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Yıl 2021, Cilt: 7 Sayı: 2, 104 - 127, 01.04.2021
https://doi.org/10.21891/jeseh.832574

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  • Ang, K. C. (2015). Mathematical modelling in Singapore schools: A framework for instruction. In N. H. Lee & D. K. E. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 57-72). Singapore: National Institute of Education.
  • Artzt, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and Instruction, 9(2), 137-175. doi:10.1207/s1532690xci0902_3
  • Azevedo, R. (2005). Computer environments as metacognitive tools for enhancing learning. Educational Psychologist, 40(4), 193–197. Bal, A. P., & Doğanay, A. (2014). Improving primary school prospective teachers’ understanding of the mathematics modeling process. Educational Sciences: Theory & Practice, 14(4), 1375–1384.
  • Bell, D. (2016). The reality of STEM education, design and technology teachers’ perceptions: A phenomenographic study. International Journal of Technology and Design Education, 26, 61–79.
  • Biggs, J. (1987). The process of learning. Sydney: Prentice Hall.
  • Birenbaum, M. (1996). Assessment 2000: Towards a pluralistic approach to assessment. In M. Birenbaum & F. Dochy, (Eds.), Alternatives in assessment of achievements, learning processes and prior knowledge (pp. 3–30). Boston: Kluwer.
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), International perspectives on the teaching and learning of mathematical modelling, trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.
  • Blum, W., & Leiss, D. (2007). How do Students and Teachers deal with mathematical Modelling Problems? The example Sugaloaf und the DISUM Project. In C. Haines, P. L.
  • Galbraith, W. Blum & S. Khan (Eds.), Mathematical Modelling (ICTMA12) - Education, Engineering and Economics. Chichester: Horwood.
  • Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  • Borba, M. C., & Villarreal, M. (2005). Humans-with-media and the reorganization of mathematical thinking. New York: Springer.
  • Brophy, S., Klein, S., Portsmore, M., & Rogers, C. (2008). Advancing engineering education in P–12 classrooms. Journal of Engineering Education 97, 269–387 . Brown, A., & De Loache, J. (1983). Metacognitive skills. In M. Donaldson, R. Grieve, & C. Pratt (Eds.), Early childhood development and education (pp. 3–35). Oxford: Blackwell.
  • Bruner, J. S. (1964). The course of cognitive growth. American psychologist, 19(1), 1.
  • Bryce, D., & Whitebread, D. (2012). The development of metacognitive skills: Evidence from observational analysis of young children’s behavior during problem-solving. Metacognition Learning, 7, 197–217.
  • Cai, J., Cirillo, M., Pelesko, J. A., Ferri, R. B., Stillman, G., English, L. D., Wake, G., Kaiser, G., & Kwon, O. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional, and teacher educational perspectives. In Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 145-172). Canada: PME-NA.
  • Cardelle-Elawar, M. (1992). Effects of teaching metacognitive skills to students with low mathematical ability. Teaching and Teacher Education, 8(2), 109-121.
  • Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating a Models and Modeling Perspective with Existing Research and Practice. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Chan, E. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
  • Clement, L. (2004). A model for understanding, using, and connecting representations. Teaching Children Mathematics, 11(2), 97-102.
  • Cramer, K. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. Doerr (Eds.), Beyond constructivism (pp. 449-463). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Cramer, K. A., Monson, D. S., Wyberg, T., Leavitt, S., & Whitney, S. B. (2009). Models for Initial Decimal Ideas. Teaching Children Mathematics, 16(2), 106-117.
  • De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491-549). New York, NY, US: Macmillan Library Reference Usa; London, England: Prentice Hall International.
  • Deniz, D., & Akgün, L. (2014). Ortaöğretim öğrencilerinin matematiksel modelleme yönteminin sınıf içi uygulamalarına yönelik görüşleri. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 4(1), 103-116.
  • Dewaters, J., & S. E. Powers. (2006). Improving science and energy literacy through project-based K-12 outreach efforts that use energy and environmental themes. In Proceedings of the 113th Annual ASEE Conference & Exposition. Chicago, IL.
  • Diefes-Dux, H. A., & Imbrie, P. K. (2008). Modeling activities in a first-year engineering course. In J. S. Zawojewski, H. A. Diefes-Dux, & K. J. Bowman (Eds.), Models and modeling in engineering education: Designing experiences for all students (pp. 55-92). The Netherlands: Sense Publishers.
  • Diefes-dux, H., Hjalmarson, Miller, & Lesh, R. (2008). Model-eliciting for engineering education. In J. Zawojewski, H. Diefes-Dux, & K. Bowman (Eds.), Models and modeling in engineering education: Designing experiences for all students (pp. 17–35). Rotterdam, the Netherlands: Sense Publishers.
  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modeling? In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (1st ed., pp. 69–78). New York: Springer.
  • Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi (Unpublished doctoral dissertation). Hacettepe Üniversitesi, Ankara.
  • Driscoll, M. P. (2000). Psychology of Learning for Instruction (2nd ed.). Boston, MA: Allyn and Bacon.Duffy, T., & Cunningham, D. (1996). Constructivism: Implications for the design and delivery of instruction. Handbook of research for educational communications and technology, 170–198.
  • Dunlosky, J., & Metcalfe, J. (2009). Metacognition. Thousand Oaks, CA: Sage Publications, Inc.
  • English, L. D., Fox, J. L., & Watters, J. J. (2005) Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12(3), 156-163.
