Lexical ambiguity in probability: knowledge of elementary school students about chance, random and uncertainty
Keywords:
Probabilistic language, Lexical ambiguity, Elementary School, Multivariate textual analysisAbstract
The objective of this work was to establish possible lexical ambiguities related to the words chance, random and uncertainty by 61 students of the fifth year of Elementary School (9 to 11 years old) of a public school in Barueri, São Paulo, Brazil, seeking find out what probabilistic meanings do they indicate based on everyday knowledge and/or what they learned at school. This was exploratory research, with a qualitative and quantitative approach, in which multivariate textual analyzes were carried out, such as Similarity Analyzes and Descending Hierarchical Classification - CHD, using the IRaMuTeQ software (R Interface for Multidimensional Text and Questionnaire Analysis). The results indicate that children have formalized, even if intuitively, since the early years of basic education, probabilistic notions such as, for example, determining the meaning of the words chance, random and uncertainty, and there should be concern in working on these concepts. We conclude that, lexical ambiguities are presented in relation to the terms under study, starting from the intuitive meaning that is constituted as a basic element that the students presented for then, to build a connection with the probabilistic language, allowing them to start using a precise language and specialized.
Downloads
References
Alsina, A., & Vásquez, C. (2016). Análisis de los conocimientos probabilísticos del profesorado de Educación Primaria. Revista Digital Matemática, Educación e Internet, 16(1). https://doi.org/10.18845/rdmei.v16i1.2475
Almico, T., & Faro, A. (2014). Enfrentamento de cuidadores de crianças com câncer em processo de quimioterapia. Psicologia, Saúde & Doenças, 15(3), 723-737. https://doi.org/10.15309/14psd150313
Batanero, C., & Diaz, C. (2007). Meaning and understanding of mathematics. The case probability. In J P. Van Bendengen, & K. François (Eds.), Philosophical Dimmensions in Matehematics Education, pp. 107-128. Spinger.
Brasil. (2018). Ministério da Educação. Base Nacional Comum Curricular (BNCC): Educação é a Base. http://basenacionalcomum.mec.gov.br/images/BNCC_EI_EF_110518_versaofinal_site.pdf
Bryant, P., & Nunes, T. (2012). Children’s understanding of probability: a literature review. Nuffield Foundation. http://www.nuffieldfoundation.org/sites/default/files/files/Nuffield_CuP_FULL_REPORTv_F INAL.pdf. Acesso em: 22 jan. 2022
Camargo, B. V. (2005). Alceste: um programa informático de análise quantitativa de dados textuais. In A. S. P. Moreira, B. V. Camargo, J. C. Jesuino & S. M. Nóbrega (Orgs.). Perspectivas teórico-metodológicas em representações sociais (pp. 511-539). João Pessoa: EdUFPB.
Camargo, B. V., & Justo, A. M. (2013). Iramuteq: um software gratuito para análise de dados textuais. Temas em Psicologia, 21(2), 513-518. https://doi.org/10.9788/TP2013.2-16
Chamorro, M. C. P. (2003). Didáctica de las Matemáticas para Primaria. In Vecino Rubio, F. El desarrollo del pensamiento aleatorio en Educación Primaria, pp. 329-351. Pearson.
Coutinho, C. de Q. e S. (2007). Conceitos probabilísticos: quais contextos a história nos aponta? Revista Eletrônica de Educação Matemática, 2-3, 50-67. https://doi.org/10.5007/%25x
Creswell, J. W., & Clark, V. L. P. (2013). Pesquisa de métodos mistos. Penso.
DeVeaux, R. D., Velleman, P. F., & Bock, D. E. (2009). Intro Stats. Pearson Education, Inc.
Durkin, K., & Shire, B. (1991). Primary school children’s interpretations of lexical ambiguity in mathematical descriptions. Journal of Research in Reading, 14(1), 46-55.
Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. D. Reidel Publishing Company.
