THE CONCEPT OF CHANCE IN EARLY CHILDHOOD EDUCATION: AN ANALYSIS FROM THE PERSPECTIVE OF THE REGISTER OF SEMIOTIC REPRESENTATIONS

This article aims to investigate the teaching of chance in the context of tactile models (TM) from the perspective of the Theory of Register of Semiotic Representations. In this qualitative research, we sought to identify the different types of semiotic registers and transformations (treatment and conversion), in the solutions of the tasks of the Jefferson’s Random Walks Teaching Sequence of children in early childhood education (aged 5 years). We found the presence of different registers, most frequently mother tongue and figurative language, and of conversions. Finally, the TM proved versatile, particularly in addressing the concept of chance, for the mobilization of different semiotic registers and transformations, which can encourage teachers to use this material to work concepts in the school context. Abstract: Portuguese Neste artigo tem-se como objetivo investigar o ensino de Probabilidade no contexto da maquete tátil (MT) sob a ótica da teoria de Registro de Representações Semióticas. Nesta pesquisa de cunho qualitativo, buscou-se identificar os diferentes tipos de registros semióticos e de transformações (tratamento e conversão), nas soluções das tarefas da Sequência de Ensino Passeios Aleatórios do Jefferson de crianças da educação infantil (5 anos). Verificou-se a presença dos diferentes registros, mais frequentemente a lingua materna e figural, e das conversões. Por fim, a MT mostrou-se versátil, em particular na abordagem do conceito de chance, para a mobilização de diferentes registros semióticos e de transformações, o que pode estimular os professores no uso desse material para trabalhar conceitos probabilísticos no âmnbito escolar.

PRIMARY SCHOOL STUDENTS’ READING LEVELS OF LINE GRAPHS

The aim of this research was to describe the errors and reading levels that 6th and 7th grade Chilean primary school children reach when working with line graphs. To achieve this objective, we gave a questionnaire, previously validated by experts with two open-ended tasks, to a sample of 745 students from different Chilean cities. In the first task, we asked the children to read the title of the graph, describe the variables represented and perform a direct and inverse reading of a data value. In the second task, where we address the visual effect of a scale change in a representation, the students had to select the line graph more convenient to a candidate. Although both tasks were considered easy for the grade levels targeted, only some of the students achieved the highest reading level and many made occasional errors in the reading of the graphs. Abstract: Spanish El objetivo de esta investigación es describir los errores y niveles de lectura que alcanzan estudiantes chilenos de 6º y 7º grado de Educación Primaria al trabajar con gráficos de líneas. Para lograr este objetivo, se aplicó un cuestionario, previamente validado por expertos, con dos tareas abiertas a una muestra de 745 estudiantes de diferentes ciudades chilenas. En la primera tarea, se pidió que leyeran el título del gráfico, indicaran las variables representadas y realizaran una lectura directa y otra inversa de un valor de datos. En la segunda tarea, los estudiantes deben seleccionar y justificar el gráfico de líneas más conveniente para respaldar a un candidato, donde se aborda el efecto visual de cambio de escala en una representación. Aunque ambas tareas fueron fáciles, solo una parte de los estudiantes logró el máximo nivel de lectura y aparecieron errores ocasionales en la lectura de los gráficos.

