The conceptual field of measures of central tendency: A first approximation

Irene Mauricio Cazorla; Miriam Cardoso Utsumi; Sandra Maria Magina

doi:10.29333/iejme/13571

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Irene Mauricio Cazorla ¹ ^* , Miriam Cardoso Utsumi ² , Sandra Maria Magina ¹

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¹ Universidade Estadual de Santa Cruz, Ilhéus, BA, BRAZIL² Universidade Estadual de Campinas, Campinas, SP, BRAZIL^* Corresponding Author

Abstract

This article aims to present a first approximation of the conceptual field of measures of central tendency (MCT), grounded in the theory of conceptual fields. We propose six situations according to type of variable, data presentation (raw or grouped) and amount of data. We revisit specific situations for the mean and exemplify several possibilities for introducing these measures. This is a theoretical reflection and a systematization of the knowledge produced in the area with a view to aiding it teaching in Brazilian basic education (PreK-12). We argue that from the early school years, students should collect data, use concrete and manipulable material, analyze the types of variable and context of data, transform them into different representations and based on the visual observation of data distribution, intuit the location of MCT to then calculate them.

Keywords

measures of central tendency
theory of conceptual fields
basic education
statistics education
teaching of statistics

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 18, Issue 4, November 2023, Article No: em0748

https://doi.org/10.29333/iejme/13571

Publication date: 01 Oct 2023

Online publication date: 11 Aug 2023

Article Views: 1310

Article Downloads: 969

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References

Andrade, V. (2013). Os conceitos de medidas de tendência central e de dispersão na formação estatística no ensino médio no Brasil e na França. Abordagem exploratória no quadro da teoria antropológica do didático e da teoria dos campos conceituais [The concepts of measures of central tendency and dispersion in statistical training in high school in Brazil and France. Exploratory approach within the framework of the anthropological theory of didactics and the theory of conceptual fields] [PhD thesis,. Universidade Federal Rural de Pernambuco].
Arteaga, J. (2011). Evaluación de conocimientos sobre gráficos estadísticos y conocimientos didácticos de futuros profesores [Assessment of knowledge about statistical graphs and didactic knowledge of future teachers] [PhD thesis, Universidade de Granada].
Batanero, C. (2000). Significado y comprensión de las medidas de posición central [Meaning and understanding of measures of central position]. Uno, 25, 41-58.
Cazorla, I., Henriques, A., & Santana, C. (2020). O papel dos Ostensivos na representação de variáveis estatísticas qualitativas [The Role of the Ostensives in Understanding Qualitative Statistical Variables]. Bolema, 34(68), 1243-1263. https://doi.org/10.1590/1980-4415v34n68a19.
Cazorla, I., Henriques, A., Correia, G., & Santana, C. (2021a). The role of the Ostensives in understanding quantitative statistical variables. Acta Scientiae, 23(4), 46-70. https://doi.org/10.17648/acta.scientiae.6532
Cazorla, I., Magina, S., & Santana, C. (2021b). Potencialidades de uma sequência para ensinar as medidas de tendência central nos anos iniciais do ensino fundamental [Potentialities of a didactical sequence to teach measures of central tendency in the early school years]. Em Teia, 12(3), 1-26. https://doi.org/10.51359/2177-9309.2021.250551
Cazorla, I., Santana, E., & Utsumi, M. (2019). O campo conceitual da média aritmética: uma primeira aproximação conceitual [The conceptual field of arithmetic media: A first conceptual approach]. Revemat, 14, Edição Especial Educação Estatística, 1-21. http://doi.org/105007/1981-1322.2019.e62827
Cazorla, I., Utsumi, M. & Magina, S. (2021c). Revisitando o conceito de Mediana na perspectiva dos Campos Conceituais: uma aproximação teórica [Revisiting the concept of Median from the perspective of conceptual fields: a theoretical approach]. Seminário Internacional de Pesquisa em Educação Matemática. https://www.even3.com.br/anais/viiisipemvs2021/380382-revisitando-o-conceito-de-mediana-na-perspectiva-dos-campos-conceituais--uma-aproximacao-teorica/
Cazorla, I., Utsumi, M., & Monteiro, C. (2021d). Variáveis estatísticas e suas representações em gráficos: reflexões para seu Ensino [Statistical variables and its representations in graphs: reflections for teaching]. Números, 106, 23-32. http://funes.uniandes.edu.co/23578/
Cobo, B. (2003). Significados de las medidas de posición central para los estudiantes de secundaria [Meanings of central position measures for high school students] [PhD thesis, Universidade de Granada].
Cobo, B., & Batanero, C. (2000). La mediana en la educación secundaria obligatoria: ¿Un concepto sencillo? [The median in compulsory secondary education: A simple concept?] Uno, 23, 85-96.
Figueiredo, T. (2017). Mediana e quartis: Um caso de estudo das dificuldades de aprendizagem de alunos do 8.º ano de escolaridade [Median and quartiles: A case study of the learning difficulties of 8th grade students] [Master’s theis, Universidade de Aveiro].
Lopes, C. (2008). O ensino da estatística e da probabilidade na educação básica e a formação dos professors [The teaching of statistics and probability in basic education and teacher training]. Caderno Cedes [Cedes Notebook], 28(74), 57-73. https://doi.org/10.1590/S0101-32622008000100005
Lopes, C. (2013). Educação estatística no curso de licenciatura em matemática [Statistical education in the degree course in mathematics]. Bolema, 27(47), 901-915. https://doi.org/10.1590/S0103-636X2013000400010
Magina, S., Lautert, S., & Cazorla, I. (2022). A teoria dos campos conceituais na sala de aula [The theory of conceptual field in the classroom]. In S. Magina, S. Lautert, & A. Spinillo (Eds.) Processos Cognitivos e Linguísticos na Educação Matemática. Teorias, Pesquisas e Salas de Aula (pp. 55-97). Biblioteca de Educador.
Mayén, S., Cobo, B., Batanero, C., & Balderas, P. (2017). Comprensión de las medidas de posición cesntral en estudiantes Mexicanos de bachillerato [Understanding measures of central position in Mexican high school students]. Unión, 9, 187-201.
MEC. (1997). Parâmetros curriculares nacionais matemática [Mathematics national curriculum parameters]. Ministério da Educação [Ministry of Education].
MEC. (2018). Base nacional comum curricular [Common national curriculum base]. Ministério da Educação [Ministry of Education].
Morettin, P. A., & Bussab, W. O. (2010). Estatística básica [Basic statistics]. Saraiva.
Oliveira, T. (2020). Contribuições das disciplinas de estatística na formação do futuro professor de matemática para a educação básica [Contributions of the disciplines of statistics in the formation of the future teacher of mathematics for basic education] [Master’s thesis, Universidade Estadual de Santa Cruz].
Piaget, J. (1966). A epistemologia genética [The genetic epistemology]. Martins Fontes.
Piaget, J., & Inhelder, B. (1995). A psicologia da criança [Child’s psychology]. Bertrand Brasil.
Rodrigues, C., Ferreira, A., Carrara, A., Silva, H., & Leite, V. (2021). Educação estatística: O conceito de média móvel no ensino fundamental na pandemia da COVID-19 no Brasil [Statistical education: The concept of moving average in elementary education in the COVID-19 pandemic in Brazil]. Educação Matemática em Pesquisa: Perspectivas e Tendências [Mathematics Education in Research: Perspectives and Trends], 3, 186-204. https://doi.org/10.37885/21050451
Rodrigues, M., & Silva, L. (2019). Disciplina de estatística na matriz curricular dos cursos de licenciatura em matemática no Brasil [Discipline of statistics in the curriculum of undergraduate courses in mathematics in Brazil]. Revemat, 14, 1-21. https://doi.org/10.5007/1981-1322.2019.e62829
Silva, M. A. (2011). A presença da estatística e da probabilidade no currículo prescrito de cursos de licenciatura em matemática: Uma análise do possível descompasso entre as orientações curriculares para a educação básica e a formação inicial do professor de matemática [The presence of statistics and probability in the prescribed curriculum of undergraduate courses in mathematics: An analysis of the possible mismatch between curricular guidelines for basic education and the initial training of mathematics teachers]. Bolema, 24(40), 747-764.
Vergnaud, G. (1982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In T. Carpenter, & J. Moser (Eds.), Addition and subtraction: A cognitive perspective (pp. 39-59). Lawrense Erlbaun. https://doi.org/10.1201/9781003046585-4
Vergnaud, G. (1987). Conclusion. In C. Janvier (Ed.), Problem of representation in the teaching and learning of mathematics (pp. 227-232). LEA Publishers.
Vergnaud, G. (1990). Epistemology and psychology of mathematics education. In P. Nesher, & J. Kilpatrick (Eds.), Cognition and practice (pp. 14-30). Cambridge University Press. https://doi.org/10.1017/CBO9781139013499.003
Vergnaud, G. (1996). A teoria dos campos conceituais [The theory of conceptual fields]. In J. Brun (Ed.), Didáctica das matemáticas [Didactics of mathematics] (pp. 155-191). Instituto Piaget.
Vergnaud, G. (1998). Comprehensive theory of representation for mathematics education. Journal of Mathematics Behavior, 2(17), 167-181. https://doi.org/10.1016/S0364-0213(99)80057-3
Vygotsky, L. (2001). A construção do pensamento e da linguagem [The construction of thought and language] (Trans. P. Bezerra). Martins Fontes.

