement. In Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 175-205). Boston: Springer.

    Berg, B.L. (2001). Qualitative research methods for the social sciences (4th ed.). Boston: Allyn & Bacon.

    Beswick, K. (2011). Putting context in context: An examination of the evidence for the benefits of ‘contextualised’tasks. International Journal of Science and Mathematics Education, 9(2), 367-390. http://dx.doi.org/10.1007/s10763-011-9323-y.

    Beswick, K., & Goos, M. (2012). Measuring pre-service primary teachers' knowledge for teaching mathematics. Mathematics Teacher Education and Development, 14(2), 70-90.

    Bloom, B.S., Engelhart, M.D., Furst, E.J., Hill, W.H., & Krathwohl, D.R. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook 1: Cognitive domain. New York: David McKay.

    Bloom, B.S. (1994). Reflections on the development and use of the taxonomy. In L. W. Anderson & L. A. Sosniak (Eds.). Bloom's taxonomy: A forty-year retrospective (1-61). Chicago: University of Chicago Press.

    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(1), 37-68. https://doi.org/10.1007/BF00302716.

    Borko, H., & Putnam, R. (1996). Learning to teach. In D. C. Berliner, R. C. Calfee (Eds.). Handbook of educational psychology (673-708). New York: Simon & Schuster Macmillan.

    Borasi, R., & Fonzi, J. (2002). Professional development that supports school mathematics reform. Foundations series of monographs for professionals in science, mathematics and technology education. Arlington, VA: National Science Foundation.

    Bray, A., & Tangney, B. (2016). Enhancing student engagement through the affordances of mobile technology: a 21st century learning perspective on Realistic Mathematics Education. Mathematics Education Research Journal, 28(1), 173-197. https://doi.org/10.1007/s13394-015-0158-7.

    Brousseau, G. (1987). Les differents roles du maitre. Colloque des P.E.N. Angers. In S. A. Martin (Ed.). Reconstructing mathematics pedagogy from a constructivist perspective. Washington, DC: National Science Foundation.

    Bruner, J.S. (1961). The act of discovery. Harvard Educational Review, 31, 21-32.

    Cai, J., & Howson, G. (2013). Toward an international mathematics curriculum. In M. A. K. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 949–974). New York: Springer.

    Creswell, J.W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousands Oaks, CA: Sage.

    Davis, R.B. (1990). Discovery Learning and Constructivism. Journal for Research in Mathematics Education: Monograph (4): Constructivist Views on the Teaching and Learning of Mathematics, (pp. 93-106+195-21). Association Drive, Reston, VA 22091.

    Dawkins, P.C. (2015). Explication as a lens for the formalization of mathematical theory through guided reinvention. The Journal of Mathematical Behavior, 37, 63-82.

    De Corte, E. (1995). Fostering cognitive growth: A perspective from research on mathematics learning and instruction. Educational Psychologist, 30(1), 37-46. https://doi.org/10.1207/s15326985ep3001_4.

    De Lange, J. (1987). Mathematics, insight, and meaning. The Netherlands, Utrecht: OW&OC.

    De Lange, J. (1996). Using and applying mathematics in education. In A. J. Bishop et al. (Eds.). International handbook of mathematics education (pp. 49-97). The Netherlands: Kluwer Academic Publishers.

    Doorman, M., Drijvers, P., Dekker, T., van den Heuvel-Panhuizen, M., de Lange, J., & Wijers, M. (2007). Problem solving as a challenge for mathematics education in the Netherlands. ZDM, 39(5-6), 405-418. https://doi.org/10.1007/s11858-007-0043-2.

    Dreyfus, T., & Tsamir, P. (2004). Ben's consolidation of knowledge structures about infinite sets. The Journal of Mathematical Behavior, 23(3), 271-300. https://doi.org/10.1016/j.jmathb.2004.06.002.

    Driscoll, M.P. (2005). Psychology of learning for instruction. (3th Ed.) Boston, MA: Pearson.

    English, L.D. (1995). Cognitive psychology and mathematics education. In L. D. English, G. S. Halford (Eds.). Mathematics education: Models and processes (pp. 1-20). Lawrence Erlbaum Associates, Mahwah: NJ.

    English, L.D. (2003). Problem posing in the elementary curriculum. In F. Lester, R. Charles (Eds.). Teaching mathematics through problem solving. Reston, Virginia: National Council of Teachers of Mathematics.

