Graph Literacy
Graph literacy is the ability to identify the important features of a wide variety of graphs and relate those features to the context of the graphs—in other words, to increase students' understanding of the meaning of graphs.
Graph Literacy App
Our new app for iPad is designed for middle school students to investigate equivalent graphs, learn to interpolate values, discover the difference between dependent and independent variables and more.
Graph literacy is emphasized in both the Common Core State Standards for Mathematics and the Next Generation Science Standards. For example, the math standards suggest that by the eighth grade, students should learn about lines of best fit and what they mean. The project's primary goals are to:
- Develop and pilot test three to six free computer-based instructional activities that improve student graph comprehension, aimed especially at science students in grades 7 and 8, and
- Develop a pilot assessment instrument focusing on students' comprehension of graphs.
The activities and the assessment instrument will be pilot tested in Maine, and then made available to others. We will build on the work of the ongoing SmartGraphs project.
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During the winter of the 2013-2014 school year we conducted a randomized experimental trial of six graph literacy software activities in Maine. We created these activities as part of the Piloting Graph Literacy Activities in Maine (“Graph Literacy”) project, funded by NSF grant # DRL-125649, in order to teach graph literacy to middle school science students. The primary research question was whether use of the software activities would increase experimental students’ understanding of graphs, compared to the control group that did not use the software.
The overall conclusion of the study was that the approach used to teach graph literacy is promising. A summary is provided below; for the full report see Improving Students’ Graph Literacy: Report of an Experiment in Maine.
Nine teachers in Maine were recruited to participate in the study. All of them taught science or math in grades 6-9. Five teachers were randomly selected for the experimental group and four for the control group. Data were collected from all teachers about the experiences of three sections of students. In total, more than 500 students in 27 classes participated in the research. With assistance from an expert item writer, the project developed a 20-item multiple-choice assessment of students’ understanding of graphs. The same assessment, which was delivered online, was used as a pre-test in November 2013 and as a post-test in February 2014. In all, 378 students completed both the pre-test and post-test. Each item was matched to one of seven learning objectives that were established for this project, based on a review of research about how people learn to “read” and understand graphs. (An example of a learning objective is, “The student will understand how zooming, panning, stretching, and shrinking do not change the data within a graph.”) Statistical tests established that the assessment is reliable.
The other instrument used for the study is a weekly log. Teachers were asked to describe instructional activities each week in which students used graphs. Experimental teachers also answered questions about their use of the six software activities. All the teachers submitted weekly logs for three sections of students. More than 300 logs were submitted.
Pre-test scores for the students in the experimental and control groups were not statistically different. However, the mean gain from pre to post for the 214 experimental students was 1.23 (median = 1.5, mode = 2, sd = 3.09), which was statistically significant. The gain from pre to post for the 164 control students was 0.17 (median = 0, mode = 0, sd = 2.99), which was not statistically significant. The effect size of the difference in gain scores is 0.35, which is considered a small to medium size effect, and this result is statistically significant (t = -3.347, df = 376, p = .001). We conclude that the experimental treatment—use of the six software activities—had a statistically significant positive impact on students’ understanding of graphs, as assessed using the pre/post test.
The secondary research question for this study is whether, after using the activities, the experimental teachers believe they are valuable to students, easy to use, and worth the time and effort to include in the STEM curriculum. Teachers reported that it took students an average of 20 minutes to complete an activity. In 75% of the instances when teachers used an activity with a class they reported they would use the activity again “as is” or “with minor changes.” In 75% of the trials teachers agreed or strongly agree that the content was accessible to their students, and 80% of the time they agreed or strongly agreed that the software activities helped their students achieve the learning objectives for that activity.
In this pilot project, we are focusing especially on students' understanding of scatter plots and line graphs, both of which are widely used in STEM subjects. Click the icon below for a list of the goals and objectives we believe middle school students need to achieve if they are to become graph literate, meaning they are able to "read" and understand a wide variety of graphs. The free online software activities we have developed in this project address six of these objectives. Click on the icon for activities to find links to the web-based activities and accompanying teacher guides. A brief guide to using activities is available here.
Students' graph literacy develops as a result of practice based on three steps or cognitive processes. The activities we are developing are each associated with one of these steps. (Click the "twistie" next to each step to see more specific goals and objectives for student learning.):
- ► Identify and encode prominent graph features. This "bottom-up" process focuses on features such as the graph title, the axes and their titles, the shapes of the graph(s), and any other visual cues, such as color or grouping.
- ► Link prominent graph features to quantitative facts, trends, or other relationships. The second step involves associating visual features with information that might apply to any graph with similar features. For instance, for a rising, straight-line distance-time graph, the viewer might associate "rising" with an increase of the y-value over time, and "straightness" with constant, steady change.
- ► Integrate the features and relationships with the context of the graph. When understanding does not come with steps 1 and 2, it requires a more complex process of inference. The general, context-free associations made about the graph in the first two steps must be linked to the specific contextual clues provided by the labels, axes, graph shapes, captions, and any information or knowledge about the context in long-term memory. For example, this step might result in the viewer seeing a graph as a story about Sally walking at a constant speed from home to the bus stop.
- 1.2 Equivalent Graphs
Students investigate graphs that are equivalent, in the sense that they represent the same data, though they look different because they employ different scales. (Addresses Graph Literacy Objective 1.2: Understand how zooming, panning, stretching, and shrinking do not change the data within a graph.)
» A Lesson Plan is also available. - 1.3 Interpolation
Students explore experimental data of cricket chirping rate to find linear trends on graphs. They use this trend to interpolate values and then find the corresponding linear equations. (Addresses Graph Literacy Objective 1.3: Interpolate between points on a graph.)
» A Lesson Plan is also available. - 1.4 Independent and Dependent Variables
For various scenarios students select which of two variables should be considered independent and which dependent, and to explain their choice. (Addresses Graph Literacy Objective 1.4: Determine the dependent and independent variables for display on a graph.)
» A Lesson Plan is also available. - 2.1 Graphs Tell a Story
Students match a word story to the correct set of graphs involving temperature change over time. (Addresses Graph Literacy Objective 2.1: Identify the overall shape and direction of a line graph, and connect the shape with the real-world meaning.)
» A Lesson Plan is also available. - 2.2 Hurricane Katrina
Students are given graphs relating to Katrina, the hurricane that devastated New Orleans and much of the gulf coast in 2005, and are asked to identify various events, such as the moment when the hurricane made its closest approach to New Orleans. (Addresses Graph Literacy Objective 2.2: Identify the maxima and minima of a graph and interpret their meaning.)
» A Lesson Plan is also available. - 2.3 Growing Up
This activity asks students to interpret the slope of sections of a line graph of the height of U.S. girls and boys from ages two to twenty. (Addresses Graph Literacy Objective 2.3: Estimate the slope of a line and describe its real-world meaning.)
» A Lesson Plan is also available. - 4.1 Population Curve: Significance of Breakpoints
The logistic curve, or S-curve, is important in understanding how populations change over time. It's a complex curve that can be analyzed with a linear fit to help identify the breakpoints where changes of growth rate occur. This activity brings together many graph interpretation skills, and puts them to use to design and analyze a population experiment using the ubiquitous aquatic plant, duckweed.
» A Lesson Plan is also available.