Demonstrates how microcomputers can be used in teaching differential calculus, iteration, integral calculus, graphs, and statistics. Several ideas for putting this information into practice are outlined. Sample computer programs are included for the discussions on differential calculus, integral calculus, and iteration. (JN)
Description of a study which formulated a model of the cognitive processes involved in learning statistics material via computer assisted learning (CAL) focuses on mode of presentation (aural or visual), sequence of the material, and previous mathematical experience. Textual analysis is discussed and implications of the results for design of CAL are presented. (LRW)
Discussion of the effects of group aptitudes on achievement during small group learning highlights two studies that examined the effects of group composition on high and low aptitude college students. Heterogeneous and homogeneous aptitude groups are described, and an individual mastery contingency in the second study is explained. (21 references) (LRW)
Discusses the use of the computer software MINITAB in teaching statistics to explore concepts, simulate games of chance, transform the normal variable into a z-score, and stimulate small and large group discussions. (MDH)
Classroom demonstrations can help students gain insights into statistical concepts and phenomena. After discussing four kinds of demonstrations, the authors present three possible approaches for determining how much data are needed for the demonstration to have a reasonable probability for success. (Author/LMO)
The author states that the reason why students have major difficulty in learning statistics and that distinguishes statistics from other disciplines is that the important fundamental concepts of statistics are quintessentially abstract. In his view, concepts that are fundamental in statistics cannot be directly demonstrated, experienced, or drawn. Other factors are listed as making the problem worse: 1) intro stats courses involve more abstract concepts which are used frequently; 2) students must deal with truly abstract concepts AND immediately relate and apply these concepts to reality; 3) problems in statistics are always open to interpretation and have several solutions, none of which are truly known as being the correct ones; 4) the difference between statistics and mathematics lies in the type of numbers that are obtained- in mathematics, the numbers are obtained from calculations whereas in statistics, numbers are obtained from experiments; and 5) statistical notation and terminology are ambiguous and confusing. Watt's solution to the above problem is for statisticians to improve the notation and terminology by making the terms more meaningful and removing ambiguities.
General principles on how statistics should be taught and how those who learn statistics can and should use statistics in society are discussed. According to the author mathematics should be the servant of statistics, not the master. Moreover, the ultimate content must be philosophical - data analysis without a problem is a pure waste.
According to the author, there are five main components of teaching a statistics class. First, the importance of the subject matter must be demonstrated and conveyed to students by illustrating its application to the real world. It is suggested that teachers start the lecture with a few remarks about some real world problem that uses the specific method to be taught in the day's lecture. Second, a demonstration must be worked out prior to class presentation for a higher rate of success. Teachers should get students involved by having them gather and analyze their own data in class. Third, teachers should provide students with concrete real life problems that use the technique to be taught in the lesson. The author suggests that applications or activities are drawn from the students' own interests. To an extent, components 1-3 are similar to "examples training" and components 4 & 5 are similar to "formal training" (see Fong, Krantz, Nisbett; 1986). The fourth and fifth components refer to the actual lesson or lecture beginning with instruction of statistical and probability principles and ending with presentation of proofs or plausibility arguments.
The Learning/Teaching of Statistics Working Group of the National Center Research in Mathematical Sciences Education (NCRMSE) is studying the ways in which statistical content can best be integrated into the school mathematics curriculum. While NCRMSE Director Thomas Romberg initiated the Working Group, Susanne Lajoie of McGill University now chairs the group. Statistics is the seventh and final NCRMSE Working Group. It began its activities early in 1993. The operation and research of this Working Group is described.
The late introduction of conditional probability in the curriculum statements is probably related to the automatic association of conditional probability with Bayes's theorem and the complicated analyses involving Venn diagrams or tree diagrams to work out the inverse probabilities in conditional problems. No doubt Bayes's theorem is a complex topic that is likely to be mastered by most students only at the senior secondary level. However, several other more straightforward uses can be made of conditional probability earlier in the curriculum. The examples that follow illustrate how conditional statement can be used to introduce conditional probabilities, how early applications can be found in sporting data, how independence can be introduced naturally, and how conditional probability can be related to data collection and presentation in two-way tables. These four topics can be introduced in grades 8 through 10.