Research

  • In the past, K-12 mathematics students' exposure to statistical concepts has been rather impoverished, consisting primarily of measures of center-mean, median, mode-and perhaps some graphical representations of data. Both the Curriculum and Evaluation Standards (NCTM, 1989) and the Principles and Standards for School Mathematics (NCTM, 2000) advocate for a much wider and deeper role for statistics in school mathematics, including reasoning about data in context and making data-based decisions. An understanding of the role of variability in various contexts-e.g., in sampling, in data sets, and in probability experiments-is one of the critical components students need for statistical reasoning. The research reported here on students' conceptions of variability is part of a three-year NSF grant The Development of Secondary Students' Conceptions of Variability (Shaughnessy, 2003).

  • This study utilized teacher development experiment methodology to support, and deeply examine, three teachers' understandings and practices regarding content, pedagogy, and technology as they learn about and strive to integrate Fathom, data analysis software, into their curriculum and instruction. Surveys, observations, and interviews were utilized to gather data in order to research the interactions among these three factors and how they were associated with the effectiveness of the three teachers' integration of technology. Pictures of weak, developing, and exemplary facilitation of Technology-Supported Inquiry Learning, as outlined by an effective learning environment conceptual framework, resulted from this study. Exemplary practices occurred in teachers who held strong understandings and practices in all areas; content, pedagogy, and technology. This implies that professional development must be provided in such a way that teachers can learn about, practice with, and reflect on all areas simultaneously.

  • This thesis aims to analyze factors that determine success when reading statistical graphics, based on Krutetskii's mathematical ability theory and Pinker's graphical comprehension theory. 814 undergraduate students attending Statistical courses were investigated. Six instruments were used: a questionnaire; two attitudes scale towards Statistics and Mathematics; and mathematical, statistics, and verbal aptitude tests. Findings show that success when reading statistical graphics lie on the understanding of the statistical concept, level of knowledge of graphics, visual-pictorial ability, and gender. Male students show more positive attitudes, and higher scores at cognitive tests, except at the verbal aptitude test. Instruction also shows to play a significant role on the development of statistical and graphic abilities.

  • En esta Tesis nos hemos interesado por el estudio de los conocimientos y las actitudes hacia la estadística de los profesores en formación, justificando el interés del estudio por la influencia de estas variables sobre la planificación de la acción educativa que cubra tanto los conocimientos matemáticos y didácticos como la educación de la afectividad del profesor. El trabajo se ha llevado a cabo en dos fases. En la primera presentamos los resultados de pasar una escala de actitudes de construcción propia a una muestra de 66 profesores en ejercicio y 74 profesores en formación de educación primaria. No encontramos diferencias por género, aunque si una mejoría en aquellos alumnos que la estudiaron previamente. Contrariamente a nuestra hipótesis inicial, tampoco encontramos unas diferencias acusadas en las actitudes de profesores en formación y profesores en ejercicio, por lo que decidimos continuar el trabajo centrándonos exclusivamente en el primer grupo, que es sobre el que recae principalmente nuestra acción formativa. Para la segunda fase del estudio, realizada con una muestra de 367 profesores en formación elegimos la escala SATS, después de realizar un comparativo de escalas de medición de actitudes. Asimismo utilizamos una parte del cuestionario Statistics Reasoning Assessment, construido por Konold y Garfield para obtener algunos datos sobre los conocimientos estadísticos de los profesores. Se confirma que la actitud de los profesores en formación es en general positiva independientemente del genero y de la especialidad. Aporta ademas una evaluación orientativa de los conocimientos estadísticos de los profesores en formación, encontrando errores conceptuales sobre los promedios, muestreo, valor atípico, así como en las interpretaciones de la probabilidad. En estos errores influye la especialidad cursada en los estudios de Magisterio. Se observa también una relación moderada entre actitudes y conocimientos estadísticos. Pensamos que esto sugiere la necesidad de apoyo desde los departamentos de didáctica y facultades de educación. Todos estos resultados se comparan con otros estudios previos de actitudes hacia la estadística. La Memoria incluye también un estudio detallado de las investigaciones previas sobre actitudes hacia la estadística y errores en conceptos estadísticos elementales, así como un análisis del concepto actitud, sus componentes y medición y de las principales escalas de actitudes hacia la estadística.