  • Erbaş, A. K., Kertı̇l, M., Çetı̇nkaya, B., Çakiroğlu, E., Alacaci, C., & Baş, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory & Practice, 14(4), 1621–1627.
  • Eric, C. C. M. (2010). Tracing primary 6 students’ model development within the mathematical modeling process. Journal of Mathematical Modeling and Applications, 1, 40-57.
  • Ferguson, R. L. (2007). Constructivism and social constructivism. In G. M. Bodner & M. Orgill (Eds.), Theoretical frameworks for research in chemistry/science education (pp. 28-49). Upper Saddle River, NJ: Prentice Hall.
  • Fox, J. (2006). A justification for mathematical modelling experiences in the preparatory classroom. In Grootenboer, P., Zevenbergen, R., & Chinnappan, M., (Eds.), Proceedings 29th annual conference of the Mathematics Education Research Group of Australasia. 1, 21-228.
  • Frykholm, J., & Glasson, G. (2005). Connecting science and mathematics instruction: Pedagogical context knowledge for teachers. School Science and Mathematics, 105(3), 127-141.
  • Gagne, R. M., Medsker, K. L. (1996). The Conditions of Learning: Training Applications. Harcourt Brace College Publishers: Fort Worth.
  • Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163-176.
  • Glancy, A. W., & Moore, T. J. (2013). Theoretical foundations for effective STEM learning environments. Education Working Papers (1-1-2013), School of Engineering Education, Purdue University. Accessed on 10/04/2016. http://docs.lib.purdue.edu/enewp/1
  • Goldin, G. A. (2007). Aspects of affect and mathematical modelling processes. Foundations for the future in mathematics education, 281-299.
  • Goos, M. (1994). Metacognitive decision making and social interactions during paired problem solving. Mathematics Education Research Journal. 6(2), 144-165.
  • Goos, M. (2002). Understanding metacognitive failure. The Journal of Mathematical Behavior, 21(3), 283-302.
  • Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30, 229-260.
  • Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49(2), 193-223. doi:10.1023/A:1016209010120
  • Gould, H., & Wasserman, N. (2014). Striking a balance: Student’s tendencies to oversimplify or overcomplicate in mathematical modeling. Journal of Mathematics Education at Teachers College, 5(1), 27-34.
  • Gurbin, T. (2015). Metacognition and technology adoption: Exploring influences. Procedia - Social and Behavioral Sciences, 191, 1576–1582. doi.org/10.1016/ j.sbspro.2015.04.608
  • Haines, C., & Crouch, R. (2007). Mathematical modeling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: e 14th ICMI study (pp. 417-424). New York, NY: Springer.
  • Hıdıroğlu, Ç. N., & Bukova-Güzel, E. (2014). Matematiksel modellemede GeoGebra kullanımı: Boy-ayak uzunluğu problemi. Pamukkale Üniversitesi, Eğitim Fakültesi Dergisi, 36(2), 29-44.
  • Hıdıroğlu, Ç. N. ve Bukova Güzel, E. (2015). Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education, 6(2), 179-208.
  • Hıdıroğlu, Ç. N., & Bukova-Güzel, E. (2016). Transitions between Cognitive and Metacognitive Activities in Mathematical Modelling Process within a Technology Enhanced Environment. Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education, 10(1), 313-350.
  • Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. In 11th International Congress on Mathematical Education. Monterrey, Nuevo Leon, Mexico.
  • Jacobse, A. E., & Harskamp, E. G. (2009). Student-controlled metacognitive training for solving word problems in primary school mathematics. Educational Research and Evaluation, 15(5), 447-463.
  • Jacobse, A. E., & Harskamp, E. G. (2012). Towards efficient measurement of metacognition in mathematical problem solving. Metacognition and Learning, 7(2), 133-149.
  • Johnson, T., & Lesh, R. (2003). A models and modeling perspective on technology-based representational media. Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching, 265-278.
  • Johnson, D. W., Johnson, R. T., & Smith, K. (2007). The state of cooperative learning in postsecondary and professional settings. Educational Psychology Review, 19(1), 15-29.
  • Joseph, N. (2010). Metacognition needed: Teaching middle and high school students to develop strategic learning skills. Preventing School Failure. 54(2), 99–103. Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38, 196–208.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
  • Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. ZDM, 38(2), 82-85.
  • Kaiser, G., Blum, W., Ferri, R. B., & Stillman, G. (2011). International perspectives on the teaching and learning of mathematical modelling, Trends in teaching and learning of mathematical modelling. Dordrecht: Springer.
  • Kaput, J., Hegedus, S., & Lesh, R. (2007). Technology becoming infrastructural in mathematics education. In R. A. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 173–191). Mahwah, NJ: Lawrence Erlbaum.
  • Kertil, M., & Gurel, C. (2016). Mathematical modeling: A bridge to STEM education. International Journal of Education in mathematics, science and Technology, 4(1), 44-55. Doi:10.18404/ijemst.95761
  • Kim, Y. R., Park, M. S., Moore, T. J., & Varma, S. (2013). Multiple levels of metacognition and their elicitation through complex problem-solving tasks. Journal of Mathematical Behavior, 32(3), 377–396. doi: 10.1016/j.jmathb.2013.04.002.
  • Koellner-Clark, K., & Lesh, R. (2003). Whodunit? Exploring proportional reasoning through the footprint problem. School Science and Mathematics, 103(2), 92-98. doi:http:// dx.doi.org/10.1111/j.1949-8594.2003 .tb18224.x
  • 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. doi:10.1023/A:1016282811724
  • Lamon, S. J. (2003). Modelling in elementary school: Helping young students to see the world mathematically. In Mathematical Modelling (pp. 19-33). Woodhead Publishing.