Gal, I. (2002). Adult´s Statistical Literacy: meanings, components, responsibilities. International Statistical Review, 70(1), 1-5. https://doi.org/10.2307/1403713
Gal, I. (2004). Statistical literacy: meanings, components, responsibilities. In D. Ben-Zvi, & J. Garfield (Ed.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47-78). Kluwer Academic Publishers.
Gal, I. (2005). Towards “Probability literacy” for all citizen: building blocks and instructional dilemmas. A. J. Graham (Ed.), Exploring probability in school: Challenges for teaching and learning, pp. 43-70. Kluwer Academic Publishers.
García, I., & García, J. (2009). Enseñanza de la estadística y lenguaje: un estudio en Bachillerato. Educación Matemática, 21(3), 95-126. https://www.redalyc.org/articulo.oa?id=40516671005
Godino, J. D., Batanero, C., & Cañizares, M. J. (1996). Azar y Probabilidad. Fundamentos Didácticos y Propuestas Curriculares. Editorial Síntesis.
Hand, D. J. (2014). The improbability principle: Why coincidences, miracles, and rare events happen every day. Scientific American.
Hyland, K., & Tse, P. (2007). Is there an “academic vocabulary”? TESOL Quarterly, 41(2), 235-252.
Kaplan, J. J., Fisher, D. G., & Rogness, N. T. (2009). Lexical ambiguity in statistics: What do students know about the words: association, average, confidence, random and spread. Journal of Statistics Education, 17(3), 1-19. https://doi.org/10.1080/10691898.2009.11889535
Kaplan, J., Fisher, D. G., & Rogness, N. T. (2010). Lexical ambiguity in statistics: how students use and define the words: association, average, confidence, random and spread. Journal of Statistics Education, 18(2), 5–32. https://doi.org/10.1080/10691898.2010.11889491
Kaplan, J. J., Rogness, L. N. T., & Fisher, D. G. (2014). Exploiting lexical ambiguity to help students understand the meaning of random. Statistics Education Research Journal, 13(1), 9-24. https://doi.org/10.52041/serj.v13i1.296
Kazak, S., & Leavy, A. M. (2018). Emergent Reasoning About Uncertainty in Primary School Children with a Focus on Subjective Probability. In: A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou, E. (Eds.), Statistics in Early Childhood and Primary Education. Early Mathematics Learning and Development, pp. 37-54. Singapore: Springer. https://doi.org/10.1007/978-981-13-1044-7_3
Kazima, M. (2007). Malawian Students’ Meanings for Probability Vocabulary. Educational Studies in Mathematics, 64, 169–189. https://doi.org/10.1007/S10649-006-9032-6
Lee, C. (2010). El lenguaje en el aprendizaje de las matemáticas. Ediciones Morata.
Lopes, C. A. E. (2003). O conhecimento profissional dos professores e suas relações com Estatística e Probabilidade na Educação Infantil. [Tese de Doutorado em Educação, Faculdade de Educação, Universidade Estadual de Campinas]. https://doi.org/10.47749/T/UNICAMP.2003.283441
Lopes, C. A. E. (2008). O ensino da estatística e da probabilidade na educação básica e a formação dos professores. Caderno Cedes, 28(74), 57-73. https://doi.org/10.1590/S0101-32622008000100005
Makar, K., & Confrey, J. (2005). Variation-talk: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27-54. http://iase-web.org/documents/SERJ/SERJ4(1)_Makar_Confrey.pdf
Marchand, P., & Ratinaud, P. (2012). L'analyse de similitude appliquée aux corpus textuelles: les primaires socialistes pour l'élection présidentielle française. Actes des 11eme Journées internationales d’Analyse statistique des Données Textuelles, pp. 687-699. Liége, Belgique. https://n9.cl/ip96d
Moore, D. (2007). The Basic Practice of Statistics. W. H. Freeman and Company.
