Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications

Friel, S. N., F. R. Curcio, and G. W. Bright. 2001. “Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications.” Journal for Research in Mathematics Education 32 (2): 124–58. doi:10.2307/749671.

Authors Friel, Curcio, and Bright (faculty at University of North Carolina at Chapel Hill, Queens College of the City University of New York, and University of North Carolina at Greensboro respectively), argues for teaching graph comprehension and proposes the term “graph sense” to describe the ability to interpret and apply concepts from graphs. Provides a history of guidelines and research about creating graphical displays. Claims educators focus on having kids create graphs, but that it is important to teach why we use graphs. Suggests how to teach graph comprehension at the K-8 grades. Students demonstrate graph comprehension across three abilities: extracting information, interpreting information, and extrapolating or interpolating patterns from graphs. Shares guidelines about what skills kids can do and understand at each age/grade. During grades K-2 emphasis is on tallying frequencies.

Related Research and Readings

  • Curcio, Frances, and National Council of Teachers of Mathematics. 2010. Developing Data Graph Comprehension. Third Edition. National Council of Teachers of Mathematics.
  • Curcio, Frances R. 1987. “Comprehension of Mathematical Relationships Expressed in Graphs.” Journal for Research in Mathematics Education 18 (5): 382–93.

Beyond the School Doors: The Literacy Needs of Job Seekers Served by the U.S. Department of Labor

Kirsch, Irwin S., Ann Jungeblut, and Anne Campbell. 1992. Beyond the School Doors: The Literacy Needs of Job Seekers Served by the U.S. Department of Labor.

The authors write for the U.S. Department of Labor and Princeton Educational Testing Service, reporting on how adults respond to three types of literacy tasks often required in jobs: prose literacy (articles, stories), document literacy (job applications, graphs, maps), and quantitative literacy (invoices, loan advertisements). In the report’s section on document literacy, the authors point out that adults spend more time reading and working with documents (tables, forms, schedules, charts) than they spend on other reading materials. Provides reasons (relevant then and now) why document and quantitative literacy is important for success in a career and in life. People must be able to understand where on the document to find various types of information, how to avoid being misled by inaccurate or confusing documents, and be able to assess how relevant a document is for their needs. The gist of this report is in line with the idea that students should be spending more time reading informational texts in the K-12 curriculum. The authors create five levels of complexity or difficulty for tasks that require use of documents: the easiest level includes locating or entering literal information, the second easiest level requires making inferences or integrate information, and as the levels increase, the task requires making more inferences or navigating more complex displays.

Infographics Part 1 & 2: Invitations to Inquiry

Lamb, Annette, and Larry Johnson. 2014. “Infographics Part 1: Invitations to Inquiry.” Teacher Librarian 41 (4): 54–58.

Lamb, Annette, and Larry Johnson. 2014. “Infographics Part 2: Practical Ideas for Your School Library.” Teacher Librarian 41 (5): 64–67.

Students are often working on visual displays or reports in a school library. One way to convey information graphically is to create an infographic, and a library can introduce this type of document to students. These two articles suggest practical ways librarians can have students interpret and create infographics.

Reading Visual Representations

Rubenstein, Rheta N., and Denisse R. Thompson. 2012. “Reading Visual Representations.” Mathematics Teaching in the Middle School 17 (9): 544–50. doi:10.5951/mathteacmiddscho.17.9.0544.

The authors are teacher educators at the University of Michigan–Dearborn and the University of South Florida, Tampa. The authors argue that students need to learn how to understand visual representations, and suggest that a framework used for learning how to read can be applied to learning how to “read” images. Like reading literature, interpreting visual representations can require making inferences and going “beyond the data” by predicting and extrapolating. The Question-Answer-Relationship (QAR) framework is from reading theory, and can be used to ask students more meaningful questions when they interpret visual representations like graphs and charts. They describe several question types: “Orientation” (what is on the surface), “Right There” (stated explicitly within the text), “Think and Search” (found after considering symbols or making calculations or comparisons), “Author and You” (student synthesizes the author’s information with what the student already knows), and “On Your Own” (student uses only background knowledge).

Zoos, Aquariums, and Expanding Students’ Data Literacy

Mokros, Jan, and Tracey Wright. 2009. “Zoos, Aquariums, and Expanding Students’ Data Literacy.” Teaching Children Mathematics 15 (9): 524–30.

The authors share suggestions for integrating mathematics and science into a fieldtrip to a zoo or aquarium: studying the animals ahead of time, visiting the location ahead of time to choose a specific area, simulate or demonstrate animal behaviors and scientist behaviors. They also offer tips for how to run the fieldtrip and what to do after the fieldtrip. The lessons and activities can be supported with a school librarian. For instance, a school librarian could introduce various graphical organizers that students can use during their fieldtrip to help them record their observations. Or, the students could do research about the animals they see on their fieldtrip.

InspireData – Data modeling software

InspireData® was originally developed by TERC in Massachusetts with grant funding from the National Science Foundation. TERC also developed and administered a program called Mixing Math, related to a published paper “How Wide Is A Squid Eye? Integrating Mathematics into Public Library Programs for the Elementary Grades.” InspireData® is aimed at students in grade 4 through 12 and lets student collect, enter, explore, and display data. The software comes with lesson plans and suggested activities. InspireData® 1.5 (as of December 2014) provides database templates and databases with sample sample data, as well as a survey tool. They claim that their lesson align with “data literacy standards”, but do not specify which standards (but they reference AASL and ISTE standards elsewhere). The company’s white paper is undated, but the most recent citation is from 2008, with most citations from the 1990’s or early 2000’s. They offer a free 30 day trial and educator pricing.


  • Electronic Education Report. 2006. “Inspiration Launches InspireData For Data Analysis by Students” 13 (13): 5–6.
  • “How digital tools prepare students for the 21st century: A CollinsConsults White Paper Prepared for Inspiration Software, Inc.” Inspiration.
  • Website citing evidence that their software is effective: