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Interpretations of Pre-service Elementary Mathematics Teachers on the Functions of Non-Textual Elements: Case Study on Algebra Learning Area

Yıl 2023, Cilt: 13 Sayı: 1, 84 - 102, 30.04.2023

Mustafa Akıncı Murat Genç

https://doi.org/10.19126/suje.1200724

Öz

The study aimed to investigate how pre-service elementary mathematics teachers perceive the intended use of non-textual elements in an algebra content area of an eighth-grade mathematics textbook. Non-textual elements in this qualitative exploratory case study refer to visual representations consisting of components that are not only verbal, numerical, or symbolic representations. Data were collected from thirty-one undergraduate students through a task-based written questionnaire including seven non-textual elements on the algebra learning domain. Data analysis was conducted using a content analysis approach to generate themes and uncover previously unspecified patterns. The results showed that pre-service teachers’ interpretations of non-textual elements could be categorized into ten themes: (i) attractiveness, (ii) organizing, (iii) embodiment, (iv) informativeness, (v) reasoning, (vi) conciseness, (vii) essentiality, (viii) decorativeness, (ix) contextuality, and (x) connectivity. Pre-service teachers were found to have diverse but sometimes overlapping interpretations of the functions of each non-textual element. However, the functional diversity of non-textual elements may have differentiated their interpretations, as visual literacy skills and strategies are required to interpret the intended use of non-textual elements. Therefore, in order for pre-service mathematics teachers to better understand the functions of non-textual elements, various teaching approaches should be developed to support pre-service teachers’ visual literacy, and these approaches to visual literacy should be incorporated into teacher education and professional development.

Anahtar Kelimeler

Non-textual elements mathematics textbook algebra learning area pre-service elementary mathematics teachers

