Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study

Detalhes bibliográficos
Autor(a) principal: Freitas, Adelaide
Data de Publicação: 2018
Outros Autores: Figueiredo, Teresa Simões, Silva, Nélia, Miranda, Maria Cristina
Tipo de documento: Artigo
Idioma: por
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.34624/id.v10i2.11313
Resumo: Last three decades studies point out some difficulties when calculating and interpreting the median for different levels of study. Yet there is still no answer to what kind of association exists among those observed difficulties or even if there are any. The study was done with a set of 81 responses of the 8º grade students relative to four situation problems proposed. A documental analysis was realized on each response. The errors found within the calculus and interpretation of median and quantiles were identified and classified. Based on a quantitative approach and using Cramer’s V coefficient as statistical measure of association, the aim was to find out if there is a statistical association between the capacity of calculating the median and quartile values and the correct interpretation of those values after changes in data either concerning the calculated value or looking at the correspondent boxplot. The statistical analysis of the responses showed weak or moderate association in some cases; moreover, the analysis suggested that there is not association between the difficulties of calculating the median value and identifying the value in a boxplot after changing the data. This lack of association might indicate the distinct way students look at each form not realizing the existing relation as if they were two different issues.
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spelling Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative studyDificuldades na aprendizagem da Mediana e Quartis por alunos do 8.º ano de escolaridade: estudo comparativo Fórmula versus GráficoLast three decades studies point out some difficulties when calculating and interpreting the median for different levels of study. Yet there is still no answer to what kind of association exists among those observed difficulties or even if there are any. The study was done with a set of 81 responses of the 8º grade students relative to four situation problems proposed. A documental analysis was realized on each response. The errors found within the calculus and interpretation of median and quantiles were identified and classified. Based on a quantitative approach and using Cramer’s V coefficient as statistical measure of association, the aim was to find out if there is a statistical association between the capacity of calculating the median and quartile values and the correct interpretation of those values after changes in data either concerning the calculated value or looking at the correspondent boxplot. The statistical analysis of the responses showed weak or moderate association in some cases; moreover, the analysis suggested that there is not association between the difficulties of calculating the median value and identifying the value in a boxplot after changing the data. This lack of association might indicate the distinct way students look at each form not realizing the existing relation as if they were two different issues.Investigaciones realizadas en las últimas tres décadas señalan dificultades en el cálculo e interpretación de la mediana en estudiantes de distintos niveles de enseñanza. A pesar de que puedan existir interacciones entre las causas que originan tales dificultades, todavía no se han averiguado si las dificultades (observables) en el cálculo y en la interpretación de la mediana y cuartiles, están conectadas ni el cómo lo están. En el presente trabajo son analizadas las respuestas de 81 estudiantes, del 2º ESO (con 8 años de la escolaridad), frente a cuatro problemas involucrando el cálculo y la interpretación de la mediana, primero cuartil y tercer cuartil sobre los datos dados y sujetos a una modificación de un dato. En los cuatro problemas los datos son presentados como una colección y representados por un diagrama de caja. Basado en una análisis documental de las respuestas incorretas, son identificados y clasificados los errores cometidos en el cálculo y en la interpretación de mediana y cuartiles.Basado en una perspectiva cuantitativa y utilizando el coeficiente de asociación V de Cramer, el análisis estadístico de las respuestas indicó situaciones con asociaciones débiles y moderadas; más aún, el análisis subrayó que no hay asociación entre la dificultad de obtener la mediana analíticamente (via fórmula) y gráficamente (via diagrama de cajas) ante la modificación de un dato. Esta constatación sugiere que para los alumnos la interpretación de resultados obtenidos por fórmula o por diagrama de cajas son dos temas distintos, que no se entrelazan.Investigações realizadas nas últimas três décadas reportam a existência de fragilidades na aplicação de algoritmos de cálculo da mediana e na sua interpretação, em alunos de diferentes níveis de ensino. Embora possam existir interações entre as causas que originam tais dificuldades, escasseiam estudos se e como as dificuldades (observáveis) no cálculo e na interpretação da mediana e dos quartis estão interligadas. Partindo de quatro situaçõesproblemas, são analisadas as respostas dadas por 81 alunos do 8.