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Speaking Mathematically: Communication in Mathematics Classrooms (Language, Education and Society), by David Pimm
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David Pimm examines the school teaching of mathematics from the perspective of mathematics as a language.
- Sales Rank: #3150458 in Books
- Published on: 1987-08
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 240 pages
Most helpful customer reviews
3 of 3 people found the following review helpful.
Recommended for every math teacher
By J. Turner
In spite of being 25 years old, this book has valuable insights about communicating mathematics in the classroom that do not seem to have been well-circulated in the teacher community. If for nothing else, Pimm points out many conventions that are so ingrained in math teachers (starting in elementary grades) that the teachers do not think to explain them to students.
For example, the way that mathematicians think of the words "any," "some" and "all" are different from the way that students often do. Students typically think of "some" and "all" as contrasting words; thus, the statment "some rational numbers are real numbers" was taken by students in a poll to be false, since ALL rational numbers are real numbers. And the question, "Is any even number prime?" can be quite ambiguous--it could mean either "Is there even one number that is prime?" or "Are all even numbers prime?" And even more advanced students can misunderstand math vocabulary--Pimm gives an example where, after defining a set of 2 x 2 matrices, the assignment directs "For any matrix A in W, show that A^2 = A." Many student answers contained particular numerical matrices for A for which they had derived the result for only one chosen instance. When asked about his answer, one student commented "Well, it said to show it for any, so I just picked one. I thought that was what it meant."
The book is filled with examples of how teachers' assumptions about language, mental imagery, and symbolic representations can be confusing, if not actually misleading, to students. I highly recommend this book to all math teachers from elementary grades through college.
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