ATTITUDES RELATED TO STUDENTS’ PERFORMANCE IN STATISTICS IN UNIVERSITY PROGRAMS IN ARGENTINA

Students from non-statistics degree programs often perceive statistics as a burden, underestimating its usefulness and encountering difficulties that cause them anxiety and stress, among others, which leads many of them to fail the course. Students’ attitudes can hinder their learning and development of useful skills associated with statistical thinking, which should be later applied outside the classroom. The aim of this study was to analyze students’ attitudes towards statistics in introductory courses in three schools of Argentina, grouped in Agricultural Sciences and Biological Sciences. We analyzed students’ attitudes at the beginning and at the end of the course, the differences between pre- and post-course attitudes and the relationship between these changes and students’ performances. The sample consisted of 436 students and their attitudes were measured using the Survey of Attitudes Towards Statistics (SATS-28), considering four components: Affect, Cognitive Competence, Value and Difficulty. Students’ performances were classified as: passed (and exempt from final exam), intermediate (but not exempt from final exam), and failed. Difficulty was not related to students’ performance, as opposed to what was detected with the other components. Cognitive competence was the only component that classified students’ performance in the correct order. Students who failed the course differed from the rest in that they developed more negative feelings towards statistics at the end of the course; in contrast, students with good performance showed an increase in the value given to statistics. Biological Sciences students presented higher average in the four components studied. Abstract: Spanish Los estudiantes de carreras universitarias no estadísticas a menudo perciben a estadística como una imposición, subestimando su utilidad, encontrando dificultades que les causan, entre otros, ansiedad y estrés y muchos desaprueban la materia. Las actitudes de los estudiantes pueden dificultar su aprendizaje y el desarrollo de habilidades útiles asociadas al pensamiento estadístico que deberían aplicarse posteriormente fuera del aula. El objetivo de este estudio fue analizar las actitudes de los estudiantes hacia la estadística en cursos introductorios en tres facultades de Argentina, agrupadas en Ciencias Agrícolas y Ciencias Biológicas. Analizamos sus actitudes al principio y al final del curso, las diferencias entre las actitudes posteriores y previas al curso y la relación entre estos cambios y el rendimiento del alumno. La muestra estaba compuesta por 436 estudiantes y sus actitudes se midieron utilizando la Encuesta de Actitudes Hacia la Estadística (SATS-28), considerando cuatro componentes: Afecto, Competencia Cognitiva, Valor y Dificultad. El rendimiento de los estudiantes se clasificó en promoción, intermedio y reprobación. Dificultad no se relacionó con el rendimiento del estudiante a diferencia con lo detectado con las otras componentes. La Competencia Cognitiva fue la única componente que clasificó el rendimiento en el orden correcto. Los estudiantes que reprobaron el curso se diferenciaron del resto en que desarrollaron más sentimientos negativos hacia la estadística al final del curso; en contraposición los que tuvieron un buen rendimiento, mostraron un aumento en el valor dado a la estadística. Los estudiantes de Ciencias Biológicas presentaron un promedio más alto en las cuatro componentes.

THE NEPSO AND OPINION EDUCATIVE SURVEY IN LATIN AMERICA: DISCUSSIONS ON STATISTICAL LITERACY IN THE PERSPECTIVE OF THIS APPROACH

In this paper, the objective is to discuss some aspects of statistical literacy in the context of conducting an educative project of opinion survey in the perspective of the teaching-learning approach of the Nossa Escola Pesquisa Sua Opinião (Nepso) Program or “our school survey your opinion”, in English. This Program, with centers created in some regions of Brazil, Latin America and Europe, consists of the dissemination of the use of opinion survey as a pedagogical tool through an eight-step methodology. This discussion is supported by a qualitative research, of participant observation, whose empirical research was based on the holding of eight meetings for the development of an opinion survey based on a theme chosen by a group of 16 students aged 13-14 years at a public school from Belo Horizonte city, state of Minas Gerais, Brazil. Of these eight meetings, one was selected to explore the analysis model we call the Nepso Process, which was based on the non-fragmentation of this teaching-learning approach to the detriment of a fragmented analysis. For such, the data were analyzed in a descriptive and interpretive manner, coherent with the qualitative nature of the research. Thus, it was found that Nepso is a methodology capable of stimulating statistical literacy in students through steps that link competencies and skills needed to work with projects. Abstract: Portuguese Neste artigo, objetivamos discutir alguns aspectos do letramento estatístico no âmbito da realização de um projeto educativo de pesquisa de opinião na perspectiva da abordagem de ensino-aprendizagem do Programa Nossa Escola Pesquisa Sua Opinião (Nepso). Esse Programa, com polos criados em algumas regiões do Brasil, América Latina e Europa, consiste na disseminação do uso da pesquisa de opinião como ferramenta pedagógica por meio de uma metodologia baseada em oito etapas. Tal discussão está amparada em uma investigação qualitativa, de observação participante, cuja pesquisa empírica baseou-se na realização de oito encontros para o desenvolvimento de uma pesquisa de opinião a partir de um tema escolhido por um grupo de 16 estudantes de 13-14 anos de uma escola pública da cidade de Belo Horizonte, Estado de Minas Gerais, Brasil. Desses oito encontros, um foi selecionado para perscrutar o modelo de análise que chamamos de Processo Nepso que consistiu na não-fragmentação dessa abordagem de ensino-aprendizagem em prol de estratos de análise. Para tanto, os dados foram analisados de forma descritiva e interpretativa, coerente com a natureza qualitativa da pesquisa. Destarte, verificou-se que o Nepso é uma metodologia capaz de estimular algum letramento estatístico nos estudantes por meio das suas etapas de trabalho que vinculam competências e habilidades necessárias ao trabalho com projetos.

