Journals / Necmettin Erbakan Üniversitesi Ereğli Eğitim Fakültesi Dergisi / 2026 / Cilt: 5 Sayı: Özel Sayı Özel Sayı

Constructing Mental Models: Mathematical Communication and Discourses in Conceptual Understanding

Zihinsel Modeller İnşa Etmek: Kavramsal Öğrenmede Matematiksel İletişim ve Söylemler

Mahir Biber(HASAN ALİ YÜCEL EĞİTİM FAKÜLTESİ)0000-0003-4044-6966
Pages
271–305
Publication Date
2023-10-29
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The investigation draws insights from pertinent literature, culminating in a comprehensive exploration of how mathematical communication-oriented learning environments serve as catalysts for the profound realization of conceptual understanding.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the realm of challenging subjects like mathematics, communication-driven learning environments assume paramount significance.
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Key Findings & Data:Within these environments, gauging students' grasp of mathematical concepts solely through immediate responses can prove to be a daunting task for educators.
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Conclusion & Impact:The investigation draws insights from pertinent literature, culminating in a comprehensive exploration of how mathematical communication-oriented learning environments serve as catalysts for the profound realization of conceptual understanding.
🔬Design:Derleme
📍Scope:Comprehensive Sample
⚙️Variables:kavramsal öğrenme · söylemler · matematiksel iletişim

Abstract

In the realm of challenging subjects like mathematics, communication-driven learning environments assume paramount significance. Within these environments, gauging students' grasp of mathematical concepts solely through immediate responses can prove to be a daunting task for educators. The unveiling of students' intricate mathematical insights necessitates a platform of reciprocal dialogues, thought-provoking discussions, and engaging discourses. Mathematics pedagogy revolves around two distinct forms of learning: conceptual and procedural. The former, conceptual learning, empowers learners to organically construct intricate mathematical frameworks within their mental landscapes, interlinking various concepts harmoniously. It is within this context that the cultivation of students' dialogues and interactive exchanges, integral components of a mathematically communicative learning environment, is believed to profoundly enhance their grasp of conceptual dimensions. This study endeavors to underscore the pivotal role of communication and discourses in education. It delves into the profound influence wielded by communication-centric learning settings in nurturing and actualizing conceptual learning. The investigation draws insights from pertinent literature, culminating in a comprehensive exploration of how mathematical communication-oriented learning environments serve as catalysts for the profound realization of conceptual understanding.

Özet

Matematik gibi algılanması güç bir alan için iletişim temelli öğrenme ortamlarının önemi büyüktür. Öğrenme ortamlarında öğretmenlerin öğrencilerinin anlık tepkilerinden matematiksel anlayışlarına dair fikir sahibi olmaları zordur. Öğrencilerin matematiksel fikirlerinin ortaya çıkarılması, karşılıklı diyaloglar, tartışmalar ve iletişimin önemli bir parçası olan söylemlerle mümkün olmaktadır. Diğer yandan, matematik öğretimi kavramsal ve işlemsel öğrenme olmak üzere iki öğrenme türüne dayanmaktadır. Bireylerin matematiksel kavramları ve kavramlar arasındaki ilişkileri zihinlerinde yapılandırmalarını sağlayan ve anlamlı öğrenmenin anahtarı olan öğrenme türü kavramsal öğrenmedir. Matematiksel iletişim temelli bir öğrenme ortamının ayrılmaz bileşenleri olan öğrencilerin diyaloglarının ve etkileşimli alışverişlerinin geliştirilmesinin, onların kavramsal öğrenmelerini derinden geliştirdiğine inanılmaktadır. Bu çalışma, eğitimde iletişim ve söylemlerin merkezi rolünün altını çizmeye çalışmaktadır. Bu bağlamda araştırma, kavramsal öğrenmeyi beslemek ve gerçekleştirmek için iletişim merkezli öğrenme ortamlarının kullandığı derin etkiyi incelemeyi amaçlamaktadır. Araştırma, matematiksel iletişim odaklı öğrenme ortamlarının, kavramsal anlayışın derinden gerçekleştirilmesi için nasıl katalizör görevi gördüğüne dair ilgili literatür ışığında kapsamlı bir değerlendirmeyi içermektedir.

