Graphing calculators and their potential for teaching and learning statistics

The world today is described as a world based on information (National Council of Teachers of Mathematics, 1989), and reports on the rapid increase of information use figures such as " doubling every four years " or " increasing exponentially. Technology is not only responsible for producing much of this information, it is a critical tool in the way information is analyzed. Processing information often falls into the domain of statistics, and, although statistics has recently become a part of the mainstream curriculum in the United States, lessons are often focused on simple plots and finding standard measures of center, not on the task of processing information into useful and meaningful statements that can aid in understanding situations and making decisions. Recent developments in technology, including graphing calculators and statistics software packages with simulation capability, have the potential to transform the statistical content in the curriculum and how this content is taught. In general, the potential for graphing calculators to radically change the teaching of mathematics is enormous. On a voluntary basis, secondary teachers in the United States have embraced them as an exciting and useful tool for the classroom. Hundreds of workshops are given each year, usually by teachers teaching other teachers, where participants learn to use the spreadsheet functions, graphing capabilities, and the programming logic of the calculators. The secondary mathematics curriculum has begun to reflect the changes made possible by the calculator; for example, students study functions in great detail, collect and analyze data from scientific experiments, and use programs to do complicated sorting and analyses. These changes also have an affect on the statistics curriculum. Technology makes statistics and statistical reasoning accessible to all students. Students can analyze data numerically and graphically, compare expected results to observed results, create models to describe relationships, and generate simulations to understand probabilistic situations in ways that would not be possible without technology. Technology allows students to use real data in real situations. It also allows students to move easily between tabular representations, graphical representations, and symbolic representations of the data, and provides the opportunity to think about how each representation contributes to understanding the data. Students learn to recognize that considering either number summaries or graphical representations alone can be misleading. The plots in Figure 1 were created from a dataset generated by John McKenzie from Babson College. Number summaries alone of these data are misleading; in each case, …