Kaynakça

  • Alsina, C., & Nelsen, R. B. (2006). Math made visual: Creating images for understanding mathematics. Washington D. C.: Mathematical Association of America. https://doi.org/10.5948/UPO9781614441007
  • Araya, R., Farsani, D., & Hernández, J. (2016). How to attract students’ visual attention. In K. Verbert, M. Sharples, T. Klobučar (Eds.), Adaptive and adaptable learning. EC-TEL 2016. Lecture notes in computer science (pp. 843–908). Springer, Cham. https://doi.org/10.1007/978-3-319-45153-4_3
  • Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/A:1024312321077
  • Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14–18.
  • Bazerman, C. (2006). Analyzing the multidimensionality of texts in education. In J. L. Green, G. Camilli, & P. B. Elmore (Eds.), Handbook of complementary methods in education research (pp.77–94). New York, NY: Routledge. https://doi.org/10.4324/9780203874769
  • Biron, D. (2006). Fonctions de l’image dans les manuels scolaires de mathématiques au primaire. In M. Lebrun (Dir.) Le manuel scolaire, un outil à multiples facettes. (pp. 191–208). Quebec: Presses Université du Québec.
  • Boling, E., Eccarius, M., Smith, K., & Frick, T. (2004). Instructional illustrations: Intended meanings and learner interpretations. Journal of Visual Literacy, 24(2), 185–204. https://doi.org/10.1080/23796529.2004.11674612
  • Borwein, P., & Jörgenson, L. (2001). Visible structures in number theory. The American Mathematical Monthly, 108(10), 897–910. https://doi.org/10.1080/00029890.2001.11919824
  • Bosse, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal for Mathematics Teaching and Learning, 17(3), 1–20.
  • Böge, H. & Akıllı, R. (2019). Ortaokul ve imamhatip ortaokulu matematik 8 ders kitabı [Middle school and imamhatip middle school 8th-grade mathematics textbook]. Ankara: Milli Eğitim Bakanlığı Yayınları.
  • Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Durán, R., Reed, B. S., & Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663–689. https://doi.org/10.3102/00028312034004663
  • Carney, R. N., & Levin, J. R. (2002). Pictorial illustrations still improve students' learning from text. Educational psychology review, 14(1), 5–26. https://doi.org/10.1023/A:1013176309260
  • Corbin, J. M., & Strauss, A. L. (2015). Basics of qualitative research: Techniques and procedures for developing grounded theory (4th ed.) Thousand Oaks, CA: SAGE. https://doi.org/10.4135/9781452230153
  • Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage Publications.
  • Demircioğlu, H., & Polat, K. (2015). Ortaöğretim matematik öğretmen adaylarının “sözsüz ispat” yöntemine yönelik görüşleri [Secondary mathematics pre-service teachers’ opinions about “proof without words"]. The Journal of Academic Social Science Studies, 41, 233–254.
  • Duchastel, P., & Waller, R. (1979). Pictorial illustration in instructional texts. Educational Technology, 19(11), 20–25. https://www.jstor.org/stable/44421421
  • Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109–122). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
  • Elia, I., & Philippou, G. (2004). The functions of pictures in problem solving. In: M.J. Hoines, & A.B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the psychology of mathematics education. (Vol. 2, pp. 327–334). University College.
  • Farmaki, V., & Paschos, T. (2007). The interaction between intuitive and formal mathematical thinking: a case study. International Journal of Mathematical Education in Science and Technology, 38(3), 353–365. https://doi.org/10.1080/00207390601035302
  • Ferratti, R. P., & Okolo, C. M. (1996). Authenticity in learning: multimedia design projects in the social studies for students with disabilities. Journal of Learning Disability, 29(5), 450–460. https://doi.org/10.1177/002221949602900501
  • Filloy, E., Rojano, T., & Puig, L. (2008). Educational algebra: A theoretical and empirical approach. New York, NY: Springer. https://doi.org/10.1007/978-0-387-71254-3
  • Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2(3), 209–219. https://doi.org/10.1207/S15327833MTL0203_3
  • Goldin, G. A., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics. Reston, VA: NCTM.
  • Herbert, K., & Brown, R. H. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340–344. https://doi.org/10.5951/TCM.3.6.0340
  • Herman, M. (2007). What students choose to do and have to say about use of multiple representations in college algebra. Journal of Computers in Mathematics and Science Teaching, 26(1), 27–54. https://www.learntechlib.org/primary/p/21086/
  • Hershkowitz, R., Arcavi, A., & Bruckheimer, M. (2001). Reflections on the status and nature of visual reasoning-the case of the matches. International Journal of Mathematical Education in Science and Technology, 32(2), 255–265. https://doi.org/10.1080/00207390010010917
  • Kamii, C., Lewis, B., & Kirkland, L. (2001). Manipulatives: When are they useful? Journal of Mathematical Behavior, 20(1), 21–31. https://doi.org/10.1016/S0732-3123(01)00059-1
  • Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Karakaya, İ. (2011). Dokuzuncu sınıf matematik ders kitaplarındaki fonksiyon kavramıyla ilgili görsel objelerin incelenmesi [Investigating visual objects related to the function concept in high school mathematics textbooks]. Yayınlanmamış Yüksek Lisans Tezi, İstanbul: Marmara Üniversitesi Eğitim Bilimleri Enstitüsü.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The mathematics educator, 8(1), 139–151.
  • Kim, R. Y. (2009). Text + book = textbook? Development of a conceptual framework for non-textual elements in middle school mathematics textbooks. Unpublished doctoral dissertation, Michigan State University, USA.
  • Kim, R. Y. (2012). The quality of non-textual elements in mathematics textbooks: An exploratory comparison between South Korea and the United States. ZDM—The International Journal on Mathematics Education, 44(2), 175–187. https://doi.org/10.1007/s11858-012-0399-9
  • Lee, J. E., & Ligocki, D. (2020). Analysis of pre-service teachers' interpretation and utilization of non-textual elements in mathematics curriculum materials. Research in Mathematical Education, 23(4), 181–217.
  • Levin, J. R., & Mayer, R. E. (1993). Understanding illustrations in text. In B. K. Britton, A. Woodward, & M. R. Binkley (Eds.), Learning from textbooks: Theory and practice (pp. 95–111). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Milli Eğitim Bakanlığı [Ministry of National Education]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum: Elementary and middle school grades 1, 2, 3, 4, 5, 6, 7 and 8]. Ankara: MEB.
  • Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and Implementation (4th ed.). San Francisco, CA: Jossey Bass.
  • Metros, S. E. (2008). The educator’s role in preparing visually literate learners. Theory into Practice, 47(2), 102–109. https://doi.org/10.1080/00405840801992264
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Thousand Oaks, CA: Sage.
  • National Council of Teachers of Mathematics (NCTM). (2018). Catalyzing change in high school mathematics: Initiating critical conversations. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
  • Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation(s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127. https://doi.org/10.1207/s15430421tip4002_6
  • Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage Publications.
  • Peeck, J. (1993). Increasing picture effects in learning from illustrated text. Learning and Instruction, 3(3), 227–238. https://doi.org/10.1016/0959-4752(93)90006-L
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İlköğretim Matematik Öğretmen Adaylarının Metin Dışı Öğelerin İşlevlerine Yönelik Görüşleri: Cebir Öğrenme Alanına Ait Durum Çalışması

