Levels of graph comprehension1

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Although literal reading of data presented in graphical form is an important component of graph-reading ability, the maximum potential of the graph is realized when the reader is capable of interpreting and generalizing from the data. A graph is a picture, and therefore “speaks a thousand words.” We want students to see not just a few of the pointwise “words,” but also see the global- and trend-features of the graph. Three levels of graph comprehension were proposed by Curcio in 1987.2 Regardless of the graph form used (pie, line, bar, etc.), the three levels of graph comprehension are reading the data, reading between the data, and reading beyond the data.

Reading the Data

This level of comprehension requires a literal reading of the graph. The reader simply “lifts” the facts explicitly stated in the graph, or the information found in the graph title and axis labels, directly form the graph. There is no interpretation at this level. Reading that requires this type of comprehension is a very low level cognitive task. In terms of functions, reading-the-data generally means (a) given an input, find the output, or (b) given an output, find the input(s).

Reading between the Data

This level of comprehension includes the interpretation and integration of the data in the graph. It requires the ability to compare quantities (e.g., greater than, tallest, smallest) and the use of other mathematical concepts and skills (e.g., addition, subtraction, multiplication, division) that allow the reader to combine and integrate data and identify the mathematical relationships expressed in the graph. This is the level of comprehension most often assessed on standardized tests. Ideas include: comparison of values, maximums/minimums, where are values increasing/decreasing/constant, where are the values increasing the most, given a set of inputs, find the outputs, or given a set of outputs, find the inputs.

Reading between the data requires “at least one step of logical or pragmatic inferring necessary to get from the question to the response and both question and response are derived from the text” (Pearson and Johnson, 19783).
Reading beyond the Data

This level of comprehension requires the reader to predict or infer from the data by tapping existing schemata (i.e., background knowledge, knowledge in memory) for information that is neither explicitly nor implicitly stated in the graph. Whereas reading between the data might require that the reader make an inference based on the data presented in the graph, reading beyond the data requires that the inference be made on the basis of a “data base” in the reader’s head, not just in the graph.

Graph Interpretation Activity

Use the graph above to answer the following questions:
1. At what time did the sun set in mid-October?

a. 8:00 p.m. c. 6:30 p.m.

b. 7:15 p.m. d. 5:30 p.m.

2. 8:30 p.m. is the average time of sunset during which month?

a. July c. September

b. August d. November

3. As the months progress form July to December, which of the following is true about the average time of sunset?

a. It gets earlier

b. It gets later

c. It remains the same

d. It first gets earlier and then later

4. How much longer do you have to play outside (before it gets dark) in July than you have in October?

a. 1 ¼ hours c. 2 ½ hours

b. 1 ½ hours d. 4 ½ hours

5. As the months progress form June to December what do you expect to happen to the average number of daylight hours?

a. Increases

b. Decreases

c. Remains the same

  1. First decreases, and then increases

6. Which of the following graphs represent the average time of sunset form January to June that would make the graph above represent one complete year?





7. During which month is there the greatest change in the time of sunset?

a. August c. October

b. September d. November

8. From the beginning of July to the end of September, what is the average number of minutes of evening sunlight lost per month.

a. 20 min. per mon. c. 39 min. per mon.

b. 45 min. per mon. d. 1 hr. 58 min. per mon.

1Adapted from Developing Graph Comprehension, by Frances R. Curcio, published by the N.C.T.M., 1989.

2Curcio, Frances R. “Comprehension of Mathematical Relationships Expressed in Graphs.” Journal for Research in Mathematics Education 18(1987): 382-93.

3Pearson, P David, and Dale D Johnson. Teaching Reading Comprehension. New York: Holt, Rinehart & Winston, 1978.

J.R.Olsen ~ W.I.U.

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