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Cite This Article

Biber, M. (2023). Constructing Mental Models: Mathematical Communication and Discourses in Conceptual Understanding. Necmettin Erbakan Üniversitesi Ereğli Eğitim Fakültesi Dergisi, Cilt: 5 Sayı: Özel Sayı Özel Sayı, 271–305. https://ajindex.com/articles/1532155

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References (148)

  1. Abrahamson, D., & Abdu, R. (2020). Towards an ecological-dynamics design framework for embodied-interaction conceptual learning: The case of dynamic mathematics environments. Educational Technology Research and Development, 69. https://doi.org/10.1007/s11423-020-09805-1
  2. Afrianti, R. E. N., & Qohar, A. (2020). Improving student’s mathematical communication ability through think talk write learning model on geometry materials. JIPM (Jurnal Ilmiah Pendidikan Matematika), 8(2), Article 2. https://doi.org/10.25273/jipm.v8i2.6184
  3. Akkuş, R. (2015). Language and discourse in mathematics. Elementary Education Online, 14(1), Article 1.
  4. Altun, M. (2008). Teaching mathematics 6-7-8. classes (6th ed.). Alpha Publications.
  5. Andamon, J., & Tan, D. (2018). Conceptual understanding, attitude and performance in mathematics of grade 7 students. International Journal of Scientific & Technology Research, 07(8), 96–105.
  6. Ansori, H., Budayasa, I. K., & Suwarsono, t. (2019). Mathematical communication profile of female student who is mathematics teacher candidate in implementing teaching practice program. Math Didactic: Jurnal Pendidikan Matematika, 5, 145–153. https://doi.org/10.33654/math.v5i2.605
  7. Apriliyanto, B., Saputro, D., & Riyadi, R. (2018). Student’s social interaction in mathematics learning. Journal of Physics: Conference Series, 983(1). https://doi.org/10.1088/1742-6596/983/1/012130
  8. Ata Baran, A., & Kabael, T. (2021). An investigation of eighth grade students’ mathematical communication competency and affective characteristics. The Journal of Educational Research, 114(4), 367–380. https://doi.org/10.1080/00220671.2021.1948382
  9. Ata Baran, A., & Kabael, T. (2023). An investigation of eighth-graders’ mathematical communication competency and mathematical literacy performance. The Journal of Educational Research. https://doi.org/10.1080/00220671.2023.2250752
  10. Ata Baran, A., & Yenilmez, K. (2014). Investigation of prospective teachers’ conceptual and procedural knowledge of types of events. The Journal of Academic Social Science Studies, 28, 465–480. http://dx.doi.org/10.9761/JASSS2525
  11. Aufa, M., Saragih, S., & Minarni, A. (2016). Development of learning devices through problem based learning model based on the context of ACEH cultural to improve mathematical communication skills and social skills of SMPN 1 Muara Batu students. Journal of Education and Practice, 7(24), 232–248.
  12. Aydın, S., Ural Keleş, P., Haşıloğlu, M. A., & Aydın, L. (2016). Academicians’ views on conceptual and procedural learning in science education. Participatory Educational Research, 16(2), 121–129. https://doi.org/10.17275/per.16.spi.2.13
  13. Aydın, S., & Yeşi̇lyurt, M. (2007). Student’s view about the language used in mathematics teaching. Elektronic Journal of Social Sciences, 6(22), Article 22.
  14. Baki̇, A., Gürbüz, R., Ünal, S., & Atasoy, E. (2009). The effects of activities based on the multiple intelligence theory on students’ conceptual learning: A case of basic operations in the integer numbers. The Journal of Turkish Educational Sciences, 7(2), Article 2.
  15. Bali̇ Çalıkoğlu, G. (2002). Language scale in mathematics teaching. Hacettepe University Journal of Education Faculty, 2002(23), Article 23.
  16. Balka, D. S., Hull, T. H., & Miles, R. H. (2014). What is conceptual understanding? Retrieved October 24, 2023, from https://studylib.net/doc/7941770/what-is-conceptual-understanding?
  17. Bandura, A. (1969). Principles of behavior modification. Holt, Rinehart and Winston.
  18. Baroody, A. J. (1993). Problem solving, reasoning and communicating, K-8: Helping children think mathematically. Macmillan.
  19. Barwell, R., Leung, C., & Morgan, C. (2005). Applied linguistics and mathematics education: more than words and numbers. Language and Education, 19, 141–146. https://doi.org/10.1080/09500780508668670
  20. Baxter, J. A., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms. The Elementary School Journal, 101(5), 529–547.
