Öz
Different modes of thinking and reasoning with them is
important. Interactive Diagrams (ID) are compact programs enabling multiple
representations with translations between representational modes. IDs are all
over the Internet, and covers one or more misconceptions and sometimes enables
in-depth understanding. Inside an ID, same mod translations are named as
“treatments” while different mod translations are named as “conversions”.
Student, first deduce meaning from the static representation. Then, she or he
interacts with the ID, meanwhile, translation types and representation modes
are analyzed. Individual parameters are detected for their prospective effects
on the system. This in turn leads to identification of mathematical
relationships to be synthesized. Patterns are analyzed with pattern ends.
Student, uses the insight that she /he receives from this example, on different
but same topic IDs. In the analytical geometry
course, after the topic; “vector representation of lines in the space”, 9
open-ended questions related to ID, were asked. Students were informed that
they would get 5 points from this work in case they do it personally. From 18
volunteer students, answer sheets were analyzed with content analysis method.
Specifically, the effect of the direction of conversions on the mathematical
thinking was investigated
Anahtar Kelimeler
interactive diagrams mathematical thinking treatments conversions
Kaynakça
- Akkuş, O. & Çakıroğlu, E. (2006). Seventh grade students’ use of multiple representations in pattern related algebra tasks, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi (31), 13-24.
- Berger, M. (2010). A semiotic view of mathematical activity with a computer algebra system, Relime (13), 2, 159-186.
- Cezikturk, O. (2003). The effect of interactive diagrams on secondary students’ understandings of selected mathematical representations based on van Hiele Theory and Representation Theory, Unpublished doctoral dissertation, University at Albany, SUNY, listed in UMI Dissertation Abstracts
- Cheng, P.C.H. (1999). Interactive law encoding diagrams for learning and instruction, Learning and Instruction,9(4), 309-326.
- D’Amore, B. (2002).Conceptualisation, registers of semiotic representation and noetic in mathematical education, http://math.math.unipa.it/~grim/Jdamoreingl.PDF adresinden 1. Ocak 2016 tarihinde alınmıştır.
- Devlin, K. (2012). Introduction to Mathematical Thinking, http://profkeithdevlin.com. Adresinden 15 Nisan 2017 de alınmıştır.
- Duval, R. (2017a). How to learn to understand Mathematics?, JIEEM(10), 2, 114-122.
- Duval, R.(2017b). Mathematical activity and the transformations of semiotic representations,In (Ed.R. Duval) Understanding the Mathematical Way of Thinking-The registers of semiotic representations,(pp. 21-43)Springer International Publishing. DOI 10.1007/978-3-319-56910-9_2
- Duval, R. (2006c). A cognitive analysis of problems of comprehension in a learning of mathematics, Educational Studies in Mathematics(61), 103-131.
- Fendt, W. (2015). Vector equation of a line in three-dimensional space, ID in HTML-5 app, http://www.walter-fendt.de/html5/men/line3d_en.htm adresinden 1Mart 2018 tarihinde alınmıştır.
- Gomez, J.L.L.(2001). Technology and semiotic representations in learning Mathematics, http://funes.uniandes.edu.co/588/1/LupiannezJ01-2698.pdf adresinden 10 ocak 2018 tarihinde alınmıştır.
- Janvier, C. (1987). Translation processes in mathematics education. In C. Janvier (Ed.). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Lesh, R., Post, T.& Behr, M. (1987). Representations and translations among representations in Mathematics learning and problem solving. In C. Janvier, (Ed.), Problems of representations in the teaching and learning of Mathematics (pp.33-40).Hillsdale,NJ: Lawrance Erlbaum.
- Pino-Fan, L.R., Guzman, I., Duval, R. & Font, V. (2015). The theory of registers of semiotic representation andthe onto-semiotic approach to mathematical cognition and instruction: Linking looks fort he stduy of mathematical understanding. In Beswick, K., Muir,T.,& wells,J. Eds.). Proceedings of the 39th Psychologyof Mathematics Education Conference, 4, 33-40.Hobart, Australia: PME.
- Santi, G., Sbaragil, S. (2007). Semiotic representations, “avoidable” and “unavoidable” misconceptions, La matematica e la sua didattica (21), 1, 105-110.Schoenfeld, A. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (reprint) Journal of Education (196), 2,1-39.
- Sedig, K. & Liang, H-N. (2006). Interactivity of visual mathematical representations: factors affecting learning and cognitive processes, Journal of Interactive Research, 17(2), 179-212.
- Van Hiele, P. (1986). Structure and insight, A theory of Mathematics education, Orlando, FL: Academic Press.lbaladejo, I. M. R., Garcia, M., & Codina, A., (2015). Developing mathmatical compedenciesin secendary students by introducing dynamic geometry systems in the classroom. Education and Science, 40(177), 43-58.
