Theory

  • Similarities and differences in the articles by Rumsey, Garfield and Chance are summarized. An alternative perspective on the distinction between statistical literacy, reasoning, and thinking is presented. Based on this perspective, an example is provided to illustrate how literacy, reasoning and thinking can be promoted within a single topic of instruction. Additional examples of assessment items are offered. I conclude with implications for statistics education research that stem from the incorporation of recommendations made by Rumsey, Garfield and Chance into classroom practice.

  • Similarities and differences in the articles by Rumsey, Garfield and Chance are summarized. An alternative perspective on the distinction between statistical literacy, reasoning, and thinking is presented. Based on this perspective, an example is provided to illustrate how literacy, reasoning and thinking can be promoted within a single topic of instruction. Additional examples of assessment items are offered. I conclude with implications for statistics education research that stem from the incorporation of recommendations made by Rumsey, Garfield and Chance into classroom practice.

  • While many teachers of statistics are likely to focus on transmitting knowledge, many students are likely to have trouble with statistics due to non-cognitive factors, such as negative attitudes or beliefs towards statistics. Such factors can impede learning of statistics, or hinder the extent to which students will develop useful statistical intuitions and apply what they have learned outside the classroom. This paper reviews the role of affect and attitudes in the learning of statistics, critiques current instruments for assessing attitudes and beliefs of students, and explores assessment methods teachers can use to gauge students' dispositions regarding statistics.

  • Changes in educational assessment are currently being called for, both within the fields of measurement and evaluation as well as in disciplines such as statistics. Traditional forms of assessment of statistical knowledge provide a method for assigning numerical scores to determine letter grades but rarely reveal information about how students actually understand and can reason with statistical ideas or apply their knowledge to solving statistical problems. As statistics instruction at the college level begins to change in response to calls for reform (e.g., Cobb 1992), there is an even greater need for appropriate assessment methods and materials to measure students' understanding of probability and statistics and their ability to achieve more relevant goals, such as being able to explore data and to think critically using statistical reasoning. This paper summarizes current trends in educational assessment and relates these to the assessment of student outcomes in a statistics course. A framework is presented for categorizing and developing appropriate assessment instruments and procedures.

  • This paper defines statistical reasoning and reviews research on this topic. Types of correct and incorrect reasoning are summarized, and statistical reasoning about sampling distributions is examined in more detail. A model of statistical reasoning is presented, and suggestions are offered for assessing statistical reasoning. The paper concludes with implications for teaching students in ways that will facilitate the development of their statistical reasoning.

  • Computationally intensive methods of statistical inference do not fit the current canon of pedagogy in statistics. Seven pedagogical principles are proposed to accommodate those methods and the logic underlying them. These include defining inferential statistics as techniques for reckoning with chance; distinguishing 3 types of research (sample surveys, experiments, and correlational studies); teaching random-sampling theory in the context of sample surveys, augmenting the conventional treatment with bootstrapping; and noting that random assignment fosters internal but not external validity. The additional principles are explaining the general logic for testing a null model; teaching randomization tests as well as t , F , and x-sup-2 ; and acknowledging the problems of applying inferential statistics in the absence of deliberately introduced randomness. (PsycLIT Database Copyright 1996 American Psychological Assn, all rights reserved)

  • This paper critically discusses explorative data analysis (EDA) from the point of view of an empirical descriptive scientific theory. EDA deals mainly with the exploration of data by means of predominantly graphical representations, i.e. the search for striking elements and structures in data sets and for simple collective descriptions of the phenomena revealed. The proper analysis of EDA in this piece of work is intended to lay a foundation for further didactic research and development work in this field, in particular as to whether it can effectively be made available to a wider circle of people.

  • From the content: Intuition and mathematics (didactical points of view, networks related to stochastics, intuitions and mathematics as key for understanding, history of ideas and their mathematization); intuitive ideas in classic statistics (interpretation of probability; random choice; expected value; variance); intuitive ideas in the Bayes approach (ratio of chances and degree of confidence, encouragement and thinking in informations, Bayes formula structures thinking, Bayes formula structures applications); intuitive ideas by persons (research framework; symmetry and basic space; relative frequencies and probability; causal relationships and stochastic dependency; statistical assessment; consequences for empirical research and education).

  • Three aspects to be considered when teaching a one-semester beginning economics statistics course are coverage, mastery, and applications. There is a difference between coverage and mastery. Moreover, mastery is not an end in itself; instructors must consider how statistics courses will influence students' approaches to other subjects and applications. In principle, computer activities can be designed and implemented to improve any and all of these three goals. The HyperCard software for the Macintosh computer should result in an important advance in the interface between computer and user. This will be valuable for tutorial programs. Cognitive scientists are designing software which analyzes student solutions to standard problems by inferring a student's intentions from the details of her/his solution and then offering diagnostic assistance. Programs like "Stat Helper" (briefly discussed) for the Macintosh allow students to interact with the computer in solving a variety of problems. Students can learn about regressions better through hands-on experience on personal or mainframe computers. Computer experiments can exhibit a variety of points about regression applications. Computers can expand coverage and make applications more accessible to the average student. Students must develop some sense about what questions regressions can and cannot be expected to answer. Four examples, including graphs and statistical data, are given: automobile weight and fuel mileage, polynomial (quadratic), omitted independent variable, and logarithmic relationship. Nine references and numerous tables and graphs are provided. (GEA)

  • The recording of the interaction between pupil and computer is one of the data sources frequently used in research on the use of computers in teaching. Describes the analysis methodology of these recordings to determine the use of computers in statistics and its adaptation to other research work on the use of computers in education. (Author/MDH)

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