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Öz

There are several studies related to learning on the field of education, but in the recent times, they have focused on examining how students think and how their thinking becomes more complicated in time. The conception of learning trajectories consisting of mathematical purpose, progressive improvements specific to the domain of child, appropriate activities for the different levels of these improvements has emerged in this review process. Various definitions of learning trajectories have been put forward by different researchers, and it has been observed that the trajectories are utilized in the processes of learning and teaching mathematics, and evaluating the subject learned. Therefore, the aim of this compilation study is primarily to introduce the conception of learning trajectories to national literature, to discuss this subject by using definitions of learning trajectories by various researchers, and to address the fields utilizing mathematics education briefly. It is suggested to conduct different studies at all levels about learning orbits

Anahtar Kelimeler

• learning trajectory, mathematics education, learning

Öğrenme Yörüngeleri ve Matematik Eğitimindeki Yeri

Öz

Eğitim alanında öğrenme üzerine pek çok çalışma yapılmış olmakla birlikte son zamanlarda öğrenmeyle ilgili yapılan çalışmalar, öğrencilerin nasıl düşündüğünü ve düşüncelerinin zaman içerisinde nasıl karmaşık hale geldiğini inceleme üzerine odaklanmışlardır. Bu inceleme sürecinde, bireyin belirli bir  alana özgü gelişimsel ilerlemeleri ve bu ilerlemelerin farklı seviyelerde uygun aktivitelerin toplamından oluşan öğrenme yörüngesi kavramı ortaya çıkmıştır. Öğrenme yörüngesi ile ilgili araştırmacılar tarafından çeşitli tanımlar yapılmıştır. Bu tanımlardan hareketle öğrenme yörüngesinin matematikte öğrenme, öğretme ve öğrenileni değerlendirme süreçlerinde kullanıldığı görülmüştür. Bu derleme çalışmasının amacı, öncelikle öğrenme yörüngesi kavramını ulusal literatüre kazandırmak, beraberinde öğrenme yörüngelerinin ne olduğuna ilişkin çeşitli araştırmacıların tanımlarından faydalanarak bu konu üzerinde tartışmak ve matematik eğitiminde kullanım alanlarına kısaca değinmektir. Öğrenme yörüngeleriyle ilgili olarak, her düzeyde matematik konuları kapsamında çeşitli çalışmaların yapılması önerilmektedir.

Anahtar Kelimeler

• öğrenme yörüngesi, matematik eğitimi, öğrenme

Kaynakça

1. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–406.
2. Barrett, J. E., & Clements, D. H. (2003). Quantifying path length: Fourth-grade children's developing abstractions for linear measurement. Cognition and Instruction, 21(4), 475-520.
3. Barrett, J. E., Clements, D. H., Klanderman, D., Pennisi, S., & Polaki, M. V. (2006). Students' coordination of geometric reasoning and measuring strategies on a fixed perimeter task: Developing mathematical understanding of linear measurement. Journal for Research in Mathematics Education, 37(3), 187-221.
4. Battista, M. T. (2003). Levels of sophistication in elementary students' reasoning about length. Paper presented at the 27th annual conference of the International Group for the Psychology of Mathematics Education, Honolulu, HI.
5. Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843- 908). Charlotte, NC: Information Age Publishing, Inc.
6. Brown, A.L. & Campione, J.C. (1996). Psychological theory and the design of innovative learning environments: On procedures, principles, and systems. In L. Schauble & R. Glaser (Eds.), Innovations in learning: New environments for education (pp. 289-325). Mahwah, NJ: Erlbaum.
7. Brown, C. S., Sarama, J., & Clements, D. H. (2007). Thinking about learning trajectories in preschool. Teaching Children Mathematics, 14, 178-181.
8. Bumen, N. T. (2007). Effects of the original versus revised Bloom’s Taxnomy on lesson planning skills: A Turkish study among pre-service teachers. Review of Education, 53(4), 439–455.

9. Case, R., & Griffin, S. (1990). Child cognitive development: The role of central conceptual structures in the development of scientific and social thought. In E. A. Hauert (Ed.), Developmental psychology: Cognitive, perceptuo-motor, and neurological perspectives (pp. 193-230). North-Holland: Elsevier
10. Catley, K., Lehrer, R., & Reiser, B. (2004). Tracing a prospective learning progression for developing understanding of evolution. Washington, DC: National Academy Press.
11. Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical thinking and learning, 6(2), 81-89.
12. Clements D.H., & Sarama J. (2009) Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.
13. Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children's composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6(2), 163-184.
14. Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166.
15. Confrey, J. (2006). The evolution of design studies as methodology. In R. K. Sawyer (Ed.), The cambridge handbook of the learning sciences (pp. 135-152). New York: Cambridge University Press.
16. Confrey, J. (2008). A synthesis of the research on rational number reasoning: A learning progressions approach to synthesis. In Presentation at the 11th international congress of mathematics instruction Monterrey, Mexico.
17. Confrey, J., Maloney, A., Nguyen, K., Mojica, G., & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 345–353). Thessaloniki, Greece.
18. Confrey, J., & Maloney, A. P. (2010). A next generation of mathematics assessments based on learning trajectories, East Lansing, MI.
19. Corcoran, T., Mosher, F. A., & Rogat, A. (2009). Learning progressions in science: An evidence-based approach to reform. New York: Center on Continuous Instructional Improvement Teachers College–Columbia University.
20. Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in mathematics (Research Report No. 68). Madison, WI: Consortium for Policy Research in Education.Battista, M. T. (2006). Understanding the development of students’thinking about length. Teaching Children Mathematics, 13, 140–146.
21. Gilbert, M. C., & Musu, L. E. (2008). Using TARGETTS to create learning environments that support mathematical understanding and adaptive motivation. Teaching Children Mathematics, 15(3), 138–143.
22. Maloney, A. P., & Confrey, J. (2010, June–July). The construction, refinement, and early validation of the equipartitioning learning trajectory. Paper presented at the 9th International Conference of the Learning Sciences, Chicago, IL.
23. Mojica, G. (2010). Preparing pre-service elementary teachers to teach mathematics withlearning trajectories. Unpublished doctoral dissertation. North Carolina State University, Raleigh, NC. Raleigh, NC.
24. Moore, K. C. (2010). The role of quantitative reasoning in precalculus students learning central concepts of trigonometry (doctoral dissertation). Tempe, AZ:Arizona State University
25. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge.
26. Schifter, D. (1998). Learning mathematics for teaching: From a teacher's seminar to the classroom. Journal of Mathematics Teacher Education, I, 55-87.
27. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.
28. Simon, M., & Tzur, R. (2004) Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91 104.
29. Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning Trajectory Based Instruction Toward a Theory of Teaching. Educational Researcher, 41(5), 147-156.
30. Weber, E., & Lockwood, E. (2014). The duality between ways of thinking and ways of understanding: Implications for learning trajectories in mathematics education. The Journal of Mathematical Behavior, 35, 44-57.
31. Weber, E. (2012). Students’ ways of thinking about two variable functions and rate of change in space (doctoral dissertation). Tempe, AZ: Arizona State University.
32. Weber, E., & Thompson, P. W. (2014). Students’ images of two-variable functions and their graphs. Educational Studies in Mathematics,http://dx.doi.org/10.1007/s10649-014-9548-0.
33. Wilson, P. H. (2009). Teachers’ uses of a learning trajectory for equipartitioning. Unpublished doctoral dissertation. North Carolina State University. Raleigh, NC.