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Uncovering Student Thinking in Mathematics- 25 K-12 Formative Assessment Probes

The 10 assessment probes in the "Number and Operations" section of this book can be used as a CTS application to examine student thinking after conducting a CTS. Additionally, the teacher background notes provide valuable information on instructional implications (CTS Section II) and research on learning (CTS Section III). For example, the "Comparing FRactions" probe can be used with the "Fractions" CTS to examine student work related to part-whole relationships when comparing fractions.

Bibliographic Citation: 
Rose, C., Minton, L., and Arline, C. 2007. Uncovering student thinking in mathematics- 25 formative assessment probes. Thousand Oaks, CA: Corwin Press.

The Young Mathematician at Work: Fractions, Decimals and Perent (3rd in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

Bibliographic Citation: 
Fosnot, Catherine Twomey and Dolk, Maarten (2001). The Young Mathematician at Work, Portsmouth, NH: Heinemann.

The Young Mathematician at Work: Addition and Subtraction (1st in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

Bibliographic Citation: 
Fosnot, Catherine Twomey and Dolk, Maarten (2001). The Young Mathematician at Work, Portsmouth, NH: Heinemann.

Teaching for K-12 Mathematical Understanding Using the Conceptual Change Model

Chapter 3 of this resource can be used to supplement Section IV: Research on Student Learning for topics in the Numbers and Operations Category. The Chapter includes information about 1) Student difficulties, confusion, and misconceptions and 2) Factors contributing to students' difficulties, confusion, and misconceptions.

Bibliographic Citation: 
Stepans, S, Schmidt, D., Welsh, K., Reins, K., and Saigo, B. (2005), St. Cloud, MN: Saiwood Publications

Number and Operations Annenberg Media

Description: A series of video clips (? hour each) with accompanying support materials such as problem solving activities, online and print resources, interactive activities and demonstrations which help increase teachersí expertise and content knowledge as it relates to number and operations. The online series is a useful resource to supplement section I.

Bibliographic Citation: 
WGBH Education Foundation (2003). Annenberg Media Learner.org To view these video clips: http://www.learner.org/channel/courses/learningmath/number/overview/index.html

How Students Learn: Mathematics in the Classroom

How Students learn uses the principles and findings from How People Learn within the context of the mathematics classroom. An introduction to the principles as they apply to mathematics is included in chapter 2, whole numbers at the elementary level is the focus of chapter 3, rational numbers at the middle level is the focus of chapter 4 and chapter 5 focuses on functions at the high school level. This would be an additional reference to sections II, III and IV.

Bibliographic Citation: 
Bibliographic Citation: The National Research Council. ( 2005) Washington, D.C: National Academies Press. The read this book online: http://darwin.nap.edu/books/0309089492/html
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