  • Lapp, D. A., & Cyrus, V. F. (2000). Using data-collection devices to enhance students’ understanding. Mathematics Teacher, 93(6), 504-510.
  • Lehrer, R., & Schauble, L. (2000). Developing model-based reasoning in mathematics and science. Journal of Applied Developmental Psychology, 21(1), 39–48. doi:10.1016/S0193-3973(99)00049-0
  • Lesh, R. (1979). Mathematical learning disabilities: Consideration for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied mathematical problem solving (pp. 166-175). Columbus, OH: ERIC/SMEAC.
  • Lesh, R., Post, T., & Behr, M. (1987). Representation and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2-3), 109-129.
  • Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The handbook of research on mathematics teaching and learning (2nd ed.) (pp. 763-804). Reston, VA/Charlotte, NC: National Council of Teachers of Mathematics.
  • Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J., (2003) Using a translation model for curriculum development and classroom instruction. In Lesh, R. & Doerr, H. (Eds.) Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Lawrence Erlbaum Associates, Mahwah, New Jersey.
  • Lesh, R., & Doerr, H. M. (2003). In what ways does a models and modeling perspective move beyond constructivism? In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R., & Fennewald, T. (2010). Introduction to part I modeling: What is it? Why do it? In Richard Lesh, C. Haines, P. L. Galbraith, & A. Hurford (Eds.), Modeling Students’ MM competencies (pp. 5-10). New York: Springer.
  • Lesh, R., & Harel, G. (2003). Problem solving modeling and local conceptual development. Mathematical Thinking and Learning 5(2-3), 157-189.
  • Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models & modelling perspectives on mathematics problem solving, learning, and teaching? In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 161-170). New York: Springer.
  • Lesh, R., Amit, M., & Schorr, R. Y. (1997). Using 'real-life' problems to prompt students to construct conceptual models for statistical reasoning. In I. Gal, & J. B. Garfield (Eds.), The Assessment Challenge in Statistics Education (pp. 65-84). Burke, VA: International Statistical Institute.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Research Design in mathematics and science education (pp. 591–646). New Jersey: Lawrence Erlbaum Associates, Inc.
  • Lester, F. K. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for research in mathematics education, 25(6), 660-675.
  • Lester, F. Jr., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and meta-cognition: Key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving (pp. 75-88). New York, NY: Springer-Verlag. doi:10.1007/978-1-4612-3614-6_6
  • Lingefjärd, T. (2000). Mathematical modeling by prospective teachers using technology (Electronically published doctoral dissertation). University of Georgia. http://ma-serv.did.gu.se/matematik/thomas.htm
  • Lingefjärd, T. (2007a). Mathematical modelling in teacher education– Necessity or unnecessarily. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 333-340). New York: Springer.
  • Lingefjärd, T. (2007b). Modelling in teacher education. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 475-482). New York: Springer.
  • Lowery, N. (2002). Construction of teacher knowledge in context: Preparing elementary teachers to teach mathematics and science. School Science and Mathematics, 102(2), 68-83.
  • Lucangeli, D., & Cornoldi, C. (1997). Arithmetic education and learning in Italy. Journal of Learning Disabilities, 37(1), 42-49.
  • MaaB, K. (2007). Modelling in class: What do we want the students to learn. Mathematical modelling: Education, engineering and economics, 63-78.
  • Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional science, 26(1-2), 49-63.
  • Magiera, M. T., & Zawojewski, J. (2011). Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modelling. Journal for Research in Mathematics Education, 42(5), 486-520.
  • Mayer, R. E. (2003). Mathematical problem solving. In: J. M. Royer (Ed.), Mathematical Cognition (pp. 69–92). Connecticut: Information Age Publishing.
  • Maiorca, C. (2016). A case study: Students’ mathematics-related beliefs from integrated STEM model-eliciting activities. Retrieved from Digital Scholarship UNLV. (2702)
  • Milanović, I., Vukobratović, R., & Raičević, V. (2012). Mathematical modelling of the effect of temperature on the rate of a chemical reaction. Croatian Journal of Education, 14(3), 681-709.
  • Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers college record, 108(6), 1017.
  • Montague, M., & Bos, C. S. (1990). Cognitive and metacognitive characteristics of eighth grade students' mathematical problem solving. Learning and individual differences, 2(3), 371-388.
  • Moore, T. J., & Smith, K. A. (2014). Advancing the state of the art of STEM integration. Journal of STEM Education: Innovations and Research, 15(1), 5-10.
  • Moore, T. J., Miller, R. L., Lesh, R. A., Stohlmann, M. S., & Kim, Y. R. (2013). Modeling in engineering: The role of representational fluency in students' conceptual understanding. Journal of English Education, 102, 141-178. doi:10.1002/jee.20004.
  • Morrison, J. (2006). TIES STEM education monograph series, attributes of STEM education. Baltimore, MD: TIES, 3.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer.
  • Nugent, G., Bradley, B., Grandgenett, N., & Adamchuk, V. I. (2010). Impact of robotics and geospatial technology interventions on youth STEM learning and attitudes. Journal of Research on Technology in Education, 42(4), 391e408.
  • Özsoy, G., & Ataman, A. (2017). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67-82.
  • Pintrich, P. R., Anderman, E. M., & Klobucer, C. (1994). Intraindividual differences in motivation and cognition in students with and without learning disabilities. Journal of Learning Disabilities, 27(6), 360-370.
