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On the Shoulders of Giants

On the Shoulders of Giants

New Approaches to Numeracy

  • Author: Steen, Lynn Arthur
  • Publisher: National Academies Press
  • ISBN: 9780309084499
  • eISBN Pdf: 9780309537049
  • Place of publication:  United States
  • Year of digital publication: 1990
  • Month: January
  • Pages: 241
  • DDC: 507
  • Language: English

What mathematics should be learned by today's young people as well as tomorrow's workforce? On the Shoulders of Giants is a vision of richness of mathematics expressed in essays on change, dimension, quantity, shape, and uncertainty, each of which illustrate fundamental strands for school mathematics. These essays expand on the idea of mathematics as the language and science of patterns, allowing us to realize the importance of providing hands-on experience and the development of a curriculum that will enable students to apply their knowledge to diverse numerical problems.

  • On the Shoulders of Giants
  • Copyright
  • Preface
  • Contents
  • Pattern
    • FUNDAMENTAL MATHEMATICS
    • FIVE SAMPLES
    • CONNECTIONS
    • GAINING PERSPECTIVE
    • REFERENCES AND RECOMMENDED READING
  • Dimension
    • INTRODUCTION
      • The Dimensional Ladder
      • Giving Geometrical Gifts
    • MEASURING VOLUMES
      • Decomposition Models
      • Pyramid Problems
      • Cylinders and Discs
    • VISUALIZING DIMENSIONS
      • Growth Factors
      • Rates and Averages
      • Drawing Cubes
    • COORDINATES IN DIFFERENT DIMENSIONS
      • Number Lines and Circles
      • Lengths and Perimeters
      • Planes and Surfaces
      • Three-Dimensional Space
      • Higher-Dimensional Spaces
    • CONFIGURATION SPACES
      • The Fourth Dimension
      • Statics and Dynamics
    • SLICING IN DIFFERENT DIMENSIONS
      • Visitors from Higher Dimensions
    • COUNTING COMBINATIONS
      • Counting Triangles
      • Counting Squares and Cubes
      • Seeking Patterns
    • REFERENCES AND RECOMMENDED READING
  • Quantity
    • QUANTITY IN SCHOOL MATHEMATICS
      • Influence of Technology
      • Influence of Applications
      • Influence of Psychological Research
    • FUNDAMENTAL CONCEPTS
      • Numbers and Operations
      • Variables and Relations
    • PROCEDURES
      • Numerical Representation
      • Graphical Representation
      • Computer Representation
      • Algorithms
      • Conceptual and Procedural Knowledge
      • Number Sense
      • Symbol Sense
    • NUMBER SYSTEMS
      • Natural Numbers and Integers
      • Rational Numbers
      • Real Numbers
      • Complex Numbers
      • New Number Systems
    • APPLICATIONS
      • Modeling
      • Measurement
    • GOALS
    • REFERENCES AND RECOMMENDED READING
  • Uncertainty
    • INTRODUCTION
      • Data
      • Chance
      • Calculators and Computers
      • From Data to Inference
    • DATA ANALYSIS
      • Displaying Data
      • Numerical Description
      • Mathematical Models
    • PRODUCING DATA
      • Measurement
      • Statistical Designs
      • Some Cautions
    • PROBABILITY
      • Basics
      • Further Study
      • Transition to Inference
    • INFERENCE
      • Bayesian or Classical?
      • Confidence Intervals
      • Significance Tests
    • STATISTICAL THINKING
    • REFERENCES AND RECOMMENDED READING
  • Shape
    • INTRODUCTION
    • CLASSIFICATION
      • Congruence and Similarity
        • Symmetry and Self-Similarity
        • Combinatorial Properties
        • Topology
      • Naming
    • ANALYSIS
      • Discovering Symmetry
      • Mirror Geometry
      • Using Symmetry
      • Lattices
      • Dissection
      • Combinatorial Tools
    • REPRESENTATION
      • Models
      • Maps
      • Shadows and Lenses
      • Drawing
      • Image Reconstruction
      • Computer Graphics
    • VISUALIZATION
    • CURRICULAR ISSUES
      • Forging Connections
      • Geometry
      • Studying Shape
        • The Study of Shape is Interdisciplinary
        • The Study of Shape is a Laboratory Subject
        • The Study of Shape is for Everyone
        • The Study of Shape is Fun
        • The Study of Shape is Open Ended
    • REFERENCES AND RECOMMENDED READING
  • Change
    • THE MATHEMATICS OF CHANGE
      • Variety of Styles
      • Approaches to Teaching
      • Levels of Description
    • POPULATION DYNAMICS
      • Limits to Growth
      • Levels of Analysis
      • Dynamical Systems
      • Numerical Experiments
      • The Irregular Fruit Fly
      • Moving on to Calculus
    • METEORITES
      • Stability
      • Rubber Sheet Dynamics
      • Phase Portraits
      • Resonance
      • Gaps and Clumps
    • THE TIGER'S STRIPES
      • Curie Was Right . . .
      • Curie Was Wrong . . .
      • Turing's Tiger
    • IMPLICATIONS
    • REFERENCES AND RECOMMENDED READING
  • Biographies
  • Index

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