Journal Article

  • Providing students with opportunities to find their own databases creates an environment of participation and involvement where students experience what it is to do statistics. Creating their own databases also gives students experience with real world problems. In doing so, students can learn to observe and discuss the influence of missing data and outliers as they occur in day to day situations. The author gives an example of how students at University of Wisconsin dealt with obtaining their own data for Buffon's needle problem, and how they analyzed the data. Suggestions for possible activities for students learning statistics include using statistics to estimate how many words are in an article and strategies for guessing on various kinds of multiple choice tests.

  • This article states that there are two considerations for learning to graph data: 1) the structure of the phenomenon, and 2) the limitations of the format of graphical representation used. This paper provides historical examples of how graphic data has been used, highlights aspects of a display theory, and identifies concrete steps to improve the tabular quality of graphs. According to the author, a graph has the power to answer most commonly asked questions about data, and invite deeper questions as long as it is properly drawn. Bertin's (1973) levels of questions that can be asked from a graph are described. The first level deals with elementary questions which involve simple extractions of data from the graphs. The second level deals with intermediate questions. These refer to trends among multiple points in the data, and the identification of outliers. The third level involves overall questions which requires an understanding of the deep structure of the data in its totality, often comparing trends or groups in the data, and the overall message of what is being said in the picture. Questions that involve retrieving data from tables are almost always elementary questions. These only require that students understand discrete units of data. Wainer states that most tables do a disservice by confusing the kinds of data presented. Columns are often placed without much thought to the relevancy of their order. The order within the columns is similarly vulnerable to irrelevance. For example, criterion variables (like countries) are often presented in alphabetical order when they should be arranged on a concept that is more useful (like size of GNP or population). The author therefore recommends that rows and columns are ordered in a way that makes sense and that numbers be rounded off as much as possible.

  • This article describes a class taught in the summer of 1988, an introduction to probability and statistics for a heterogeneous group of 12 academically talented secondary students. The main focus was on the concepts of sampling and binomial distributions. The approach was based on simulation, including extensive use of the Boxer computer language. We present the work of a group of 3 students who had minimal prior exposure to computer programming. During the course, these students used, modified, and created computer tools to produce a sophisticated simulation. This project demonstrates the value of integrating programming with teaching subject matter.

  • The students' interaction with the computer poses new problems of research in Mathematics Education and also offers new methodological resources. One of these is the possibility to employ the recording of the students' interaction with the computer as a technique to gather data on the processes that the students follow to solve the proposed tasks. In this work, different examples of the use of these records in research on Mathematics Education are analyzed, showing the diversity of the obtainable data and the dependence of the same with respect to the "roles" carried out by the computer and the student. We end by presenting the method of analysis of these records that we have used in our own research, that combines qualitative and quantitative elements and can be easily adapted to other research.

  • This paper presents a framework for the design and analysis of introductory statistics courses. This framework logically precedes the usual process of putting together the syllabus for an introductory statistics course. Four approaches, or paradigms, of statistics teaching are put forward, together with tools for deciding which blend of approaches is most useful in any particular case. These approaches do not correspond to the two traditional schools of thought in statistics education -- probability-driven or data-driven -- but rather constitute a new approach.

  • Previous studies of correlational reasoning have focused on the interpretation of 2 x 2 tables. The research in this article examined age trends in responses to problems involving more than 2 continuous variables. Instruments were developed and administered to Ss from Grade 4 through postgraduate (n = 20 in each grade) to produce multidimensional profiles of student growth. Experiment 1 found that correlational reasoning skills increased with age. Experiments 2 and 3 found that students performance could be improved through instruction. Evidence of convergent and discriminant validity of the instruments was obtained. Although there were similarities between results obtained with 2 x 2 data problems and results on continuous data problems, the evidence in support of a single correlational schema underlying both was ambiguous. There was no transfer, and correlations between the 2 types of performance were weak.

  • Students in four statistics classes received different amounts of guidance and instruction in interpretive skills. Students who wrote press releases free of statistical jargon acquired better computational and interpretive skills than did students in a traditional class. Emphasis on interpretation was not associated with greater conceptual knowledge. Writing assignments appear to focus students' attention on the context and rationale for the statistics. This technique can also be used in other courses.

  • In this curriculum and evaluation standards for School Mathematics (1989), the National Council of Teachers of Mathematics recommends that the K-12 mathematics curriculum be broadened and designates statistics as an area deserving increased attention. The standards document promotes the concept that statistics be learned through the study of real problems with real data collected by the students. Rather than focus on developing formulas from which answers are simply computed, teachers should present statistics in a coherent fashion and develop the topic as a whole problem-solving process. The standards also encourage the use of appropriate technologies for learning mathematics. Appropriate technology allows us not only to expand what mathematics is taught but also to enhance how that mathematics is learned.

  • Ways of knowing statistical concepts are reviewed. A general three-category structure for knowing is proposed: (a) calculations, (b) propositions, and (c) conceptual understanding. Test items were developed that correspond to the first category and to a partitioning of the two latter categories into words and symbols. Thirty-one items covering the five types were administered to 57 graduate students. Correlation of student scores on the 10-item calculations subtest and the 10-item propositions subtest was . 61, whereas the other two intercategory correlations were .40 (Calculations vs. Conceptual Understanding) and .37 (Propositions vs. Conceptual Understandings). The result suggest that students should be tested in more than one domain, and that instructors should expect students to develop conceptual understanding in addition to skills in computation.

  • This article classifies and discusses some of the common technical and conceptual mistakes found in the entries to student statistical project competitions in Hong-Kong.

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