    Ertmer, P.A., & Newby, T.J. (1993). Behaviorism, cognitivism, constructivism: Comparing critical features from an instructional design perspective. Performance Improvement Quarterly, 6(4), 50-72. https://doi.org/10.1111/j.1937-8327.1993.tb00605.x

    Fauzan, A. (2002). Applying Realistic Mathematics Education (RME) in teaching geometry in Indonesian primary schools. Unpublished Doctoral Dissertation. Enschede: University of Twente.

    Feijs, E. (2005). Constructing a learning environment that promotes reinvention. In R. Nemirovsky, A. S. Rosebery, J. Solomon, & B. Warren (Eds.). Everyday matters in science and mathematics: Studies of complex classroom events. Mahwah, NJ: Lawrence Erlbaum.

    Feiman-Nemser, S. (2001). From preparation to practice: Designing a continuum to strengthen and sustain teaching. Teachers College Record, 103(6), 1013-1055.

    Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel.

    Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer Academic.

    Granello, D. H. (1995). Encouraging the cognitive development of supervisees: Using Bloom's taxonomy in supervision. Counselor Education and Supervision, 40(1), 31-46. https://doi.org/10.1002/j.1556-6978.2000.tb01797.x.

    Granello, D. H. (2001). Promoting cognitive complexity in graduate written work: Using Bloom’s taxonomy as a pedagogical tool to improve literature reviews. Counselor Education and Supervision, 40, 292-307. https://doi.org/10.1002/j.1556-6978.2001.tb01261.x.

    Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177. https://doi.org/10.1207/s15327833mtl0102_4.

    Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: Utrecht, The Netherlands: CD-? Press.

    Gravemeijer, K.P.E. (2001). Developmental research: Fostering a dialectic relation between theory and practice. In J. Anghileri (Ed.). Principles and practice in arithmetic teaching (147-161). London: Open University Press.

    Gravemeijer, K.P.E., & Cobb, P. (2006). Design research from a learning design perspective. In J.Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 45–85). London: Routledge, Taylor Francis Group.

    Gravemeijer, K. (2008). RME theory and mathematics teacher education. International handbook of mathematics teacher education, 1, 283-302.

    Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307. https://doi.org/10.1016/S0959-4752(97)00006-6.

    Hadi, S. (2002). Effective teacher professional development for the implementation of realistic mathematics education in Indonesia. Unpublished Doctoral Dissertation. University of Twente.

    Hammer, D. (1997). Discovery learning and discovery teaching. Cognition and Instruction, 15(4), 485-529. https://doi.org/10.1207/s1532690xci1504_2.

    Hamzah, U., & Bustang, B. (2014). Constructivism versus cognitive load theory: in search for an effective mathematics teaching. In Proceeding of International Conference on Research, Implementation and Education of Mathematics and Sciences, May 18-20, 2014. Yogyakarta State University.

    Herman, P., & Gomez, L.M. (2009). Taking guided learning theory to school. In S. Tobias, D. M. Duffy (Eds.). Constructivist theory applied to instruction: Success or failure? (pp. 62-81). New York, NY: Taylor & Francis.

    Hiebert, J., & Carpenter, T.P. (1992). Learning and teaching with understanding. In J. Hiebert, T. P. Carpenter, D. A. Grouws (Eds.). Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 65-97). New York: Macmillan.

    Jacobsen, D., Eggen, P., & Kauchak, D. (1993). Methods for teaching: A skills approach (4th ed.). Columbus, OH: Merrill.

    Jonassen, D.H. (1991). Objectivism versus constructivism: Do we need a new philosophical paradigm? Educational technology research and development, 39(3), 5-14. https://doi.org/10.1007/BF02296434.

    Jonassen, D.H. (1991a). Evaluating constructivistic learning. Educational Technology, 31(9), 28-33.

    Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.). Cognitive science and mathematics education (123-148). Hillsdale. NJ: Erlbaum.

    Klein, A.S. (1998). Flexibilization of mental arithmetic strategies on a different knowledge base. Utrecht: Freudenthal Institute.

    Kraiger, K., Ford, J.K., & Salas, E. (1993). Application of cognitive, skill-based, and affective theories of learning outcomes to new methods of training evaluation. Journal of Applied Pschology, 78(2), 311-328.

    Krathwohl, D.R., Bloom, B.S., & Bertram, B.M. (1973). Taxonomy of educational objectives, the classification of educational goals. Handbook II: affective domain. New York: David McKay.

