Yıl: 2020 Cilt: 7 Sayı: 3 Sayfa Aralığı: 1111 - 1124 Metin Dili: İngilizce İndeks Tarihi: 14-11-2020

PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS

Öz:
The purpose of the present study was to propose a model for mathematics achievementconsidering the mediating role of eye tracking measurements in the relationship betweenproblem solving performance and mathematics achievement. In this sequential explanatorymixed method research design, a geometry test was conducted to 381 7th grade students. Theirproblem-solving process was recorded using eye tracking technology. Also, their mathematicsachievement scores were acquired from their schools. Afterwards, semi-structured interviewswere conducted to 15 students. Based on the results, it was observed that there was a positiverelationship among problem-solving performance and mathematics achievement while eyetracking measurements were negatively correlated to problem solving performance andmathematics achievement. Qualitative findings also confirmed these results. Moreover, thehypothesized model could approximately express 22% of the variance on mathematicsachievement.
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  • Aka, E. İ., Güven, E. & Aydoğdu, M. (2010). Effect of problem solving method on science process skills and academic achievement. Journal of Turkish Science Education, 7(4), 13–25.
  • Akuysal, N. (2007). İlköğretim 7. sınıf öğrencilerinin 7. sınıf ünitelerindeki geometrik kavramlardaki yanılgıları. Yayınlanmamış yüksek lisans tezi, Selçuk Üniversitesi, Konya.
  • Alatorre, S., & Saiz, M. (2009). Teachers and triangles. Proceedings of Congress of Educational Research in Mathematics Education. 28 January- 1 February, Lyon; France.
  • Andrá, C., Lindström, P., Arzarello, F., Holmqvist, K., Robutti, O., & Sabena, C. (2015). Reading mathematics representations: an eye-tracking study. International Journal of Science and Mathematics Education, 13(2), 237–259.
  • Bao, Y., Kiss, M., & Wittmann M. (2002). Effects of age and memory grouping on simulated car driving. In Proceedings of the Human Factors and Ergonomics Society 46th Annual Meeting (pp. 1853-1857). Santa Monica, CA: Human Factors and Ergonomics Society.
  • Bransford, J., Sherwood, R., Vye, N., & Rieser, J. (1986). Teaching thinking and problem solving: Research foundations. American Psychologist, 41(10), 1078–1089.
  • Cheng, S. C., She, H. C., & Huang, L. U. (2018). The Impact of Problem-Solving Instruction on Middle School Students’ Physical Science Learning: Interplays of Knowledge, Reasoning, and Problem Solving. EURASIA Journal of Mathematics, Science and Technology Education, 14(3), 731-743.
  • Clements, D., Swaminathan, S., Hannibal, M., & Sarama, J. (1999). Young children’s concepts of shape. Journal for Research in Mathematics Education, 30(2), 192–212.
  • Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem solving transfer. Journal of Educational Psychology, Vol 79(4), 347-362.
  • Creswell, J. W. (2013). Qualitative inquire and research design: Choosing among five approaches. Los Angeles, CA: Sage.
  • Devichi, C., & Munier, V. (2013). About the concept of angle in elementary school: misconceptions and teaching sequences. Journal of Mathematical Behavior, 32, 1–19.
  • De Waard, D. (1996). The measurement of drivers’ mental workload. Groningen, the Netherlands: Traffic Research Center Groningen University.
  • Dhillon, A. S. (1998). Individual differences with problem-solving strategies used in physics. Science Education, 82(3), 379–405.
  • Doyuran, G. (2014). Ortaokul öğrencilerinin temel geometri konularinda sahip olduklari kavram yanilgilari. Yayımlanmamış yüksek lisans tezi, Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir.
  • Epelboim, J., & Suppes, P. (2001). A model of eye movements and visual working memory during problem solving in geometry. Vision Research, 41(12), 1561-1574.
  • Erez, M. & Yerushalmy, M. (2006). If you can turn a rectangle into a square, you can turn a square into a rectangle: young students' experience the dragging tool. International Journal of Computers for Mathematical Learning, 11(3), 271-299.
  • Fujita, T. & Jones, K. (2008). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3–20.
  • Gok, T. (2014). Students’ Achievement, Skill and Confidence in Using Stepwise Problem Solving Strategies. Eurasia Journal of Mathematics, Science & Technology Education, 10(6), 617-624.