  • This is a collaborative research linking researcher and teachers working together at schools. Our assumption is that teachers' professional knowledge, resulting from the integration of theory and practice, is personal and can be mainly observed from teacher's work while developing the curriculum. Moreover, teachers' professional development emerges when they intentionally engage in an educational project, and reflect on their practice, as individuals and as a group. We also took into account the relevance of researchers' participation, professional knowledge, questioning capacity and empathy when encouraging teachers to learn more about themselves and their practice.<br>Freire's concept of reflective teacher was taken into account to investigate the contributions that Statistics and Probability concepts can bring to a group of Kindergarten teachers' professional education and pedagogical practice in a private school in Campinas. A planned intervention led to collaborative production, which allowed the enlargement of professional knowledge concerning Mathematics and Statistics, the curriculum, and the teaching learning process for these teachers. Information was collected along three years of teaching, using questionnaires, interviews, papers, the researcher's notes, collective discussion of texts, videotaped lessons and analysis of activities planned and performed by the teachers. Case study of teachers and coordinators participating in the experience when trying to identify important points in their mathematics, statistics and didactics knowledge and their professional development were used.<br><br>Main conclusions were: The curriculum knowledge was linked to teachers' conception about the meaning of statistics and probability in Kindergarten education. Teachers were aware of the curricula goals, and were capable to design projects related to their context. Their didactical knowledge was visible in solving the problems and in the diversity of strategies and solutions. Their professional development increased through their ethical and solidary work when jointly producing concept developments and didactics knowledge for Mathematics and Statistics. Consequently, we suggest an educational process that values the teachers' knowledge, challenges their reasoning, encourage teachers' research on their own practice and allow them to contribute to collective production of knowledge.

  • New software tools for data analysis provide rich opportunities for representing and understanding data. However, little research has been done on how learners use thse tools to think about data, nor how that affects teaching. This paper describes several ways that learners use new software tools to deal with variability in analyzing data, specifically in the context of comparing groups. The two methods we discuss are 1) reducing the apparent variability in a data set by grouping the values usig numerical bins or cut points and 2) using proportions to interpret the relationship between bin size and group size. This work is based on our observations of middle- and high-school teachers in a professional development seminar, as well as of students in these teachers' classrooms, and in a 13-week sixth grade teaching experiment. We conclude with remarks on the implications of these uses of new software tools for research and teaching.

  • Variability stands in the heart of statistics theory and practice. Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning. The focus in this paper is on the emergence of beginners' reasoning about variation in a comparing distributions situation during their extended encounters with an Exploratory Data Analysis (EDA) curriculum in a technological environment. The current case study is offered as a contribution to understanding the process of constructing meanings and appreciation for variability within a distribution and between distributions and the mechanisms involved therein. It concentrates on the detailed qualitative anlaysis of the ways by which two seventh grade students started to develop views (and tools to support them) of variability in comparing groups using various statistical representations. Learning statistics is conceived as cognitive development and socialization processes into the culture and values of "doing statistics" (enculturation). In the light of the anlaysis, a description of what it may mean to begin reasoning about variability in comparing distributions of equal size is proposed, and implications are drawn.

  • This paper examines ways in which coherent reasoning about key concepts such as variability, sampling, data, and distribution can be developed as part of statistics education. Instructional activities that could support such reasoning were developed through design research conducted with students in grades 7 and 8. Results are reported from a teaching experiments with grade 8 students that employed two instructional activities in order to learn more about their conceptual development. A "growing a sample" activity had students think about what happens to the graph when bigger samples are taken, followed by an activitiy requiring reasoning about shape of data. The results suggest that the instructional activities enable conceptual growth. Last, implications for teaching, assessment and research are discussed.

  • Variation is a key concept in the study of statistics and its understanding is a crucial aspect of most statistically related tasks. This study aimed to extend and apply a hierarchy for describing students' understanding of variation that was developed in a sampling context to the context of a natural event in which variation occurs. Students aged 13 to 17 engaged in an inference task that necessitated the description of both rainfall and temperature data. The SOLO Taxonomy was used as a framework for analyzing student responses. Two cycles of Unistructural-Multistructural-Relational levels, one for qualitative descriptions and the other for quantitative descriptions, were identified in responses. Implications of the extended hierarchy for describing understanding of variation for research, teaching and assessment are outlined.

  • This study compares students' performance and attitudes in a hybrid (blend of online and face-to-face) model of Elementary Statistics and a traditional (face-to-face) model of the same course. Performance was measured by test, quiz, project, and final exam grades. Attitude was measured by the results of a course survey administered at the end of the semester. Both models of the course required the same textbook and statistical computer package, were taught by the same instructor, and had similar demographic characteristics such as gender, major, and classification. Significant differences were found in an extra credit grade comprised of points earned on interactive worksheets, and attitudes toward the course. There was no significant difference in students' performance as measured by grades. The value of hybrid courses as a viable option in distance education and their potential benefits to students and the educational institution are discussed.

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