    Krathwohl, D. R. (2002). A revision of Bloom's taxonomy: An Overview. Theory into Practice, 41(4), 212-218. https://doi.org/10.1207/s15430421tip4104_2.

    Kwon, O.N. (2002). Conceptualizing the Realistic Mathematics Education approach in the teaching and learning of ordinary differential equations. In Proceedings of the International Conference on the Teaching of Mathematics Hersonissos, July 1-6. Crete, Greece.

    Lesh, R., Doerr, H.M., Carmona, G., & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking and Learning, 5(2&3), 211–233. http://dx.doi.org/10.1080/10986065.2003.9680000.

    Lianghuo, F. (2014). Investigating the pedagogy of mathematics: How do teachers develop their knowledge?. Imperial College Press, London.

    Lincoln, Y.S., & Guba, E.G. (1985). Naturalistic inquiry (Vol. 75). California: Sage.

    Makonye, J. P. (2014). Teaching functions using a realistic mathematics education approach: A theoretical perspective. International Journal of Educational Sciences, 7(3), 653-662. https://doi.org/10.1080/09751122.2014.11890228.

    National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

    Noddings, N. (1990). Constructivism in mathematics teaching. In R. B. Davis, C. A. Maher, N. Noddings (Eds). Constructivist views on the learning and teaching of mathematics (7-18). Reston, VA: National Council of Teachers of Mathematics. (J for Res in Math Edu. Monograph Number 4).

    OECD. (2003). The PISA 2003 assessment framework. mathematics, reading, science and problem solving knowledge and skills. Paris: OECD.

    OECD. (2009). PISA 2006 Technical report. Paris: OECD.

    Patton, M.Q. (1990). Qualitative evaluation and research methods. (2nd ed.) Newbury Park, CA: Sage.

    Pearson, P.D., & Johnson, D.D. (1978). Teaching reading comprehension. New York: Holt, Rinehart, & Winston.

    Piaget, J. (1973). To understand is to invent: The future of education. New York: Grossman.

    Putnam, R.T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Research, 29(1), 4-15. https://doi.org/10.3102%2F0013189X029001004.

    Rasmussen, C.L., & King, K.D. (2000). Locating starting points in differential equations: A realistic mathematics education approach. International Journal of Mathematical Education in Science and Technology, 31(2), 161-172. https://doi.org/10.1080/002073900287219.

    Richards, J. (1991). Mathematical Discussion. In E. von Glasersfeld (Ed.). Radical constructivism in mathematical education (pp. 13-52). Dortrecht: Kluwer.

    Sadler, T.D., & Zeidler, D.L. (2009). Scientific literacy, PISA, and socioscientific discourse: Assessment for progressive aims of science education. Journal of Research in Science Teaching, 46(8), 909-921. https://doi.org/10.1002/tea.20327.

    Selter, C. (1997). Instructional design for teacher education. In M. Beishuizen, K.P.E. Gravemeijer, & E.C.D.M. van Lieshout (Eds.), The role of contexts and models in the development of mathematics strategies and procedure (pp. 55-77). Utrecht:CD-B Press/Freudenthal Institute.

    Selter, C. (2001). Understanding-the underlying goal of teacher education. In M. Van den Heuvel-Panhuizen (Ed.), Proceeding of 25th conference international group of psychology of mathematics education, 12-17 July, Utrecht, the Netherlands.

    Sembiring, R.K, Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM, 40, 927-939. https://doi.org/10.1007/s11858-008-0125-9.

    Simon, M.A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematical Education, 26(2), 114-145. https://doi.org/10.2307/749205.

    Simons, R.J., Van der Linden, J., & Duffy, T. (Eds.) (2000). New learning. Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1-23.

    Sowder, J.T. (2007). The mathematics education and development of teachers. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157-223). Charlotte, NC: Information Age.

    Sriraman, B., & English, L. (2010). Surveying theories and philosophies of mathematics education. In B. Sriraman & L. English (Eds). Theory of mathematics education. Advances in mathematics education (pp. 7-32). Berlin Heidelberg: Springer-Verlag.

    Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behavior, 24, 341–350. https://doi.org/10.1016/j.jmathb.2005.09.004.

    Streefland, L. (1991). Fraction in Realistic Mathematics Education, A paradigm of developmental research. Dordrecht: Kluwer Academic Publisher.

    Svinicki, M.D. (1998). Theoretical Foundation for Discovery Learning. Advances in Psychological Education, 20(1), S4-S7. https://doi.org/10.1152/advances.1998.275.6.S4.

    Szydlik, J.E., Szydlik, S.D., & Benson, S.R. (2003). Exploring changes in pre-service elementary teachers’ mathematical beliefs. Journal of Mathematics Teacher Education, 6(3), 253-279. https://doi.org/10.1023/A:1025155328511

    Treffers, A., & Goffree, F. (1985). Rational analysis of realistic mathematics education - The Wiskobas Program. In L. Streefland (Ed). Proceedings of the 9th International Conference for the Psychology of Mathematics Education, July 22-29; Noordwijkerhout. Utrecht, The Netherlands.

    Treffers, A. (1991). Realistic mathematics education in the Netherlands 1980 - 1990. In L. Streefland (Ed.). Realistic Mathematics Education in primary schools (pp. 11–20). Utrecht: Freudenthal Institute.

    Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics education. Dordrecht: Reidel.

    Tsamir, P. (2008). Using Theories as Tools in Mathematics Teacher Education, In D. Tirosh & T. Wood (Eds.). Tools and Processes in Mathematics Teacher Education (pp. 221-232). Rotterdam: Sense Publishers.

    Van den Heuvel-Panhuizen, M. (1996). Assessment and Realistic Mathematics Education. Utrecht: Freudenthal Institute.

    Van den Heuvel-Panhuzen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9-35. https://doi.org/10.1023/B:EDUC.0000005212.03219.dc.

    Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets & Zeitlinger, Lisse.

    Von Glasersfeld, E. (1987). Learning as a constructive activity, In C. Janvier (Ed.). Problems of representation in the teaching and learning of mathematics (pp. 3-18). Hillsdale, NJ: Lawrence Erlbaum Associate.

    Wang P.L. (1990). Assessment of Cognitive Competency. In D. E. Tupper and K. D. Cicerone (Eds.) The Neuropsychology of Everyday Life: Assessment and Basic Competencies. Foundations of Neuropsychology (pp. 219-228). Springer, Boston, MA.

    Webb, N. (1997). Criteria for alignment of expectations and assessments on mathematics and science education. Council of Chief State School Officers and National Institute for Science Education Research Monograph No. 6. Washington, DC: CCSSO.

    Webb, N. (1999). Alignment of science and mathematics standards and assessments in four states. Council of Chief State School Officers and National Institute for Science Education Research Monograph No.18. Washington, DC: CCSSO.

    Widjaja, W. (2008). Local instruction theory on decimals: The case of Indonesian pre-service teachers. Doctoral dissertation. Melbourne: The University of Melbourne.

    Widjaja, W. (2013). The use of contextual problems to support mathematical learning. Journal on Mathematics Education, 4(2), 157-168. http://dx.doi.org/10.22342/jme.4.2.413.151-159.

    Wu, H. (1999). Basic skills versus conceptual understanding. American Educator, 23(3), 14-19.

    Wubbels, T., Korthagen, F., & Broekman, H. (1997). Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32, 1–28. https://doi.org/10.1023/A:100290052.

    Yackel, E., & Cobb, P. (1996). Sociomath norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematical Education, 27, 75-190. https://www.jstor.org/stable/749877

    Yackel, E., Gravemeijer, K., & Sfard, A. (2011). A journey in mathematics education research. Dordrecht: Springer.

    Y?ld?r?m, A., & ?im?ek, H. (2005). Sosyal bilimlerde nitel ara?t?rma yöntemleri (Qualitative research methods for social sciences). Ankara: Seçkin Yay?nc?l?k.

    Zulkardi. (2002). Developing a learning environment on realistic mathematics education for Indonesian student teachers. Doctoral Dissertation. Enschede: University of Twente.




    DOI: https://doi.org/10.22342/jme.11.1.8690.17-44

    Refbacks

    • There are currently no refbacks.


    Creative Commons License
    This work is licensed under a Creative Commons Attribution 4.0 International License.

    Journal on Mathematics Education
    Doctoral Program on Mathematics Education
    Faculty of Teacher Training and Education, Universitas Sriwijaya
    Kampus FKIP Bukit Besar
    Jl. Srijaya Negara, Bukit Besar
    Palembang - 30139
    email: jme@unsri.ac.id
    p-ISSN: 2087-8885 | e-ISSN: 2407-0610

    Creative Commons License
    Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.


    View My Stats