Developing Data Graph Comprehension

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Curcio, Frances, and National Council of Teachers of Mathematics. 2010. Developing Data Graph Comprehension. Third Edition. Reston, VA: National Council of Teachers of Mathematics.

Frances Curcio is clearly the expert in teaching young people how to understand data and graphs. Since at least the late 1980’s, Curcio has worked with the National Council of Teachers of Mathematics (NCTM) to publish various iterations of a book focused on data and graph comprehension. Curcio has also written academic articles about the same topic. The 2010 edition features 30 activities for the classroom that involve mathematical reasoning and communication. Based on the publisher’s description on Amazon, the book encourages ways for students to take information from their daily lives and the media, and then process and understand and visualize that information.

Prior/Related Editions and Reviews:

Curcio, Frances R. 2001. Developing Data-Graph Comprehension in Grades K-8. Reston, VA: National Council of Teachers of Mathematics.

  • Harkey, Cecilia. 2002. “Developing Data-Graph Comprehension in Grades K-8″ (Review of Second edition). Teaching Children Mathematics 8 (9): 552.
  • Laing, Leneda J. 2002. “Developing Data-Graph Comprehension in Grades K-8, 2ND ED.” Mathematics Teaching in the Middle School 8 (2): 122.
  • Moritz, Jonathan. 2002. “Developing Data-Graph Comprehension in Grades K-8 (Book).” Australian Primary Mathematics Classroom 7 (3): 22.
  • Curcio, Frances R., and National Council of Teachers of Mathematics. 1989. Developing Graph Comprehension: Elementary and Middle School Activities. Reston, VA: National Council of Teachers of Mathematics.
  • Carman, Robert E. 1990. “Developing Graph Comprehension: Elementary and Middle School Activities.” The Mathematics Teacher 83 (6): 480
  • Goodman, B Joan. 1991. “Developing Graph Comprehension: Elementary and Middle School Activities.” The Arithmetic Teacher 39 (3): 58-59.

Tracking Media Use

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Lesson Overview

Lesson plan in which students calculate the number of hours they spend each day using digital media, and input their data on bar graphs. This lesson applies the strategy of data modeling to a real-life situation that students can relate to. This lesson was created with teenagers in mind, but the lesson can be adapted for children who are not using tablets and phones as much (they can track watching TV for example).

Lesson Goals:

“Students will be able to …

  • assess how much time they spend with media activities.
  • record and compare the time they spend with different forms of digital media (cell phones, Internet, etc.) and in different activities (texting, posting, and watching or creating videos).
  • formulate a viewpoint on the role that digital media play in their lives.”

Lesson Plan Materials

Common Core State Standards this Lesson Supports

The original lesson was aimed at middle school students, and Common Sense Media suggests it targets CCSS.ELA.SL.6-8.2 (Interpret information in diverse media, including quantitatively) and CCSS.ELA.SL.6-8.5 (Use displays, including graphics, to present information). Adapted to younger grades, it could support:

  • CCSS.ELA.SL.5.2 Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
  • CCSS.ELA.SL.5.5 Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes.
  • CCSS.Math.Practice.MP4 Model with mathematics.

AASL Standards for the 21st Century Learner

  • AASL 2.1.3 Use strategies to draw conclusions from information and apply knowledge to curricular areas, real-world situations, and further investigations.
  • AASL 2.1.4 Use technology and other information tools to analyze and organize information.

Mathematics in the K-8 Classroom and Library

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McKinney, Sueanne and KaaVonia Hinton. 2010. Mathematics in the K-8 Classroom and Library. Santa Barbara, CA: Linworth.

Authors Sueanne E. McKinney and Kaavonia Hinton are both assistant professors at Old Dominion University in STEM Education and Professional Studies and the Darden College of Education, respectively. Their book describes how school librarians can integrate literature into math in order to support students develop a “conceptual understanding of math.” The book is a great resource to help a school librarian use the books already in the library for math lessons. A school librarian could build connections with teachers by sharing selected books and lessons with them, or offering to teach the lesson in the library. The authors also offer suggestions for how to use any book in a math lesson. Another important area that gets good coverage is how school librarians can collaborate with math teachers.

