Monday, August 07, 2006
Cognition in Practice, J. Lave (1991, Spanish translation)
La cognición en la práctica came as a surprise. The title in Spanish did not include the subtitle it had in English, Mind, Mathematics and Culture in Everyday Life, so when I read the Table of Contents and the Preface it was a positive feature I was not expecting.
Still, I was troubled by the way Lave treats the concept of transfer in mathematics and that kept me paying special attention to the reasons she would present to support her argument. This book is not about learning mathematics; it is about how adults use arithmetic (the lowest level content area in mathematics, taught in grade school) in everyday activities: such as home finances, supermarket shopping, diet meal preparation, and others.
Two theories of transfer are presented by Lave: first, many specific tools are used to solve specific problems; second, a few general tools can be used to solve many different problems.
An example that is presented in the book is related to the preparation of a recipe, where 3/4 of 2/3 of a cup needs to be used. The person did not use paper and pencil to solve the problem (multiplying fractions will give 1/2 cup), instead measured 2/3 of a cup and then used a circle to take three fourths of the total. But isn’t this something learned in school when working with fractions? The mathematical algorithm is not used, but concretely it is solve as with manipulatives. In this case, I believe transfer has occurred.
How much mathematics do we remember after we leave school? How much mathematics we need to use in our work? How much mathematics/arithmetic we need to use in everyday activities? In school, students are expected to find solutions to specific problems, to find exact solutions. But Lave’s research shows in real life, approximations are usually enough. For example, in the supermarket, when trying to choose between two articles, an exact solution is not necessary.
One might think that it is not important to have students go over so much trouble, trying to learn so many algorithms. But mathematics is not only used in real live activities, it is also used in different ways in our jobs. Being precise is being accurate, correct. And because we never know what are we doing in the future I truly believe it is better to be safe and learn as much as we can.
Anyway, at this moment this book doesn’t seem to help me much with my research, as it is related to how people use mathematics more than to how people learn mathematics outside the school building. One thing I can say, the discussion forum I will be analyzing is more an extension of the classroom/school, a place where students go to get help, to be tutored by more knowledgeable others. Up to a certain point, it works as a zone of proximal development where novice and expert interchange ideas, and working together try to find a solution to a problem posed by the student. Students that participate in the discussion forum are internally motivated, they are going beyond their own means to understand the math they study at school. Now the question remains, up to what point is this informal learning?
Lave, J. (1991). La cognición en la práctica. Buenos Aires, Argentina: Paidós. [Translation by Luis Botella; original title: Cognition in Practice, 1988].
Still, I was troubled by the way Lave treats the concept of transfer in mathematics and that kept me paying special attention to the reasons she would present to support her argument. This book is not about learning mathematics; it is about how adults use arithmetic (the lowest level content area in mathematics, taught in grade school) in everyday activities: such as home finances, supermarket shopping, diet meal preparation, and others.
Two theories of transfer are presented by Lave: first, many specific tools are used to solve specific problems; second, a few general tools can be used to solve many different problems.
An example that is presented in the book is related to the preparation of a recipe, where 3/4 of 2/3 of a cup needs to be used. The person did not use paper and pencil to solve the problem (multiplying fractions will give 1/2 cup), instead measured 2/3 of a cup and then used a circle to take three fourths of the total. But isn’t this something learned in school when working with fractions? The mathematical algorithm is not used, but concretely it is solve as with manipulatives. In this case, I believe transfer has occurred.
How much mathematics do we remember after we leave school? How much mathematics we need to use in our work? How much mathematics/arithmetic we need to use in everyday activities? In school, students are expected to find solutions to specific problems, to find exact solutions. But Lave’s research shows in real life, approximations are usually enough. For example, in the supermarket, when trying to choose between two articles, an exact solution is not necessary.
One might think that it is not important to have students go over so much trouble, trying to learn so many algorithms. But mathematics is not only used in real live activities, it is also used in different ways in our jobs. Being precise is being accurate, correct. And because we never know what are we doing in the future I truly believe it is better to be safe and learn as much as we can.
Anyway, at this moment this book doesn’t seem to help me much with my research, as it is related to how people use mathematics more than to how people learn mathematics outside the school building. One thing I can say, the discussion forum I will be analyzing is more an extension of the classroom/school, a place where students go to get help, to be tutored by more knowledgeable others. Up to a certain point, it works as a zone of proximal development where novice and expert interchange ideas, and working together try to find a solution to a problem posed by the student. Students that participate in the discussion forum are internally motivated, they are going beyond their own means to understand the math they study at school. Now the question remains, up to what point is this informal learning?
Lave, J. (1991). La cognición en la práctica. Buenos Aires, Argentina: Paidós. [Translation by Luis Botella; original title: Cognition in Practice, 1988].
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To have more information about this book, you might want to look at the following book reviews available through the UF library online resources in:
Contemporary Sociology, 19 (1), pp. 150-151.
Applied Cognitive Psychology, 4 (6), Nov/Dec 1990, pp. 504-506.
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Contemporary Sociology, 19 (1), pp. 150-151.
Applied Cognitive Psychology, 4 (6), Nov/Dec 1990, pp. 504-506.
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