اعتبار سازی ابزار با استفاده از نظریه های فعالیت و پرسش و پاسخ برای ارزشیابی درک دانش آموزان از دست ورزی های مجازی در یادگیری ریاضی

نویسنده

دکترای آموزش ریاضی، کارشناس توسعه و کاربرد نرم‌افزارهای آموزشی، پژوهشکدة برنامه‌ریزی درسی و نوآوری‌های آموزشی، سازمان پژوهش و برنامه‌ریزی آموزشی

چکیده

پدیدۀ تکنولوژی های جدید، دست ورزی های فیزیکی را، که مدل هایی ملموس برای بازنمایی مفاهیم هستند، جایگزین دست ورزی های مجازی کرده است که بسیاری از فراگیران و معلمان آن ها را در کلاس های ریاضی سودمند می دانند. مطالعة حاضر، انگیزۀ دانش آموزان را برای کار با دست ورزی های مجازی، به عنوان ابزارهایی در آموزش ریاضی، بررسی کرده است. از «نظریۀ فعالیت» برای تهیۀ ابزار چندمؤلفه ای، برای انجام پیمایشی در خصوص دست ورزی های مجازی در آموزش ریاضی، استفاده شد. در پیمایش 442 نفر دانش آموز دبیرستانی، به منظور آزمون کردن درک آن ها از ویژگی های مختلف این دست ورزی ها شرکت داده شدند. با استفاده از مدل مقیاس رتبه بندی راش اندریچ بر اساس نظریة پرسش پاسخ، جنبه های روان سنجی ابزار ازجمله قابل قبول بودن نشانگر، توانایی فراگیر، برازش و تک بعدی بودن بررسی شد و ابزاری رواشده برای اندازه گیری انگیزة دانش آموزان در استفاده از دست ورزی های مجازی تهیه شد. این ابزار می تواند برای پیدا کردن عواملی به کار رود که درک دانش آموزان از دست ورزی های مجازی را در کلاس ریاضی نشان می دهد. همچنین با استفاده از این ابزار می توان روابط بین سازه های این پرسش نامه را بررسی کرد که با تولید مدل هایی در خصوص انگیزۀ دانش آموزان برای استفاده از دست ورزی های مجازی می تواند علاوه بر گسترش مرز دانش در این حوزه، کیفیت فرآیند یاددهی و یادگیری ریاضی را ارتقا دهد.

کلیدواژه‌ها


عنوان مقاله [English]

The validation of an instrument using the activity theory for the evaluation of the students’ comprehension of virtual manipulatives in mathematics learning

نویسنده [English]

  • Fereshte Zeinivandneghād
PhD, mathematics education, Organization for Educational Research and Planning, Institute of Curriculum Planning and Educational Innovation, Tehran, Iran
چکیده [English]

The advent of new technologies has replaced physical manipulatives—which are physical models of equivalent representation of concepts—by virtual manipulatives which many learners and teachers find useful in the mathematics classroom. In the current study, I investigated students’ motivation to engage with virtual manipulatives as a tool in the mathematics education.

The activity theory was used to develop a multi-componential instrument to be used in a survey of virtual manipulatives in education and it was administered among 442 Iranian high school students with the aim of examining students’ perception of various aspects of the manipulatives. Using the Rasch-Andrich rating scale model (RSM), an item response theory model, psychometric features of the instrument including item endorsibility, learners’ ability, fit, and unidimensionality was examined and a valid instrument  was developed for measuring students’ motivation in using virtual manipulation. The validated instrument can be used to find the factors that could improve students’ perceptions of virtual manipulatives in the mathematics classroom. Investigating the relationship between the constructs in the validated instrument can cross the boundary of knowledge and enhance the quality of teaching and learning mathematics as well.

