|Andrew Ahlgren (USA)||email@example.com|
|Ideas in statistics, mathematics, and
the natural and social sciences are so closely interwoven that designing
education in any one area has to be coordinated with design of the others.
Instruction for statistical literacy is properly undertaken in a cross-disciplinary
setting of natural and social sciences, not in mathematics alone. Although
there are obvious mathematical aspects to statistics, the underlying motivation
for literacy in statistics is not mathematical. Rather it is how to describe
and interpret the world.
The basic proposition is that statistical literacy requires not just a collection of ideas, but a fabric of understanding-a pattern of where ideas come from and where they lead, where they support one another, and where they converge. At the American Association for the Advancement of Science we have sketched how that understanding would have to grow over time. Our basic recommendations in the book Science for All Americans represents ideas that are (a) learnable by most adults, (b) important in understanding the world, and (c) part of a fabric of connected and mutually supporting ideas. In sections Probability, Summarizing Data, Sampling, Correlation, and Critical Skills - we specified just what few central ideas are most useful and feasible for all adults to understand. In the subsequent Benchmarks for Science Literacy, that adult-literacy content was analyzed into plausible steps of understanding in elementary and secondary curriculum. The implied connections among the K-12 steps are now displayed explicitly in conceptual-strand maps- for which feedback was sought at PME and ICOTS meeting - in the new AAAS publication Atlas of Science Literacy. The maps are labeled "Statistical Reasoning," "Correlation," and "Averages and Comparison."
Conceptual-map displays of connections among ideas throw light on how mathematics and science interact in learning statistics. For example, the scientific notion of experimental control of variables, which springs from an earlier notion of "fairness" in physical comparisons, relates directly to the statistical notion of fair comparison of group data and sampling bias. From the beginning, close attention was given to the research in learning statistics, science, and mathematics - and especially to findings about common difficulties in understanding. (Even getting students to care about summary description of groups, rather than individuals, was found to require more time than is commonly recognized.) Students' difficulties in learning the notion of controlling variables in science sheds light on planning instruction about sampling. Sampling and control of variables both play a part in making sense of results of scientific studies reported in the news media. Similarly, students' difficulties in learning to reason proportionally in mathematics-even just when to multiply and when to divide - sheds light on planning instruction in probability.
The consideration of conceptual connections is stimulated and facilitated by the array of inter-connected conceptual maps. Educators have found study of these conceptual maps to be thought-provoking and helpful in designing outcome goals, curriculum, instruction, assessments, and further research on learning. I believe that all conference participants interested in defining or promoting statistical literacy should benefit, perhaps significantly, from them.
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