Yıl 2023, Cilt: 13 Sayı: 1, 84 - 102, 30.04.2023

Mustafa Akıncı Murat Genç

https://doi.org/10.19126/suje.1200724

Öz

Öz. Bu araştırmada, ilköğretim matematik öğretmen adaylarının sekizinci sınıf matematik ders kitabındaki cebir öğrenme alanına ait metinsel olmayan öğelerin işlevlerini nasıl yorumladıkları incelenmek amaçlanmıştır. Nitel keşfetmeye dayalı durum çalışması olarak yürütülen çalışmada, metinsel olmayan öğeler, yalnızca sözel, sayısal veya sembolik temsiller olmayan bileşenlerden oluşan görsel temsilleri ifade etmektedir. Araştırmanın verileri cebir öğrenme alanına ilişkin yedi metinsel olmayan öğeyi içeren göreve dayalı açık uçlu sorulardan oluşan bir anket formu aracılığıyla otuz bir lisans öğrencisinden toplanmıştır. Çalışmada veri analizi toplanan verilerin derinlemesine analiz edilmesini gerektiren ve önceden belirli olmayan temaların ve boyutların ortaya çıkarılmasına olanak tanıyan içerik analizi yöntemi kullanılarak yapılmıştır. Elde edilen bulgular öğretmen adaylarının metinsel olmayan öğelerin işlevlerine ilişkin yorumlarının on tema altında kategorize edilebileceğini göstermiştir: (i) dikkat çekme, (ii) organize etme, (iii) somutlaştırma, (iv) açıklayıcılık, (v) akıl yürütme, (vi) özlülük, (vii) zorunluluk, (viii) dekoratiflik, (ix) bağlamsallık, (x) ilişkilendirme. Öğretmen adaylarının, metinsel olmayan her bir öğenin işlevleri için farklı, bazen örtüşen yorumlara sahip oldukları tespit edilmiştir. Bununla birlikte, metinsel olmayan öğelerin amaçlanan kullanımını yorumlamak için görsel okuryazarlık becerileri ve stratejileri gerektiğinden, metinsel olmayan öğelerin işlevsel çeşitliliği öğretmen adaylarının yorumlarını farklılaştırmış olabilir. Bu nedenle, ilköğretim matematik öğretmen adaylarının metinsel olmayan öğelerin işlevlerini daha iyi anlayabilmeleri için öğretmen adaylarının görsel okuryazarlığını destekleyen çeşitli öğretim yaklaşımları geliştirilmeli ve görsel okuryazarlığa yönelik bu yaklaşımlar öğretmen eğitimi ve mesleki gelişime dahil edilmelidir.

Anahtar Kelimeler

Metinsel olmayan öğeler matematik ders kitabı cebir öğrenme alanı ilköğretim matematik öğretmen adayları

