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Understanding Graphs

Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158.

Data and graphical displays are everywhere in today's society. Newspapers and magazines are filled with numbers and displays of information on topics from economics to crime. Friel et al.'s article discusses the research on graph comprehension and its implications for teaching. The focus of their article is graphing comprehension at the elementary and middle school level.

The authors have done an extensive search of the research on understanding graphs, and provide "a synthesis of information about the nature and structure of graphs." They then define graph comprehension and graph sense.

  • Graph comprehension involves "the abilities of graph readers to derive meaning from graphs created by others and themselves."
  • Graph sense "develops gradually as the result of one's creating graphs and using already designed graphs in a variety of problem contexts that require making sense of data."

They provide some interesting historical notes. For example, "William Playfair (late 1700s) has been credited with inventing most of the currently used statistical graphs, including picture graphs, line plots, bar graphs, and histograms." And "Tukey introduced displays that are now considered important in the school curriculum: stem-and-leaf plots (or stem plots) and box-and-whisker plots (or box plots)." (p. 126)

They claim that all graphs share four components:

  • framework - information on the kind of measurements used and data measured,
  • specifiers - used to represent data values,
  • labels - for naming, and
  • background - includes coloring grid, and pictures

They discuss the research literature on the kinds of questions that graphs can be used to answer, providing a table with an overview of five different researchers' work.

Much of the article is devoted to the characteristics of the task of graph comprehension, the characteristics of the "discipline" of working with data, and the characteristics of graph readers. They provide some interesting examples of graphs and uses of graphs. One example from the work of Carpenter and Shah illustrates the importance of a graph's visual characteristics. With the same information on age, vocabulary, and hours of TV watching displayed in two different ways, two very different graphs appear. Teachers might find the graphs that appear on page 139 a particularly interesting challenge in interpretation that they could share with their students.

Teachers will be most interested in Part II (pp. 145-153), "Instructional Implications."

"Number sense and symbol sense can be considered as representing certain ways of thinking rather than as bodies of knowledge that can be transmitted to others. A similar approach seems to be a profitable way to think about graph sense. Graph sense develops gradually as a result of one's creating graphs and using already designed graphs in a variety of problem contexts that require making sense of data." (p. 145)

Friel et al. provide a list of behaviors that indicate graph sense (p. 146) and a chart with a suggested progression for introducing different types of graphs through the elementary and middle grades (p. 147).

Another interesting and practical part of the article for teachers is the recounting of an activity involving graphing raisins. One of the authors worked with students in an 8th grade science class.

"The students carried out an activity that involved estimating and counting the number of raisins in several half-ounce boxes of a specific brand of raisins. Boxes of a different brand of raisins were also available; one student wondered when they would find a similar distribution for that brand. In fact, students found two different distributions; this finding motivated them to weigh the raisins in each box for each of the two brands (sample size was 24 boxes of raisins). In the end, they had two sets of 24 pairs, that is, number or raisins and mass in grams. For homework, their teacher asked them to represent the data in some way that would permit them to compare these two brands of raisins." (p.150)

The role of the teacher is essential in such an activity to "help students understand the richness of possible questions to be explored." (p.151)

Questions related to Math Tools.

  • How do you develop graph sense in young children?
  • What online tools for developing graph sense do you recommend?
  • What is your favorite graphing activity?

Please reply on the discussion section.

Graph Tool: Check out this applet from the Utah State Virtual Manipulative site that generates histograms

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