  • Gokkurt, B., Şahin, Ö., Soylu, Y. & Doğan, Y. (2015). Pre-service teachers’ pedagogical content knowledge regarding student mistakes on the subject of geometric shapes. Elementary Education Online, 14(1), 55-71.
  • Hayes, A. F. (2009): Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76(4), 408-420. doi:10.1080/03637750903310360
  • Hayes, A. F. (2012). Process: A versatile computational tool for observed variable mediation, moderation, and conditional process modelling. Retrieved from http://www.processmacro.org/download.html
  • Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis A regression based approach. USA: The Guilford Press.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70–95). Cambridge, UK: Cambridge University Press.
  • Hu, R., Xiaohui, S., & Shieh, C. J. (2017). A study on the application of creative problem solving teaching to statistics teaching. Eurasia Journal of Mathematics, Science and Technology Education, 13(7), 3139–3149.
  • Hyönä, J. (2010). The use of eye movements in the study of multimedia learning. Learning and Instruction, 20, 172–176.
  • Jackson, K. L. (1975). The art of problem solving. London: Heinamann, Bk. Ltd.
  • Jacob, R. J. K. & Karn, K. S. (2003). Eye Tracking in Human—Computer Interaction and Usability Research: Ready to Deliver the Promises. In R. Radach, J. Hyona, & H. Deubel (Eds.). The mind's eye: Cognitive and applied aspects of eye movement research. Elsevier.
  • Jang, Y.-M., Mallipeddi, R., & Lee, M. (2014). Identification of human implicit visual search intention based on eye movement and pupillary analysis. User Modeling and UserAdapted Interaction, 24(4), 315–344.
  • Jarodzka, H., Scheiter, K., Gerjets, P., & van Gog, T. (2010). In the eyes of the beholder: How experts and novices interpret dynamic stimuli. Learning and Instruction, 20(2), 146-154.
  • Johnson, C. I., & Mayer, R. E. (2012). An eye movement analysis of the spatial contiguity effect in multimedia learning. Journal of Experimental Psychology-Applied, 18, 178– 191.
  • Irwanto, Saputro, A. D., Rohaetti, E. & Prodjo Santoso, A. K. (2018). Promoting critical thinking and problem solving skills of preservice elementary teachers through processoriented guided-ınquiry learning (POGIL). International Journal of Instruction, 11(4), 777-794.
  • Kester, L., Kirschner, P. A., and van Merriënboer, J. J. G. (2005). The management of cognitive load during complex cognitive skill acquisition by means of computer simulated problem solving. Br. J. Educ. Psychol. 75: 71–86.
  • Knoblich, G., Ohlsson, S. & Raney, E. G. (2001). An eye movement study of insight problem solving. Memory & Cognition, 29, 1000–1009.
  • Lin, J. J. H., & Lin, S. S. J. (2014a). Cognitive load for configuration comprehension in computer-supported geometry problem solving: An eye movement perspective. International Journal of Science and Mathematics Education, 12, 605–627.
  • Liversedge, S. P., & Findlay, J. M. (2000). Saccadic eye movements and cognition. Trends in Cognitive Sciences, 4(1), 6–14.
  • Mayer, R. E. (2010). Unique contributions of eyetracking research to the study of learning with graphics. Learning and Instruction, 20(2), 167-171
  • McGivney, J. M., & DeFranco T. C. (1995). Geometry proof writing: A problem solving approach a la Polya. Mathematics Teacher, 89, 552-555, Reston, Virginia: National Council of Teachers of Mathematics.
  • Metallidou, P. (2009). Pre-service and in-service teachers’ metacognitive knowledge about problem-solving strategies. Teaching and Teacher Education, 25, 76-82.
  • Monaghan, F. (2000). What difference does it make? Children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42 (2),179-196.
  • Muldner, K., & Burleston, W. (2015). Utilizing sensor data to model students’ creativity in a digital environment. Computers in Human Behavior, 42, 127–137.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Noy, Y.I., Lemoine, T.L., Klachan, C. & Burns, P.C. (2005). Task interruptability and duration as a measure of visual distraction. Applied Ergonomics, 35, 207-213.
  • Obersteiner, A. & Tumpek, C. (2016). Measuring fraction comparison strategies with eyetracking. ZDM—Mathematics Education, 48(3), 255-266.
