Using Graphs as More Than Pretty Pictures
by Bob Coulter
National, state, and local curriculum standards in science and mathematics all support the development of classes filled with students collecting and analyzing data drawn from a variety of real-world phenomena. The challenge teachers inevitably face is that as students engage in these inquiries the data sets involved can become quite large. Finding the average for five measurements is a comparatively trivial task, best done with paper and pencil or a calculator. When students are working with hundreds or even thousands of data points, as is common in many data sets available through the Internet, these tools may prove to be inefficient.
Recently a range of moderately priced data analysis software packages have become available to schools. These tools are, however, all too often used to make a "final graph" displaying the data students have collected. While these graphs inevitably look professional and give students a chance to make use of the technology resources that schools have invested in so heavily in the past few years, this "collect your data and make a graph of it" type of assignment rarely reaches the depths of inquiry envisioned by current math and science standards. To maximize the educational benefit of data-rich investigations, graphs need to serve as more than a pretty picture made at the end of the project.
When data analysis software is used effectively, it allows students to meet the standards more readily as they focus on the substantial questions they are investigating. By greatly simplifying students efforts to manage their data and freeing them from worrying about the mechanics of the calculations and plotting, the meaning of the data becomes central. Equally important, new questions can be posed of the core data set without students being discouraged by the need to perform elaborate new calculations or redraw a graph in which they have already invested a great deal of time.
More broadly our goal should be, of course, the development of thoughtful, data-literate students who are critical consumers of the mass of data we all encounter on a daily basis. Investigations such as the ones described below and those you read in the rest of this issue are a good start, and can serve as models for similar investigations of topics relevant to your curriculum.
Data representation: which graph is best?
Teachers who have worked with students making graphs know the challenge of helping students make good choices about whether to draw a line graph, a bar graph, or a pie chart (or any of a number of other graph formats). Instead of simply telling the students which format to use, or giving them abstractand somewhat arbitraryguidelines to go by, students can use the flexibility of the software to try several alternatives. Imagine a second or third grade class investigation into pet ownership among the members of the class. If 7 students have cats, 5 have dogs, and 3 have hamsters, which graph format is best? A bar graph shows most clearly that cats are the most popular pet, but a pie chart (or circle graph) shows the proportions of pet ownership best.
Students leading the investigation will need to choose which presentation is most effective, depending on the question they are investigating and the message they hope to convey. The importance for the teacher is that once the data is entered a single time in the computer, the creation of each graph takes only a few seconds. Such comparative graphing isnt a particularly suitable option for paper and pencil graphing, as the constraints of time make the generation of alternative graphs difficult. Without the opportunity to generate and discuss alternative representations, students wont have the experiences needed to become literate users of data. Thus, for practical (time-saving) and pedagogic reasons, data analysis software can be an essential tool for even the simplest student investigations.
Using graphs to highlight or mislead
One who is comfortable using basic data analysis tools can selectively present their information to highlight certain aspects, focusing attention where it needs to be. Just as easily, statistical sleights of hand can be used to mislead an unsuspecting reader. Developing data literacy skills in our students is essential, both to equip them to make effective presentations and to provide them with the means to detect misleading graphs.
One of the simplest tools used to selectively present information is to alteror even omitthe axes used in the graph. Imagine a graph which presents the average February temperature in St. Louis for the past five years. Both of the graphs shown above present the same data, but each gives a very different impression of how much the average temperature varies from year to year. This is only one of many cases where the axes can be used subtly to convey different impressions. I have found that it is very educational to have students discuss alternative graphs such as these to see how two representations of the same data can be employed for different purposes.
Filtering the data
A few years ago, I had the pleasure of teaching two very bright and ambitious fourth graders who developed a science fair project investigating the accuracy of weather forecasts over the past fifty years. By comparing the predicted high temperature for each day with the actual temperature recorded, Ben and Matt were able to document the improved accuracy in modern forecasts. Based on their data, the forecast error in 1998 was shown to be only half what it was in 1948. In conducting this data project, they were able to engage in the critical thinking described here, as they considered alternative ways to represent their data and selected the methods they considered to be the most accurate and effective.
One tool which wasnt readily available to them at the time but which is now commonly found in data analysis software is a filter. Just as graphs can be used to choose how the data set is presented, filtering tools can be used earlier in the process as students consider which data to include in that set. This tool does what one would expect of a filterit screens out data from the original data table students created, based on certain criteria. In this case, the filter could be used to select, analyze, and present the data for each of the three years in their study (1948, 1973, and 1998) individually. In this case, the smaller error (defined as the difference between the predicted and observed high temperatures) in 1998 can be seen much more clearly than raw numbers such as means or medians convey.
As these three brief examples and others in this issue have shown, there is considerably more to be done in investigating data than simply collecting it, displaying a table, and graphing it with appealing colors. Using data analysis software is often the best tool for the job, as it allows students to manipulate the data as needed with only a few mouse clicks. When the tool makes the mechanics of working with data tables and graphs nearly transparent, the focus can be placed where it belongson the meaning of the data being studied.
The examples here use Graph Master, a data analysis software package for grades 4-8 from Tom Snyder Productions (http://www.tomsnyder.com). While more advanced students may need the power found in formal spreadsheet or statistics programs, the comparative ease of use makes a program designed specifically for your students' age a more appropriate choice for many schools.
©Synergy Learning International, Inc., 2002, All Rights Reserved.
- Bob Coulter is director of Mapping the Environment, a program at the Missouri Botanical Garden's Litzsinger Road Ecology Center that supports teachers' efforts to enhance their science curriculum through the use of the Internet and geographic information system (GIS) software. Previously, Bob taught elementary grades for 12 years.