Anderson-Pence, K. L., Moyer-Packenham, P. S., Westenskow, A., Shumway, J., & Jordan, K. (2014). Relationships between visual static models and students’ written solutions to fraction tasks. International Journal for Mathematics Teaching and Learning, 15, 1-18. http://www.cimt.plymouth.ac.uk/journal/default.htm
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573. doi: 10.1007/bf02293814
Ayalon, M., Watson, A., & Lerman, S. (2017). Students’ conceptualisations of function revealed through definitions and examples. Research in Mathematics Education, 19(1), 1-19. doi: 10.1080/14794802.2016.1249397
Baki, A., Kosa, T., & Guven, B. (2011). A comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualization skills of pre‐service mathematics teachers. British Journal of Educational Technology, 42(2), 291-310.
Biggs, J., Kember, D., & Leung, D. Y. (2001). The revised two‐factor study process questionnaire: R‐SPQ‐2F. British journal of educational psychology, 71(1), 133-149.
Bond, T., & Fox, C. M. (2015). Applying the Rasch model: Fundamental measurement in the human sciences. London: Routledge.
Boone, William J., Staver, John R., & Yale, Melissa S. (2014). Person Reliability, Item Reliability, and More Rasch Analysis in the Human Sciences (pp. 217-234). Dordrecht: Springer Netherlands.
Bouck, E. C., & Flanagan, S. M. (2010). Virtual Manipulatives: What They Are and How Teachers Can Use Them. Intervention in School and Clinic, 45(3), 186-191.
Burns, B. A., & Hamm, E. M. (2011). A comparison of concrete and virtual manipulative use in third‐and fourth‐grade mathematics. School Science and Mathematics, 111(6), 256-261.
Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.
Chao, T., Chen, J., Star, J. R., & Dede, C. (2016). Using Digital Resources for Motivation and Engagement in Learning Mathematics: Reflections from Teachers and Students. Digital Experiences in Mathematics Education, 2(3), 253-277.
Cope, L. (2015). Math manipulatives: Making the abstract tangible. Delta Journal of Education, 5(1), 10-19.
Coupland, M. (2004). Learning with new tools (Unpublished PhD thesis). Department of Information Systems, University of Wollongong. Retrieved from http://adt.caul.edu.au/.
Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand Oaks, CA: Sage publications.
Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: Defining "Gamification". Proceedings from MindTrek '11. Tampere, Finland: ACM.
Dreyfus, T. (1991). Advanced mathematical thinking processes. In Tall D. (ed) Advanced mathematical thinking (pp. 25-41). Springer Netherlands.
Durksen, T. L., Way, J., Bobis, J., Anderson, J., Skilling, K., & Martin, A. J. (2017). Motivation and engagement in mathematics: a qualitative framework for teacher-student interactions. Mathematics Education Research Journal, 29(2), 163-181.
Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.
Furner, J. M., & Worrell, N. L. (2017). The Importance of Using Manipulatives in Teaching Math Today. Transformations, 3(1), 1-25.
Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219.
Gay, L. R., Mills, G. E., & Airasian, P. W. (2011). Educational research: Competencies for analysis and application (10th ed). Boston: Pearson.
Gravetter, F. J., and Wallnau, L. B. (2007). Statistics for the behavioral sciences. Belmont, CA: Thompson Learning.
Ha, O., & Fang, N. (2018). Interactive Virtual and Physical Manipulatives for Improving Students’ Spatial Skills. Journal of Educational Computing Research, 55(8), 1088-1110.
Hardman, J. (2005). An exploratory case study of computer use in a primary school mathematics classroom: new technology, new pedagogy? Research: information and communication technologies. Perspectives in Education, 23(1), 99-111.
Jurdak, M. (2016). Learning and teaching real world problem solving in school mathematics: A multiple-perspective framework for crossing the boundary. New York: Springer
Kaput, J. J. (1992). Technology and mathematics education. In D. Grouws (Ed.) Handbook on research in mathematics teaching and learning. NCTM Yearbook on Mathematics Education (pp. 515–556). New York: Macmillan.
Karadag, Z., & McDougall, D. (2011). GeoGebra as a cognitive tool. In L. Bu & R. Schoen (Eds.), Model-Centered Learning (pp. 169-181). SensePublishers.
Karakırık, E. (2016). Developing Virtual Mathematics Manipulatives: The SAMAP Project. In Moyer-Packenham P. (ed), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (Vol 17, pp. 147-170). Springer International Publishing.
Kontas, H. (2016). The Effect of Manipulatives on Mathematics Achievement and Attitudes of Secondary School Students. Journal of Education and Learning, 5(3), 10-20.
Ladel, Silke, & Kortenkamp, Ulrich. (2016). Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives. In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp. 25-40). Cham: Springer International Publishing.
Lee, Chun-Yi, & Chen, Ming-Jang. (2016). Influence of Prior Knowledge and Teaching Approaches Integrating Non-routine Worked Examples and Virtual Manipulatives on the Performance and Attitude of Fifth-Graders in Learning Equivalent Fractions. In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp. 189-212). Cham: Springer International Publishing.
Leont’ev, A. N. (1981). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37–71). Armonk, NY: ME Sharpe.
Lerman, S. (2001). A Review of Research Perspectives on Mathematics Teacher Education. In F.-L. Lin & T. J. Cooney (Eds.), Making Sense of Mathematics Teacher Education (pp. 33-52). Dordrecht: Springer Netherlands.
Linacre, J.M. (2015). A user’s guide to WINSTEPS. Chicago, IL: Winsteps.com.
Moyer-Packenham, Patricia S., & Bolyard, Johnna J. (2016). Revisiting the Definition of a Virtual Manipulative. In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp. 3-23). Cham: Springer International Publishing.
Pallant, J. F., & Tennant, A. (2007). An introduction to the Rasch measurement model: an example using the Hospital Anxiety and Depression Scale (HADS). British Journal of Clinical Psychology, 46(1), 1-18.
Tall, D., (2013). How humans learn to think mathematically: exploring the three worlds of mathematics. New York: Cambridge University Press.
Van Zile-Tamsen, C. (2017). Using Rasch Analysis to Inform Rating Scale Development. Research in Higher Education, 58(8), 922-933.
Wan, Z. H., & Lee, J. C. K. (2017). Hong Kong secondary school students’ attitudes towards science: a study of structural models and gender differences. International Journal of Science Education, 39(5), 507-527.
Wertsch, J. V. (1979). The concept of activity in soviet psychology: An introduction. In J. V. Wertsch (ED), The concept of activity in soviet psychology (pp.03-36). New York: M.E. Sharpe.
Wright, B. D., and Masters, G. N. (1982). Rating Scale Analysis: Rasch Measurement. Chicago: MESA Press.
Yuan, Y., Lee, C. Y., & Wang, C. H. (2010). A comparison study of polyominoes explorations in a physical and virtual manipulative environment. Journal of Computer Assisted Learning, 26(4), 307-316.
Zeynivandnezhad, F., & Bates, R. (2017). Explicating mathematical thinking in differential equations using a computer algebra system. International Journal of Mathematical Education in Science and Technology, 1-25. DOI: 10.1080/0020739X.2017.1409368
Zimmermann, W. & Cunningham, S. (1991). Editor's introduction: What is mathematical visualization? In W. Zimmermann and S. Cunningham (eds.), Visualization in Teaching and Learning Mathematics, (pp. 1-8). Washington, DC: Mathematical Association of America.