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Numbers and Operations

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.

Using Everyday Knowledge of Decimals to Enhance Understanding

This article discusses the role of students' everyday knowledge of decimals in supporting the development of their knowledge of decimals. Students using contextual problems with decimals are able to build on their understanding of decimals. The problems used tap common misconceptions about decimal fractions so could be used to supplement section IV.

Bibliographic Citation: 
Irwin, Kathryn C. (2001). Using Everyday Knowledge of Decimals to Enhance Understanding. Journal for Research in Mathematics July Issue: 399-420

Upper Elementary School Pupils' Difficulties in Modeling and Solving Nonstandard Additive Word Problems Involving Ordinal Numbers.

This article provides information about the scope and nature of studentsí difficulties with modeling and solving non-routine word problems using addition or subtraction. Highlighted misconceptions about numbers and arithmetic operations can be used to supplement section IV.

Bibliographic Citation: 
Verschaffe, Lieven, Corte, Erik De and Vierstraete, Heidi (1999). Upper Elementary School Pupilsí Difficulties in Modeling and Solving Nonstandard Additive Word Problems Involving Ordinal Numbers. Journal for Research in Mathematics Education May Issue: 265-285

Upper Elementary School Pupils' Difficulties in Modeling and Solving Nonstandard Additive Word Problems Involving Ordinal Numbers.

This article provides information about the scope and nature of studentsí difficulties with modeling and solving non-routine word problems using addition or subtraction. Highlighted misconceptions about numbers and arithmetic operations can be used to supplement section IV.

Bibliographic Citation: 
Verschaffe, Lieven, Corte, Erik De and Vierstraete, Heidi (1999). Upper Elementary School Pupilsí Difficulties in Modeling and Solving Nonstandard Additive Word Problems Involving Ordinal Numbers. Journal for Research in Mathematics Education May Issue: 265-285

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.

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
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