  • Peterson, G. W., Sampson, Jr., J. P., Reardon, R. C., & Lenz, J. G. (1996). Acognitive information processing approach to career problem solving anddecision making. In D. Brown, L. Brooks, & Associates (Eds.), Career choiceand development (3rd ed., pp. 423– 476). San Francisco: Jossey-Bass.
  • Pickreign, J. (2007). Rectangle and rhombi: How well do pre-service teachers know them? Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-7.
  • Polya, G. (1945). How to solve it. New Jersey: Princeton University Press.
  • Rayner, K. (1998). Eye movements in reading and information processing: 20 years of research. Psychological Bulletin, 124, 372–422.
  • Sampson, J. P., Jr., Peterson, G. W., Lenz, J. G., & Reardon, R. C. (1992). A cognitive approach to career services: Translating concepts into practice. The Career Development Quarterly, 41, 67-74.
  • Saputro, A. D., Irwanto, I., Atun, S. & Wilujeng, I. (2019). The impact of problem solving instruction on academic achievement and science process skills among prospective elementary teachers. Elementary Education Online, 18(2), 496-507.
  • Schindler, M., Lilienthal, A.J., Chadalavada, R., & Ögren, M. (2016). Creativity in the eye of the student. Refining investigations of mathematical creativity using eye-tracking goggles. In Csíkos, C., Rausch, A., & Szitányi, J. (Eds.). Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 163–170. Szeged, Hungary: PME.
  • Serway, R. A., & R.J. Beichner. 2000. Physics for Scientists and Engineers, with Modern Physics. Fort Worth, Tex.: Saunders College Publishing.
  • Simon, D. P. & Simon, H. A. (1978). Individual differences in solving physics problems. In R. S. Siegler (Eds.), Children thinking: What develop? (pp.325-348). New Jersey: Lawrence Erlbaum Associates.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Boston: Pearson.
  • Thomas, L. E. & Lleras, A. (2007). Moving eyes and moving thought: On the spatial compatibility between eye movements and cognition. Psychonomic Bulletin & Review, 14, 663–668.
  • Tsai, M.-J., Hou, H.-T., Lai, M.-L., Liu, W.-Y., & Yang, F.-Y. (2012). Visual attention for solving multiple-choice science problem: An eye-tracking analysis. Computers & Education, 58, 375-385.
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2014). Early‑years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDMMathematics Education, DOI 10.1007/s11858-014-0641-8.Uygun, T. &
  • Akyuz, D. (2019). Developing subject matter knowledge through argumentation. International Journal of Research in Education and Science (IJRES), 5(2), 532-547. Woolfolk A. (1993). Educational psychology. Fifth Ed. Allyn and Bacon.
APA Simsek I, uygun t, Güner P (2020). PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. , 1111 - 1124.
Chicago Simsek Irfan,uygun tuğba,Güner Pınar PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. (2020): 1111 - 1124.
MLA Simsek Irfan,uygun tuğba,Güner Pınar PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. , 2020, ss.1111 - 1124.
AMA Simsek I,uygun t,Güner P PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. . 2020; 1111 - 1124.
Vancouver Simsek I,uygun t,Güner P PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. . 2020; 1111 - 1124.
IEEE Simsek I,uygun t,Güner P "PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS." , ss.1111 - 1124, 2020.
ISNAD Simsek, Irfan vd. "PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS". (2020), 1111-1124.
APA Simsek I, uygun t, Güner P (2020). PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. IOJET, 7(3), 1111 - 1124.
Chicago Simsek Irfan,uygun tuğba,Güner Pınar PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. IOJET 7, no.3 (2020): 1111 - 1124.
MLA Simsek Irfan,uygun tuğba,Güner Pınar PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. IOJET, vol.7, no.3, 2020, ss.1111 - 1124.
AMA Simsek I,uygun t,Güner P PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. IOJET. 2020; 7(3): 1111 - 1124.
Vancouver Simsek I,uygun t,Güner P PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS. IOJET. 2020; 7(3): 1111 - 1124.
IEEE Simsek I,uygun t,Güner P "PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS." IOJET, 7, ss.1111 - 1124, 2020.
ISNAD Simsek, Irfan vd. "PROBLEM-SOLVING PERFORMANCE AND MATHEMATICS ACHIEVEMENT: THE MEDIATING ROLE OF EYE TRACKING MEASUREMENTS". IOJET 7/3 (2020), 1111-1124.