Math constructivism

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.

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

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.

Zoos, Aquariums, and Expanding Students’ Data Literacy

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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.