I thought I knew math fairly well.

I thought arithmetic was boring.

I thought the reason other nations beat America in international math tests was that their students worked harder than ours.

I thought all sorts of silly things before I read Liping Ma’s Knowing and Teaching Elementary Mathematics. Now this must-read book is coming out in a new edition, due in bookstores next week.

I can hardly wait!

In American elementary mathematics education, arithmetic is viewed as negligible, sometimes even with pity and disdain—like Cinderella in her stepmother’s house. Many people seem to believe that arithmetic is only composed of a multitude of “math facts” and a handful of algorithms. . . Who would expect that the intellectual demand for learning such a subject actually is challenging and exciting?

— Liping Ma

Arithmetic in American Mathematics Education: An Abandoned Arena?

## What’s So Hard about Arithmetic?

If you have not yet read Ma’s original work, these articles will give you a taste of her topic:

- Knowing and Teaching Elementary Mathematics

Thorough review by Richard Askey in the American Educator.

- What Do You Need to Know to Teach Your Child Elementary Mathematics?

Another review, this one directed at homeschoolers, by Jennifer Dees.

- Liping Ma’s Knowing and Teaching Elementary Mathematics

A short outline of the book’s key points.

## Related Resources

- Arithmetic in American Mathematics Education: An Abandoned Arena?

Remarks by Liping Ma at the National Summit on the Mathematical Education of Teachers.

- Three Ways To Think about Addition

Before you click, can you guess what the three ways are? Bar models provide insight into one of the most basic operations in arithmetic.

- What Does Liping Ma REALLY say?

Notes from a lecture at Rutgers University.

- Basic Skills Versus Conceptual Understanding

Hung-Hsi Wu examines a “bogus dichotomy in mathematics education.”

## What Does It Take To Teach Elementary Math?

- Knowing Mathematics for Teaching

Who knows mathematics well enough to teach 3rd grade?

- What’s Sophisticated about Elementary Mathematics?

Hung-Hsi Wu argues that schools need specialized math teachers at the elementary level.

- What Is So Difficult about the Preparation of Mathematics Teachers?

“Our universities do not adequately prepare mathematics teachers for their mathematical needs in the school classroom. . . Mathematics is by its very nature a subject of transcendental clarity. In context, there is never any doubt as to what a concept means, why something is true, or where a certain concept or theorem is situated in the overall mathematical structure. Yet mathematics is often presented to school students as a mystifying mess. . .”

- Beyond Singapore’s Mathematics Texbooks

A look at how one nation successfully prepares and supports math teachers with clearly-defined content, a flexible educational structure, and a focus on teacher development.

[**Hat tip:** kitchen table math, the sequel.]

## Update

I finally got the new edition through my library, and it was somewhat disappointing. They hardly added anything new, where I was hoping for at least a couple chapters expanding on the idea of PUFM. If your budget is tight, you won’t miss anything by ordering a used copy of the original version.

Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

Truly a great book, and every time I go back and read a chapter again it further convicts me about how my students can really

learnmath and not just learn algorithms or tricks.Thanks for the web links; I definitely want to check out some of those resources.

Denise, thanks for all the good links.

Only thing is, it’s messing up my schedule.

I am spending too much time reading these articles!

The article by Jennifer Dees was especially interesting–thank you! I’ve linked.

Like Rich, I love to re-read Liping Ma’s book, since it seems like I learn something new (or at least am reminded of something I’ve forgotten) each time. I especially admire the variety of word problems the Chinese teachers came up with to represent the calculation .

I am hoping (or perhaps just dreaming?) that one of the things added to the new book will be a framework of connections between arithmetic topics, like the “knowledge package for multiplication” on p. 47 of the first edition. I have tried making my own list of such connections, but I get bogged down in the possibilities. I would love to see what Ma might suggest.

My problem now is that our dysfunctional state government has cut all funds to the library loan system. In order to read the new edition of this book, I may actually have to buy it. I don’t know if I can bear such a drastic reduction in my reading diet as will result from being limited to my own pocketbook. 😦

Thanks for your entry to the Carnival of Educators: http://nfahm.blogspot.com/2010/02/carnival-of-educators-14th-edition.html