º ano de escolaridade de uma escola, identificando e classificando os erros cometidos no cálculo e interpretação da mediana e dos quartis. Usando o coeficiente de associação V de Cramer, investiga-se também, numa perspetiva quantitativa, a interdependência entre a capacidade de obter os valores da mediana, primeiro quartil e terceiro quartil e a de interpretar o efeito sobre a mediana de uma alteração de um dado, tendo por base um conjunto de dados e um diagrama de extremos e quartis. A análise estatística das respostas assinalou situações onde existem associações fracas ou moderadas; mais ainda, não revelou associação entre a dificuldade de obtenção analítica (via fórmula) e gráfica (via diagrama de extremos e quartis) da mediana, perante uma alteração de dados. Esta constatação leva a crer que os alunos veem a interpretação de resultados obtidos segundo aquelas duas abordagens (via fórmula versus via gráfica) como se de dois tópicos diferentes, não interligados, se tratasse.Centro de Investigação Didática e Tecnologia na Formação de Formadores (CIDTFF) / Universidade de Aveiro2018-07-27info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.34624/id.v10i2.11313https://doi.org/10.34624/id.v10i2.11313Indagatio Didactica; Vol 10 No 2 (2018); 109-132Indagatio Didactica; Vol. 10 Núm. 2 (2018); 109-132Indagatio Didactica; Vol. 10 No 2 (2018); 109-132Indagatio Didactica; vol. 10 n.º 2 (2018); 109-1321647-3582reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAPporhttps://proa.ua.pt/index.php/id/article/view/11313https://proa.ua.pt/index.php/id/article/view/11313/7371Freitas, AdelaideFigueiredo, Teresa SimõesSilva, NéliaMiranda, Maria Cristinainfo:eu-repo/semantics/openAccess2023-09-22T10:18:17Zoai:proa.ua.pt:article/11313Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:30:22.171335Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
Dificuldades na aprendizagem da Mediana e Quartis por alunos do 8.º ano de escolaridade: estudo comparativo Fórmula versus Gráfico
title Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
spellingShingle Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
Freitas, Adelaide
title_short Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
title_full Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
title_fullStr Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
title_full_unstemmed Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
title_sort Learning difficulties with median and quartiles concepts in the 8th grade students: formula versus plot comparative study
author Freitas, Adelaide
author_facet Freitas, Adelaide
Figueiredo, Teresa Simões
Silva, Nélia
Miranda, Maria Cristina
author_role author
author2 Figueiredo, Teresa Simões
Silva, Nélia
Miranda, Maria Cristina
author2_role author
author
author
dc.contributor.author.fl_str_mv Freitas, Adelaide
Figueiredo, Teresa Simões
Silva, Nélia
Miranda, Maria Cristina
description Last three decades studies point out some difficulties when calculating and interpreting the median for different levels of study. Yet there is still no answer to what kind of association exists among those observed difficulties or even if there are any. The study was done with a set of 81 responses of the 8º grade students relative to four situation problems proposed. A documental analysis was realized on each response. The errors found within the calculus and interpretation of median and quantiles were identified and classified. Based on a quantitative approach and using Cramer’s V coefficient as statistical measure of association, the aim was to find out if there is a statistical association between the capacity of calculating the median and quartile values and the correct interpretation of those values after changes in data either concerning the calculated value or looking at the correspondent boxplot. The statistical analysis of the responses showed weak or moderate association in some cases; moreover, the analysis suggested that there is not association between the difficulties of calculating the median value and identifying the value in a boxplot after changing the data. This lack of association might indicate the distinct way students look at each form not realizing the existing relation as if they were two different issues.
publishDate 2018
dc.date.none.fl_str_mv 2018-07-27
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.fl_str_mv https://doi.org/10.34624/id.v10i2.11313
https://doi.org/10.34624/id.v10i2.11313
url https://doi.org/10.34624/id.v10i2.11313
dc.language.iso.fl_str_mv por
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dc.relation.none.fl_str_mv https://proa.ua.pt/index.php/id/article/view/11313
https://proa.ua.pt/index.php/id/article/view/11313/7371
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dc.publisher.none.fl_str_mv Centro de Investigação Didática e Tecnologia na Formação de Formadores (CIDTFF) / Universidade de Aveiro
publisher.none.fl_str_mv Centro de Investigação Didática e Tecnologia na Formação de Formadores (CIDTFF) / Universidade de Aveiro
dc.source.none.fl_str_mv Indagatio Didactica; Vol 10 No 2 (2018); 109-132
Indagatio Didactica; Vol. 10 Núm. 2 (2018); 109-132
Indagatio Didactica; Vol. 10 No 2 (2018); 109-132
Indagatio Didactica; vol. 10 n.º 2 (2018); 109-132
1647-3582
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