As part of the project Design, Development and Assessment in Mathematics Education, I spent four weeks at Whitnall High School in Milwaukee, Wisconsin, testing a booklet on descriptive statistics called Data Visualization.
As part of the project Design, Development and Assessment in Mathematics Education, I spent four weeks at Whitnall High School in Milwaukee, Wisconsin, testing a booklet on descriptive statistics called Data Visualization.
Authors will strive to present information to help teachers (1) understand students' conceptions or misconceptions of important ideas, (2) consider various approaches to teaching, and (3) offer activities that probe students' understanding. Although research offers no one correct answer to the many perplexing problems surrounding teaching and learning mathematics, the suggestions and perspectives may help teachers pursue their work with new insights. It is hoped that the department will also stimulate researchers to reflect on connecting research to the classroom. Communication and collaboration between teachers and researchers will benefit both groups and help each grow in appreciation of the other's tasks.
This paper discusses the dilemma in the cooperation between teachers and scientists and introduces the cooperative project which should help to improve the understanding between them.
The traditional role of educational research and theory for the mathematical teaching practice has been increasingly and extensively questioned during the last decade. There is something wrong with the usual understanding of the theory-practice-relation. Theories - be they as detailed and comprehensive as possible - cannot be transferred directly into the teacher's practice nor can they be applied immediately. Educational research cannot automatically improve teaching practice. Research results cannot be disseminated into teacher's practice simply in a strategy "from the top down". In one word, the old idea that the relationship of theory to practice is of a linear nature in a way that the theoretical results developed in research - if they are only adequately elaborated and made explicit - can be handed over to practice for immediate use will not longer work.
Some understanding of statistics is needed at all levels in society from the individual in his or her personal life to the professional statistician in the university or research institute, in Government or in business. Simple statistical and experimental principles underlie the understanding and interpretation of many everyday phenomena. There is a very strong case for improving the level of numeracy and statistical understanding at all levels in our society.
Content 1. Changing conceptions of statistics 2. Meta-knowledge as part of teachers professional knowledge 2.1 The relevance of meta-knowledge 2.2 Meta-knowledge for teachers 3. Elements of teacher knowledge about developments related to Exploratory Data Analysis 3.1 Data and their context 3.2 Activity of data analysis 3.3 Graphs 4. Concluding remarks References
Expanding any kind of education has challenging difficulties, and expanding statistical education a very generous share. Then there has been the nature of the subject itself. The concepts and thought processes are rather subtle, not easy to grasp in the first place and rapidly lost if not well reinforced.
Statistical educators do not always agree on whether the real roots of statistics lie in theory or applications, and so will not always concur on what constitutes success and failure in Statistical Education. Students' understanding should be developed to include both aspects, but statistical education programmes still emphasise the manipulation rather than the development of relevant statistical models, and students therefore have great difficulty relating theory to application. Changes in technology, and hence in professionals', and now increasingly lay-persons', practice of statistics, have made our views of statistical education unclear. Delegates at the International Statistical Institute's Round Table Conference, "Training Teachers to Teach Statistics" (Budapest, 1988), had difficulty determining training priorities because what teachers should or would teach was not clearly defined.
The main focus of the second Quantitative Literacy Project was to provide secondary teachers with a week-long workshop on the quantitative literacy materials and on techniques to use in teaching those materials. The participants modelled the roles of students and the staff the role of the teacher, using techniques that could be transported to a secondary school classroom. One unique aspect of the workshops was the involvement of professionals statisticians contacted through the local ASA chapters who served as speakers, provided on-site visits and were role models for those interested in statistics as a profession. Another key element was to involve participants in planning, designing and carrying out a project with the guidance of one of the statisticians.
I will describe here the plans of the American Association for the Advancement of Science to incorporate basic ideas of statistics into K-12 curricula that more or less integrate science, technology, and mathematics. Rather than adding simply statistics topics to the curriculum, the curriculum design involves a mapping of ideas in these fields as they interconnect and increase in sophistication.