kitchen table math, the sequel: Part II of MathNotations Interview

Monday, September 17, 2007

Part II of MathNotations Interview

You have to read it to believe it. I thought question 18 was most telling.


"18. Here’s an innocent little question, Prof. Steen! The current conflicts in mathematics education are usually referred to as the Math Wars. In your opinion, what were the major contributing factors in spawning this conflict and how would you resolve it?"


"There are many factors involved. I think I can identify a few, but I have no confidence that I could resolve any of them. One is the natural tendency of parents to want their children to go through the same education that they received—even when, as often is the case with mathematics, they admit that it was a painful and unsuccessful ordeal. This makes many parents critical of any change, most especially if it introduces approaches that they do not understand and which therefore leaves them unable to help their children with homework."

[Number one: Parents are stupid.]


"Another source were scientists and mathematicians who pretty much breezed through school mathematics and who were increasingly frustrated with graduates (often their own children) who did not seem to know what these scientists knew (or thought they knew) when they had graduated from high school. Our weak performance on international tests appeared to provide objective confirmation of these concerns, and they came to pubic notice just as the NCTM standards became widely known in the early to mid-1990s. Even though very few students had gone through an education influenced by these standards, the confluence of events led many to believe that the standards contributed to the decline."

[Number two: Lower expectations started long ago. The standards just codified them and gave them a pedagogical foundation.]


"A third source can be traced to the way in which the NCTM Standards upset the caste system in mathematics education. Mathematicians are accustomed to a hierarchy of status and influence with internationally recognized researchers at the top, ordinary college teachers in the middle, below them high school teachers, and at the very bottom teachers in elementary grades. The gradient is determined by level of mathematics education and research. So it came as somewhat of a shock to research mathematicians when the organization representing elementary and secondary school teachers, seemingly without notice or permission, deigned to issue "standards" for mathematics. Mathematicians would say, and did say, "we define mathematics, not you."

[Number three: College professors are stupid.]

[Screw the professors. Screw the kids. Full steam ahead. It doesn't matter if kids aren't prepared for college.]


"I could go on, but won't. But I do want to add that, as with any contentious issue, face-to-face dialog helps bridge differences. With some exceptions, I believe that has happened with protagonists of the math wars. Achieve was one of the first organizations to bring to one table people from all these different perspectives. Subsequently, other groups have made similar efforts, generally with good results. As mathematicians and educators roll up their sleeves to work together on common projects, each learns from the other and the frictions that led to the math wars begin to reduce."


[They do what they want without asking the people who have to teach the product of their actions, and then claim that the solution is to work together. Incredible. I've said before that this is about academic turf and here it is, plain as day.]

16 comments:

Instructivist said...

I came across this surreal comment in the Steen interview:

"Factoring is one of the topics on the borderline of the two perspectives on Algebra II—preparation for life vs. preparation for higher mathematics. For life (e.g., citizenship and personal living) factoring is a relatively useless skill."

Preparation for life is so vague that it can include or exclude everything. It's jarring to encounter "preparation for life" in connection with factoring.

Catherine Johnson said...

Number two: Lower expectations started long ago. The standards just codified them and gave them a pedagogical foundation.

This was the implied thesis of my own comment.

Catherine Johnson said...

The missing parties here are parents, teachers, and students.

There's not going to be an end to the math wars until teachers, parents, and students have a place at the table.

Anonymous said...

There won't be an end to the math wars - because the side with the most at stake does not have the FUNDING to end it.

And that would be the parents.

Anyone think the NSF wants to fund Kumon for my kids elementary school years, my tutoring costs for afterschooling (time, materials), and then pay for the LOST time of my kids?

I read this on a website (cant recall where at the moment).

Educators are academically intellectual but they are NOT EXPERTS.