DISCUSSION CIRCLE FOR THE TEACHING-LEARNING OF STATISTICS

Conceptual appropriation is central to the teaching-learning and development processes. The intellectual stage is expressed by writing, verbalization and the use of the object under construction, among other means of expression. This paper discusses the conceptual appropriation by means of the creation of collaborative situations in which the argumentative language mediates the construction of knowledge. Supported by Vygotsky’s cultural-historical theory, Discussion Circle is an activity that consists of presenting some conceptual questions for the class to discuss in small groups initially, and then in a larger group, as a general meeting. Hence, we present the central ideas and theoretical support for the development of this activity and comment on a practice that took place during a course of Basic Statistics, part of the Teaching Program in Mathematics. Results indicate the conceptual development of students, which allows for the improvement of elementary school mathematics’ teacher education in terms of statistics studies, which is a strategic matter of importance for the broadening of society’s knowledge about this area. Abstract: Portuguese No processo de ensino-aprendizagem e desenvolvimento, a apropriação conceitual é central. O estágio intelectual se expressa, entre outras formas, pela escrita, verbalização e uso do objeto em construção. Este artigo discute a apropriação conceitual por meio da criação de situações colaborativas em que a linguagem da argumentação medeia a construção do conhecimento. A atividade Roda de Conversa, apoiada na teoria Histórico-Cultural de Vygotsky, consiste em propor algumas questões conceituais para a classe discutir, inicialmente em pequenos grupos e, a seguir, em uma reunião geral. Apresentamos as ideias centrais e os suportes teóricos para o desenvolvimento dessa atividade e comentamos sobre uma realização prática ocorrida em uma disciplina de Estatística Básica do curso de Licenciatura em Matemática. Os resultados encontrados indicam o desenvolvimento conceitual dos estudantes, colaborando com a melhoria da formação estatística do professor de Matemática da Educação Básica, questão estratégica na ampliação do conhecimento da sociedade sobre a área.

A SURVEY OF THE TEACHING OF STATISTICAL LITERACY, REASONING AND THINKING: TEACHERS’ CLASSROOM PRACTICE IN MEXICAN HIGH SCHOOL EDUCATION

This paper presents partial results of a one-year project funded by a grant from Mexico’s National Science and Technology Council and the National Institute for the Evaluation of Education that was designed to characterize the teaching of statistics in Mexican high school education. Work was organized in two 6-month phases. The first stage involved documentary research that consisted of analyzing the study programs of statistics courses used at 12 high school-level educational systems. The second used the field research technique to design and administer a survey called “Teaching Statistical Literacy, Reasoning and Thinking” (TSLRT), that was answered by 754 high school statistics teachers at those 12 educational systems. Both phases were based on the theoretical ideas of statistical literacy, reasoning and thinking, and were conducted with the aim of constructing a reference framework to analyze the study programs (phase one) and design the items included in the TSLRT survey (phase two). Here, we report results from the survey applied, which was comprised of 18 items on sociodemographic variables and 65 Likert scale items that measured the degree to which teachers’ classroom practice focused on elements of statistical literacy, reasoning and thinking, or shared elements. Confirmatory factor analysis was applied to the responses to the 65 Likert scale items. Results indicate that the responses fit a one-dimensional model. Finally, we discuss the pedagogical and theoretical implications of the TSLRT survey results. Abstract: Spanish En este artículo, reportamos parte de los resultados de un Proyecto de investigación de un año, el cual fue financiado por el Consejo Nacional de Ciencia y Tecnología y el Instituto Nacional para la Evaluación Educativa. El Proyecto fue diseñado para caracterizar la enseñanza de la estadística en la Educación Media Superior mexicana, y se organizó en dos fases de 6 meses cada una. La primera etapa involucró un estudio documental que consistió en analizar los programas de estudio de la materia de estadística utilizados en 12 diferentes sistemas educativos de educación media superior. La segunda usó la técnica de investigación de campo para diseñar y administrar un cuestionario llamado “Enseñanza de una Cultura, Razonamiento y Pensamiento Estadístico” (TSLRT, por sus siglas en inglés). El cuestionario fue respondido por 754 profesores de educación media superior que imparten la materia de estadística y laboran en escuelas de los 12 sistemas educativos mencionados. Ambas fases estuvieron basadas en las ideas teóricas de cultura, razonamiento y pensamiento estadístico con el objetivo de construir un marco de referencia para analizar los programas de estudio (fase uno) y diseñar los ítems incluidos en el cuestionario TSLRT (fase dos). Aquí, reportamos los resultados del cuestionario aplicado, el cual consistió en 18 ítems sobre variables sociodemográficas y 65 ítems de escala Likert que midieron el grado en que la enseñanza del profesor se centra en elementos de una cultura, razonamiento y pensamiento estadístico, o en elementos comunes. Se aplicó un análisis factorial de confirmación a las respuestas de los 65 ítems. Los resultados indican que las respuestas se ajustan a un modelo unidimensional. Finalmente, discutimos las implicaciones pedagógicas y teóricas de los resultados del cuestionario.