Kaynakça

  • Alsina, C., & Nelsen, R. B. (2006). Math made visual: Creating images for understanding mathematics. Washington D. C.: Mathematical Association of America. https://doi.org/10.5948/UPO9781614441007
  • Araya, R., Farsani, D., & Hernández, J. (2016). How to attract students’ visual attention. In K. Verbert, M. Sharples, T. Klobučar (Eds.), Adaptive and adaptable learning. EC-TEL 2016. Lecture notes in computer science (pp. 843–908). Springer, Cham. https://doi.org/10.1007/978-3-319-45153-4_3
  • Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/A:1024312321077
  • Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14–18.
  • Bazerman, C. (2006). Analyzing the multidimensionality of texts in education. In J. L. Green, G. Camilli, & P. B. Elmore (Eds.), Handbook of complementary methods in education research (pp.77–94). New York, NY: Routledge. https://doi.org/10.4324/9780203874769
  • Biron, D. (2006). Fonctions de l’image dans les manuels scolaires de mathématiques au primaire. In M. Lebrun (Dir.) Le manuel scolaire, un outil à multiples facettes. (pp. 191–208). Quebec: Presses Université du Québec.
  • Boling, E., Eccarius, M., Smith, K., & Frick, T. (2004). Instructional illustrations: Intended meanings and learner interpretations. Journal of Visual Literacy, 24(2), 185–204. https://doi.org/10.1080/23796529.2004.11674612
  • Borwein, P., & Jörgenson, L. (2001). Visible structures in number theory. The American Mathematical Monthly, 108(10), 897–910. https://doi.org/10.1080/00029890.2001.11919824
  • Bosse, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal for Mathematics Teaching and Learning, 17(3), 1–20.
  • Böge, H. & Akıllı, R. (2019). Ortaokul ve imamhatip ortaokulu matematik 8 ders kitabı [Middle school and imamhatip middle school 8th-grade mathematics textbook]. Ankara: Milli Eğitim Bakanlığı Yayınları.
  • Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Durán, R., Reed, B. S., & Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663–689. https://doi.org/10.3102/00028312034004663
  • Carney, R. N., & Levin, J. R. (2002). Pictorial illustrations still improve students' learning from text. Educational psychology review, 14(1), 5–26. https://doi.org/10.1023/A:1013176309260
  • Corbin, J. M., & Strauss, A. L. (2015). Basics of qualitative research: Techniques and procedures for developing grounded theory (4th ed.) Thousand Oaks, CA: SAGE. https://doi.org/10.4135/9781452230153
  • Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage Publications.
  • Demircioğlu, H., & Polat, K. (2015). Ortaöğretim matematik öğretmen adaylarının “sözsüz ispat” yöntemine yönelik görüşleri [Secondary mathematics pre-service teachers’ opinions about “proof without words"]. The Journal of Academic Social Science Studies, 41, 233–254.
  • Duchastel, P., & Waller, R. (1979). Pictorial illustration in instructional texts. Educational Technology, 19(11), 20–25. https://www.jstor.org/stable/44421421
  • Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109–122). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
  • Elia, I., & Philippou, G. (2004). The functions of pictures in problem solving. In: M.J. Hoines, & A.B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the psychology of mathematics education. (Vol. 2, pp. 327–334). University College.
  • Farmaki, V., & Paschos, T. (2007). The interaction between intuitive and formal mathematical thinking: a case study. International Journal of Mathematical Education in Science and Technology, 38(3), 353–365. https://doi.org/10.1080/00207390601035302
  • Ferratti, R. P., & Okolo, C. M. (1996). Authenticity in learning: multimedia design projects in the social studies for students with disabilities. Journal of Learning Disability, 29(5), 450–460. https://doi.org/10.1177/002221949602900501
  • Filloy, E., Rojano, T., & Puig, L. (2008). Educational algebra: A theoretical and empirical approach. New York, NY: Springer. https://doi.org/10.1007/978-0-387-71254-3
  • Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2(3), 209–219. https://doi.org/10.1207/S15327833MTL0203_3
  • Goldin, G. A., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics. Reston, VA: NCTM.
  • Herbert, K., & Brown, R. H. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340–344. https://doi.org/10.5951/TCM.3.6.0340
  • Herman, M. (2007). What students choose to do and have to say about use of multiple representations in college algebra. Journal of Computers in Mathematics and Science Teaching, 26(1), 27–54. https://www.learntechlib.org/primary/p/21086/
  • Hershkowitz, R., Arcavi, A., & Bruckheimer, M. (2001). Reflections on the status and nature of visual reasoning-the case of the matches. International Journal of Mathematical Education in Science and Technology, 32(2), 255–265. https://doi.org/10.1080/00207390010010917
  • Kamii, C., Lewis, B., & Kirkland, L. (2001). Manipulatives: When are they useful? Journal of Mathematical Behavior, 20(1), 21–31. https://doi.org/10.1016/S0732-3123(01)00059-1
  • Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Karakaya, İ. (2011). Dokuzuncu sınıf matematik ders kitaplarındaki fonksiyon kavramıyla ilgili görsel objelerin incelenmesi [Investigating visual objects related to the function concept in high school mathematics textbooks]. Yayınlanmamış Yüksek Lisans Tezi, İstanbul: Marmara Üniversitesi Eğitim Bilimleri Enstitüsü.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The mathematics educator, 8(1), 139–151.
