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Multiplication and Division

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: Multiplication and Division (2nd 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: 
Bibliographic Citation: Fosnot, Catherine Twomey and Dolk, Maarten (2001). The Young Mathematician at Work, Portsmouth, NH: Heinemann.

Enhancing Prospective Teachers' Knowledge of Children's Conceptions: The Case of Division of Fractions

This article discusses teacherís own subject-matter knowledge of division of fractions as well as the likely sources of common misconceptions held by children. The reading can be used to supplement sections I, II and IV.

Bibliographic Citation: 
Tirosh, Dina (2000). Enhancing Prospective Teachers' Knowledge of Children's Conceptions: The Case of Division of Fractions. Journal for Research in Mathematics Education January Issue: 5-25

Alternative Algorithms: Increasing Options, Reducing Errors

This article describes a variety of computational techniques for addition, subtraction, multiplication and division of whole numbers. This resource could be used in conjunction with sections I, II and III.

Bibliographic Citation: 
Randolph, Tamela D., Sherman, Helene J. (2001). Alternative Algorithms: Increasing Options, Reducing Errors Teaching Children Mathematics. April Issue: 480-484.

A Mathematics Source Book for Elementary and Middle School Teachers

This book discusses many mathematical topics providing key concepts, connections, teaching tips and learning pitfalls. Corresponding NAEP and/or TIMSS are also given. This book would be an additional resource to sections II, III and IV.

Bibliographic Citation: 
University School Support for Educational Reform(1999) A Mathematics Source Book for Elementary and Middle School Teachers, Arena Press, Novato CA (1999)

Looking at Learning Again Part 1

A short video clip (4 minutes) reflecting estimation and computation skills in a fourth grade classroom setting. Students are shown solving math problems, using multiplication of whole numbers, as a group. Estimation strategies, problem solving and communication skills are stressed. This short video clip could be used to supplement section II.

Bibliographic Citation: 
Harvard-Smithsonian Center for Astrophysics (2001). Annenberg CPB. To view this video clip: http://www.hsdvl.org/video.php?record_serial=141&state_serial=13581&source=3
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