Newsletter for the Section on Statistical Education
Volume 2, Number 1 (Winter 1996)
As educators struggle to implement the standards, statistics, under the guise of quantitative literacy, has become an accepted component of elementary, middle, and secondary mathematics programs. Exploratory data analysis modeled on Exploring Data by James Landwehr and Ann Watkins from the Quantitative Literacy Series can be found in nearly every middle and high school text series; box plots, stem-and- leaf plots, exercises on the mean, median, range and interquartile range. The February 1990 issue of the Mathematics Teacher was a special focus issue on statistics. NCTM published an addenda series to help teachers implement the Standards. The sales of the three addenda books on statistics, Making Sense of Data (grades K-6), Dealing with Data and Chance (grades 5-8), and Data Analysis and Statistics Across the Curriculum (grades 9-12), indicate they have been purchased by a very large number of teachers and schools around the country and in Canada. Many sessions at NCTM annual and regional meetings have been devoted to statistics, probability and data analysis. Two all day "conferences within a conference" devoted to elementary and secondary statistics were held at the 1995 Annual NCTM Meeting in Boston. Many of the examples used to illustrate the NCTM Assessment Standards are based in statistics. The council has, indeed, supported efforts to promote statistics as a component of the curriculum.
The critical question, however, is what is actually happening in classrooms? Are we preparing students to deal with data and chance in meaningful ways? There are several issues that seem to need addressing before our efforts can begin to be successful. First, despite the existence of statistics and probability strands in the curriculum, there is no guarantee that they are being taught. And even then, in many instances, only the procedures have become a part of the curriculum. Despite being embedded in context, textbook exercises ask process questions, independent of the context and devoid of interpretation: what is the mean; make a box plot. The problems provide data on high school drop out rates but ask students only to "find the median," which can be done without any context. There is little attempt to make "sense" out of a situation or to use data to help advance an argument or to make a decision.
The statistical view put forth is often limited. Little attention is paid to the concept of variability, to enable students to develop a sense of how important it is to capture not only measures of center but measures of how things vary, and what patterns in this variation might indicate. Little attention is paid to thinking carefully about how to design an experiment or to collect data. The emphasis is shifting from teaching students to think statistically about situations to teaching a prescribed and limited list of procedures.
A further issue is the current "rush" to teach "real" statistical concepts. Even at the elementary level, probability is introduced on page one; on page two students learn to use "and" and "or," and at the middle school, on the third page they use combinations and permutations to answer probability questions. There is little opportunity nor curriculum provisions that allow students to investigate, to experiment with different probability situations, to look at results over many trials, to develop an understanding of probability rather than memorizing rules and formulas.
Because the graphing calculator has become readily available, curve fitting has recently become a part of the curriculum. Instead of carefully building student understanding of what it means to choose a line to "best fit" a set of data, students are taught to punch a button. In grade 7 students with little or no preparation for thinking about what it means to fit a line to data and use their line to describe a relationship are finding a least squares regression line. Just because we can do something is not necessarily a reason for doing it! Without the mathematical foundation, a concept is likely to be used incorrectly. Repeatedly in texts and in publications, the concept of correlation is misused and misunderstood. A high correlation does not mean a line (or curve) is the "best fit" for a set of data. Fitting curves to data involves careful analysis of the context for clues about the relationship.
(Contextually, the diameter of a tree and the volume of wood might be related by a cubic; if they are not, you might want to raise a question.) The context, graph, residuals and their graphs as well as numerical summaries are all part of the process of finding a "good" fit for data.
The Standards paint a picture of statistics that is not yet a reality in classrooms. There is progress, but there is a long way to go. Technology is now readily available to allow students to explore statistical situations. Materials are being developed through the curriculum projects of the National Science Foundation that will provide teachers with exemplars. In particular, Data Driven Mathematics, a series of modules designed to integrate statistics into standard mathematical topics in the secondary curriculum and the elementary series, Elementary Quantitative Literacy, (both to be published by Dale Seymour) are designed to help teachers understand and incorporate statistics into their classes.
Making statistics a true component of the curriculum presents a challenge for 1996 and beyond -- an even greater challenge, however, is to help teachers, students, and textbook writers understand that "statistics is the art of making numerical conjectures about puzzling questions," an exciting and fascinating way to think about numbers and mathematics and to ensure that it is this view of statistics that takes root in the classroom.
University of Wisconsin, Madison
President-elect of the National Council of Teachers of Mathematics
PHONE: (608) 263-4288