Research in Mental Computation:
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Institution Price: AUD $101.50

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Research in Mental Computation:

Multiple Perspectives

By Rosemary A. Callingham and Jane M. Watson.
ISBN: 978-1921214-36-3 A4 122pp
AUD $67.50 + p&p.

About

This book makes a valuable and important contribution to developing the evidence base for mental computation by drawing together several varied research projects in Australia that provide different perspectives on the issues surrounding students' successes and difficulties with mental computation... Where other research has been carried out on calculation strategies it has usually been small scale–qualitative interviews with a limited number of students. And the research has usually provided a snapshot of student understanding at a moment in time. Large scale, quantitative analyses of students' mental computations over time are rare. This book presents one of those rarities...

I love finding research that surprises me and surprises were in store here, as different student strategies emerge from those that might be expected in written computation, for both whole and part-whole numbers. Together the quantitative and qualitative analysis on fractions, decimals, and percents I think surpasses any previous research in the area of mental computation.

Dr Mike Askew, Professor of Mathematics Education, King's College London.

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Contents

  • Foreword
  • Acknowledgements
    Chapter 1: Introduction
    Mental Computation in the Mathematics Curriculum
    Research in Mental Computation
    Strategies for Mental Computation
    Teaching Mental Computation
    Mental Computation with Part-whole Numbers
    This Publication
    Chapter 2: Measuring Mental Computation Competence
    The Rasch Measurement Model
    Interpreting the Rasch Model
    Instruments
    Schools and Students
    A Developmental Scale of Mental Computation Competence
    Description of the Identified Levels of Mental Computation Competence
    Discussion of the Levels Identified
    Distribution of Students Across Levels
    Sub-domains of Mental Computation
    Summary
    Chapter 3: Performance and Growth in Mental Computation
    Growth and Performance across the Grades of Schooling
    Performance by Grade
    Performance by Grade within Schools
    Longitudinal Study of Individual Students
    Students Starting in Grade 3
    Students Starting in Grade 5
    Students Starting in Grade 7
    Summary
    Chapter 4: Error Analysis from Mental Computation Tests
    Analysis of Level B Mental Computation Items
    Whole Number Single-digit Addition and Subtraction
    Two-digit Addition and Subtraction
    Whole Number Single-digit Multiplication and Division
    Analysis of Level D Mental Computation Items
    Whole Number Single-digit Multiplication and Division
    Multi-digit Addition and Subtraction
    Two-digit Multiplication and Division
    Fractions Addition and Subtraction
    Fractional Operators
    Analysis of Level F Mental Computation Items
    Whole Number Single-digit Multiplication and Division
    Two-digit Addition and Subtraction
    Two-digit Multiplication and Division
    Decimals Addition and Subtraction
    Decimals Multiplication and Division
    Fractions Addition and Subtraction
    Fractional Operators
    Percent
    Analysis of Level H Mental Computation Items
    Two-digit Multiplication and Division
    Decimals Multiplication and Division
    Fractions Addition and Subtraction
    Fractions Multiplication and Division
    Percent
    Links among Errors
    Chapter 5: Strategy Use in Whole Number Mental Computation
    Whole Number Two-digit Addition and Subtraction
    Addition
    Subtraction
    Whole Number Multiplication and Division
    Multiplication
    Division
    Halving and Doubling
    Discussion
    Chapter 6: Mental Computation with Fractions, Decimals and Percents
    A Scale of Mental Computation Competence with Part-whole Numbers
    Interpretation of the Part-whole Competence Scale
    Misfitting Items
    Performance across Grades
    Error Analysis from the Tests
    Strategies for Mental Computation with Part-whole Numbers
    Strategy Use with Fraction Problems
    Strategy Use with Decimal Problems
    Strategy Use with Percent Problems
    Summary
    Chapter 7: Developing Mental Computation Programs
    Key Teachers and Resource Development
    Structure for Working with Teachers
    Outcomes for Teachers
    • Organisation and Curriculum
    • Impact on Teachers
    • Factors that Made a Difference
    Focus on the Interface between Mental and Written Computation
    Outcomes from the Project
    Implementing a Whole School Approach in One Primary School
    Outcomes from the Whole School Program
    Common Features of the Projects
    Teacher Ownership
    Underpinning Framework
    Links between Research and Practice
    Systemic Support
    Implications for Computation in the Classroom
    Chapter 8: Implications for Schooling and Further Research
    Implications for Curriculum Development
    Standards and Benchmarks of Performance
    Development of Strategies for Part-whole Mental Computation
    Implications for Schools and Classrooms
    School organisation
    Developing a Mental Computation Program
    Implications for Future Research
    Final Remarks
  • References

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