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 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.

Principal Investigators

Carolyn Staudt
Andrew Zucker

Project Inquiries

cstaudt@concord.org

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This material is based upon work supported by the National Science Foundation under Grant No. DRL-1256490. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

During the first year, 2012-2013, we will conduct formative research trials in a small number of Maine classrooms. During the second year, 2013-2014, we plan to conduct an experimental trial of several graph literacy activities. For that study, a group of 10 teachers will be randomly split into experimental and control groups. A pre- and post-test focusing on graph literacy will be used to measure student outcomes.

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. Listed below are 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. Links to the online activities, as well as accompanying teacher guides, are available at concord.org/gl.

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:

  1. ▼ Identify and encode superficial 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.

    GOAL 1. Identify and Use Scales

    The first step in graph comprehension involves focusing on the scales and noticing and correctly interpreting the quantity graphed, units (if any), and numerical range.

    Objective 1.1: The student will correctly name the coordinate values of any point on any single line graph or scatter-plot, including units, if any.

    Objective 1.2: The student will understand how zooming, panning, stretching, and shrinking do not change the data within a graph.

    Objective 1.3: The student will be able to interpolate between points on a graph.

    Objective 1.4: The student will be able to determine the dependent and independent variables.

    GOAL 2. Identify General Graph Features

    The other part of the first step in graph comprehension involves visual processing of the overall graph shape. This also includes relating graph shapes and meanings. We expect that instruction that focuses on specific kinds of features will help students acquire this skill.

    Objective 2.1: Identify the overall shape and direction of a line graph, and connect the shape with the real-world meaning.

    Objective 2.2 Identify the maxima and minima of a graph and interpret their meaning.

    Objective 2.3: Estimate the slope of a line and describe its real-world meaning.

  2. ▼ Link superficial 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.

    GOAL 3. Recognize Basic Functions and their Significance

    This goal focuses on mathematical functions that often match (or "model") the data. One advantage of modeling data in this way is that the function provides a way to extrapolate beyond the data.

    Objective 3.1: The student will be able to identify a graph or scatter plot of data that can be approximated by sections of linear functions.

    Objective 3.2: The student will be able to identify a graph or scatter plot of data that can be approximated by sections of quadratic functions.

    Objective 3.3: The student will be able to extrapolate a linear function beyond available data and describe the behavior of the extrapolated function.

    GOAL 4. Recognize the Significance of Breakpoints

    GOAL 5. Identify Trends in Noise

  3. ▼ 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.

    GOAL 6. Link Stories and Graphs—Piecewise Linear

    This goal focuses on mathematical functions that often match (or "model") the data. One advantage of modeling data in this way is that the function provides a way to extrapolate beyond the data.

    Objective 6.1: The student will be able to connect specific sections of a graph with specific portions of a story.

    Objective 6.2: The student will be able to connect multiple representations — including the graph, table, function, and animation — to specific portions of a story.

    GOAL 7. Link Stories and Graphs—Any Common Function

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