  21. Baxter, J. A., Woodward, J., & Olson, D. (2005). Writing in mathematics: An alternative form of communication for academically low‐achieving students, Learning Disabilities Research and Practice, 20(2), 119–135. https://doi.org/10.1111/j.1540-5826.2005.00127.x
  22. Becerra Labra, C., Gras Marti, A., & Torregrosa, J. M. (2012). Effects of a problem-based structure of physics contents on conceptual learning and the ability to solve problems. International Journal of Science Education, 34(8), 1235–1253. https://doi.org/10.1080/09500693.2011.619210
  23. Bergsten, C., Engelbrecht, J., & Kagesten, O. (2017). Conceptual and procedural approaches to mathematics in the engineering curriculum – comparing views of junior and senior engineering students in two countries. EURASIA Journal of Mathematics, Science and Technology Education, 13. https://doi.org/10.12973/eurasia.2017.00631a
  24. Birgin, O., & Gürbüz, R. (2009). İlköğretim II. Kademe öğrencilerinin rasyonel sayılar konusundaki işlemsel ve kavramsal bilgi düzeylerinin incelenmesi [Investigation of operational and conceptual knowledge levels of secondary school students on rational numbers]. Journal of Uludag University Faculty of Education, 22(2), Article 2.
  25. Boaler, J. (2000). Mathematics from another world: Traditional communities and the alienation of learners. The Journal of Mathematical Behavior, 18, 379–397. https://doi.org/10.1016/S0732-3123(00)00026-2
  26. Bondurant, L. (2020). Equitable mathematics classroom discourse. Journal of Practitioner Research, 5(2). https://doi.org/10.5038/2379-9951.5.2.1146
  27. Brendefur, J. L., & Frykholm, J. (2000). Promoting mathematical communication in the classroom: two preservice teachers’ conceptions and practices. Journal of Mathematics Teacher Education, 3(2), 125–153. https://doi.org/10.1023/A:1009947032694
  28. Brenner, M. E. (1998). Development of mathematical communication in problem solving groups by language minority students. Bilingual Research Journal, 22(2), 149–174. https://doi.org/10.1080/15235882.1998.10162720
  29. Bruner, J. (1974). Toward a theory of instruction: Belknap Press.
  30. Cai, F. (2017). Challenges and strategies of Chinese higher education under the globalization background. Advances in Computer Science Research, 76, 659–662.
  31. Cai, J., Jakabcsin, M. S., & Lane, S. (1996). Assessing students’ mathematical communication. School Science and Mathematics, 96(5), 238–246. https://doi.org/10.1111/j.1949-8594.1996.tb10235.x
  32. Canobi, K. H. (2009). Concept–procedure interactions in children’s addition and subtraction. Journal of Experimental Child Psychology, 102(2), 131–149. https://doi.org/10.1016/j.jecp.2008.07.008
  33. Çaycı, B., Demi̇r, M. K., Başaran, M., & Demi̇r, M. (2007). Concept teaching with cooperative learning in social studies lesson. Kastamonu Journal of Education, 15(2), Article 2.
  34. Çelik, H., & Ekşi, H. (2013). Discourse analysis. Marmara University Atatürk Education Faculty Journal of Educational Sciences, 27(27), 99 - 117.
  35. Cesar, M. (1998). Social interactions and mathematics learning (SE065789; p. 15). https://eric.ed.gov/?id=ED463156
  36. Chapin, S. H., Anderson, N. C., & O’Connor, C. (2003). Classroom discussions: Using math talk to help students learn: Grades 1-6 (1st ed.). Blindpig Books.
  37. Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13(2), 145–182. https://doi.org/10.1016/0364-0213(89)90002-5
  38. Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28, 258–277. https://doi.org/10.2307/749781
  39. Everyday Mathematics. (2022). The University of Chicago School Mathematic Project Resource and Information Center. Retrieved October 24, 2023, from https://everydaymath.uchicago.edu/
  40. Farokhah, L., Ari̇setyawan, A., & Jupri̇, A. (2017). The effect of ethnomathematics-based SAVI (somatic, auditory, visualization, intellectually) approach on mathematical communication skill on geometry in elementary school. IJAEDU- International E-Journal of Advances in Education, 3(9), Article 9. https://doi.org/10.18768/ijaedu.370417
  41. Fernández-Millán, E., & Molina, M. (2017). Secondary students’ implicit conceptual knowledge of algebraic symbolism. An exploratory study through problem posing. International Electronic Journal of Mathematics Education, 12(3), 799–826. https://doi.org/10.29333/iejme/649
  42. Forrester, P., & Chinnappan, M. (2010). The predominance of procedural knowledge in fractions. Faculty of Education - Papers (Archive), 185–192.
