Teaching Fractions through Situations: A Fundamental Experiment

1. Front Matter

   Pages i-xiii

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2. Why These Adventures?

   • Guy Brousseau, Nadine Brousseau, Virginia Warfield

   Pages 1-8

3. The Adventure as Experienced by the Students

   • Guy Brousseau, Nadine Brousseau, Virginia Warfield

   Pages 9-125

4. The Adventure as Experienced by the Teachers

   • Guy Brousseau, Nadine Brousseau, Virginia Warfield

   Pages 127-163

5. The Adventure as Experienced by the Researchers

   • Guy Brousseau, Nadine Brousseau, Virginia Warfield

   Pages 165-199

6. Expansions and Clarifications

   • Guy Brousseau, Nadine Brousseau, Virginia Warfield

   Pages 201-210

7. Back Matter

   Pages 211-215

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This work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries.

• Constructivism in Mathematics Education
• Mathematics Education
• Scientific Observation in Mathematics Education
• Teaching Fractions and Decimals
• The didactique method
• Theory of Situations
• learning and instruction

From the reviews:

 

“This book, intended for teachers, mathematics education researchers, and mathematicians, is about developing and teaching a curriculum for teaching fractions. … the book describes three ‘adventures’ –– the adventure of the researchers while discovering and testing a curriculum for rational number learning, developed using the theory of didactical situations (Chapter 4), the adventure of the teachers implementing that curriculum (Chapter 3), and the adventures of the students experiencing that curriculum (Chapter 2).” (Annie Selden, MAA Reviews, February, 2014)

• Université de Bordeaux, Bordeaux, France

  Guy Brousseau

• Bordeaux, France

  Nadine Brousseau

• Mathematics, University of Washington, Seattle, USA

  Virginia Warfield

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