They are not experts in CONTENT. (my vote is for the PHD in the content area - say, like a Math Professor from NYU or Harvard or JHU or Stanford)

They are not experts in HOW the BRAIN acquires knowledge (see PHD etc.. in psycology, cognitive development)

They are teachers and need the BEST materials. Pedogogy SHOULD NEVER drive THE MATERIALS.

It is then making the teachers "seem" like experts.

And they are not.

SteveH said...

"Preparation for life is so vague that it can include or exclude everything."

It bothered me that he sees no middle ground. It's either some sort of terminal Algebra II course in high school or the AP calculus track for math brains going on to major in "higher mathematics".

The real problem is that many students don't go into certain degree programs in college because they can't deal with the math requirements. Back when I taught college math, students (obviously not on a technical path) would comment about each degree program and how much math was required. Statistics was the killer course for many students in non-technical degree programs. Statistics done right is difficult and all of the silly stuff done in lower grades won't help students one bit. They need real math skills.

Our Math and Computer Science department would work with other departments to help them decide on the terminal math course. In the old days, all students would have to take the traditional math sequence of algebra, trig, calculus, and/or statistics. Changes were made to offer different courses (perhaps in some integrated way) to make these courses more appropriate for students not continuing on in math. The key was to maintain the rigor and expectations of the courses and not water them down into math appreciation. These were good changes for the most part. (But I don't know what's happening lately.)

However, K-12 educators should be thinking very little about "life skills" when so many kids want to go to college. Educators need to think about preparing kids for the next level. They don't do this by making unilateral changes based on their own opinions.

PaulaV said...

While at Kumon yesterday, I noticed this on the bullentin board: Why You Should Choose Math in High School

You can find the article at www.acm.org/ubiquity. Search for 12 reasons to do math.

Sorry I don't know how to link.

Catherine Johnson said...

So it came as somewhat of a shock to research mathematicians when the organization representing elementary and secondary school teachers, seemingly without notice or permission, deigned to issue "standards" for mathematics. Mathematicians would say, and did say, "we define mathematics, not you."

Which has the underappreciated virtue of being true.

Catherine Johnson said...

Heck - I just tried to write directions & couldn't get them to show up.

Anonymous said...

why you should choose math,
by espen anderson in ubiquity.

PaulaV said...

Thank you anonymous!

Catherine Johnson said...

Thanks so much for the article link - I'll get that up. Must get Steve's comment up front, too.

He's right; students CONSTANTLY gatekeep themselves out of careers because of the math requirements.

CONSTANTLY.

Our K-12 schools have no concept that this occurs. They seem to think: if your kid isn't going to be a mathematician, then there's no call for a serious K-12 math education.

I get this CONSTANTLY, from parents, too (and have had this thought myself --- the difference being that I banish it at once).

This is a question of knowing what you don't know, which is never easy.

Catherine Johnson said...

Factoring is one of the topics on the borderline of the two perspectives on Algebra II—preparation for life vs. preparation for higher mathematics. For life (e.g., citizenship and personal living) factoring is a relatively useless skill

Actually, this observation was helpful to me.

Saxon fairly often will tell you that a procedure you're learning won't be used in life -- meaning the arithmetic you use in everyday life -- but will be used in future math courses.

I always find that a terrifically helpful clarification (in part because I'll be feeling vaguely stupid that I don't see where factoring a polynomial is leading - I'll sit there thinking that other people know these things, but I have somehow missed them.)

Anonymous said...

Excuse me, but when did I start sending my children to school to learn life skills?

I send my children to school to learn academic skills.

Schools seem to forget this.

Anne Dwyer

SteveH said...

"... students CONSTANTLY gatekeep themselves out of careers because of the math requirements.

CONSTANTLY.

Our K-12 schools have no concept that this occurs. ..."


Then they have short memories. Education is is a typical "fall-back" degree because of math.

Catherine Johnson said...

Education is is a typical "fall-back" degree because of math.

Is that right???

SteveH said...

Education is is a typical "fall-back" degree because of math.

"Is that right???"

Yes. Nursing was tougher.