  43. Garba, A., Ismail, N., Osman, S., & Mohd Rameli, M. R. (2019). Exploring peer effect on mathematics anxiety among secondary school students of Sokoto State, Nigeria through photovoice approach. Eurasia Journal of Mathematics, Science and Technology Education, 16. https://doi.org/10.29333/ejmste/112622
  44. Geary, D. (1994). Children’s mathematical development: Research and practical applications. American Psychological Association. https://doi.org/10.1037/10163-000
  45. Gelman, R., & Williams, E. M. (1998). Enabling constraints for cognitive development and learning: Domain specificity and epigenesis. In D. Kuhn & R. S. Siegler (Eds.), Handbook of child psychology: Cognition, perception, and language (5th ed, Vol. 2). J. Wiley.
  46. Gürbüz, R., & Gülburnu, M. (2013). Effect of Teaching Geometry with Use Cabri 3D in Eighth Grade on Conceptual Learning. Turkish Journal of Computer and Mathematics Education, 4. https://doi.org/10.16949/turcomat.60325
  47. Halford, G. S. (1993). Children’s understanding: The development of mental models. Psychology Press. https://doi.org/10.4324/9781315801803
  48. Harianja, J. K., Hernadi, S. L., & Indah, I. (2020). Students’ mathematical conceptual understanding and its relation to the mathematical communication skills. Jurnal Penelitian Pendidikan Dan Pengajaran Matematika, 6(1), 1–12.
  49. Hussein, Y. F., & Csíkos, C. (2023). The effect of teaching conceptual knowledge on students’ achievement, anxiety about, and attitude toward mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 19(2), Article em2226. https://doi.org/10.29333/ejmste/12938
  50. Hyde, R., & Jain, P. (2020). Myths and legends of mastery in the mathematics curriculum (R. Hyde & P. Jain, Eds.). SAGE, Learning Matters.
  51. Işıkdoğan Uğurlu, N., & Kayhan, N. (2018). Examination to attitudes of classroom teachers towards educational evaluation process of students with special needs. Journal of Adıyaman University Social Sciences Institute, 29, Article 29. https://doi.org/10.14520/adyusbd.398385
  52. İşleyen, T., & Işik, A. (2005). On conceptual learning of the concept of sub-vector space. Journal of Kazım Karabekir Education Faculty, 11, Article 11.
  53. İşleyen, T., & Işık, A. (2003). Conceptual and procedural learning in mathematics. Journal of Korea Society of Mathematical Education Series D: Research in Mathematical Education, 7(2), 91–99.
  54. Jazuli, A., Setyosari, P., Sulthon, & Kuswandi, D. (2017). Improving conceptual understanding and problem-solving in mathematics through a contextual learning strategy. Global Journal of Engineering Education, 19, 49–53.
  55. Kabael, T., & Ata Baran, A. (2017). Prospective middle school mathematics teachers’ mathematical communication, mathematical and pedagogical knowledge. Kastamonu Eğitim Dergisi, 25(5), Article 5.
  56. Uygur Kabael, T., & Ata Baran, A. (2016). Matematik öğretmenlerinin matematik dili becerilerinin gelişimine yönelik farkındalıklarının incelenmesi. İlköğretim Online, 15(3), 868-881,. https://doi.org/10.17051/io.2016.78518
  57. Kandemi̇r, M. (2004). The permanent concepts in mathematics. Kastamonu Educational Journal, 12(2), Article 2. Kanselaar, G., van Boxtel, C., & Linden, J. L. (2000). Collaborative Learning tasks and the elaboration of conceptual knowledge. Learning and Instruction, 10. https://doi.org/10.1016/S0959-4752(00)00002-5
  58. Kanz, M. (2020). Assessing conceptual learning in mathematics classrooms, [Master Thesis, Massey University].
  59. Kaya, D., & Aydın, H. (2016). Elementary mathematics teachers’ perceptions and lived experiences on mathematical communication. Eurasia Journal of Mathematics, Science and Technology Education, 12(6), 1619–1629. https://doi.org/10.12973/eurasia.2014.1203a
  60. Kaymak, S., Balta, N., Almas, A., Kazmagambet, B., & Mbala, O. (2020). The impact of peer instruction on students’ achievement in mathematics analysis. Journal of Psychology Research, 10(12). https://doi.org/10.17265/2159-5542/2020.12.003
  61. Kersaint, G. (n.d.). Orchestrating mathematical discourse whitepaper. I-Ready classroom mathematics. Retrieved October 24, 2023, from https://www.curriculumassociates.com/programs/i-ready-learning/classroom-math/orchestrating-mathematical-discourse-whitepaper
  62. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academies Press.
