Teaching

  • 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.

  • The first volume of these conference proceedings includes an introductory talk (on why statistics should be taught), three plenary papers (discussing stochastics at the school level in the age of the computer, optimum balance between statistical theory and applications in teaching, and the relevance of statistical training), and 35 invited papers. The papers are organized under nine topic headings. These topic areas are: (1) teaching statistics in schools (6-11 years age group); (2) teaching statistics in schools (12-15 years age group); (3) teaching statistics in schools (16-18 years age group); (4) teaching statistics to non-statisticians; (5) development of teaching materials at the school level; (6) training of teachers in statistics; (7) use of calculators and computers in teaching; (8) teaching statistics with the help of case studies; and (9) training statistical practitioners. Topics addressed in the individual papers summarize the situation in statistical education around the world and point the way to future developments. (JN)

  • 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.

  • In a recent issue of this journal, Hart [2] mentioned that "she made a habit of asking students of all levels what a standard deviation is". She complained that in most students the only answer was: "It's a measure of spread", upon which they provide a formula. We are still more pessimistic. We doubt whether most students do realize that the standard deviation is a special measure of spread: one that measures how strongly the data depart from central tendency. Our doubt has been induced by the way in which many textbooks introduce the concept of variability. Most introductions put a stronger emphasis on the heterogeneity among the observations than on their deviations from the central tendency. An example may illustrate our point.

  • The following classroom examples illustrate how to teach statistics in connection with mathematical concepts already present in the curriculum. Each examples begins with material for middle school or junior high school students and is extended in ways that are appropriate for students throughout the high school grades.

  • This book (written in Spanish) is the result of a research on the students' difficulties on learning Combinatorics and of our theoretical reflections about the teaching methodology and curricular development in Mathematics Education. It is intended to be a basic didactical instrument for teachers, students and researchers. The first chapter includes the description of the combinatorial problems, concepts and models, from a mathematical, historical and phenomenological perspective, establishing the connections of these aspects with the didactical units presented in chapter 3. Chapter 2 contains a summary of the research on teaching and learning Combinatorics that has been carried out in Psychology and Mathematics Education. Finally, in chapter 3 a detailed combinatorial curriculum for the different levels of primary and secondary education (10 - 18 year-olds pupils) is proposed. Each unit includes objectives, introductory problem situations, drill and practice and application problems with their solution, as will as methodological orientations for teachers.

  • Skill in the critical reading of data, which is a component of quantitative literacy, is becoming a necessity in our highly technological society. In particular, processing information presented in newspapers, magazines, commercial reports, and on television is dependent on a reader's ability to comprehend graphs. To meet the needs of society, industry, and business, our students must become adept at processing information. As stated in the Curriculum and Evaluation Standards for School Mathematics, children must be involved in collecting, organizing, and describing data. They should be able to construct, read, and interpret graphs as well as analyze trends and predict from the data (NCTM 1989, pp. 54, 105). This book is intended to provide elementary and middle school teachers and teacher educators with practical ideas on incorporating the graph-reading component of quantitative literacy into the instructional program. It can be used to supplement the teachers' editions of K-8 textbooks or as an elementary methods text for preservice and in-service teachers. It provides many suggestions for activities that can be used with youngsters in both small-group and large-group instruction. In support of the Standards (NCTM 1989), the activities presented in this book provide teachers with ideas to emphasize exploration, investigation, reasoning, and communication in mathematics. Furthermore, suggestions for using the computer as a tool are presented in many activities. This material can be used at different grade levels, depending on the learners' prior experiences with collecting and analyzing data. The data generated and collected by the students should be interesting and meaningful to them.

  • The classroom activity described here is a structured problem series developed for students to discover concepts themselves. Among psychology students, introductory statistics is a course which often is less appealing than other courses. As a result, one of the major challenges in teaching it to undergraduates is making the material both interesting and relevant to the student's personal experience. This is particularly true in relation to other courses in the major, where the self-referential nature of the content insures at least some degree of relevance. During the past three years, I have taught introductory statistics courses to classes which included not only psychology majors but also education and biology students. The students of these courses and feedback from students has convinced me that a few key features of the course structure and manner of presentation of the material are primarily responsible for making the courses effective and enjoyable. These features all relate the material to the direct experience of the students. This approach has a strong justification of both educational theory (e.g., Dewey, 1938) and from psychological research (e.g., Craik & Lockhart, 1972); material made meaningful in this way is more likely to be assimilated and retained. In particular, the aspect of individual experience to which the statistical material is conceptually related is the manner in which knowledge is gained. This will be elaborated later in the article; the justification of this approach can be made in terms of the nature of the discipline as well as pedagogically. Statistical inference is directly concerned with specifying principles by which scientific knowledge is gained; be relating the content of statistics to one's own experience of gaining knowledge, one sees more clearly the core of the discipline. This paper first describes the classroom activities which have been features of this approach; it then reviews the manner in which statistical principles have been conceptually related to the students' experience of gaining knowledge.

  • Students in a small experimental design class obtained information about statistical and research applications concerning a variety of products advertised by different companies. The resulting data were perceived to have several advantages for the students: (a) it made collecting and interpreting data more interesting and less mysterious, (b) it helped them to understand how research design and statistics are used in real-life situations, and (c) it helped them to make more discerning judgments about advertisers' claims for their products.

  • Explaining abstract, theoretical distributions to beginning students is sometimes difficult. This article describes a demonstration that helps to make the central limit theorem for generating sampling distributions concrete and understandable.

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