Öz
Temsil yolları ile gösterim çeşitliliği ve bunlarla
akıl yürütme önemlidir. Etkileşimli diyagramlar (ID); sınırlı, farklı
temsillerle aynı konuya dikkat çekilen, konuya özel, temsiller arasında
geçişlerle küçük bilgisayar yazılımlarıdır. Internet üzerinde ücretsiz,
kullanıcı dostu butik programlar; bir veya birkaç kavram yanılgısına cevap
aramak için yazılmış olabileceği gibi anlaşılması zor ve çoklu gösterim
ihtiyacı duyan konular için de hazırlanmış olabilir. ID içinde, aynı gösterim modu arasındaki geçişler
“treatment” (geçiş) diye adlandırılırken, farklı temsil modları arası geçişler
“conversion” (dönüştürme) olarak adlandırılabilmektedir. Öğrenci önce görselin
statik görüntüsünden anlam çıkarır. Daha sonra ID ile etkileşimde bulunarak
gösterim geçişleri ve gösterim özelliklerinden sistem analiz edilir. Tek tek
parametrelerin sistemde nasıl değişiklikler yaptığı bulunmaya çalışılır. Bunun
sayesinde de matematiksel bağlantılar –bağlantılı gösterim sistemleri-
sentezlenerek bir sonuca ulaşır ve ortaya çıkan örüntüler – örüntü sonları ile
birlikte araştırılır. Öğrenci, buradan elde edeceği öngörüyü farklı ama benzer
konuyu hedefleyen ID ler de de kullanmak durumunda kalacaktır. Analitik
geometri dersinde, “Uzayda doğrunun vektörel gösterimi” konusunun ardından ID
ve onunla ilgili 9 açık uçlu soruyla ID nin uygun kullanımına dikkat çekildi.
Bu ödevden +5 bonus alacakları için bireysel yapmaları istendi. 18 gönüllü
öğrencinin cevap kâğıdı fenomenolojik içerik analizi yöntemiyle incelendi.
Özellikle farklı temsil modları arası olan dönüştürmelerin yönünün matematiksel
düşünceyi nasıl etkilediği araştırıldı. 10 punto büyüklüğünde, tek satır
aralıklı, iki yana yaslı ve en çok 250 sözcük olmalıdır. “Öz” metni içinde kaynak verilmemelidir
Anahtar Kelimeler
etkileşimli Diyagramlar matematiksel düşünme dönüştürmeler geçişler
Kaynakça
- Akkuş, O. & Çakıroğlu, E. (2006). Seventh grade students’ use of multiple representations in pattern related algebra tasks, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi (31), 13-24.
- Berger, M. (2010). A semiotic view of mathematical activity with a computer algebra system, Relime (13), 2, 159-186.
- Cezikturk, O. (2003). The effect of interactive diagrams on secondary students’ understandings of selected mathematical representations based on van Hiele Theory and Representation Theory, Unpublished doctoral dissertation, University at Albany, SUNY, listed in UMI Dissertation Abstracts
- Cheng, P.C.H. (1999). Interactive law encoding diagrams for learning and instruction, Learning and Instruction,9(4), 309-326.
- D’Amore, B. (2002).Conceptualisation, registers of semiotic representation and noetic in mathematical education, http://math.math.unipa.it/~grim/Jdamoreingl.PDF adresinden 1. Ocak 2016 tarihinde alınmıştır.
- Devlin, K. (2012). Introduction to Mathematical Thinking, http://profkeithdevlin.com. Adresinden 15 Nisan 2017 de alınmıştır.
- Duval, R. (2017a). How to learn to understand Mathematics?, JIEEM(10), 2, 114-122.
- Duval, R.(2017b). Mathematical activity and the transformations of semiotic representations,In (Ed.R. Duval) Understanding the Mathematical Way of Thinking-The registers of semiotic representations,(pp. 21-43)Springer International Publishing. DOI 10.1007/978-3-319-56910-9_2
- Duval, R. (2006c). A cognitive analysis of problems of comprehension in a learning of mathematics, Educational Studies in Mathematics(61), 103-131.
- Fendt, W. (2015). Vector equation of a line in three-dimensional space, ID in HTML-5 app, http://www.walter-fendt.de/html5/men/line3d_en.htm adresinden 1Mart 2018 tarihinde alınmıştır.
- Gomez, J.L.L.(2001). Technology and semiotic representations in learning Mathematics, http://funes.uniandes.edu.co/588/1/LupiannezJ01-2698.pdf adresinden 10 ocak 2018 tarihinde alınmıştır.
- Janvier, C. (1987). Translation processes in mathematics education. In C. Janvier (Ed.). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Lesh, R., Post, T.& Behr, M. (1987). Representations and translations among representations in Mathematics learning and problem solving. In C. Janvier, (Ed.), Problems of representations in the teaching and learning of Mathematics (pp.33-40).Hillsdale,NJ: Lawrance Erlbaum.
- Pino-Fan, L.R., Guzman, I., Duval, R. & Font, V. (2015). The theory of registers of semiotic representation andthe onto-semiotic approach to mathematical cognition and instruction: Linking looks fort he stduy of mathematical understanding. In Beswick, K., Muir,T.,& wells,J. Eds.). Proceedings of the 39th Psychologyof Mathematics Education Conference, 4, 33-40.Hobart, Australia: PME.
- Santi, G., Sbaragil, S. (2007). Semiotic representations, “avoidable” and “unavoidable” misconceptions, La matematica e la sua didattica (21), 1, 105-110.Schoenfeld, A. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (reprint) Journal of Education (196), 2,1-39.
- Sedig, K. & Liang, H-N. (2006). Interactivity of visual mathematical representations: factors affecting learning and cognitive processes, Journal of Interactive Research, 17(2), 179-212.
- Van Hiele, P. (1986). Structure and insight, A theory of Mathematics education, Orlando, FL: Academic Press.lbaladejo, I. M. R., Garcia, M., & Codina, A., (2015). Developing mathmatical compedenciesin secendary students by introducing dynamic geometry systems in the classroom. Education and Science, 40(177), 43-58.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Eğitim Üzerine Çalışmalar |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2019 |
| Kabul Tarihi | 25 Haziran 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 1 Sayı: 1 |