  • Post, T., & Cramer, K. (1989). Knowledge, representation, and qualitative thinking. In M. Reynolds (Ed.), Knowledge base for the beginning teacher-Special publication of the AACTE (pp. 221-231). Oxford: Pergamon Press.
  • Post, T. R., Behr, M., & Lesh, R. (1986). Research-based observations about children’s learning of rational number concepts. Focus on Learning Problems in Mathematics, 8, 39–48.
  • Polya, G. (1957). How to Solve it: A New Aspect of Mathematical Method. 2d Ed. Doubleday.
  • Presmeg, N. (2002). Beliefs about the nature of mathematics in the bridging of everyday and school mathematical practices. In G Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 293 -312), Boston, MA: Kluwer Academic Publishers.
  • Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236-245. doi:10.1111/j.1949-8594.2001.tb18026.x
  • Revlin, R. (2013). Cognition: Theory and Practice. New York: Worth Publishers.
  • Rodgers, K. J., Diefes-Dux, H. A., Kong, Y., & Madhavan, K. (2015, June). Framework of basic interactions to computer simulations: Analysis of student developed interactive computer tools. Proceedings from the 122nd ASEE Annual Conference & Exposition: Making Value for Society, Seattle, WA.
  • Roehrig, G. H., Moore, T. J., Wang, H. H., & Park, M. S. (2012). Is adding the E enough? Investigating the impact of K‐12 engineering standards on the implementation of STEM integration. School Science and Mathematics, 112(1), 31-44.
  • Roth, W. M. (2007). Mathematical modeling ‘in the wild’: A case of hot cognition. In R. Lesh, J. J. Kaput, E. Hamilton, & J. Zawojewski (Eds.), Users of mathematics: Foundations for the future. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Rysz, T. (2004). Metacognition in learning elementary probability and statistics (Doctoral dissertation). University of Cincinnati, Ohio.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York, NY: Macmillan.
  • Stacey, K. (1991). Making optimal use of mathematical knowledge. Australian Journal of Remedial Education, 22(4), 6-10.
  • Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications tasks. Mathematics Education Research Journal, 16(1), 41–71.
  • Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), International perspectives on the teaching and learning of mathematical modelling, Trends in teaching and learning of mathematical modelling (pp. 165–180). Dordrecht: Springer.
  • Stillman, G. A., & Galbraith, P. L. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157-194.
  • Stillman, G., & Mevarech, Z. (2010). Metacognition research in mathematics education: From hot topic to mature field. ZDM-International Journal on Mathematics Education, 42(2), 145–148.
  • Stohlmann, M. S., Moore, T. J., & Cramer, K. (2013). Preservice elementary teachers’ mathematical content knowledge from an integrated STEM modelling activity. Journal of Mathematical Modelling and Application, 1(8), 18-31.
  • Stohlmann, M., Maiorca, C., & Olson, T. A. (2015). Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards. Mathematics Educator, 24(1), 21-43.
  • Tam, K. C. (2011). Modeling in the Common Core State Standards. Journal of Mathematics Education at Teacher College, 2(1), 28–33.
  • Tan, L. S., & Ang, K. C. (2013). Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling- A Case Study. In Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 373-383). Springer Netherlands.
  • Teague, D., Levy, R., & Fowler, K. (2016). “The GAIMME report: Mathematical Modeling in the K-16 curriculum.” In C. Hirsch (Ed.), Annual perspectives in mathematics education (APME): Mathematics modeling and modeling with mathematics (pp. 249-261). Reston, VA: National Council of Teachers of Mathematics.
  • Teong, S. K. (2003). The effect of metacognitive training on mathematical word‐problem solving. Journal of computer assisted learning, 19(1), 46-55.
  • Trainin, G., & Swanson, H. L. (2005). Cognition, metacognition, and achievement of college students with learning disabilities. Learning Disability Quarterly, 28(4), 261-272. doi:10.2307/4126965
  • Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling competencies: Empirical verification of theoretical assumptions. ZDM Mathematics Education, 50(1-2), 343-354. https://doi.org/10.1007/s11858-017-0909-x
  • Wolf, N. (2015). Modeling with mathematics: Authentic problem solving in middle school. Portsmouth, New Hampshire: Heinemann.
  • Yimer, A., & Ellerton, N. F. (2006). Cognitive and metacognitive aspects of mathematical problem solving: An emerging model. Identities, cultures, and learning spaces, 575-582.
  • Yu, P. W. D., & Tawfeeq, D. A. (2011). Can a kite be a triangle? Bidirectional discourse and student inquiry in a middle school interactive geometric lesson. New England Mathematics Journal, 43, 7-20.
  • Zawojewski, J. S., Diefes-Dux, H., & Bowman, K. (2008). Models and modeling in engineering education. Sense Publishers.

Pre-Service Teachers’ Cognitive and Metacognitive Processes in Integrated STEM Modeling Activity

Yıl 2021, Cilt: 7 Sayı: 2, 104 - 127, 01.04.2021
https://doi.org/10.21891/jeseh.832574

Öz

This study was conducted during two educational technology courses in spring term of 2016-2017 academic years. The participants of the study were pre-service teachers who were in mathematics teaching program in a university located at the west part of Turkey. Pre-service teachers were asked to solve a complex problem that requires mathematical model eliciting activities and report their solution. While pre-service teachers were solving the problem and writing their report, they were audio recorded. Additionally, their solutions and reports for problem were collected as data sources. All three various data sources used for triangulation to make the data collection process more reliable. The problem-solving behavior from the study conducted by Kim et al. (2013) was used as the theoretical framework. First, the behavior is classified as cognitive or metacognitive. Then the behavior (either cognitive or metacognitive) is also classified as at individual, social, or environmental levels. Additionally, Lesh Translation Model was used to decide the representations of mathematical content knowledge codes for metacognitive activities. The implications of this study are the developed metacognitive activities for pre-service teachers. Additionally, there is potential usage of technology for the role of metacognition in mathematics education.

