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Computation and Operations

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.

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

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

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.

Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.

Description: A summary of the structures used by students for adding and subtracting mulitdigit numbers. The article identifies and describes categories of methods devised by students to sovle the problems as well as typical errors that may arise with each method. This article can be used to supplement sections II and IV.

Bibliographic Citation: 
Fuson, Karen C. , Wearne, Diana, Hiebert, James C., Murray, Hanlie G. , Human, Pieter G., Olivier, Alwyn I. , Carpenter, Thomas P., and Fennema, Elizabeth (1997).Childrenís Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction. Journal for Research in Mathematics March Issue: 130-162

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)
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