A DIAGNOSIS OF STATISTICAL SERVICE COURSES IN MEXICO

Statistical education is a very important area of research because it builds knowledge and promotes innovation in the courses of this discipline. Based on the advances in this area, changes in the content and approaches of the courses at all educational levels have been promoted in several countries. In this study, we examine programs of introductory statistics courses at the higher education level, seeking to characterize the state of statistical education for non-statisticians in Mexico. The extent to which the Statistical Learning Goals (MAEs) were addressed was explored. Included in the study were 410 statistics course programs from various Mexican institutions. A checklist was constructed to assess the extent to which MAEs were considered in the programs; that is, indicators of the degree of consideration of each of the goals were constructed. Exploratory and descriptive analyses were carried out to identify the extent the goals were met, followed by multiple correspondence analysis to identify associations with the program identification variables. The results showed that the MAEs were applied very little in Mexico, especially those that refer to the development of statistical thinking and culture; the exceptions were the goals of organizing data, building tables and graphs, as well as calculating descriptive statistics. For all this, it was concluded that there is much work to be done on this issue in Mexico. Abstract: Spanish La educación estadística es un área de investigación muy importante porque permite obtener conocimiento y promover la innovación en los cursos de esta disciplina. A partir de los avances en esta área, en varios países se han promovido cambios en los contenidos y enfoques de los cursos en todos los niveles educativos. En este estudio examinamos programas de cursos introductorios de estadística en el nivel superior, buscando caracterizar el estado que mantiene la educación estadística para no estadísticos en México. Se exploró la medida en la que se consideran las Metas de Aprendizaje de la Estadística (MAE) propuestas por Gal y Garfield (1997). Se recopilaron 410 programas de cursos de estadística de diversas instituciones mexicanas. Se construyó una lista de cotejo para evaluar qué tanto se consideran las MAE en el programa; es decir, se construyeron indicadores del grado de consideración de cada una de las metas. Se realizaron análisis exploratorios y descriptivos para identificar qué tanto se atiende cada una de las metas, seguidos de análisis de correspondencia múltiple para identificar asociaciones con las variables de identificación de los programas. Los resultados muestran que las MAE se han aplicado muy poco en México, sobre todo las que se refieren al desarrollo del pensamiento y la cultura estadística; la excepción es la meta que se refiere organizar los datos, construcción de tablas y gráficas, así como calcular estadísticas descriptivas. Por todo esto, se concluye que hay mucho trabajo por hacer en este tema en México.