Mutombo, E. (2013). A bird’s-eye view on the EC environmental policy framing: Ten years of Impact assessment at the commission. Proceedings of 1st International Conference on Public Policy, Grenoble. http://www.icpublicpolicy.org/IMG/pdf/panel17_s1_mutombo.pdf
Nascimento-Schulze, C. M., & Camargo, B. V. (2000). Psicologia social, representações sociais e métodos. Temas de Psicologia, 8(3), 287-299.
Pereira, A. G. C. et al. (2020). Algumas reflexões sobre a definição de probabilidade. Revista Eletrônica de Educação Matemática, 15(1), 1-22. https://doi.org/10.5007/1981-1322.2020.e70030
Pilz, J. (2017). What is statistics about. In Borovcnik, M. Research report of the department of statistics AAU Klagenfurt, pp. 31-39. Klagenfurt: University of Klagenfurt. https://www.researchgate.net/publication/324222525_The_Relevance_of_Statistics
Reinert, M. (1990). Alceste une methodologie d'analyse des donnees textuelles et une application: Aurélia de G. de Nerval. Bulletin de Méthodologie Sociologique, (28), 24-54.
Salviati, M. E. (2017). Manual do Aplicativo IRaMuTeQ (Apostila de Curso). Planaltina, DF: Embrapa Cerrados. http://www.IRaMuTeQ.org/documentation/fichiers/manual-do-aplicativo-IRaMuTeQ-par-maria-elisabeth-salviati
Shultz, T., & Pilon, R. (1973). Development of the ability to detect linguistic ambiguity. Child Development, 44(4),728–733.
Skoumpourdi, C., & Kalavassis, F. (2003). The development of elementary students’ thinking regarding the probabilistic expressions. Proceedings of 20th Hellenic Congress of Mathematical Education: The development of the child in mathematics from preschool age to adulthood (pp. 509-518), Veroia (Greek).
Sousa, Y. S. O. (2021). O Uso do Software IRaMuTeQ: Fundamentos de Lexicometria para Pesquisas Qualitativas. Estudos e Pesquisas em Psicologia, 21(4). https://doi.org/10.12957/epp.2021.64034
Triola, M. F. (2006). Elementary Statistics, Pearson Education, Inc.
Tsakiridou, H., & Vavyla, E. (2015). Probability Concepts in Primary School. American Journal of Educational Research, 3(4), 535-540. https://doi.org/10.12691/education-3-4-21
Vásquez, C. O. (2018). Surgimiento del lenguaje probabilístico en el aula de educación primaria. REnCiMa, 9(2), 374-389. https://doi.org/10.26843/rencima.v9i2.1675
Vásquez, C. O., & Alsina, A. (2017). Lenguaje probabilístico: un camino para el desarrollo de la alfabetización probabilística. Un estudio de caso en el aula de Educación Primaria. Bolema, 31(57), 454 - 478. https://doi.org/10.1590/1980-4415v31n57a22
Downloads
Published
How to Cite
Issue
Section
License
This journal provides free, immediate access to its content under the principle of making research freely available to the public, which fosters a greater exchange of global knowledge.
Authors who publish in Areté, Revista Digital del Doctorado en Educación, agree to the following terms:
- Authors retain copyright and grant the journal the right to be the first publication of the work, as well as licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of authorship of the work and initial publication in this journal.
- Authors may separately establish additional agreements for the non-exclusive distribution of the version of the work published in the journal (for example, placing it in an institutional repository or publishing it in a book), with an acknowledgement of its initial publication in this journal and not to be used for commercial purposes.
- The contents and images included in the articles are the responsibility of the author(s). Areté, Revista Digital del Doctorado en Educación, is not responsible for the information included in them.
- Authors agree with the license of use used by the journal, with the self-archiving conditions and with the open access policy.
- Authors are allowed to disseminate electronically (e.g., in institutional repositories or on their own website) the published version of their work, as it favors its earlier circulation and dissemination and thus a possible increase in its citation and reach among the academic community.
- In case of reuse of published works, the existence and specifications of the license of use must be mentioned, as well as the authorship and original source of publication.