  63. Köğce, D., Yıldız, C., & Aydın, M. (2019). An investigation of preservice mathematics teachers’ opinions on determining and eliminating of mathematical misconceptions and concept teaching. Cumhuriyet International Journal of Education, 8(2), 453–478.
  64. Konyalioğlu, A. C., Tortumlu, N., Kaplan, A., Işık, A., & Hizarcı, S. (2011). On pre-service mathematics teachers’ conceptual understanding of the integral concept. Journal of Bayburt Educational Faculty, 6(1), Article 1.
  65. Kosko, K. W., & Wilkins, J. L. M. (2010). Mathematical communication and its relation to the frequency of manipulative use. International Electronic Journal of Mathematics Education, 5(2), 79–90. https://doi.org/10.29333/iejme/251
  66. Kushwaha, S. S. (2014). Trend in researches on mathematics achievement. IOSR Journal of Research & Method in Education, 4, 53–62. https://doi.org/10.9790/7388-04625362
  67. Kusumah, Y., Kustiawati, D., & Herman, T. (2020). The effect of GeoGebra in three-dimensional geometry learning on students’ mathematical communication ability. International Journal of Instruction, 13, 895–908. https://doi.org/10.29333/iji.2020.13260a
  68. Lee, J. (2015). “Oh, I just had it in my head”: Promoting mathematical communications in early childhood. Contemporary Issues in Early Childhood, 16(3), 284–287. https://doi.org/10.1177/1463949115600054
  69. Lindquist, M. M., & Elliott, P. C. (1996). Communication-an imperative for change: A conversation with Mary Lindquist. In Communication in mathematics, K-12 and beyond (pp. 1–10). NCTM.
  70. Lisnani, L. (2018). Design research on plane figure learning by using picture story and pairing game to improve mathematical communication skills of second grade of primary school students. Journal of Physics: Conference Series, 1040, 012027. https://doi.org/10.1088/1742-6596/1040/1/012027
  71. Lobato, J., Hohensee, C., Rhodehamel, B., & Diamond, J. (2012). Using student reasoning to inform the development of conceptual learning goals: The case of quadratic functions. Mathematical Thinking and Learning, 14, 85–119. https://doi.org/10.1080/10986065.2012.656362
  72. Lomibao, L. S., Luna, C. A., & Namoco, R. A. (2016). The influence of mathematical communication on students’ mathematics performance and anxiety. American Journal of Educational Research, 4(5), 378–382. https://doi.org/10.12691/education-4-5-3
  73. Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422–441. https://doi.org/10.2307/749431
  74. Makgakga, T. (2023). Twinned teachers’ mathematical discourse using problem-solving. Journal of Culture and Values in Education, 6(2), 138–157. https://doi.org/10.46303/jcve.2023.13
  75. Malatjie, F., & Machaba, F. (2019). Exploring mathematics learners’ conceptual understanding of coordinates and transformation geometry through concept mapping. Eurasia Journal of Mathematics, Science and Technology Education, 15(12), Article em1818. https://doi.org/10.29333/ejmste/110784
  76. Mareschal, D. (2016). The neuroscience of conceptual learning in science and mathematics. Current Opinion in Behavioral Sciences, 10, 114–118. https://doi.org/10.1016/j.cobeha.2016.06.001
  77. Marinopoulos, D., & Stavridou, H. (2002). The influence of a collaborative learning environment on primary students’ conceptions about acid rain. Journal of Biological Education, 37. https://doi.org/10.1080/00219266.2002.9655841
  78. Martin, D. (2001). Mathematics success and failure among african-american youth: the roles of sociohistorical context, community forces, school influence, and individual agency. Contemporary Sociology, 30. https://doi.org/10.2307/3089793
  79. Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21, 10–32. https://doi.org/10.1007/BF03217543
  80. Maspe, P. W., Awaluddin, Dassa, A., & Rosidah. (2021). The effect of self-efficacy and self-esteem on students’ mathematical communication skills. 409–415. https://doi.org/10.2991/assehr.k.211211.069
  81. Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507–528. https://doi.org/10.2167/le678.0
  82. Merriam Webster Dictionary. (2022). Definition of concept. In Merriam webster dictionary. https://www.merriam-webster.com/dictionary/concept
  83. Mohd Yatim, S. S. K., Saleh, S., Zulnaidi, H., Yew, W., & Yatim, S. A. M. (2022). Effects of brain-based teaching approach integrated with GeoGebra (b-geo module) on students’ conceptual understanding. International Journal of Instruction, 15, 327–346. https://doi.org/10.29333/iji.2022.15119a
  84. MoNE, (Ministry of National Education). (2013). Middle school mathematics course (5, 6, 7, and 8th Grades) Curriculum. Ministry of National Education.
