0
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Exploring the linguistic factors influencing concept identification

ORCID Icon &
Received 31 Dec 2023, Accepted 11 Jul 2024, Published online: 20 Jul 2024

References

  • Ben-Yehuda, M., Lavy, I., Linchevski, L., & Sfard, A. (2005). Doing wrong with words: What bars students’ access to arithmetical discourses. Journal for Research in Mathematics Education, 36(3), 176–247.‏.
  • Bozkurt, A. (2018). Analysis of the teaching process of cylinder and prism in mathematics curricula and textbooks in Turkey. International Online Journal of Educational Sciences, 10(3), 22–41. https://doi.org/10.15345/iojes.2018.03.002
  • Charmaz, K., & Belgrave, L. L. (2007). Grounded theory. John Wiley & Sons.
  • Chierchia, G. (2006). Formal semantics. In K. Brown (Ed.), Encyclopedia of language and linguistics (Vol. 1, pp. 564–579). Elsevier. https://doi.org/10.1016/B0-08-044854-2/01114-7
  • Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Sage Publications.
  • Crystal, D. (2010). The Cambridge encyclopedia of language (3rd ed.). Cambridge University Press.
  • de Villiers, M. (1998). To teach definitions in geometry or teach to define? In A. Olivier & K. Newstead (Eds.), Proceedings of the Conference of the International Group for the Psychology of Mathematics Education, Stellenbosch, South Africa (pp. 248−255). PME.
  • Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1–2), 3–20. https://doi.org/10.1080/14794800008520167
  • Greiner-Petter, A., Youssef, A., Ruas, T., Miller, B. R., Schubotz, M., Aizawa, A., & Gipp, B. (2020). Math-word embedding in math search and semantic extraction. Scientmetrics, 125(3), 3017–3046. https://doi.org/10.1007/s11192-020-03502-9
  • Gros, H., Thibaut, J. P., & Sander, E. (2020). Semantic congruence in arithmetic: A new conceptual model for word problem solving. Educational Psychologist, 55(2), 69–87. https://doi.org/10.1080/00461520.2019.1691004
  • Gutiérrez, A., & Jaime, A. (1999). Preservice primary teachers’ understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253–275. https://doi.org/10.1023/A:1009900719800
  • Haj-Yahya, A. (2019). Can classification criteria constitute a correct mathematical definition? Preservice and In-service teachers’ perspectives. International Journal of Research in Education & Science, 5(1), 88–101.‏.
  • Haj-Yahya, A. (2021). Students’ conceptions of the definitions of congruent and similar triangles. International Journal of Mathematical Education in Science and Technology, 53(10), 2703–2727.‏. https://doi.org/10.1080/0020739X.2021.1902008
  • Haj-Yahya, A., Daher, W., & Swidan, O. (2019). In-service teachers’ conceptions of parallelogram definitions. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedingsof the CERME11 (pp. 797–804). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME‏.
  • Haj-Yahya, A., & Hershkowitz, R. (2013). When visual and verbal representations meet the case of geometrical figures. In A. M. Lindmeier & A. Heinz (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Kiel, Germany (pp. 409–416). PME.
  • Haj-Yahya, A., Hershkowitz, R., & Dreyfus, T. (2023). Investigating students’ geometrical proofs through the lens of students’ definitions. Mathematics Education Research Journal, 35(3), 607–633.‏. https://doi.org/10.1007/s13394-021-00406-6
  • Hershkowitz, R. (1987). The acquisition of concepts and misconceptions in basic geometry - or when “a little learning is a dangerous thing”. In J. D. Novak (Ed.) Proceedings of the Second International Seminar on Misconceptions and Educational Strategies in Science and Mathematics, Itacha, NY (pp. 238–251). Cornell University.
  • Hershkowitz, R. (1989). Visualization in geometry - two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61–76.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70–95). Cambridge University Press.
  • Hetzron, R. (1997). Semitic languages. Routledge.
  • Johnson, R. E., Grove, A. L., & Clarke, A. (2019). Pillar integration process: A joint display technique to integrate data in mixed methods research. Journal of Mixed Methods Research, 13(3), 301–320. https://doi.org/10.1177/1558689817743108
  • Kocak, M., Özdemir, B. G., & Soylu, Y. (2017). An investigation of the pedagogical content knowledge of primary mathematics prospective teachers about the concept of cylinder. Cukurova University Faculty of Education Journal, 46(2), 711–765.‏.
  • Kohlhase, M. (2014). A data model and encoding for a semantic, multilingual terminology of mathematics. In S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka, & J. Urban (Eds.), Intelligent computer mathematics – Proceedings of the 2014 International Conference on Intelligent Computer Mathematics, Coimbra, Portugal (pp. 169–183). Springer Cham.