Kaynakça

  • Ang, K. C. (2015). Mathematical modelling in Singapore schools: A framework for instruction. In N. H. Lee & D. K. E. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 57-72). Singapore: National Institute of Education.
  • Artzt, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and Instruction, 9(2), 137-175. doi:10.1207/s1532690xci0902_3
  • Azevedo, R. (2005). Computer environments as metacognitive tools for enhancing learning. Educational Psychologist, 40(4), 193–197. Bal, A. P., & Doğanay, A. (2014). Improving primary school prospective teachers’ understanding of the mathematics modeling process. Educational Sciences: Theory & Practice, 14(4), 1375–1384.
  • Bell, D. (2016). The reality of STEM education, design and technology teachers’ perceptions: A phenomenographic study. International Journal of Technology and Design Education, 26, 61–79.
  • Biggs, J. (1987). The process of learning. Sydney: Prentice Hall.
  • Birenbaum, M. (1996). Assessment 2000: Towards a pluralistic approach to assessment. In M. Birenbaum & F. Dochy, (Eds.), Alternatives in assessment of achievements, learning processes and prior knowledge (pp. 3–30). Boston: Kluwer.
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), International perspectives on the teaching and learning of mathematical modelling, trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.
  • Blum, W., & Leiss, D. (2007). How do Students and Teachers deal with mathematical Modelling Problems? The example Sugaloaf und the DISUM Project. In C. Haines, P. L.
  • Galbraith, W. Blum & S. Khan (Eds.), Mathematical Modelling (ICTMA12) - Education, Engineering and Economics. Chichester: Horwood.
  • Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  • Borba, M. C., & Villarreal, M. (2005). Humans-with-media and the reorganization of mathematical thinking. New York: Springer.
  • Brophy, S., Klein, S., Portsmore, M., & Rogers, C. (2008). Advancing engineering education in P–12 classrooms. Journal of Engineering Education 97, 269–387 . Brown, A., & De Loache, J. (1983). Metacognitive skills. In M. Donaldson, R. Grieve, & C. Pratt (Eds.), Early childhood development and education (pp. 3–35). Oxford: Blackwell.
  • Bruner, J. S. (1964). The course of cognitive growth. American psychologist, 19(1), 1.
  • Bryce, D., & Whitebread, D. (2012). The development of metacognitive skills: Evidence from observational analysis of young children’s behavior during problem-solving. Metacognition Learning, 7, 197–217.
  • Cai, J., Cirillo, M., Pelesko, J. A., Ferri, R. B., Stillman, G., English, L. D., Wake, G., Kaiser, G., & Kwon, O. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional, and teacher educational perspectives. In Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 145-172). Canada: PME-NA.
  • Cardelle-Elawar, M. (1992). Effects of teaching metacognitive skills to students with low mathematical ability. Teaching and Teacher Education, 8(2), 109-121.
  • Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating a Models and Modeling Perspective with Existing Research and Practice. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Chan, E. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
  • Clement, L. (2004). A model for understanding, using, and connecting representations. Teaching Children Mathematics, 11(2), 97-102.
  • Cramer, K. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. Doerr (Eds.), Beyond constructivism (pp. 449-463). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Cramer, K. A., Monson, D. S., Wyberg, T., Leavitt, S., & Whitney, S. B. (2009). Models for Initial Decimal Ideas. Teaching Children Mathematics, 16(2), 106-117.
  • De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491-549). New York, NY, US: Macmillan Library Reference Usa; London, England: Prentice Hall International.
  • Deniz, D., & Akgün, L. (2014). Ortaöğretim öğrencilerinin matematiksel modelleme yönteminin sınıf içi uygulamalarına yönelik görüşleri. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 4(1), 103-116.
  • Dewaters, J., & S. E. Powers. (2006). Improving science and energy literacy through project-based K-12 outreach efforts that use energy and environmental themes. In Proceedings of the 113th Annual ASEE Conference & Exposition. Chicago, IL.
  • Diefes-Dux, H. A., & Imbrie, P. K. (2008). Modeling activities in a first-year engineering course. In J. S. Zawojewski, H. A. Diefes-Dux, & K. J. Bowman (Eds.), Models and modeling in engineering education: Designing experiences for all students (pp. 55-92). The Netherlands: Sense Publishers.
  • Diefes-dux, H., Hjalmarson, Miller, & Lesh, R. (2008). Model-eliciting for engineering education. In J. Zawojewski, H. Diefes-Dux, & K. Bowman (Eds.), Models and modeling in engineering education: Designing experiences for all students (pp. 17–35). Rotterdam, the Netherlands: Sense Publishers.
  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modeling? In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (1st ed., pp. 69–78). New York: Springer.
  • Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi (Unpublished doctoral dissertation). Hacettepe Üniversitesi, Ankara.
  • Driscoll, M. P. (2000). Psychology of Learning for Instruction (2nd ed.). Boston, MA: Allyn and Bacon.Duffy, T., & Cunningham, D. (1996). Constructivism: Implications for the design and delivery of instruction. Handbook of research for educational communications and technology, 170–198.