  85. Mosckhovich, J. (2007). Using two languages when learning mathematics. Educational Studies in Mathematics, 64, 121–144. https://doi.org/10.1007/s10649-005-9005-1
  86. Moseley, B. (2005). Students’ early mathematical representation knowledge: the effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 37–69.
  87. Mujiasih, M., Waluyo, B., Kartono, K., & Mariani, S. (2021). The students’ mathematics communication skill performance after GeoGebra-assisted epic-r learning implementation. International journal of learning, Teaching and Educational Research, 20(10), Article 10. https://doi.org/10.26803/ijlter.20.10.14
  88. Nahdi, D. S., & Jatisunda, M. G. (2020). Conceptual understanding and procedural knowledge: A case study on learning mathematics of fractional material in elementary school—iopscience. Journal of Physics: Conference Series, 1477, 1–5. https://doi.org/10.1088/1742-6596/1477/4/042037
  89. Nakamura, K. (2008). Language and affect: Japanese children’s use of evaluative expressions in narratives. In Crosslinguistic approaches to the psychology of language: Research in the traditions of Dan Slobin. Lawrence Erlbaum Associates.
  90. Nathan, M., & Knuth, E. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21, 175–207. https://doi.org/10.1207/S1532690XCI2102_03
  91. NCTM. (1989). Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics.
  92. NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  93. Ng, O. L. (2016). The interplay between language, gestures, dragging and diagrams in bilingual learners’ mathematical communications. Educational Studies in Mathematics, 91(3), 307–326. https://doi.org/10.1007/s10649-015-9652-9
  94. Nurjanah, N., Dahlan, J., & Wibisono, Y. (2021). The effect of hands-on and computer-based learning activities on conceptual understanding and mathematical reasoning. International Journal of Instruction, 14, 143–160. https://doi.org/10.29333/iji.2021.1419a
  95. Pape, S. J., Bell, C. V., & Yetkin, İ. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 53(3), 179–202. https://doi.org/10.1023/A:1026062121857
  96. Paridjo, P., & Waluya, S. (2017). Analysis mathematical communication skills students in the matter algebra based NCTM. IOSR Journal of Mathematics, 13, 60–66. https://doi.org/10.9790/5728-1301056066
  97. Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2), 165–190. https://doi.org/10.1007/BF01273662
  98. Pourdavood, R. G., & Wachira, P. (2015). Importance of mathematical communication and discourse in secondary classrooms. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 15(10), 9–20.
  99. Pourdavood, R., McCarthy, K., & McCafferty, T. (2005). The impact of mental computation on children’s mathematical communication, problem solving, reasoning and algebraic thinking. Athens Journal of Education, 7(3), 241–254. https://doi.org/10.30958/aje.7-3-1
  100. Pugalee, D. K. (2001). Spotlight on the standards: Using communication to develop students’ mathematical literacy. Mathematics Teaching in the Middle School, 6(5), 296–299. https://doi.org/10.5951/MTMS.6.5.0296
  101. Pujiastuti, H., Haryadi, R., & Rosyana, R. F. (2021). The use of set magnetic teaching aids to improve mathematical communication ability. Unnes Journal of Mathematics Education, 10(1), Article 1. https://doi.org/10.15294/ujme.v10i1.43588
  102. Rillero, P. (2016). Deep conceptual learning in science and mathematics: Perspectives of teachers and administrators. The Electronic Journal of Science Education, 20(2), 14–31.
  103. Roble, D. B., Lomibao, L. S., & Luna, C. A. (2018). Promoting students’ achievement and mathematical flexibility through pre-within-post problem posing tasks. International Journal of Science and Research (IJSR), 7(1), 1830–1834.
  104. Ross, A., & Willson, V. (2012). The effects of representations, constructivist approaches, and engagement on middle school students’ algebraic procedure and conceptual understanding. School Science and Mathematics, 112. https://doi.org/10.1111/j.1949-8594.2011.00125.x
  105. Ryve, A. (2006). Making explicit the analysis of students’ mathematical discourses – revisiting a newly developed methodological framework. Educational Studies in Mathematics, 62(2), 191–209. https://doi.org/10.1007/s10649-006-4834-0
  106. Sammons, L. (2018). Teaching students to communicate mathematically. ASCD.
  107. Sari, D. P., & Darhim, D. (2020). Implementation of react strategy to develop mathematical representation, reasoning, and disposition ability. Journal on Mathematics Education, 11(1), Article 1. https://doi.org/10.22342/jme.11.1.7806.145-156
  108. Sari, S. I., & Yuberta, K. R. (2022). Analysis of mathematical communication ability in terms of student’s numerical ability. Rangkiang Mathematics Journal, 1(2), Article 2. https://doi.org/10.24036/rmj.v1i2.7
  109. Savaş, E., Taş, S., & Duru, A. (2010). Factors affecting students' achievement in mathematics. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 11(1), Article 1.