  • Kontorovich, I. (2018). Why Johnny struggles when familiar concepts are taken to a new mathematical domain: Towards a polysemous approach. Educational Studies in Mathematics, 97(1), 5–20.‏. https://doi.org/10.1007/s10649-017-9778-z
  • Kontorovich, I., & Zazkis, R. (2017). Mathematical conventions: Revisiting arbitrary and necessary. For the Learning of Mathematics, 37(1), 29–34‏.
  • Kosslyn, S. (1981). The medium and the message in mental imagery: A theory. Psychological Review, 88(1), 46–66. https://doi.org/10.1037/0033-295X.88.1.46
  • Lansdell, J. M. (1999). Introducing young children to mathematical concepts: Problems with new terminology. Educational Studies, 25(3), 327–333. https://doi.org/10.1080/03055699997837
  • Lewins, A., & Silver, C. (2007). Using software in qualitative research: A step-by-step guide. Sage.
  • Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. John Wiley & Sons.‏.
  • Miller, K. F., Kelly, M., & Zhou, X. (2005). Learning mathematics in China and the United States. Handbook of Mathematical Cognition, 8(35), 163–178.
  • Naveh, J., & Shaked, S. (1982). Amulets and magic bowls: Aramaic incantations of late antiquity. Brill.‏.
  • Okazaki, M., & Fujita, T. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul, South Korea (pp. 8–41). PME.
  • Owens, J. (2001). Arabic sociolinguistics: Topics in Diglossia, gender, identity, and politics. Georgetown University Press.
  • Pickreign, J. (2007). Rectangles and rhombi: How well do pre-service teachers know them? Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1–7.
  • Pimm, D. (1993). Just a matter of definition. Educational Studies in Mathematics, 25(3), 261–277. https://doi.org/10.1007/BF01273865
  • Presmeg, N. C. (1992). Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595–610. https://doi.org/10.1007/BF00540062
  • Pylyshyn, Z. (1981). The imagery debate: Analogue media versus tacit knowledge. Psychological Review, 88(1), 16–45. https://doi.org/10.1037/0033-295X.88.1.16
  • Pylyshyn, Z. (1985). Computation and cognition toward a foundation for cognitive science. MIT Press.
  • Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235–252. https://doi.org/10.1080/10573569.2015.1030995
  • Rosch, E. (1975). Cognitive reference points. Cognitive Psychology, 7(4), 532–547. https://doi.org/10.1016/0010-0285(75)90021-3
  • Rosch, E., & Mervis, C. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7(4), 605–773. https://doi.org/10.1016/0010-0285(75)90024-9
  • Saldaña, J. (2015). The coding manual for qualitative researchers. Sage.
  • Sapir, E. (1985). Culture, language, and personality: Selected essays by Edward Sapir. University of California Press.
  • Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. Journal of the Learning Sciences, 16(4), 565–613. https://doi.org/10.1080/10508400701525253
  • Stock, W. G. (2010). Concepts and semantic relations in information science. Journal of the American Society for Information Science and Technology, 61(10), 1951–1969. https://doi.org/10.1002/asi.21382
  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619
  • Tsamir, P., & Ovodenko, R. (2013). University students’ grasp of inflection points. Educational Studies in Mathematics, 83(3), 409–427.‏. https://doi.org/10.1007/s10649-012-9463-1
  • Ulusoy, F. (2019). Early-years prospective teachers’ definitions, examples and non-examples of cylinder and prism. International Journal for Mathematics Teaching and Learning, 20(2), 149–169.‏. https://doi.org/10.4256/ijmtl.v20i2.213
  • Usiskin, Z. (1996). Mathematics as a language. In P. Elliott & M. Kenny (Eds.), Communication in mathematics: K-12 and beyond (pp. 231–243). National Council of Teachers of Mathematics.
  • Van Dormolen, J., & Zaslavsky, O. (2003). The many facets of a definition: The case of periodicity. Journal of Mathematical Behavior, 22(1), 91–106. https://doi.org/10.1016/S0732-3123(03)00006-3
  • Viholainen, A. (2008). Incoherence of a concept image and erroneous conclusions in the case of differentiability. The Montana Mathematics Enthusiast, 5(2&3), 231–248. https://doi.org/10.54870/1551-3440.1104
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65–81). Kluwer Academic Publishers.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356–366. https://doi.org/10.2307/749441
  • Vinner, S., & Hershkowitz, R. (1980). Concept image and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the 4th Conference of the International Group for Psychology of Mathematics Education, Berkeley, CA (pp. 177–184). Lawrence Hall of Science, University of California.
  • Vygotsky, L. S. (1986). Thought and language. MIT Press.
  • Whorf, B. L. (1956). Language, thought, and reality. MIT Press.
  • Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal of Research in Mathematics Education, 36(4), 317–346.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.