# Singapore Math in AFT magazine

The American Educator (current issue, Winter 2010) has an article, not on the texts that some home schoolers and traditionalists use or support here, but on teacher training and professional development in Singapore (Beyond Singapore’s Math Textbooks).

Also, to rile some bloggers, E. D. Hirsch addresses the need for curricula, and along the way takes a few shots at “progressive education.” Creating a Curricula for America: Our Democracy Depends on Shared Knowledge.

And while we’re looking at The American Educator, I owe some sort of review of What’s Sophisticated about Elementary Mathematics (*Plenty—That’s Why Elementary Schools Need Math Teachers) *(Fall 2009) by Hung-Hsi Wu. It’s a major piece, lead article.

For the record, I love the Wu piece. I am curious about the Singapore professional development, but have no idea how much could be translated. And I have mixed feelings about Hirsch. Agree with him, disagree with him, anyone dealing with standards and content in American schools should be familiar with what he espouses.

The magazine comes out quarterly, and it has regular archives going back to Fall 1997 (though not all articles are available), when I started my first regular teaching assignment. Watching what’s changed, what hasn’t, makes interesting reading. As does noticing that there is an article from 1999 challenging “learning styles” or consistent articles on pedagogy in math going back over a decade.

I’ve been working with Carol Seaman who defined mathematical sophistication as a list of attitudes for her elementary and middle school teacher preparation research. It is quite interesting. If you’d like, I can give you more detailed references and quotes.

Please do.

I don’t know that I will agree. But I do choose to wall myself off….

I would be interested to know what you think about this list. Here is a somewhat rephrased piece from: Szydlik, J., Kuennen, E., & Seaman, C. (2009). Development of an Instrument to Measure Mathematical Sophistication. In Conference on Research in Undergraduate Mathematics Education Proceedings.

“The following overarching values support mathematical sophistication:

1. Understanding patterns based on underlying mathematical structures

2. Finding the same essential structure in seemingly different mathematical objects

3. Constantly making and testing conjectures about mathematical objects and structures

4. Using precise mathematical definitions of objects to provide necessary and sufficient criteria for classifying objects, to create taken-as-shared meanings, and to make arguments

5. Creating models, examples, and non-examples of mathematical objects as a way to create and understand definitions of objects.

6. Understanding relationships and structures of relationships among objects

7. Using logical arguments and counterexamples as sources of conviction

8. Using precise language with fine distinctions for communicating assertions and for making and evaluating arguments

9. Employing symbolic representations of objects and ideas, and using powerful notation for organizing thinking and for communication

We stress that mathematical sophistication belongs to the domain of attitudes and beliefs, and does not directly follow from, nor imply, an understanding of any specific piece of mathematical content knowledge. Rather, it means possessing the avenues of knowing of the mathematical community that allow one to construct mathematics for oneself. We also note that mathematical sophistication in the context of practicing mathematics does not automatically and directly translate into the pedagogical knowledge of how to help students develop mathematical sophistication.”

Your link to the article on learning styles seems to be broken. Can you check it and repost?

Thanks! It should work fine now.

Maria,

so your list is interesting. It seems to place a lot of emphasis on structure. At first blush, that seems right to me.

When I teach problem solving, I have a list of characteristics of strong mathematical problem solvers (I’ll find it one day and put it up here). That list overlaps yours, considerably.

I’m struck by some ideas that are not present.

The ability to ignore non-essential information (or even to determine what that is)

The ability to retain “executive control” ie to get deeply involved in a subtask, but not lose sight of the big idea.

The ability to pluck useful information out of a sea of muck.

I should look for my list. And maybe they should only partially overlap. What do you think?

“The following overarching values support mathematical sophistication:1. Understanding patterns based on underlying mathematical structures

2. Finding the same essential structure in seemingly different mathematical objects

3. Constantly making and testing conjectures about mathematical objects and structures

4. Using precise mathematical definitions of objects to provide necessary and sufficient criteria for classifying objects, to create taken-as-shared meanings, and to make arguments

5. Creating models, examples, and non-examples of mathematical objects as a way to create and understand definitions of objects.

6. Understanding relationships and structures of relationships among objects

7. Using logical arguments and counterexamples as sources of conviction

8. Using precise language with fine distinctions for communicating assertions and for making and evaluating arguments

9. Employing symbolic representations of objects and ideas, and using powerful notation for organizing thinking and for communication

JD, I agree that lists should overlap only partially. Carol Seaman’s list of Mathematical Sophistication I posted captures some of the “content” values – as you said, it’s about structure. Your items capture “executive control” and management. My own lists usually focus on authoring and ownership:

– Creating your own math entities

– Naming and defining math creations

– Standing on the shoulders of giants when you engage in building mathematics

– Connecting math making with general culture development, including sciences and arts

– Personal meaning and significance of math constructions, connecting math creations with your life and that of your family, communities and networks

I expect this discussion to come up in the Online Family Studies I will be leading this Spring.

one curriculum, two or more curricula.

don’t let “datum” and “data” fool ya.

I stubbed my toe on a datum once…

With Hirsch, I find I agree on the need for content and shared knowledge — but I find his idea of what it should be rather dry. And it sometimes seems as if he assumes that if students today don’t learn the same things they did 50 years ago, they must not be learning anything.

Rachel, I think you’ve articulated part of my gut reaction to him…