This paper describes a recent and on-going development intended to enhance student learning by making use of individualised computerised assignments for a class of first year students at the University of Witwatersrand, Johannesburg.
This paper describes a recent and on-going development intended to enhance student learning by making use of individualised computerised assignments for a class of first year students at the University of Witwatersrand, Johannesburg.
"Simulations in Mathematics-Probability and Computing", (SIM-PAC), is a three year project funded by the United States' National Science Foundation's Materials Research and Development program. This paper describes the background and rationale for the project, its goals and objectives and the instructional strategy utilized by SIM-PAC. An example of a typical learning activity and the capabilities of the software are illustrated.
The basic principles of experimental design, as it is usually taught today, both to students specialising in statistics and to those in other disciplines, were established nearly fifty years ago. For many statisticians and users of statistics, the major textbook on Design is still Cochran and Cox (1957), written before the advent of the computer. During the last twenty-five years, our computational habits have changed radically, and it is important to ask whether the fundamental ideas of experimental design remain unchanged, or whether these ideas were influenced by the computational environment in which they were developed. I shall not be talking about design by computer, but about the teaching of design liberated by the computer from restrictions imposed by the need to analyse the data. I shall attempt to consider not only the teaching of design now, but into the future.
Courses in experimental design usually provide students with a set of possible designs and corresponding methods of analysis but fail to offer them opportunities for using these new "tools" to solve actual problems. This situation is unfortunate since some of these students may eventually be required to give advice to researchers planning experiments without ever having experience the joys, frustrations, or compromises involved in conducting an experiment. In fact, with the advent of cooperative, internship, and work-study programs, the student is being requested to give advice even sooner than in the past. How can these students, who have never been confronted by time or cost constraints, choice of appropriate factors, or design of follow-up experiments fully appreciate the problems their clients face? This paper describes in detail the computer package which we have developed for this purpose and outlines its use as a teaching aid. Following more than ten years of combined experience with this package, we believe that it is a unique, extremely versatile, and powerful tool not only for use in experimental design courses, but in regression, sampling, multivariate, and introductory courses as well.
The purpose of this paper is to suggest how Dienes' stages of concept development can be applied as a framework for organising probability teaching. If we try to organise probability teaching globally in this manner, it turns out too complicated and inadequate; too many concepts are involved at the same time. So I believe that for the sake of didactical analysis it may be useful to separate particular concepts and to model the teaching according to Dienes' stages - each concept separately - and finally combine these models.
The following will outline a stochastics course which essentially differs from the usual ones in theory, concepts, proceeding, notation and models. The paper is divided into global remarks on the theoretical background and the procedure in the classroom.
We view understanding of mathematical material as a function of (1) connections of text concepts and formulas to real-world referents; (2) integration of concepts and formulas within the text; and (3) explanation of formulas. This view has provided a basis for constructing three written treatments of elementary probability, presumably varying in the degree to which they convey understanding. Our view of the processes involved in solving problems has led us to use both formula and story problems, and to emphasize analyses of error protocols. A research study is described involving 48 undergraduate students, randomly assigned to three text conditions. Results indicated that very different patterns of knowledge appear to be present in subjects in the non-explanatory (standard and low-explanatory texts) and explanatory conditions. Subjects in the two non-explanatory groups performed considerably less well on story than on formula problems, and often used the correct formula for a problem (that is, met the lenient criterion) but failed to solve it. A closer look at answers to story problems revealed that subjects in the non-explanatory conditions often required the explicit presence of key words which unambiguously pointed to certain operations, tended to misclassify problems in the presence of irrelevant or redundant information, and made many errors when the values in the story required modification before insertion into the formula. In contrast, subjects in the highly explanatory condition performed equally well on story and formula problems, tended to solve whenever they showed evidence of knowing the appropriate formula, and were considerably less hindered by absence of key words, the presence of irrelevant information, and the need to translate values in the story.
Learning mathematical terms like "frequency", "random event", "probability" and the like is closely connected with the means of illustration that you - the teacher or the pupil- choose. In solving descriptive mathematical problems, school children can be grouped into two different types: those who prefer graphs and graphical procedures like situational outlines or diagrams and the like; and those who prefer to choose a verbal form of expression and who like to work with symbolic means. Examples are offered of suitable activities for the first type of learner.
The author discusses the potential of the magazine "Consumer Reports" as a source of data for Shopping Statistics. This magazine provides alot of data on prices and various aspects of product quality for many different makes and brands for all sorts of products. Such a data source can allow students to learn about statistics using information found in every day life. Real world data can serve to contextualize student learning.
This article illustrates some common applications of probability and statistics in the field of epidemiology as they may presented to an undergraduate class in probability and statistics.