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Subjects:
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Mathematics
Arithmetic. Concept formation. Decimals. Fractions. Instructional issues. Misconceptions. Percentage. Process skills. Professional development. Ratios. Teachers. Teaching methods. |
Resource Type:
Professional development. Media Type:
Print material.
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Abstract:
This collection of mathematics teaching cases, written by and for teachers of grades 4 through 8, is intended to serve as a catalyst for improving curriculum and instruction specific to fractions, decimals, ratios, and percents. These short cases are designed to stimulate discussion and collaborative reflection. The accompanying facilitator's discussion guide contains suggestions for structuring a teacher study group as well as a series of questions and issues raised by each of the cases. Each case story describes the events that created a problem, the classroom context in which the problem occurred, and the teacher's attempts to resolve the problem. For example, in Six-Tenths or Four-Fifths of a Dollar, a grade 4 teacher discovers that 26 of her 30 students would rather have six-tenths of a dollar. The teacher suspects that this problem may have been difficult for the students because the solution was not geometrically motivated; in other words, the dollar was not physically divided. Questions raised in the facilitator's discussion guide include, Why might students focus only on the numerator?, Which are more difficult to understand, parts of a set or parts of a whole?, and What are the strengths and weaknesses associated with the use of manipulatives when representing fractions? In How Can 100% of Something Be Just One Thing?, a grade 5 teacher addresses the importance of making sense of percentages and of conceptual understanding. She recognizes that her students need additional experiences with the concept of 100% but is unsure as to how to proceed. Issues raised in the facilitator's discussion guide include the differences between conceptual understanding and procedural knowledge, the colloquial use of one hundred percent, and the possibility that curriculum materials reinforce the idea that 100% is 100. Each case story is followed by a list of suggested readings. (Author/CMS) |
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Table of Contents:
[Casebook text:]
Foreword, by Judith H. Shulman and Lee S. Shulman
Preface
Acknowledgments
Teacher to teacher: introduction to cases
Inside student thoughts
Take one-third
Language
Student drawings
Connections
Bean, rulers, and algorithms
Connections
Representations
There's no one-half here
Manipulatives
Building concepts
Everything I know about decimals
Part one
Part two
Epilogue
Assessment
Student writing
Equity
How can 100% of something be just on thing?
Mathematical relationships
Assessment
Equity
Making sense or memorizing rules?
Point seven plus four is point eleven
Connections
Classroom discourse
Calculators
I still don't see why my way doesn't work
Invented algorithms
Mathematical relationships
Decimal wall
Representations
Number sense
Knocking off zeroes
Invented algorithms
Mathematical relationships
Lining up the decimal
Manipulatives
Connections
Building concepts
A proportion puzzle
Intuitive thinking
Problem solving
Alternative strategies
Teaching as questioning
Zeroes sometimes make a difference
Assessment
Building concepts
Six-tenths or four-fifths of a dollar
Connections
Student writing
Assessment
Testing theories
Patterns and relationships
Alternative strategies
Classroom discourse
Hugh's invention
Proportional reasoning
Number sense
Intuitive thinking
Thirteen can't fit over twelve
Epilogue
Classroom discourse
Teacher reflection
Student disposition
Reflecting
Problem of the week
Bounce, bounce
Assessment
Student writing
Student disposition
Function machine
Patterns and functions
Student writing
Student theories
Why isn't one less?
Proportional reasoning
Intuitive thinking
Problem solving
Manipulatives aren't magic
Rote manipulatives?
Proportional reasoning
Connections
Number sense
Two green triangles
Classroom discourse
Manipulatives
Mathematical relationships
What next?
Where do I go from here?
Student drawings
Assessment
Representations
Favorite food circle graph
Mathematical relationships
Calculators
Graphing
What's my grade?
Proportional reasoning
Language
Mathematical relationships
Connections
Percents, proportions, and grids
Proportional reasoning
Representations
Mathematical relationships
Six hours isn't one-sixth of a day
Spatial visualization
Representations
Connections
This wasn't my plan
Bubbles to kickball
Part one
Part two
Mathematical relationships
Calculators
Teacher reflections
The beauty of math
Mathematical relationships
Student disposition
The ratio of girls to boys
Connections
Language
Appendix
Advisory Board Members
References
[Facilitator guide:]
Contents duplicate casebook text's except for extra appendices
Appendices
Case discussion process assessment
Facilitator feedback
Advisory Board Members
Reviews and Awards:
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Eisenhower National Clearinghouse. (2000). The reality of change. ENC Focus, 07(01).
Learn more about this source of information.
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(1999). Review of Fractions, decimals, ratios, and percents :hard to teach and hard to learn?. Teacher Education Materials Project: A Database for K-12 Mathematics and Science Professional Development Providers. (See specific review or award data.)
Learn more about this source of information.
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User Comments:
Pricing Information:
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Description: 1 facilitator guide (paperback) |
Cost: $25.00 |
ISBN: |
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Description: 1 casebook (paperback) |
Cost: $23.00 |
ISBN: |
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Publisher:
Heinemann
Contributor(s):
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Authors: Carne Barnett; Babette Jackson; Donna Goldenstein. |
Funding Agency:
US Department of Education (DED) Stuart Foundations
Specifications:
1 casebook text (xx, 127 pages : illustrations ; 26 cm.)
1 facilitator guide (xxv, 93 pages : illustrations ; 26 cm.)
Record Created: 05/02/1997; Last Modified: 02/18/2004;
© 1997-
2004 ENC. All information in this catalog record was verified and accurate when it was first made available to the public. ENC updates catalog records when resources are featured in special projects or when we learn that the information in the record is out of date.
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