Conference Paper

How Do Tertiary Students Assess Sampling on Social Contexts and Media Reports? Exploring Students’ Statistical Literacy With Relation to Sampling

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Sampling is a foundational concept for a proper development of students’ statistical literacy. This paper focuses on the evaluation of Mexican tertiary students’ abilities to evaluate statistical conclusions or claims in relation to sampling found in a social and media report context. The SOLO taxonomy is used to evaluate the richness of students’ responses in relation to sampling for two scenarios. General results reveal students have trouble correctly identifying or calculating sample size for a given study and a tendency to accept claims based on inappropriate sampling, even if the selection method has an evident source of bias. Implications for teaching in relation to sampling and statistical literacy are discussed.

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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.
Conference Paper
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In this article we analyze the fundamental ideas of statistics in the Mexican curriculum of basic and high school education, with the purpose of establishing relationships with some curricula and recommendations of organizations that promote statistical education. The results show that statistics are present from kindergarten to high school, as established by international recommendations; however, statistical inference is absent from the secondary school curriculum, including high school. The methodology of teaching in basic education gives importance to real contexts and to the posing of statistical questions to respond with the data, but in high school there is a greater emphasis on statistical procedures. Technology for data analysis and simulation is practically absent in the curriculum of all levels.
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Ideas of statistical inference are being increasingly included at various levels of complexity in the high school curriculum in many countries and are typically taught by mathematics teachers. Most of these teachers have not received a specific preparation in statistics and therefore, could share some of the common reasoning biases and misconceptions about statistical inference that are widespread among both students and researchers. In this chapter, the basic components of statistical inference, appropriate to school level, are analysed, and research related to these concepts is summarised. Finally, recommendations are made for teaching and research in this area.
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.
Context provides meaning for data analysis and the evaluation of evidence but may be distracting to students. This research explores the role of context in students' reasoning about sampling: specifically, the relationship between the strength of students' opinions about a topic, which provides the context for a study, and their ability to judge the quality of the sampling method and the scope of the conclusions in the study. Data were collected at four diverse institutions in both a testing environment and through individual interviews. Student responses were analyzed using a grounded theory approach. Testing environment results showed little evidence of the use of context whereas interview results showed more evidence of reliance on context-based opinions rather than statistical principles. © International Association for Statistical Education (IASE/ISI), November, 2013.
Multimodal learning and the quality of intelligent behavior
  • J Biggs
  • K Collis
Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behavior. In H. Rowe (Ed.), Intelligence, reconceptualization and measurement (pp. 57-76). Laurence Erlbaum.
Planes de Estudio de Referencia del Marco Curricular Común de la Educación Media Superior
  • Secretaría De Educación Pública
Secretaría de Educación Pública. (2017). Planes de Estudio de Referencia del Marco Curricular Común de la Educación Media Superior [Reference study plans of the common curriculum framework for higher middle education].
Development of understanding of sampling for statistical literacy
  • J Watson
  • J Moritz
Watson, J., & Moritz, J. (2000). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behavior, 19(1), 109-136.