Learning mathematical symbolization: conceptual challenges and instructional strategies in secondary schools

Referencias

ABABNEH, M. A. R.; KHASAWNEH, A. A. Symbol Sense Among Undergraduate Students. Journal of Al-Quds Open University for Educational & Psychological Research & Studies, Palestine, v. 11, n. 32, p. 102-120, dec. 2020. ABONYI, J.; FEIL, B. Cluster analysis for data mining and system identification. Berlin: Springer Science & Business Media, 2007. ADAMS, T. L. Reading mathematics: More than words can say. The Reading Teacher, Newark, v. 56, n. 8, p. 786-795, may. 2003. ARCAVI, A. Symbol sense: Informal sense making in formal mathematics. For the learning of Mathematics, Hamburg, v. 14, n. 3, p. 24-35, nov. 1994. ARCAVI, A. Developing and using symbol sense in mathematics. For the learning of mathematics, Hamburg, v. 25, n. 2, p. 42-47, jul. 2005. BAKER, T. L. Doing social research. 2. ed. New York: McGraw-Hill, may. 1994. BARDINI, C.; PIERCE, R. Assumed mathematics knowledge: the challenge of symbols. International Journal of Innovation in Science and Mathematics Education, Bhopal, v. 23, n. 1, p. 1-9, feb. 2015. BOLARINWA, O. A. Principles and methods of validity and reliability testing of questionnaires used in social and health science researches. Nigerian Postgraduate Medical Journal, Ilorin, v. 22, n. 4, p. 195-201, oct. 2015. BRUNER, J. S.; HASTE, H. (Eds.). Making Sense (Routledge Revivals): The Child’s Construction of the World. New York: Routledge, 2010. CRESWELL, J. W.; CLARK, V. L. P. Designing and conducting mixed methods research. Wiley Online Library, 2007. DUBINSKY, E.; MCDONALD, M. A. APOS: A constructivist theory of learning in undergraduate mathematics education research. In: HOLTON, D. (Ed.). The teaching and learning of mathematics at university level 2001. Dordrecht: Springer, 2001. p. 275-282. Dubinsky, E. A theory and practice of learning college mathematics. In: SCHOENFELD, A. (Ed.). Mathematical Thinking and Problem Solving. Hillsdale: Erlbaum, 1994. p 221-243. DUBINSKY, E.; WELLER, K.; MCDONALD, M. A.; BROWN, A. Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 2. Educational Studies in Mathematics, Berlin, v. 2, p. 253-266, mar. 2005. FAGNANT, A. The use of mathematical symbolism in problem solving: An empirical study carried out in grade one in the French community of Belgium. European Journal of Psychology of Education, Berlin, v. 20, n. 4, p. 355-367, dec. 2005. GILLHAM, B. Case study research methods. London: Bloomsbury Publishing, 2000. GODINO, J. D.; BATANERO, C.; FONT, V. The onto-semiotic approach to research in mathematics education. International Journal on Mathematics Education (ZDM), Berlin, v. 39, n. 1-2, p. 127- 135, mar. 2007. GÜÇLER, B. The role of symbols in mathematical communication: the case of the limit notation. Research in Mathematics Education, v. 16, n. 3, p. 251-268, 2014. GRAY, E. M.; TALL, D. O. Duality, ambiguity, and flexibility: A “proceptual” view of simple arithmetic. Journal for research in Mathematics Education, Reston, VA, v. 25, n. 2, p. 116-140, mar. 1994. GUIN, D; RUTHVEN, K.; TROUCHE, L. (Eds.). The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument Berlin: Science & Business Media, v. 36, 2006. HAMMILL, L. The interplay of text, symbols, and graphics in mathematics education. Transformative Dialogues: Teaching & Learning Journal, Surrey, BC, v. 3, n. 3, p. 1-8, mar. 2010. HEEFFER, A. Surmounting obstacles: circulation and adoption of algebraic symbolism. Philosophica (Gent), Ghent, v. 87, n. 4, p. 5-25. dec. 2012. HENDERSON, F.; RASMUSSEN, C.; ZANDIEH, M.; WAWRO, M.; SWEENEY, G. Symbol sense in linear algebra: A start toward eigen theory. In: BROWN, S.; LARSEN, S.; MARRONGELLE, K.; OEHRTMAN, M. (Eds.). Proceedings of the 14th Annual Conference for Research in Undergraduate Mathematics Education. Portland: Oregon, 2010. p. 1-12. KAPUT, J. J. Teaching and Learning a New Algebra with Understanding. Washington: National Science Foundation, may. 2000. LANDY, D.; GOLDSTONE, R. L. How abstract is symbolic thought? Journal of Experimental Psychology: Learning, Memory, and Cognition, Washington, DC, v. 33, n. 4, p. 720-733, july. 2007. LAROSE, D. T. Discovering knowledge in data: an introduction to data mining. New Jersey: John Wiley & Sons, 2014. LOMMATSCH, C. W.; MOYER-PACKENHAM, P. S. Learning Logic: examining the effects of context ordering on reasoning about conditionals. International Journal of Mathematical Education in Science and Technology, London, v. 15, n. 5, p. 730-753, june. 2018. MAHARAJ, A. Some insights from research literature for teaching