### INVESTIGATING SOCIAL SCIENCE STUDENTS’ UNDERSTANDING OF LIMITS THROUGH THE LENS OF THE PROCEPT THEORY

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DOI: http://dx.doi.org/10.19166/johme.v7i1.5900

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Cornu, B. (1991). Limits. In D. O. Tall (Ed.), *Advanced Mathematical Thinking* (pp. 153 -166). Dordrecht, NL: Kluwer Academic Publishers.

Cottrill, J., Dubinsky, E., Nicholas, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: Beginning with a coordinated process scheme. *Journal of Mathematical Behavior*, *15*(2), 167–192. https://doi.org/10.1016/S0732-3123(96)90015-2

Denbel, D. G. (2014). Students’ misconceptions of the limit concept in a first calculus course. *Journal of Education and Practice, 5*(34), 24-40. Retrieved from https://core.ac.uk/download/pdf/234636567.pdf

Essien, A. A. (2021). *Rethinking exemplification in mathematics teacher education multilingual classrooms*. Retrieved from https://zenodo.org/record/5457116#.ZDZmmHZBzIU

Güçler, B. (2014).** **The role of symbols in mathematical communication: The case of the** **limit notation. *Research in Mathematics Education, 16*(3), 251-268. https://doi.org/10.1080/14794802.2014.919872

Gray E., & Tall, D. (1992). *Success and failure in mathematics: Procept and procedure - A primary perspective*. Retrieved from https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=f964d3be8ef76ebcff452d5e75984b662c0c66c7

Gray E., & Tall, D. (1994). Duality, ambiguity, and flexibility: A proceptual view of simple arithmetic. *The Journal for Research in Mathematics Education, 26*(2), 115–141. Retrieved from https://www.jstor.org/stable/749505

Gray, E., & Tall, D. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. *Proceedings of PME25, Utrecht*, 65–72. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2001i-pme25-gray-tall.pdf

Jones, S. R. (2015) Calculus limits involving infinity: The role of students’ informal dynamic reasoning. *International Journal of Mathematical Education in Science and Technology*, *46*(1), 105-126. https://doi.org/10.1080/0020739X.2014.941427

Maharaj, A. (2010). An APOS analysis of students’ understanding of the concept of a limit of a function. *Pythagoras: Journal of the Association for Mathematics Education of South Africa, 71, *41-52. Retrieved from https://pythagoras.org.za/index.php/pythagoras/article/view/6/6

Mellor, K., Clark, R., & Essien, A. A. (2018). Affordances for learning linear functions: A comparative study of two textbooks from South Africa and Germany. *Pythagoras:** **Journal of the Association for Mathematics Education of South Africa**, 39*(1). https://doi.org/10.4102/pythagoras.v39i1.378

Monaghan, J. (1991). Problems with language of limits. *For the Learning of Mathematics,* *11*(3), 20 – 24. Retrieved from https://www.jstor.org/stable/40248029

Moru, E. K. (2009). Epistemological obstacles in coming to understand the limit of a function at undergraduate level: A case from the National University of Lesotho. *International Journal of Science and Mathematics Education, 7*, 431-454. http://dx.doi.org/10.1007/s10763-008-9143-x

Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. *Educational Studies in Mathematics, 22*(1), 1-36. https://doi.org/10.1007/bf00302715

Starman, A. B. (2013). The case study as a type of qualitative research. *Journal of Contemporary Educational Studies,* *1*, 28-43. Retrieved from https://www.sodobna-pedagogika.net/en/articles/01-2013_the-case-study-as-a-type-of-qualitative-research/

Skemp, R. A. (1971). *The psychology of learning mathematics. *Harmondsworth, UK: Penguin Books.

Skemp, R. A. (1976). Relational understanding and instrumental understanding.

*Mathematics Teaching*, *77*, 20–26. Retrieved from http://www.davidtall.com/skemp/pdfs/instrumental-relational.pdf

Taback, S. (1975). The child’s concept of limit. In M.F. Rosskopf (Ed.), *Children’s mathematical concepts *(pp. 111 - 144). New York, NY: Teachers College Press.

Tall, D.O. (n.d.). *The theory of PROCEPTs: Flexible use of symbols as both PROcess and conCEPT in arithmetic, algebra, calculus*. Retrieved from http://www.davidtall.com/papers/3.procepts.pdf

Tall, D. O., & Thomas, M. O. J. (1991).* *Encouraging versatile thinking in algebra using the computer.** ***Educational Studies in Mathematics, 22*(2), 125–147. https://doi.org/10.1007/BF00555720

Tall, D. O. (1992). *Mathematical processes and symbols in the mind*. Retrieved from https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=c36bd769cf707ab940732b63571fd944585edb3e

Tall, D. O., Gray, E., Ali, M. B., Crowley, L., DeMarois, P., McGowen, M., Pitta. D., Pinto. M., Thomas, M., & Yusof, Y. (2001). Symbols and the bifurcation between procedural and conceptual thinking. *Canadian Journal of Science, Mathematics and Technology Education, 1*, 80-104. https://doi.org/10.1080/14926150109556452

Thomas, M. O. J., & Hong, Y. Y. (2001). *Representations as conceptual tools: Process and structural perspectives*. Retrieved from https://www.math.auckland.ac.nz/~thomas/index/staff/mt/My%20PDFs%20for%20web%20site/PME01YY.pdf

Viirman, O., Vivier, L., & Monaghan, J. (2022). The limit notion at three educational levels in three countries. *International Journal of Research in Undergraduate Mathematics Education, 8*(2),** **222–244. https://doi.org/10.1007/s40753-022-00181-0

*Journal for Research in Mathematics Education, 22*(3), 219 -236. https://doi.org/10.5951/jresematheduc.22.3.0219

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