  110. Schwarz, B., Prusak, N., Swidan, O., Livny, A., Gal, K., & Segal, A. (2018). Orchestrating the emergence of conceptual learning: A case study in a geometry class. International Journal of Computer-Supported Collaborative Learning, 13. https://doi.org/10.1007/s11412-018-9276-z
  111. Septiana, A., Kusmayati, T., & Fitriana, L. (2018). Mathematical communication skill of senior high school students based on their personality types. Journal of Physics: Conference Series, 1108, 012027. https://doi.org/10.1088/1742-6596/1108/1/012027
  112. Setiyani, S., Putri, D., Ferdianto, F., & Fauji, S. (2020). Designing a digital teaching module based on mathematical communication in relation and function. Journal on Mathematics Education, 11, 223–236. https://doi.org/10.22342/jme.11.2.7320.223-236
  113. Sfard, A. (2008). Thinking as communicating. Cambridge University Press.
  114. Sfard, A. (2012). Introduction: Developing mathematical discourse—Some insights from communicational research. International Journal of Educational Research, 51–52, 1–9. https://doi.org/10.1016/j.ijer.2011.12.013
  115. Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8(1), 42–76. https://doi.org/10.1207/S15327884MCA0801_04
  116. Sierpinska, A. (1994). Understanding in mathematics (1st ed.). Routledge.
  117. Simon, M. (2013). The need for theories of conceptual learning and teaching of mathematics. In Vital directions for mathematics education research (pp. 95–118). https://doi.org/10.1007/978-1-4614-6977-3_5
  118. Simon, M. A., Kara, M., Placa, N., & Avitzur, A. (2018). Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning through activity theoretical framework. Journal of Mathematical Behavior, 52, 95–112. https://doi.org/10.1016/j.jmathb.2018.04.002
  119. Soter, A. O., Wilkinson, I. A., Murphy, P. K., Rudge, L., Reninger, K., & Edwards, M. (2008). What the discourse tells us: Talk and indicators of high-level comprehension. International Journal of Educational Research, 47(6), 372–391. https://doi.org/10.1016/j.ijer.2009.01.001
  120. Soylu, Y., & Aydın, S. (2006). A study on importance of the conceptual and operational knowledge are balanced in mathematics lessons. Erzincan University Journal of Education Faculty, 8(2), Article 2.
  121. Stein, C. A. (2007). Let’s talk: Promoting mathematical discourse in the classroom. The Mathematics Teacher, 101(4), 285–289. https://doi.org/10.5951/MT.101.4.0285
  122. Sukmawati, F., Setyosari, P., Sulton, S., & Purnomo, P. (2019). The effect of project-based collaborative learning strategy and social skill towards conceptual understanding and the application of biology concept. Journal for the Education of Gifted Young Scientists, 7(4), 1325–1344. https://doi.org/10.17478/jegys.630693
  123. Sumaji̇, S., Sa’di̇jah, C., Aydın, S., & Si̇sworo, S. (2020). Mathematical communication process of junior high school students in solving problems based on apos theory. Journal for the Education of Gifted Young Scientists, 8(1), Article 1. https://doi.org/10.17478/jegys.652055
  124. Susilawati, W., Maryono, I., & Maimunah, S. (2018). The development of Adobe Flash-based interactive multimedia to enhance students’ mathematical communication skills. IOP Conference Series: Materials Science and Engineering, 434, 012011. https://doi.org/10.1088/1757-899X/434/1/012011
  125. Tahir, T. (2021). The effect of learning styles on students’ mathematical communication ability. Journal Of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 5(1), 13–21. https://doi.org/10.31331/medivesveteran.v5i1.1378
  126. Thompson, D., & Chappell, M. (2007). Communication and representation as elements in mathematical literacy. Reading & Writing Quarterly, 23, 179–196. https://doi.org/10.1080/10573560601158495
  127. Thurston, A., Roseth, C., Chiang, T. H., Burns, V., & Topping, K. (2020). The influence of social relationships on outcomes in mathematics when using peer tutoring in elementary school. International Journal of Educational Research Open, 1(100004). https://doi.org/10.1016/j.ijedro.2020.100004
  128. Tong, D. H., Uyen, B. P., & Van Anh Quoc, N. (2021). The improvement of 10th students’ mathematical communication skills through learning ellipse topics. Heliyon, 7(11), Article e08282. https://doi.org/10.1016/j.heliyon.2021.e08282