Below is a list of the mathematical topics and the children’s books which are covered in McKinney and Hinton’s book. These book titles have detailed notes or lesson ideas in the “Using Mathematics Literature” sections of each Chapter. This list will help a school librarian decide if purchasing the book will help them make more use of their existing collection. McKinney and Hinton’s book typically contains a page describing several activities for each of these titles.

Numbers and Operations

  • A Creepy Countdown
  • Fish Eyes: A Book You Can Count On
  • One Less Fish
  • The M&M’s Count to One Hundred Book
  • Dreaming: A Countdown to Sleep

Addition and Subtraction

  • How the Second Grade Got $8,205.50 to Visit the Statue of Liberty
  • The Grapes of Math
  • How Many Feet in the Bed?
  • The Hershey’s Kisses Subtraction Book
  • Subtraction Action

Multiplication and Division

  • One Hundred Hungry Ants
  • Amanda Bean’s Amazing Dream
  • A Remainder of One
  • 2×2 = Boo
  • Spaghetti and Meatballs for All!

Fractions

  • The Wishing Club
  • Full House: An Invitation to Fractions
  • Piece = Part = Portion
  • The Doorbell Rang
  • Centipede’s 100 Shoes

Algebra

  • The King’s Chessboard
  • The Number Devil: A Mathematical Adventure
  • The Adventures of Penrose the Mathematical Cat
  • Math Curse
  • Fractals, Googles and Other Mathematical Tales

Geometry

  • Sir Cumference and the First Round Table
  • Grandfather Tang’s Story
  • The Greedy Triangle
  • Draw Me a Star
  • Mummy Math: An Adventure in Geometry

Measurement

  • Twelve Snails to One Lizard: A Tale of Mischief and Measurement
  • How Tall, How Short, How Faraway
  • Clocks and More Clocks
  • Millions to Measure
  • Alexander, Who Used to Be Rich Last Sunday

Data Analysis and Probability

  • Cloudy With a Chance of Meatballs
  • Tricking the Tallyman
  • If the World Were a Village
  • Lemonade for Sale
  • Do You Wanna Bet?

“Any Literary Selection Can Be a Mathematics Selection”

  • A Perfect Snowman
  • Beetle McGrady Eats Bugs
  • Olivia … and the Missing Toy
  • Swamp Angel
  • Chicken Soup

“The Library Problem” – An Ongoing Column in Teaching Children Mathematics

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Schad, Brian, Joseph Georgeson, and Sarah Bunten. 2010. “The Library Problem.” Teaching Children Mathematics 16 (7): 387–89.

The authors, elementary and middle school math teachers, describe a math lesson plan that takes elementary age students to the local public library to gather and analyze data. The students count the number of words on a page of a picture book, and then tally the number of letters in each word on the same page. They describe two methods: older students can work in pairs where one student counts and one completes the table, and younger students can complete the activity using one page with a whole class. Once they have gathered data, they analyze it with the goal of understanding relationships between numbers (e.g. ratio, fraction, decimals, percentages) and how numbers can be visually represented (e.g. on a tally sheet). The authors claim that this exercise puts a difficult concept like rational numbers in the context of how many words you read or how difficult a book is. The authors conclude by inviting other teachers to try the same problem in their classes and share the outcomes. This lesson could be easily adapted by a school librarian or by a public children’s librarian.

Lesson Goals:

  • Students can tally the number of words on a page of a picture book
  • Students can tally the number of letters in each word on a page of a picture book
  • Students can compare these figures and discuss patterns they observe

Lesson Plan Materials

For more detailed instructions and examples, see: Schad, Brian, Joseph Georgeson, and Sarah Bunten. 2010. “The Library Problem.” Teaching Children Mathematics 16 (7): 387–89.

Common Core State Standards this Lesson Supports

  • CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP4 Model with mathematics.

AASL Standards for the 21st Century Learner

  • AASL 2.1.3 Use strategies to draw conclusions from information and apply knowledge to curricular areas, real-world situations, and further investigations.
  • AASL 2.1.4 Use technology and other information tools to analyze and organize information.

Related Articles

  • Small, Marian. 2010. “North Dakota’s Centennial Quilt and Problem Solvers: Solutions: The Library Problem.” Teaching Children Mathematics 16 (7): 386–93.