  • Dunlosky, J., & Metcalfe, J. (2009). Metacognition. Thousand Oaks, CA: Sage Publications, Inc.
  • English, L. D., Fox, J. L., & Watters, J. J. (2005) Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12(3), 156-163.
  • Erbaş, A. K., Kertı̇l, M., Çetı̇nkaya, B., Çakiroğlu, E., Alacaci, C., & Baş, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory & Practice, 14(4), 1621–1627.
  • Eric, C. C. M. (2010). Tracing primary 6 students’ model development within the mathematical modeling process. Journal of Mathematical Modeling and Applications, 1, 40-57.
  • Ferguson, R. L. (2007). Constructivism and social constructivism. In G. M. Bodner & M. Orgill (Eds.), Theoretical frameworks for research in chemistry/science education (pp. 28-49). Upper Saddle River, NJ: Prentice Hall.
  • Fox, J. (2006). A justification for mathematical modelling experiences in the preparatory classroom. In Grootenboer, P., Zevenbergen, R., & Chinnappan, M., (Eds.), Proceedings 29th annual conference of the Mathematics Education Research Group of Australasia. 1, 21-228.
  • Frykholm, J., & Glasson, G. (2005). Connecting science and mathematics instruction: Pedagogical context knowledge for teachers. School Science and Mathematics, 105(3), 127-141.
  • Gagne, R. M., Medsker, K. L. (1996). The Conditions of Learning: Training Applications. Harcourt Brace College Publishers: Fort Worth.
  • Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163-176.
  • Glancy, A. W., & Moore, T. J. (2013). Theoretical foundations for effective STEM learning environments. Education Working Papers (1-1-2013), School of Engineering Education, Purdue University. Accessed on 10/04/2016. http://docs.lib.purdue.edu/enewp/1
  • Goldin, G. A. (2007). Aspects of affect and mathematical modelling processes. Foundations for the future in mathematics education, 281-299.
  • Goos, M. (1994). Metacognitive decision making and social interactions during paired problem solving. Mathematics Education Research Journal. 6(2), 144-165.
  • Goos, M. (2002). Understanding metacognitive failure. The Journal of Mathematical Behavior, 21(3), 283-302.
  • Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30, 229-260.
  • Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49(2), 193-223. doi:10.1023/A:1016209010120
  • Gould, H., & Wasserman, N. (2014). Striking a balance: Student’s tendencies to oversimplify or overcomplicate in mathematical modeling. Journal of Mathematics Education at Teachers College, 5(1), 27-34.
  • Gurbin, T. (2015). Metacognition and technology adoption: Exploring influences. Procedia - Social and Behavioral Sciences, 191, 1576–1582. doi.org/10.1016/ j.sbspro.2015.04.608
  • Haines, C., & Crouch, R. (2007). Mathematical modeling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: e 14th ICMI study (pp. 417-424). New York, NY: Springer.
  • Hıdıroğlu, Ç. N., & Bukova-Güzel, E. (2014). Matematiksel modellemede GeoGebra kullanımı: Boy-ayak uzunluğu problemi. Pamukkale Üniversitesi, Eğitim Fakültesi Dergisi, 36(2), 29-44.
  • Hıdıroğlu, Ç. N. ve Bukova Güzel, E. (2015). Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education, 6(2), 179-208.
  • Hıdıroğlu, Ç. N., & Bukova-Güzel, E. (2016). Transitions between Cognitive and Metacognitive Activities in Mathematical Modelling Process within a Technology Enhanced Environment. Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education, 10(1), 313-350.
  • Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. In 11th International Congress on Mathematical Education. Monterrey, Nuevo Leon, Mexico.
  • Jacobse, A. E., & Harskamp, E. G. (2009). Student-controlled metacognitive training for solving word problems in primary school mathematics. Educational Research and Evaluation, 15(5), 447-463.
  • Jacobse, A. E., & Harskamp, E. G. (2012). Towards efficient measurement of metacognition in mathematical problem solving. Metacognition and Learning, 7(2), 133-149.
  • Johnson, T., & Lesh, R. (2003). A models and modeling perspective on technology-based representational media. Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching, 265-278.
  • Johnson, D. W., Johnson, R. T., & Smith, K. (2007). The state of cooperative learning in postsecondary and professional settings. Educational Psychology Review, 19(1), 15-29.
  • Joseph, N. (2010). Metacognition needed: Teaching middle and high school students to develop strategic learning skills. Preventing School Failure. 54(2), 99–103. Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38, 196–208.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
  • Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. ZDM, 38(2), 82-85.
  • Kaiser, G., Blum, W., Ferri, R. B., & Stillman, G. (2011). International perspectives on the teaching and learning of mathematical modelling, Trends in teaching and learning of mathematical modelling. Dordrecht: Springer.
  • Kaput, J., Hegedus, S., & Lesh, R. (2007). Technology becoming infrastructural in mathematics education. In R. A. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 173–191). Mahwah, NJ: Lawrence Erlbaum.
  • Kertil, M., & Gurel, C. (2016). Mathematical modeling: A bridge to STEM education. International Journal of Education in mathematics, science and Technology, 4(1), 44-55. Doi:10.18404/ijemst.95761
  • Kim, Y. R., Park, M. S., Moore, T. J., & Varma, S. (2013). Multiple levels of metacognition and their elicitation through complex problem-solving tasks. Journal of Mathematical Behavior, 32(3), 377–396. doi: 10.1016/j.jmathb.2013.04.002.