  129. Toscano, R., Gavilán-Izquierdo, J. M., & Sánchez, V. (2019). A study of pre-service primary teachers’ discourse when solving didactic-mathematical tasks. Eurasia Journal of Mathematics, Science and Technology Education, 15(11), em1762. https://doi.org/10.29333/ejmste/108631
  130. Triana, M., Zubainur, C., & Bahrun, B. (2019). Students’ mathematical communication ability through the brain-based learning approach using autograph. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 1, 1. https://doi.org/10.23917/jramathedu.v1i1.6972
  131. Tu, C. H., & McIsaac, M. (2002). The relationship of social presence and interaction in online classes. American Journal of Distance Education, 16, 131–150. https://doi.org/10.1207/S15389286AJDE1603_2
  132. Tzur, R. (2011). Can dual processing theories of thinking inform conceptual learning in mathematics? The Mathematics Enthusiast, 8(3), 597–636. https://doi.org/10.54870/1551-3440.1230
  133. Tzur, R., & Simon, M. (2004). Distinguishing two stages of mathematics conceptual learning. International Journal of Science and Mathematics Education, 2, 287–304. https://doi.org/10.1007/s10763-004-7479-4
  134. Usiskin, Z. (2015). What does it mean to understand some mathematics? In S. J. Cho (Ed.), selected regular lectures from the 12th international congress on mathematical education (pp. 821–841). Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_46
  135. Uyen, B. P., Tong, D. H., & Tram, N. T. B. (2021). Developing mathematical communication skills for students in grade 8 in teaching congruent triangle topics. European Journal of Educational Research, 10(3), 1287–1302.
  136. Uygur Kabael, T., & Ata Baran, A. (2016). Matematik öğretmenlerinin matematiksel iletişim becerilerinin gelişimine yönelik farkındalıklarının incelenmesi [Investigation of mathematics teachers’ awareness of developing mathematical communication skills]. İlköğretim Online, 15, 868–881.
  137. van de Walle, J. A. (1989). Elementary school mathematics. Longman.
  138. Vygotsky, L. S. (2012). Thought and language. MIT Press.
  139. Walid, A. (2023). Improving conceptual understanding of mathematics through blended learning using google classroom. International Journal of Education and Teaching Zone, 2(1), 130–138. https://doi.org/10.57092/ijetz.v2i1.122
  140. Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78, 516–551. https://doi.org/10.3102/0034654308320292
  141. Wells, C. (2003). A handbook of mathematical discourse. https://abstractmath.org/Handbook/handbook.pdf
  142. Yeh, C., Cheng, H., Chen, Z. H., Liao, C. Y., & Chan, T. W. (2019). Enhancing achievement and interest in mathematics learning through Math-Island. Research and Practice in Technology Enhanced Learning, 14. https://doi.org/10.1186/s41039-019-0100-9
  143. Yimam, M., & Kelkay, A. D. (2022). Evaluation of the effects of discourse-based mathematics instruction on eleventh grade students’ conceptual and procedural understanding of probability and statistics. Cogent Education, 9(1). https://doi.org/10.1080/2331186X.2021.2007742
  144. Yüksel, A. H. (2012). The concept of persuasion. In Persuasive communication (p. 18). Anadolu University Open Education Faculty Publications.
  145. Yulian, N. (2018). Developing teaching materials using comic media to enhance students’ mathematical communication. IOP Conference Series: Materials Science and Engineering, 335, Article 012110. https://doi.org/10.1088/1757-899X/335/1/012110
  146. Zakaria, E., Yaakob, M., Mistima, S., & Adnan, M. (2010). Conceptual knowledge and mathematics achievement of matriculation students. Procedia - Social and Behavioral Sciences, 9, 1020–1024. https://doi.org/10.1016/j.sbspro.2010.12.279
  147. Zengin, Y. (2017). The potential of GeoGebra software for providing mathematical communication in the light of pre-service teachers’ views. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11, 101–127.
  148. Zeybek, Z., & Açıl, E. (2018). Investigating seventh grade students’ mathematical communication skills: Student journals. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(3), Article 3. https://doi.org/10.16949/turkbilmat.367513