Literature Index

Displaying 1861 - 1870 of 3326

  • Reasoning about chance events: Assessing and changing students' conception of probability

    Author(s):
    Garfield, J. B., & delMas, R. C.
    Year:
    1989
    Abstract:
    Research on misconceptions of probability indicates that students' conceptions are difficult to change. A recent review of concept learning in science points to the role of contradiction in achieving conceptual change. A software program and evaluation activity were developed to challenge students' misconceptions of probability. Support was found for the effectiveness of the intervention, but results also indicate that some misconceptions are highly resistant to change.
    Location:
    RISE

  • Reasoning About Covariation

    Author(s):
    Moritz, J.
    Editors:
    Ben-Zvi, D. & Garfield, J.
    Year:
    2004
    Abstract:
    Covariation concerns association of variables; that is, correspondence of variation. Reasoning about covariation commonly involves translation processes among raw numerical data, graphical representations, and verbal statements about statistical covariation and causal association. Three skills of reasoning about covariation are investigated: (a) speculative data generation, demonstrated by drawing a graph to represent a verbal statement of covariation, (b) verbal graph interpretation, demonstrated by describing a scatterplot in a verbal statement and by judging a given statement, and (c) numerical graph interpretation, demonstrated by reading a value and interpolating a value. Survey responses from 167 students in grades 3, 5, 7, and 9 are described in four levels of reasoning about covariation. Discussion includes implications for teaching to assist development of reasoning about covariation (a) to consider not just the correspondence of values for a single bivariate data point but the variation of points as a global trend, (b) to consider not just a single variable but the correspondence of two variables, and (c) to balance prior beliefs with data-based observations.

  • Reasoning about data

    Author(s):
    Konold, C., & Higgins, T.
    Editors:
    Kilpatrick, J., Martin, W. G. & Schifter, D. E.
    Year:
    2003
    Abstract:
    In this article, we focus primarily on what we have learned more recently from research about how younger students reason about data, concentrating on ideas that begin developing in early elementary school. We therefore do not review the literature related to statistical inference. One reason for not reviewing that literature here is that a reasonable treatment would require us to review as well the development of probabilistic thinking (see Shaughnessy's review, this volume). But more importantly, there are core ideas in reasoning about data that tend to get shoved to the wings as soon as statistical inference takes the stage. The issues we discuss here, though basic, are still critical to statistical reasoning in the upper grades.
    Location:
    http://www.umass.edu/srri/serg/papers/KonoldHiggins72001.pdf

  • Reasoning About Data Analysis

    Author(s):
    Ben-Zvi, D.
    Editors:
    Ben-Zvi, D. & Garfield, J.
    Year:
    2004
    Abstract:
    The purpose of this chapter is to describe and analyze the ways in which middle school students begin to reason about data and come to understand exploratory data analysis (EDA). The process of developing reasoning about data while learning skills, procedures, and concepts is described. In addition, the students are observed as they begin to adopt and exercise some of the habits and points of view that are associated with statistical thinking. The first case study focuses on the development of a global view of data and data representations. The second case study concentrates on design of a meaningful EDA learning environment that promotes statistical reasoning about data analysis. In light of the analysis, a description of what it may mean to learn to reason about data analysis is proposed and educational and curricular implications are drawn.

  • Reasoning about data analysis

    Author(s):
    Ben-Zvi, D.
    Editors:
    D. Ben-Zvi & J. Garfield
    Year:
    2004
    Abstract:
    Statistics is a discipline in its own right rather than a branch of mathematics, and the knowledge needed to solve statistical problems is likely to differ from the knowledge needed to solve mathematical problems. Therefore, a framework that characterizes creative performance in learning to reason about informal statistical inference is essential. In this paper we present an initial framework to assess creative praxis of primary school students involved in learning informal statistical inference in statistical inquiry settings. In building the suggested framework, we adapt the three common characteristics of creativity in the mathematics education literature, namely, fluency, flexibility, and novelty, to the specifics of learning statistics. We use this framework to capture creative praxis of three sixth grade students in a 60-min statistical inquiry episode. The episode analysis illustrates the strengths and limitations of the suggested framework. We finally consider briefly research and practical issues in assessing and fostering creativity in statistics learning.

  • REASONING ABOUT INFORMAL STATISTICAL<br>INFERENCE: ONE STATISTICIAN'S VIEW

    Author(s):
    ALLAN J. ROSSMAN
    Year:
    2008
    Abstract:
    This paper identifies key concepts and issues associated with the reasoning of<br>informal statistical inference. I focus on key ideas of inference that I think all students<br>should learn, including at secondary level as well as tertiary. I argue that a<br>fundamental component of inference is to go beyond the data at hand, and I propose<br>that statistical inference requires basing the inference on a probability model. I<br>present several examples using randomization tests for connecting the randomness<br>used in collecting data to the inference to be drawn. I also mention some related<br>points from psychology and indicate some points of contention among statisticians,<br>which I hope will clarify rather than obscure issues.
    Location:
    http://www.stat.auckland.ac.nz/~iase/serj/SERJ7(2).pdf

  • Reasoning about Probabilistic Phenomena: Lessons Learned and Applied in Software Design

    Author(s):
    Hollylynne s. Lee, Todd J. Lee
    Year:
    2009
    Abstract:
    In this paper we provide a glimpse of the iterations of design, research and theorizing of a<br>probability simulation tool, Probability Explorer, that have occurred over the past decade. We<br>provide a brief description of the key features of the technology designed to allow young students<br>opportunities to explore probabilistic situations. This is followed by details about several research<br>observations made in multiple investigations of student explorations with this probability micro-<br>world software package. We then explicate how research results suggest that a focus on a<br>bidirectional interplay between theoretical distribution and empirical data can promote reasoning<br>about probabilistic phenomena, and offer implications for instruction. The paper concludes with a<br>discussion of a next generation innovation in the software for representing a theoretical distribution<br>that we believe may promote better students reasoning about the bidirectional connection between<br>theoretical distributions and empirical data
    Location:
    http://escholarship.org/uc/item/1b54h9s9

  • Reasoning About Sampling Distributions

    Author(s):
    Chance, B., delMas, R., &amp; Garfield, J.
    Editors:
    Ben-Zvi, D. &amp; Garfield, J.
    Year:
    2004
    Abstract:
    This chapter presents a series of research studies focused on the difficulties students experience when learning about sampling distributions. In particular, the chapter traces the seven-year history of an ongoing collaborative research project investigating the impact of students' interaction with computer software tools to improve their reasoning about sampling distributions. For this classroom-based research project, three researchers from two American universities collaborated to develop software, learning activities, and assessment tools to be used in introductory college-level statistics courses. The studies were conducted in five stages, and utilized quantitative assessment data as well as videotaped clinical interviews. As the studies progressed, the research team developed a more complete understanding of the complexities involved in building a deep understanding of sampling distributions, and formulated models to explain the development of students' reasoning.

  • Reasoning about Shape as a Pattern in Variability

    Author(s):
    Bakker, A.
    Year:
    2004
    Abstract:
    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.
    Location:
    http://www.stat.auckland.ac.nz/~iase/serj/SERJ3(2)_Bakker.pdf

  • Reasoning about Variability in Comparing Distributions

    Author(s):
    Ben-Zvi, D.
    Year:
    2004
    Abstract:
    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.
    Location:
    http://www.stat.auckland.ac.nz/~iase/serj/SERJ3(2)_BenZvi.pdf

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The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education