  • Koellner-Clark, K., & Lesh, R. (2003). Whodunit? Exploring proportional reasoning through the footprint problem. School Science and Mathematics, 103(2), 92-98. doi:http:// dx.doi.org/10.1111/j.1949-8594.2003 .tb18224.x
  • 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. doi:10.1023/A:1016282811724
  • Lamon, S. J. (2003). Modelling in elementary school: Helping young students to see the world mathematically. In Mathematical Modelling (pp. 19-33). Woodhead Publishing.
  • Lapp, D. A., & Cyrus, V. F. (2000). Using data-collection devices to enhance students’ understanding. Mathematics Teacher, 93(6), 504-510.
  • Lehrer, R., & Schauble, L. (2000). Developing model-based reasoning in mathematics and science. Journal of Applied Developmental Psychology, 21(1), 39–48. doi:10.1016/S0193-3973(99)00049-0
  • Lesh, R. (1979). Mathematical learning disabilities: Consideration for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied mathematical problem solving (pp. 166-175). Columbus, OH: ERIC/SMEAC.
  • Lesh, R., Post, T., & Behr, M. (1987). Representation and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2-3), 109-129.
  • Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The handbook of research on mathematics teaching and learning (2nd ed.) (pp. 763-804). Reston, VA/Charlotte, NC: National Council of Teachers of Mathematics.
  • Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J., (2003) Using a translation model for curriculum development and classroom instruction. In Lesh, R. & Doerr, H. (Eds.) Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Lawrence Erlbaum Associates, Mahwah, New Jersey.
  • Lesh, R., & Doerr, H. M. (2003). In what ways does a models and modeling perspective move beyond constructivism? In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R., & Fennewald, T. (2010). Introduction to part I modeling: What is it? Why do it? In Richard Lesh, C. Haines, P. L. Galbraith, & A. Hurford (Eds.), Modeling Students’ MM competencies (pp. 5-10). New York: Springer.
  • Lesh, R., & Harel, G. (2003). Problem solving modeling and local conceptual development. Mathematical Thinking and Learning 5(2-3), 157-189.
  • Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models & modelling perspectives on mathematics problem solving, learning, and teaching? In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 161-170). New York: Springer.
  • Lesh, R., Amit, M., & Schorr, R. Y. (1997). Using 'real-life' problems to prompt students to construct conceptual models for statistical reasoning. In I. Gal, & J. B. Garfield (Eds.), The Assessment Challenge in Statistics Education (pp. 65-84). Burke, VA: International Statistical Institute.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Research Design in mathematics and science education (pp. 591–646). New Jersey: Lawrence Erlbaum Associates, Inc.
  • Lester, F. K. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for research in mathematics education, 25(6), 660-675.
  • Lester, F. Jr., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and meta-cognition: Key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving (pp. 75-88). New York, NY: Springer-Verlag. doi:10.1007/978-1-4612-3614-6_6
  • Lingefjärd, T. (2000). Mathematical modeling by prospective teachers using technology (Electronically published doctoral dissertation). University of Georgia. http://ma-serv.did.gu.se/matematik/thomas.htm
  • Lingefjärd, T. (2007a). Mathematical modelling in teacher education– Necessity or unnecessarily. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 333-340). New York: Springer.
  • Lingefjärd, T. (2007b). Modelling in teacher education. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 475-482). New York: Springer.
  • Lowery, N. (2002). Construction of teacher knowledge in context: Preparing elementary teachers to teach mathematics and science. School Science and Mathematics, 102(2), 68-83.
  • Lucangeli, D., & Cornoldi, C. (1997). Arithmetic education and learning in Italy. Journal of Learning Disabilities, 37(1), 42-49.
  • MaaB, K. (2007). Modelling in class: What do we want the students to learn. Mathematical modelling: Education, engineering and economics, 63-78.
  • Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional science, 26(1-2), 49-63.
  • Magiera, M. T., & Zawojewski, J. (2011). Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modelling. Journal for Research in Mathematics Education, 42(5), 486-520.
  • Mayer, R. E. (2003). Mathematical problem solving. In: J. M. Royer (Ed.), Mathematical Cognition (pp. 69–92). Connecticut: Information Age Publishing.
  • Maiorca, C. (2016). A case study: Students’ mathematics-related beliefs from integrated STEM model-eliciting activities. Retrieved from Digital Scholarship UNLV. (2702)
  • Milanović, I., Vukobratović, R., & Raičević, V. (2012). Mathematical modelling of the effect of temperature on the rate of a chemical reaction. Croatian Journal of Education, 14(3), 681-709.
  • Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers college record, 108(6), 1017.
  • Montague, M., & Bos, C. S. (1990). Cognitive and metacognitive characteristics of eighth grade students' mathematical problem solving. Learning and individual differences, 2(3), 371-388.
  • Moore, T. J., & Smith, K. A. (2014). Advancing the state of the art of STEM integration. Journal of STEM Education: Innovations and Research, 15(1), 5-10.
  • Moore, T. J., Miller, R. L., Lesh, R. A., Stohlmann, M. S., & Kim, Y. R. (2013). Modeling in engineering: The role of representational fluency in students' conceptual understanding. Journal of English Education, 102, 141-178. doi:10.1002/jee.20004.
  • Morrison, J. (2006). TIES STEM education monograph series, attributes of STEM education. Baltimore, MD: TIES, 3.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer.
  • Nugent, G., Bradley, B., Grandgenett, N., & Adamchuk, V. I. (2010). Impact of robotics and geospatial technology interventions on youth STEM learning and attitudes. Journal of Research on Technology in Education, 42(4), 391e408.
  • Özsoy, G., & Ataman, A. (2017). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67-82.
