# Teaching

• ### Trigonal spaces with applications

What follows are some suggestions upon module developments designed to provide problem-solving experiences in developing a sequence of trigonal,numerical arrays, JE(n), which in turn give rise to sequences of discrete, fair probability spaces, P(m(JE(n))), with practical suggestions for open-ended model building. Hopefully these module developments will give some insight into teaching and learning some aspects of problem-solving, as well as naturally generating probability spaces which are discrete and fair. The intent is that the module will contribute to the student's overall ability to understand probability and statistics at a more mature level of sophistication. These ideas were initiated about 1983 by the author, have been field tested with two groups of fifth grade students successfully, and many teachers at the public school level and university level have benefited from workshops based upon these modules.

• ### Improving open-ended problem solving: Lessons learned in industry

What's needed to excite interest in mathematics? We've found a common approach useful both in industry and the schools. Focussing on open-ended problems reveals both the practical impact of quantitative thinking and the role advanced numerical methods play in improving the quality of decisions. Using examples drawn from industry, a framework will be provided to introduce statistical thought into asking questions and getting answers.

• ### Curriculum developments in German speaking countries

Data analysis can play an important role in bridging the gab between the world of mathematics and the student's world experience. Students study functions in class, but seldom have the opportunity to see these functions and their interactions exhibited in the world around them. As the students study the behavior of functions in calculus and precalculus courses, they learn how things should happen in theory. Through data analysis, the theory can be motivated and realised in the actual. The principles of curve fitting, re-expression, and residual analysis, offer a very exciting and enlightening basis for the motivation and derivation of many of the functions and functional concepts taught in high school algebra and in calculus. The Mathematics Department at the North Carolina School of Science and Mathematics has created, tested, and published an innovative data-driven precalculus text and is presently writing a calculus course involving many laboratory experiences from which the examples in this article are taken.

• ### Teaching and testing of statistics

A series of examples from experiences taken from experiments that have taken place in The Netherlands and the USA were discussed. This work has been carried out by the Research Group on Mathematics Education of Utrecht University, with the USA work a collaboration with the National Center for Research in Mathematical Sciences Education of the University of Wisconsin in Madison. Materials were developed on the subject of Data Visualisation. This subject treats skills such as drawing basic plots and calculating basic numerical summaries of data, but it also treats questions such as the following as being of at least equal importance. What graphical representation is best for this set of data? What do these data tell me? How can I communicate the message through a picture? This approach has implications for testing and evaluation as well as teaching.

• ### Selling high school juniors and seniors on taking an elective year of descriptive statistics

This talk described how a year of Descriptive Statistics could fit in a high school's course offerings. Topics include the following: building on a student's successes; games of chance; opinion surveys; US Census 1990; report writing; Galton Board Models; and much more. Classroom handouts were shown and discussed. It is also important to tell students and parents that Descriptive Statistics is necessary and fun.

• ### More cats than fish: But why?

This paper examines the importance of the social context, particularly the place of discussion, for learning statistics in New Zealand primary classrooms.

• ### Simulations in mathematics - Probability and computing

This paper describes the background and rationale for the project, its goals and objectives, and the instructional strategy utilised by SIM-PAC. An example of a typical learning activity and the capabilities of the software are illustrated. The ICOTS presentation included a demonstration of two learning activities.

• ### The computer spreadsheet: A versatile tool for the teaching of basic statistical concepts

Many students find statistics difficult and unattractive. There is therefore an urgent need for teachers to consider new approaches and tools for teaching the subject. Many have advocated the use of microcomputers as teaching tool. When using microcomputers for teaching purposes, it is necessary to consider which software could be regarded as good teaching tools. A good teaching tool should, in my opinion, satisfy at least the following three criteria: (i) It should be reasonable priced, and readily available. (ii) It should be flexible thereby allowing teachers to introduce modifications in response to the special needs of their students. (iii) It should be able to demonstrate the basic concepts of the subject. The ease in which spreadsheets can be used to convey basic statistical concept is demonstrated in what follows.

• ### Teaching the Gaussian distribution with computers in senior high school

First of all we want to review the present state and analyse some current problems of mathematics education, particularly probability and statistics education, in Japanese senior high schools.

• ### Teaching high school mathematics with computers

Our program package for computers has been constructed mainly to assist in teaching. Its characteristic features are as follows: 1) It is constructed for easy handling. 2) Its function carefully follows the content of standard textbooks of high school mathematics. 3) It is aimed at learners who are not so good at mathematics. 4) The package is, at present, restricted to assist studying of only the most fundamental concepts included in the standard textbooks. 5) The introductory parts explaining new concepts are programmed for the screen to change slowly enough. 6) Almost all of the computer screens are programmed with many colours and some with movements. 7) User-friendly manuals to operate the package are being prepared. For further details, please contact the author at the address listed in the index.