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Context 1
... working on connecting points (last question of the time plot section of the worksheet, Figure 2) they obtained a new graph ( Figure 5). This graph elicited many comments from A and D, who tried to make sense of what they saw. They first objected and claimed that "Olympiads occur only once in every four years", namely, there are no data between the points. Thus, in their view, the connecting line (as provided by the spreadsheet upon request) not only did not add any new meaning, but also contradicted their understanding of the representation in relation to the context of the data. This further supports our claim that they were much more occupied with understanding how the graph represents pointwise data, than about ...
Context 2
... Figures 5 -7 show three graphical representatives of the same situation, namely, the men's 100 meters Olympic race. Each of them shows a different aspect of the change over time, which may be difficult or impossible to infer from another representation. For example, Figure 7 shows a linear increase of record time, Figure 6 shows a slight decrease, while Figure 5 shows a non-uniform decrease. Intuitively, it might seem that such ambiguity is detrimental to learning and or development. However, our examples suggest quite the contrary, namely, that students gained from the representative ambiguity through its promotion of shared social construction of statistical meaning. Research is needed to establish the role of representatives in the construction of meaning in ...
Context 3
... Figures 5 -7 show three graphical representatives of the same situation, namely, the men's 100 meters Olympic race. Each of them shows a different aspect of the change over time, which may be difficult or impossible to infer from another representation. For example, Figure 7 shows a linear increase of record time, Figure 6 shows a slight decrease, while Figure 5 shows a non-uniform decrease. Intuitively, it might seem that such ambiguity is detrimental to learning and or development. However, our examples suggest quite the contrary, namely, that students gained from the representative ambiguity through its promotion of shared social construction of statistical meaning. Research is needed to establish the role of representatives in the construction of meaning in ...
Context 4
... A suggested using the minimum record time (9.48 sec.) as the lower limit of y (Idea III). The resulting graph ( Figure 5)
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Context 5
... data show that all of the students were able to appropriately display the immigration data: 62% used time plots (Figure 4) and 38% used bar charts 20 ( Figure 5). Although the students were encouraged in the SC to use a scatter plot to display time series, their choices in the assessment task were dispersed between five different kinds of graphs (Table III). Further, 46% of the students used a line plot (consists of connecting segments or a smoothed line), which may indicate that they conceived of the line as an artifact that could help them to observe and present patterns in the data. This is different from the initial phenomena identified in the case study, in which A and D did not conceive of the line as an artifact to support a global view, but as something foreign and disruptive. Thus, students seem to be fluent in choosing a variety of graphs to display global features of ...
Context 6
... many attempts to design graphs, supported by the computer's powerful facilities, they developed "scale sensitivity" and became critical of the false impressions that may be induced (see, for example, the graphs in Figures ...
Context 7
... teachers reported in their interviews that most students were fluent in using the computer to produce graphs and did not ask for their assistance. The teachers also reported that several pairs were experimenting with different graphs, before they made their final choice. The distribution of students' graphical choices is presented in Figure 4. Types of time plots used by students to display the immigration data. 19 Graphs of three pairs of students were not found in their files. Thus the precentages were adjusted to the new total of 37 students. 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 Immigrants Year Figure 5. Bar chart used by students to display the immigration ...
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... Researchers pay remarkable attention to the examination of cognitive processes to define and improve statistical reasoning in teaching mathematics. Many efforts are provided to ensure students consider the features of the aggregate generated by the entire data to draw meaningful conclusions from the data (Ben-Zvi, 2001;Konold et al., 2015). Some researchers argue that this approach is at the heart of statistical reasoning (Aridor & Ben-Zvi, 2019;Hancock et al., 1992). ...
... Some researchers argue that this approach is at the heart of statistical reasoning (Aridor & Ben-Zvi, 2019;Hancock et al., 1992). Since the data derived from the context are suggested to be real, the students should be exposed to authentic contexts for developing aggregate reasoning Ben-Zvi, 2001). ...