  • Pintrich, P. R., Anderman, E. M., & Klobucer, C. (1994). Intraindividual differences in motivation and cognition in students with and without learning disabilities. Journal of Learning Disabilities, 27(6), 360-370.
  • Post, T., & Cramer, K. (1989). Knowledge, representation, and qualitative thinking. In M. Reynolds (Ed.), Knowledge base for the beginning teacher-Special publication of the AACTE (pp. 221-231). Oxford: Pergamon Press.
  • Post, T. R., Behr, M., & Lesh, R. (1986). Research-based observations about children’s learning of rational number concepts. Focus on Learning Problems in Mathematics, 8, 39–48.
  • Polya, G. (1957). How to Solve it: A New Aspect of Mathematical Method. 2d Ed. Doubleday.
  • Presmeg, N. (2002). Beliefs about the nature of mathematics in the bridging of everyday and school mathematical practices. In G Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 293 -312), Boston, MA: Kluwer Academic Publishers.
  • Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236-245. doi:10.1111/j.1949-8594.2001.tb18026.x
  • Revlin, R. (2013). Cognition: Theory and Practice. New York: Worth Publishers.
  • Rodgers, K. J., Diefes-Dux, H. A., Kong, Y., & Madhavan, K. (2015, June). Framework of basic interactions to computer simulations: Analysis of student developed interactive computer tools. Proceedings from the 122nd ASEE Annual Conference & Exposition: Making Value for Society, Seattle, WA.
  • Roehrig, G. H., Moore, T. J., Wang, H. H., & Park, M. S. (2012). Is adding the E enough? Investigating the impact of K‐12 engineering standards on the implementation of STEM integration. School Science and Mathematics, 112(1), 31-44.
  • Roth, W. M. (2007). Mathematical modeling ‘in the wild’: A case of hot cognition. In R. Lesh, J. J. Kaput, E. Hamilton, & J. Zawojewski (Eds.), Users of mathematics: Foundations for the future. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Rysz, T. (2004). Metacognition in learning elementary probability and statistics (Doctoral dissertation). University of Cincinnati, Ohio.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York, NY: Macmillan.
  • Stacey, K. (1991). Making optimal use of mathematical knowledge. Australian Journal of Remedial Education, 22(4), 6-10.
  • Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications tasks. Mathematics Education Research Journal, 16(1), 41–71.
  • Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), International perspectives on the teaching and learning of mathematical modelling, Trends in teaching and learning of mathematical modelling (pp. 165–180). Dordrecht: Springer.
  • Stillman, G. A., & Galbraith, P. L. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157-194.
  • Stillman, G., & Mevarech, Z. (2010). Metacognition research in mathematics education: From hot topic to mature field. ZDM-International Journal on Mathematics Education, 42(2), 145–148.
  • Stohlmann, M. S., Moore, T. J., & Cramer, K. (2013). Preservice elementary teachers’ mathematical content knowledge from an integrated STEM modelling activity. Journal of Mathematical Modelling and Application, 1(8), 18-31.
  • Stohlmann, M., Maiorca, C., & Olson, T. A. (2015). Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards. Mathematics Educator, 24(1), 21-43.
  • Tam, K. C. (2011). Modeling in the Common Core State Standards. Journal of Mathematics Education at Teacher College, 2(1), 28–33.
  • Tan, L. S., & Ang, K. C. (2013). Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling- A Case Study. In Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 373-383). Springer Netherlands.
  • Teague, D., Levy, R., & Fowler, K. (2016). “The GAIMME report: Mathematical Modeling in the K-16 curriculum.” In C. Hirsch (Ed.), Annual perspectives in mathematics education (APME): Mathematics modeling and modeling with mathematics (pp. 249-261). Reston, VA: National Council of Teachers of Mathematics.
  • Teong, S. K. (2003). The effect of metacognitive training on mathematical word‐problem solving. Journal of computer assisted learning, 19(1), 46-55.
  • Trainin, G., & Swanson, H. L. (2005). Cognition, metacognition, and achievement of college students with learning disabilities. Learning Disability Quarterly, 28(4), 261-272. doi:10.2307/4126965
  • Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling competencies: Empirical verification of theoretical assumptions. ZDM Mathematics Education, 50(1-2), 343-354. https://doi.org/10.1007/s11858-017-0909-x
  • Wolf, N. (2015). Modeling with mathematics: Authentic problem solving in middle school. Portsmouth, New Hampshire: Heinemann.
  • Yimer, A., & Ellerton, N. F. (2006). Cognitive and metacognitive aspects of mathematical problem solving: An emerging model. Identities, cultures, and learning spaces, 575-582.
  • Yu, P. W. D., & Tawfeeq, D. A. (2011). Can a kite be a triangle? Bidirectional discourse and student inquiry in a middle school interactive geometric lesson. New England Mathematics Journal, 43, 7-20.
  • Zawojewski, J. S., Diefes-Dux, H., & Bowman, K. (2008). Models and modeling in engineering education. Sense Publishers.
Toplam 130 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Özel Eğitim ve Engelli Eğitimi
Bölüm Articles
Yazarlar

Mehmet Kandemir

İlyas Karadeniz

Yayımlanma Tarihi 1 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 7 Sayı: 2

Kaynak Göster

APA Kandemir, M., & Karadeniz, İ. (2021). Pre-Service Teachers’ Cognitive and Metacognitive Processes in Integrated STEM Modeling Activity. Journal of Education in Science Environment and Health, 7(2), 104-127. https://doi.org/10.21891/jeseh.832574