Newsletter for the Section on Statistical Education
Volume 5, Number 2 (Summer 1999)
On April 9, 1999, approximately fifty people met at Wayne State University for a conference on "Statistical Education, Mathematics Standards, and the Meaning of Statistics." The sponsors were the Michigan Department of Education, the Detroit Chapter of the American Statistical Association, Wayne State University School of Education, Macomb Intermediate School District, Oakland Schools (ISD), and Minitab, Inc. The conference brought together K-12 teachers, school administrators, teacher educators, and statisticians from academia and industry to exchange ideas about important issues facing those engaged in statistical education, including the following: (1) What is the role of statistics in the K-12 curriculum? (2) Is the view of statistics and the process of data analysis consistent and connected across all school subjects? (3) What does the research say about teaching statistical concepts? (4) What are the experiences of teachers who have taught statistics in the classroom? (5) How can today's students use statistical thinking and statistical tools to better appreciate the world and to be successful in an increasingly complex work environment? (6) What resources are available to help K-12 teachers teach statistics?
The first speaker was Dr. Glenda Lappan, President of the National Council of Teachers of Mathematics (NCTM). After an historical note on the place of statistics in the curriculum and its inclusion in the NCTM 1989 Standards, she presented the draft for the revised Standard for Statistics. The draft has a number of standards for each of four grade levels (Pre-K-2, 3-5, 6-8, and 9-12) organized into four major categories: (1) Pose questions and collect, organize, and represent data to answer those questions. (2) Interpret data using methods of exploratory data analysis. (3) Develop and evaluate inferences, predictions, and arguments that are based on data. (4) Understand and apply basic notions of chance and probability.
In addition to the accomplishments to date, she outlined future challenges in the teaching of statistics. Dr. Lappan was the first to discuss a repeated theme: the need for better teacher preparation to teach statistics. She then provided an opportunity for those attending the conference to comment on the standards for statistics. Among the concerns mentioned by conference participants were the scope and sequence of standards, the need for supplementary materials (which may be addressed in part by websites), the clarity of the standards, and whether all students could meet all of the standards. The notes from this discussion have been forwarded to NCTM.
Dr. Joan Garfield, Associate Professor at the University of Minnesota, addressed some of the reasons why students find learning statistics difficult. She indicated there are four research areas contributing to our understanding of this issue: psychology, mathematics education, statistics education, and the field of learning and cognition. The psychological studies have indicated a number of misconceptions which people have before and even after taking a statistics course. Among these are the 'gambler's fallacy' (that stochastic processes are 'self correcting' and thus a number can be 'due' to hit) and the representativeness fallacy, (that certain examples of a random process are more or less likely than others, for example, certain sequences of heads or tails). Studies in learning and cognition have indicated that these misconceptions are very difficult to overcome. For example, even people who can work a correct answer may produce errors when responding quickly to questions, that is, relying on intuition. Research in mathematics education provides information on a number of the issues that are also concerns in learning statistics: understanding averages, graphs, and ratios and appropriate use of technology and assessment. Additional information can be found on Dr. Garfield's webpage: http://edpsy.coled.umn.edu/faculty/garfield/garfield.html
Dr. J. Stuart Hunter, Statistical Consultant and a Past President of the American Statistical Association, presented an exploration of the topic "Statistics as a Language". He pointed out that as a language, statistics has both a vocabulary and syntax. He stressed that as with any language, clear communication requires careful use of the language. He stressed that students must learn the distinction between data and information and the role of statistics in obtaining information from data. In extracting this information, the user of statistics is faced with the "Two Model Problem," -- assigning some of the variation to a deterministic causal model and some to a stochastic (probability or random) model. Dr. Hunter contrasted the image of the Greeks, who were more concerned with ideas, with that of the Romans who were more concerned with realizations. Based on this he stressed the danger of confusing our expectations (unknown parameters or ideas, symbolized by Greek letters) and the realizations obtained from calculations with data (stats or statistics, symbolized by Roman letters). With this distinction in mind, he presented the illustration of the "Probability Bridge" as a link between the ideal world of theory and the realized world of data. This bridge can be 'crossed' in one direction to estimate the probability of our result (data) given our theory, that is, the degree to which the signal of the data supports the hypothesis. Crossing the bridge in the other direction, one can find the likelihood of a theory given our data.
David Fluharty, Education Chair for the Detroit Chapter, spoke briefly about a phrase in the Michigan Mathematics Standards, "analyze natural variation and sources of variability." Several speakers and panelists stressed the need for more emphasis on this topic in the standards.
The final speaker was Judy Dill, Project Leader for Education at the American Statistical Association's Center for Statistics Education. She presented an overview of the 18,000 member American Statistical Association, with emphasis on the growing role of statistical education. She outlined a number of ongoing ASA activities, including school memberships and poster and project competitions. She described the seminars and classroom materials of the Quantitative Literacy Program. In addition to the original QL Series (Exploring Data, Exploring Probability, The Art and Techniques of Simulation, Exploring Surveys and Information from Samples), Dale Seymour also publishes the Elementary Quantitative Literacy (EQL) Series, and a new series for high school entitled Data-Driven Mathematics. Further information is available at the Center's website which contains links to other websites of interest to teachers (http://amstat.org/education/index.html).
The ASA also produces the ASA/NCTM newsletter, Statistics Teacher Network. Free subscriptions are available to interested teachers around the world. To be added to the mailing list, contact the ASA Center for Statistics Education, 732 North Washington Street, Alexandria, VA 22314. The telephone number is (703) 684-1221 and e-mail can be sent to firstname.lastname@example.org.
During a panel discussion, experiences of teachers in AP statistics and college courses for K-12 teachers were discussed. Of particular interest was a discussion of a cross-curricular project, "Linking High School Math & Science through Statistical Design of Experiments" at Macomb Intermediate School District (see the website http://www.macomb.k12.mi.us/math/math.htm for more details). The conference ended with a comment by the panelists, and discussion by attendees, of the six questions at the beginning of this article.
One theme that arose repeatedly was the need for better and more extensive teacher preparation. Another was the need for more emphasis on variation. To this end, one of the participants sent the following thought starter for a standard to NCTM. "Realize that variation is a characteristic of every physical, biological, and social system or process. Analyze natural variation and sources of variability. Detect statistical signals of specific causes that stand out from the noise of natural variation in the data."