How to cite this article

APA

Cazorla, I. M., Utsumi, M. C., & Magina, S. M. (2023). The conceptual field of measures of central tendency: A first approximation. International Electronic Journal of Mathematics Education, 18(4), em0748. https://doi.org/10.29333/iejme/13571

Vancouver

Cazorla IM, Utsumi MC, Magina SM. The conceptual field of measures of central tendency: A first approximation. INT ELECT J MATH ED. 2023;18(4):em0748. https://doi.org/10.29333/iejme/13571

AMA

Cazorla IM, Utsumi MC, Magina SM. The conceptual field of measures of central tendency: A first approximation. INT ELECT J MATH ED. 2023;18(4), em0748. https://doi.org/10.29333/iejme/13571

Chicago

Cazorla, Irene Mauricio, Miriam Cardoso Utsumi, and Sandra Maria Magina. "The conceptual field of measures of central tendency: A first approximation". International Electronic Journal of Mathematics Education 2023 18 no. 4 (2023): em0748. https://doi.org/10.29333/iejme/13571

Harvard

Cazorla, I. M., Utsumi, M. C., and Magina, S. M. (2023). The conceptual field of measures of central tendency: A first approximation. International Electronic Journal of Mathematics Education, 18(4), em0748. https://doi.org/10.29333/iejme/13571

MLA

Cazorla, Irene Mauricio et al. "The conceptual field of measures of central tendency: A first approximation". International Electronic Journal of Mathematics Education, vol. 18, no. 4, 2023, em0748. https://doi.org/10.29333/iejme/13571