  • Kim, R. Y. (2009). Text + book = textbook? Development of a conceptual framework for non-textual elements in middle school mathematics textbooks. Unpublished doctoral dissertation, Michigan State University, USA.
  • Kim, R. Y. (2012). The quality of non-textual elements in mathematics textbooks: An exploratory comparison between South Korea and the United States. ZDM—The International Journal on Mathematics Education, 44(2), 175–187. https://doi.org/10.1007/s11858-012-0399-9
  • Lee, J. E., & Ligocki, D. (2020). Analysis of pre-service teachers' interpretation and utilization of non-textual elements in mathematics curriculum materials. Research in Mathematical Education, 23(4), 181–217.
  • Levin, J. R., & Mayer, R. E. (1993). Understanding illustrations in text. In B. K. Britton, A. Woodward, & M. R. Binkley (Eds.), Learning from textbooks: Theory and practice (pp. 95–111). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Milli Eğitim Bakanlığı [Ministry of National Education]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum: Elementary and middle school grades 1, 2, 3, 4, 5, 6, 7 and 8]. Ankara: MEB.
  • Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and Implementation (4th ed.). San Francisco, CA: Jossey Bass.
  • Metros, S. E. (2008). The educator’s role in preparing visually literate learners. Theory into Practice, 47(2), 102–109. https://doi.org/10.1080/00405840801992264
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Thousand Oaks, CA: Sage.
  • National Council of Teachers of Mathematics (NCTM). (2018). Catalyzing change in high school mathematics: Initiating critical conversations. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
  • Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation(s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127. https://doi.org/10.1207/s15430421tip4002_6
  • Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage Publications.
  • Peeck, J. (1993). Increasing picture effects in learning from illustrated text. Learning and Instruction, 3(3), 227–238. https://doi.org/10.1016/0959-4752(93)90006-L
  • Pettersson, R. (1990). Teachers, students and visuals. Journal of Visual Literacy, 10(1), 45–62. https://doi.org/10.1080/23796529.1990.11674450
  • Pettersson, R. (2001). Assessing image contents. In R. E. Griffin, V. S. Williams & J. Lee (Eds.), Exploring the visual future: Art design, science, and technology (pp. 233–246). Arizona: International Visual Literacy Association.
  • Presmeg, N. (2020). Visualization and learning in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Cham: Springer. https://doi.org/10.1007/978-3-030-15789-0_161
  • Q. S. R. International (2012). NVivo qualitative data analysis software (Version 10) [Computer software]. Victoria, Australia: QSR International Pty Ltd.
  • Seffah, R. (2017). Le concept de série dans les manuels au niveau collégial: Registres de représentation et activités cognitives. [Unpublished masters’ thesis, Université de Montréal, Faculté des études supérieures et postdoctorales.
  • Sinclair, N. (2006). Mathematics and beauty: Aesthetic approaches to teaching children. New York: Teachers College Press.
  • Stein, M. K., Remillard, J., & Smith, M. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Greenwich, CT: Information Age.
  • Stylianou, D. A., & Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences. Mathematical Thinking and Learning, 6(4), 353–387. https://doi.org/10.1207/s15327833mtl0604_1
  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619
  • Van de Walle, J., Karp, K., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th edition). New York, NY: Pearson Education, Inc.
  • Watkins, J. K., Miller, E., & Brubaker, D. (2004). The role of the visual image: What are students really learning from pictorial representations? Journal of Visual Literacy, 24(1), 23–40. https://doi.org/10.1080/23796529.2004.11674601
  • Wiggins, G. (1993). Assessment: Authenticity, context, and validity. Phi Delta Kappan, 75(3), 200–214.
  • Woodward, A. (1993). Do illustrations serve an instructional purpose in US textbooks? In B. K. Britton, A. Woodward & M. Binkley (Eds.), Learning from textbooks: Theory and practice (pp. 115–134). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Yilmaz, R., & Argun, Z. (2018). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics, Science and Technology, 6(1), 41–57.
  • Yin, R. K. (2014). Case study research: Design and methods (5th ed.). Thousand Oaks, CA: Sage Publications.
Toplam 60 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Alan Eğitimleri
Bölüm Makaleler
Yazarlar

Mustafa Akıncı 0000-0003-2096-7617

Murat Genç 0000-0003-4525-7507

Erken Görünüm Tarihi 30 Nisan 2023
Yayımlanma Tarihi 30 Nisan 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 13 Sayı: 1

Kaynak Göster

APA Akıncı, M., & Genç, M. (2023). Interpretations of Pre-service Elementary Mathematics Teachers on the Functions of Non-Textual Elements: Case Study on Algebra Learning Area. Sakarya University Journal of Education, 13(1), 84-102. https://doi.org/10.19126/suje.1200724
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