OVERVIEW OF BRAZILIAN RESEARCH ON STATISTICS EDUCATION INVOLVING TEACHERS: METHODOLOGICAL PATHS AND TRAINING CONTEXTS

This article aims to analyze Brazilian research on statistics education involving teachers to highlight methodological trends and training contexts mobilized by such research. To this end, a survey was carried out in the Dissertation and Thesis Bank of CAPES, considering the descriptor "Statistical Education” and the 2013-2018 timeframe. A total of ninety-nine studies were found, twenty of which met the proposed objective. This is a documentary and bibliographic study, in which an interpretative approach was adopted using the technique of content analysis. The data analysis verified that nine of those studies did not lead to training processes with teachers. In addition, the analysis of the other eleven studies, which led to training, revealed an intrinsic relationship between the methodological path and the training contexts reported. This demonstrated the expressiveness of training contexts based on epistemology of collaboration, that is, those contexts that both give voice and listen to teachers, and recognize them as producers of knowledge. Conversely, we identified two research studies that shaped the training considering the paradigm of technical rationality, and designed training courses to address certain content/concepts that teachers supposedly do not master. It was evidenced that the conception of teacher training has a direct and explicit relationship with the organization of the training spaces outlined. Finally, we identified one research study based on epistemology of practice, which focuses on the understanding of knowledge mobilized in teaching practice. Abstract: Portuguese O presente artigo tem por objetivo analisar pesquisas brasileiras de Educação Estatística que envolveram professores, com vistas a evidenciar tendências metodológicas e de contextos formativos mobilizados por tais estudos. Para tanto, realizou-se um mapeamento no Banco de Dissertações e Teses da CAPES, considerando o descritor “Educação Estatística” e o período de 2013 a 2018. Foram identificadas 99 pesquisas, dentre as quais 20 dialogam com o objetivo proposto. Trata-se de um estudo documental e bibliográfico, no qual se adotou uma abordagem interpretativa que tem como técnica a análise de conteúdo. A análise dos dados permitiu identificar que nove destes estudos não desencadearam processos formativos com os docentes. Além disso, a análise das demais 11 pesquisas, que desenvolveram processos formativos, revelou uma intrínseca relação entre o percurso metodológico e os contextos formativos relatados. Nesse sentido, evidenciou-se uma expressividade de contextos formativos pautados na epistemologia da colaboração, ou seja, aqueles que dão voz aos professores e se colocam à sua escuta; que os reconhecem como produtores de conhecimento. Em contrapartida, duas pesquisas estruturaram as formações, considerando o paradigma da racionalidade técnica e concebendo cursos de capacitação para abordar determinado conteúdo/conceito que o professor supostamente não domina. Constatou-se que a concepção de formação de professores tem relação direta e explícita com a organização dos espaços de formação delineados. Por fim, identificou-se uma pesquisa alicerçada na epistemologia da prática, que se volta para a compreensão de saberes mobilizados no fazer docente.

EDITORIAL: STATISTICS EDUCATION RESEARCH FROM A LATIN AMERICAN PERSPECTIVE

Welcome to a special issue of SERJ.

UNDERSTANDING SAMPLING BY CHILEAN SECONDARY SCHOOL STUDENTS

In statistical inference, importance of sampling is recognized as one of its key concepts, which has allowed its incorporation internationally in different curricular guidelines and specifically in the Chilean curriculum, since the first notions of sampling are introduced in 7th Grade. This paper presents an analysis of the responses to an open-ended written questionnaire, designed to evaluate understanding of sampling, that was applied to a sample of 1,241 Chilean secondary students of 8th, 10th and 12th Grades in six different secondary schools. A mixed methodology was used, with qualitative description of responses and a quantitative analysis of their frequencies. The results reflect outstanding difficulties in the use of elements related to sampling and its properties in different problem situations. For example, students can distinguish the concept of sample in contexts close to their experiences; but when faced with different sampling methods, they are not able to identify biases associated to sample selection. Thus, when deciding if a sample is representative, they mostly identify cases in which the given sample is not. Abstract: Spanish En inferencia estadística se reconoce la importancia del muestreo como uno de sus conceptos clave, lo que ha permitido su incorporación a nivel internacional en diferentes lineamientos curriculares y específicamente en el currículo chileno, dado que las primeras nociones de muestreo se introducen en el séptimo año de educación primaria. En este trabajo se presenta el análisis de las respuestas a un cuestionario de respuesta abierta, diseñado para evaluar la comprensión del muestreo, que fue aplicado a una muestra de 1241 estudiantes de secundaria chilenos, de octavo año de primaria, segundo año de secundaria y cuarto año de secundaria, en seis centros educativos. Se empleó una metodología mixta, con una descripción cualitativa de las respuestas y un análisis cuantitativo de sus frecuencias. Los resultados reflejan dificultades destacables en la utilización de los elementos relacionados al muestreo y sus propiedades en las diferentes situaciones problema planteadas. Por ejemplo, los estudiantes distinguen el concepto de muestra en contextos cercanos a sus experiencias; pero cuando se enfrentan a diferentes métodos de muestreo, no son capaces de identificar los sesgos asociados a la selección de muestras. Así, al momento de decidir si una muestra es representativa, identifican sobre todo los casos en que la muestra dada no lo es.