Understanding Numbers In Elementary School Mathematics Pdf

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ILL
I read two third of book, stop reading on chapter explaining negative number, which author use "vector", I think it is useless to explain to the children.

See extensive note on Evernote.
https://math.berkeley.edu/~wu/

1. Understanding Numbers in Elementary School Mathematics, American Mathematical Society, 2011.
Errata for Understanding Numbers in Elementary School Mathematics May 4, 2016.

2. Teaching School Mathematics: Pre-Algebra American Mathematical Society, 2016.

3. Teaching School Mathemat

ILL
I read two third of book, stop reading on chapter explaining negative number, which author use "vector", I think it is useless to explain to the children.

See extensive note on Evernote.
https://math.berkeley.edu/~wu/

1. Understanding Numbers in Elementary School Mathematics, American Mathematical Society, 2011.
Errata for Understanding Numbers in Elementary School Mathematics May 4, 2016.

2. Teaching School Mathematics: Pre-Algebra American Mathematical Society, 2016.

3. Teaching School Mathematics: Algebra American Mathematical Society, 2016.

Summary:
1. If you looking for the book explain to you why a + b = b + a, why we line up digits when doing math addition, it is not a bad book to read. However I think the explanation is too rigid, by which I mean it is too math-like, maybe not suitable explain to elementary school kids, should have better proof and explanation which are easily understood by kids.

2. For K-6 math, 10 years of experimentation in teaching math to elementary and middle school teachers.
3. pxvi Ideally (teachers) should know mathematics in the sense that mathematicians use the word "know": knowing a concept means knowing its precise definition, its intuitive content, why it is needed, and in what contexts it plays a role, and knowing a skill means knowing precisely what it does, when it is appropriate to apply it, how to prove that it is correct, the motivation for its creation, and, of course, the ability to use it correctly in diverse situations.

To the reader:
this book focus on:
1.focus on precision;
2.primacy of precise definitions, which current math in K-12 try to avoid, result in slighting of definitions. .. This book put the definitions of concepts .. as the foundation for all reasoning and discussions. A fraction is considered by some mathematics educators to be a concept so complex that its meaning should not be given succinctly...
3.reasoning, such as product of two negative numbers a positive?
4. hierarchical structure of math, that means you can't use later definition to explain former definition. It is very strict math thinking, against Jun's use physics to learn math.

Error need to be struck out,
1. 25 / 6 = 4 R 1, 21 /5 = 4 R 1, is there same 25 / 6 = 21 /5?

...more