and learning mathematics. South African Journal of Education, Pretoria, v. 28, n. 3, p. 401-414, nov. 2008. MAHER, C. A.; POWELL, A. B. Research on informal mathematics learning. Investigations in Mathematics Learning, Greensboro, NC, v. 7, v. 2, p. 36-44, may. 2013. MARACCHIA S. The importance of symbolism in the development of algebra. Lettera Matematica, Berlin, v.1, n. 3, p. 137-44, oct. 2013. MASON, J. H. Mathematics Teaching Practice: Guide for university and college lecturers. West Sussex: Elsevier, mar. 2002. MOSCHKOVICH, J. N. “I went by twos, he went by one”: Multiple interpretations of inscriptions as resources for mathematical discussions. The Journal of the Learning Sciences, London, v. 17, n. 4, p. 551-587, oct. 2008. MPHUTHI, G. T.; MACHABA, M. F. An Apos Exploration of the Conceptual Understanding of Algebraic Expressions. Pretoria: ISTE, 2018. NAGY, W.; TOWNSEND, D. Words as tools: Learning academic vocabulary as language acquisition. Reading Research Quarterly, New Jersey, v. 47, n. 1, p. 91-108, jan. 2012. NAIDOO, J. Language matters! Exploring promise’s use of pedagogic strategies in her mathematics classroom. Language Matters, Pretoria, v. 47, n. 3, p. 372-792, sept. 2016. O’NYUMBA, T.; WILSON, K.; DERRICK, C. J. MUKHERJEE, N. The use of focus group discussion methodology: Insights from two decades of application in conservation. Methods in Ecology and evolution, London, v. 9, n. 1, p. 20-32. jan. 2018. O’HALLORAN, K. L. Mathematical Discourse: Language, Symbolism and Visual Images. London: Continuum, 2005. O’TOOLE, T. Building powerful understanding by connecting informal and formal knowledge. In: GROOTENBOER, P.; ZEVENBERGEN, R.; CHINNAPPAN, M. (Eds.). Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia, Adelaide. MERGA, 2006. v. 2. p. 384-391. PETERSEN, B. S.; VERMEULEN, C. Writing and mathematical problem solving in Grade 3. South African Journal of Childhood Education, Johannesburg, v. 7, n. 1, p. 1-9, jun. 2017. PIERCE, R.; STACEY, K. A framework for algebraic insight. In: BOBIS, J.; PERRY, B.; MITCHELMORE, M. (Eds.) Numeracy and Beyond: Proceedings of the twenty-fourth annual conference of the Mathematics Education Research Group of Australasia. Sydney: MERGA. 2001. v. 2. p. 418-425. PIMM, D. Symbols and meanings in school mathematics. Oxford: Routledge, 2002. PIMPERTON, H.; NATION, K. Understanding words, understanding numbers: An exploration of the mathematical profiles of poor comprehends. British Journal of Educational Psychology, London, v. 80, n. 2, p. 255-268, june. 2010. PROBYN, M. ‘Smuggling the vernacular into the classroom’: conflicts and tensions in classroom codeswitching in township/rural schools in South Africa. International Journal of Bilingual Education and Bilingualism, London, v. 12, n. 2, p. 123-136, mar. 2009. RITTLE-JOHNSON B.; SIEGLER. R. S.; ALIBALI, M. W. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of educational psychology, London, v. 93, n. 2, p. 346-362, june. 2001. RUBENSTEIN, R. N.; THOMPSON, D. R. Learning mathematical symbolism: Challenges and instructional strategies. The Mathematics Teacher, Reston, VA, v. 94, n. 4, p. 265-271, apr. 2001. SALO, J.; SALMI, J.; CZINK, N.; VAINIKAINEN, P. Automatic clustering of nonstationary MIMO channel parameter estimates. Cape Town: ICT’05, may. 2005. SCHLEPPEGRELL, M. J. The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, London, v. 23, n. 2, p. 139-159, feb. 2007. SEKARAN, U.; BOUGIE, R. Research methods for business: A skill building approach. London: John Wiley & Sons, 2016. SELIGER, H. W.; SHOHAMY, E. G. Second language research methods. London: Oxford University Press, 1989. TALL, D. The transition to formal thinking in mathematics. Mathematics Education Research Journal, London, v. 20, n. 2, p. 5-24, sep. 2008. WASIK, B. H. (Ed.). Handbook of family literacy. New York: Routledge, 2012. WIRIHANA, L.; WELCH, A.;WILLIAMSON, M.; CHRISTENSEN, M.; BAKON, S.; CRAFT, J. Using Colaizzi’s method of data analysis to explore the experiences of nurse academics teaching on satellite campuses. Nurse Researcher, Alphen aan den Rijn, v. 25, n. 4, p. 30- 36, mar. 2018. KIZILTOPRAK, A.; KÖSE, N. Y. Relational thinking: The bridge between arithmetic and algebra. International Electronic Journal of Elementary Education, v. 10, n. 1, p. 131-145, oct. 2017. YETKIN, E. Student Difficulties in Learning Elementary Mathematics. Bloomington, IN: ERIC Digest, 2003. ZOHRABI, M. Mixed method research: Instruments, validity, reliability and reporting findings. Theory and Practice in Language Studies, Helsinki, v. 3, n. 2, p. 254-262, feb. 2013.