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In math education, we often talk about "informal" and "formal" mathematics.

In this paper, +Michael Matassa Jr. and I examine a middle-layer, which RME researchers call the "performal" layer. Preformal mathematical productions are "mathematical models, tools, and strategies that embody historic activity and social interaction. They are simultaneously general and specific, and as such they exist between students’ informal realities and formal mathematics. Through activity, preformal productions can be made general enough so as to be applicable to a wide variety of problems, but they retain contextual cues to specific situations"

Preformal productions are really important.

(1) Preformal productions help students

(2) Preformal productions help students

In this paper, +Michael Matassa Jr. and I examine a middle-layer, which RME researchers call the "performal" layer. Preformal mathematical productions are "mathematical models, tools, and strategies that embody historic activity and social interaction. They are simultaneously general and specific, and as such they exist between students’ informal realities and formal mathematics. Through activity, preformal productions can be made general enough so as to be applicable to a wide variety of problems, but they retain contextual cues to specific situations"

Preformal productions are really important.

(1) Preformal productions help students

**do**math.(2) Preformal productions help students

**learn**formal mathematicsAdd a comment...

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My talk from the NCTM research conference last week. In short, my argument is that Realistic Mathematics Education should pay more attention to the ways that mathematics artifacts and mathematical activity get intertwined.

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The first panel is particularly exquisite.

>> Nietzsche doesn't say a word, because he generally lets his fists do the talking.

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I'm looking for some examples of work on learning trajectories in high-school math. So far, very little luck. Can anyone help?

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After a terrible day yesterday, some good news from the Supreme Court today.

This quote from scotusblog, after the Court struck down DOMA (paving the way for married same-sex couple to file their taxes jointly) captures it nicely:

"Perhaps for the first time ever, many people will be eager to file their taxes next April 15."

It's crazy to me that we tolerated blatant discrimination for so long that the simple act of a married couple filing a joint tax return should be cause for celebration.

Progress is slow, hard fought, and easily lost -- as the decisions yesterday and today demonstrate.

This quote from scotusblog, after the Court struck down DOMA (paving the way for married same-sex couple to file their taxes jointly) captures it nicely:

"Perhaps for the first time ever, many people will be eager to file their taxes next April 15."

It's crazy to me that we tolerated blatant discrimination for so long that the simple act of a married couple filing a joint tax return should be cause for celebration.

Progress is slow, hard fought, and easily lost -- as the decisions yesterday and today demonstrate.

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For everyone who came to NCTM during the snowstorm, here's what it's like now in Colorado

(While, actually, it's raining

(While, actually, it's raining

*right now*but still...)Add a comment...

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**RME @ NCTM**

Thanks +Raymond Johnson for putting together a list of the RME (Realistic Mathematics Education) sessions at NCTM '12.

http://blog.mathed.net/2013/04/planning-for-nctm-2013.html

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Just thought I'd share my schedule for NCTM -- hopefully I'll see a lot of you there!

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On pi day.... a reminder that maybe we're celebrating the wrong number.

http://tauday.com/tau-manifesto

http://tauday.com/tau-manifesto

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