Fractions

Teaching Fractions with Understanding: Part-Whole Relationship

This web-based article, from The Millennium Project in the UK, identifies perspectives through which children see fractions. It can be used with CTS Sections II or IV or the B2 Fractions Module in the CTS Mathematics Leader's Guide. http://nrich.maths.org/2550

Bibliographic Citation: 
NRich. 2011. Teaching Fractions with Understanding: Part-Whole Concept. http://nrich.maths.org/2550

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.

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

How Students (Mis-)Understand Science and Mathematics

The authors propose 'intuitive rules' that students use to reason about mathematics and science concepts. The book provides many examples how these rules can be used to interpret the misconceptions many students have about mathematical concepts. This resource book can be used to supplement the readings from section IV.

Bibliographic Citation: 
Stavy, Ruth and Tirosh, Dina (2000). How Students (Mis- ) Understand Science and Mathematics. NY, NY: Teachers College Press.

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

Connecting to Develop Computational Fluency with Fractions

This article describes developing fluency with addition and subtraction of fractions by focusing instruction on the big idea of operating with like-size units. A sequence progression of addition and subtraction problems as well as some samples of student work is illustrated. This resource could be using to supplement section II.

Bibliographic Citation: 
Mack, Nancy K. (2004). Connecting to Develop Computational Fluency with Fractions. Teaching Children Mathematics. November Issue: 226-232.

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)
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