How Wide Is a Squid Eye? Integrating Mathematics into Public Library Programs for the Elementary Grades

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Kliman, Marlene, Nuria Jaumot-Pascual, and Valerie Martin. 2013. “How Wide Is a Squid Eye? Integrating Mathematics into Public Library Programs for the Elementary Grades.” Afterschool Matters, no. 17 (January): 9–15.

The authors, researchers with TERC in Massachusetts, describe an NSF funded project, Math Off the Shelf, where informal educators are given access to a bank of over 200 activities that incorporate math for elementary age students. The researchers consulted with public children’s librarians, and considered both common and uncommon characteristics of a public library, when designing the activities. They cite research showing that on the one hand, engaging children with math outside of the school improves learning math and attitudes toward math, but on the other hand, informal educators are math avoidant and do not share their own use of math in everyday tasks with children. Further, even though science is increasingly seen as a “social” activity where kids learn through working on problems together, people still see math as a subject learned through facts, not something learned socially. The activities they designed address these issues in the public library because the library allows for a place to gather opinions (making math questions more relevant), a place to share math problem-solving strategies (learning socially), and a place to incorporate literature into a math activity. They describe how an external evaluator surveyed the librarians for their perception of math and how they used math in activities before and after introducing the activity bank. After the introduction of the activities, more librarians viewed math as important in their library services and were incorporating math into their everyday interactions with children in the library.

The School Library: A Space for Critical Thinking about Data and Mathematical Questions

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Kimmel, Sue C. 2012. “The School Library: A Space for Critical Thinking about Data and Mathematical Questions.” Library Media Connection 30 (4): 38–39.

The author, a professor at Old Dominion University (Virginia) argues that the school library can and should support mathematical inquiry, because school librarians have experience with integrating curriculum across disciplines and designing and implementing inquiry-based learning opportunities. She gives school librarians examples for how a librarian can bring math into the school library: rooting math questions and math discussions in literature, using manipulatives to help learn math concepts, and exploring reference materials to gain experience with reading graphs. She cites McKinney and Hinton (2010) who advocate for including literature in math instruction to give math more meaning, encourage math conversations, allow for investing math questions, and as a source of visual math representations. She points out that such lessons can support both the National Council for Teaching Mathematics Principles and Standards for School Mathematics as well as the AASL’s Standards for the 21st-Century Learner.

Diagrams, Timelines, and Tables-Oh, My! Fostering Graphical Literacy

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Roberts, Kathryn L., Rebecca R. Norman, Nell K. Duke, Paul Morsink, Nicole M. Martin, and Jennifer A. Knight. 2013. “Diagrams, Timelines, and Tables-Oh, My! Fostering Graphical Literacy.” The Reading Teacher 67 (1): 12–24. doi:10.1002/TRTR.1174.

Argues that young children need to be able to understand graphics found in informational texts and points out that the Common Core makes references to graphical literacy. Compares graphical literacy to reading literacy by explaining how graphical literacy requires an ability to know what graphs are and “how they work”. Defines several “concepts of graphics” and explores at what ages kids demonstrate an understanding of each concept. Concepts of graphics include: “action, extension, importance, intentionality, partiality, permanence, relevance, and representation”. Suggests that teachers encourage graphical literacy using similar techniques to teaching general literacy, such as thinking out loud. Details a research project where they showed graphics to students and asked them to explain what they could know from looking at the graphic. Researchers note that some kids could understand a lot and interpret a lot from a graphic, but that most kids do not understand important concepts of graphics.

Data Modelling with First-Grade Students

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English, Lyn. 2012. “Data Modelling with First-Grade Students.” Educational Studies in Mathematics 81 (1): 15–30. doi:10.1007/s10649-011-9377-3.

Author Lyn English reports one year into a three year study on how first grade children model data. English argues that there is a need for research exploring the ways young children demonstrate statistical reasoning. Emphasizes using statistical reasoning to answer questions of interest in the classroom. Uses storytelling to explore math problems and activities. Describes aligning lessons with teachers and the students’ curriculum. Details a quasi experimental study where children use post-its to represent and organize data collected on the types of trash and recycling in a storybook, and where children describe their reasons for organizing them in certain ways. Finds that children are able to articulate what information is important to include when representing data.

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

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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

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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.