... They face statistical reports such as the media and question how the data are collected in their daily lives (Watson, 2006;Wild & Pfannkuch, 1999). Tukey (1977) defined the statistical process in terms of exploratory data analysis, including organizing, describing, representing, and analyzing data and interpreting the results with context (Ben-Zvi, 2001). Guidelines for Assessment and Instruction in Statistics Education (GAISE II) Report (Bargagliotti et al., 2020) presents a framework by combining elements such as the way of thinking and problem-solving strategies developed by students in their school years while studying statistics. ...
This paper reports on a study aiming at examining the effect of the digital storytelling approach on the aggregate reasoning of high school students. A pretest-posttest quasi-experimental design was implemented on 50 10th-grade students for five weeks to reveal the effectiveness of digital storytelling in mathematics courses regarding aggregate reasoning. Results of statistical analysis showed a significant improvement in aggregate reasoning in favor of the students in the digital storytelling group. It was also noted that aggregate reasoning was specifically enhanced to analyze data and interpret results rather than the other two components (formulate question and collect data) in the experimental group. The results support the idea that the use of digital storytelling can be an effective instructional tool for statistics education and provide implications for course designers to provide better teaching of aggregate reasoning.
... El marco muestral que hizo posible la presente caracterización se genera por muestreo de juicio. Se eligieron trece tesis (Baker, 2009;Ben-Zvi, 2001;Bif, 2014;Castellanos, 2011;Hassad, 2007;Madden, 2008;Meletiou, 2000;Noll, 2007;Porter, 2001;Reaburn, 2011;Rouan, 2001;Slauson, 2008y Zieffler, 2006, que se examinan a la luz de categorías establecidas, marcos metodológicos empleados, e ideas para guiar la enseñanza y el aprendizaje de la estadística. ...
... Según Hassad (2007) es usual que la falta de comprensión de los conceptos se atribuya a estrategias pasivas de enseñanza-aprendizaje. La enseñanza de la estadística introductoria en los trabajos de Meletiou (2000), Ben-Zvi (2001), Hassad (2007) y Slauson (2008 se propone a partir de clases activas modeladas como laboratorios, donde se descubre el conocimiento desde actividades de aprendizaje activo, tales como proyectos, discusiones en grupo, recopilación de datos reales, uso de computadores para el análisis de datos, crítica de artículos de investigación, presentaciones orales, entre otras, con intención de suscitar alfabetización estadística, haciendo hincapié en los conceptos y sus aplicaciones, en lugar de enseñar métodos, cálculos, procedimientos y fórmulas de manera aislada. Para comprender los principios que subyacen a la inferencia estadística, las tesis de Noll (2007) y Reaburn (2011) sugieren estrategias afines, como las simulaciones en computador, el muestreo, las representaciones alternativas de las pruebas de hipótesis, la escritura de explicaciones del propio razonamiento, y las reflexiones y discusiones en aula. ...
The article presents the formulation of categories aimed to review and classify doctoral theses according to their theoretical approaches, relevant topics in educational action, subjects or focus of interest, characterization of methodological principles and ideas about the teaching-learning of stochastics. The methodology mixes the hermeneutic qualitative paradigm with quantitative methods based on statistical counts. Results show the systematization of 129 theses with advisors from universities in 18 countries, their main theoretical approach being Literacy, reasoning, and statistical thinking. The qualitative paradigm is prioritized over the quantitative paradigm. The relevant focuses of interest are students from introductory courses in statistics and the disciplinary subject under study is descriptive statistics. Finally, the paper highlights the teaching of stochastics focused on real contexts in search of a critical education.
... El marco muestral que hizo posible la presente caracterización se genera por muestreo de juicio. Se eligieron trece tesis (Baker, 2009;Ben-Zvi, 2001;Bif, 2014;Castellanos, 2011;Hassad, 2007;Madden, 2008;Meletiou, 2000;Noll, 2007;Porter, 2001;Reaburn, 2011;Rouan, 2001;Slauson, 2008y Zieffler, 2006, que se examinan a la luz de categorías establecidas, marcos metodológicos empleados, e ideas para guiar la enseñanza y el aprendizaje de la estadística. ...
... Según Hassad (2007) es usual que la falta de comprensión de los conceptos se atribuya a estrategias pasivas de enseñanza-aprendizaje. La enseñanza de la estadística introductoria en los trabajos de Meletiou (2000), Ben-Zvi (2001), Hassad (2007) y Slauson (2008 se propone a partir de clases activas modeladas como laboratorios, donde se descubre el conocimiento desde actividades de aprendizaje activo, tales como proyectos, discusiones en grupo, recopilación de datos reales, uso de computadores para el análisis de datos, crítica de artículos de investigación, presentaciones orales, entre otras, con intención de suscitar alfabetización estadística, haciendo hincapié en los conceptos y sus aplicaciones, en lugar de enseñar métodos, cálculos, procedimientos y fórmulas de manera aislada. Para comprender los principios que subyacen a la inferencia estadística, las tesis de Noll (2007) y Reaburn (2011) sugieren estrategias afines, como las simulaciones en computador, el muestreo, las representaciones alternativas de las pruebas de hipótesis, la escritura de explicaciones del propio razonamiento, y las reflexiones y discusiones en aula. ...
En búsqueda de estrategias que posicionen de manera crítica la labor de grupos de investigación que trabajan en el campo de la educación estocástica4 (en especial la labor de la línea de Educación Estadística del grupo Didáctica de la Matemática de la UPN), se considera la elaboración de un panorama acerca de la investigación en dicho ámbito, como tarea que posibilita iniciar la reformulación de una agenda de trabajo investigativo afín con las tendencias actuales.La investigación inicia con la formulación de categorías que orientan la revisión y clasificación de tesis doctorales a la luz de enfoques teóricos, temas objeto de atención en la acción educativa, sujetos o focos de interés, caracterización de principios metodológicos que respaldan la indagación, e ideas acerca de la enseñanza-aprendizaje de la estocástica. La metodología de investigación del proyecto mezcla el paradigma cualitativo hermenéutico con métodos cuantitativos basados en recuentos estadísticos. El primero posibilita la acción interpretativa de las tesis, propicia la generación de categorías de análisis para su caracterización. Lo cuantitativo facilita la descripción de tendencias así como el afinamiento y la selección de una muestra de juicio de trece tesis.Entre los resultados se señala el acopio y la sistematización de 129 tesis asesoradas en universidades de 18 países. Se constata que el enfoque teórico “Alfabetización, razonamiento y pensamiento estadístico” es predominante y propio del campo. Respecto a las metodologías, la investigación cualitativa prima sobre la cuantitativa, y se reconoce el uso frecuente del “diseño de instrucción”. Los sujetos foco de interés investigativo más comunes son estudiantes de cursos introductorios de estadística, sin dejar de lado estudiantes de colegio y profesores de matemáticas (en formación inicial o continuada). En los temas disciplinares objeto de estudio, sobresale la estadística descriptiva sobre temas como la probabilidad, la inferencia y la variabilidad. Por último, se resalta la enseñanza de la estocástica centrada en contextos reales donde el aprendiz es el foco de atención en búsqueda de su formación crítica.
The aim of this study is to investigate learners’ transforming participation as they enter and engage in a learning community. To do this, we investigated the micro-development of two students’ learning and collaborative practices in the context of a unique learning community that was fostered within a graduate level course. Interpretations of the data, which were reviewed by the researchers and triangulated by a group of expert and novice peers, led us to suggest three dimensions of transforming participation that is based on a group psychotherapy framework: (a) the social microcosm—examining one’s learning and collaboration practices in the LC in comparison with one’s everyday life; (b) developing the motivation to change based on dissatisfaction or a desire to grow; and (c) making incremental changes to practices in a socio-cultural context. We discuss the intricacies and implications of this framework for future research on learning communities.
