Pipe cleaners and parabolas

In the latest adventure of “John Dewey,” who’s studying to become a math teacher, he watches videos of math teachers using the discovery method.

This lesson was about parabolas, how the various constants in the vertex form of the equation for a parabola governed its shape, location and direction. He had them split into four groups, each group exploring what happens when you vary one particular constant. They were to use colored pipe cleaners to show the various parabolas on a poster. When through, the students all convened around the central table again and the teacher asked many questions which the students answered, some correctly, some not. There was no “That’s right, that’s wrong,” just more questions.

The teachers in both videos were extremely good at what they were doing, which brought home an unsettling realization to me: You can be very good at doing something that is absolutely horrible.

An ed school classmate thought students learn more by doing a lab. Dewey disagreed.

I said that the same information could have been imparted directly while still challenging students to answer key questions all in a much shorter amount of time. Reaction: Silence. Mr. NCTM moved on to the next comment from another woman who in all seriousness and with no sarcasm intended said “The teacher was very good at not answering the students’ questions.” There was unanimous agreement.

The teacher who pioneered new new math at my daughter’s middle school was very, very good. Most students liked his approach. When less-talented teachers tried it, students hated it. Some of the parents who got involved became leaders of California’s traditional math movement.

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  1. Silly boy. Doesn’t he realize that religious doctrine isn’t subject to discussion?

  2. The saying is that a good football can take his team and beat yours or switch and take your team and beat his.

    A good teacher can make virtually any program work and a weak one can fail with just about any program.

    Maybe it would be good to remember this during debates about Singapore math, constructivism, Reading First, etc.

  3. Miller Smith says:

    This is a serious problem at my high school in Prince George’s County, Maryland. I have honors students in chemistry with transcripts (we have direct access from our desktop computers to the complete records of all students) that show wonderful grades in every math class.

    They can’t do anything! Literally! Calculating a percentage blew their minds. My county decided to delay Chapter 3 of the new Chemistry (Prentice hall, Wilbraham) text due to the math. Oh, and dig this: If a student is failing your chemistry class due to math issues, the teacher is in trouble. I kid you not. We are to teach chemistry from a qualitative POV only with very little math involved at all.

    This is sad as all get out. We are-on purpose-deciding to not have competent students at math but give them high grades.

  4. Indigo Warrior says:

    The teacher who pioneered new new math at my daughter’s middle school was very, very good. Most students liked his approach. When less-talented teachers tried it, students hated it. Some of the parents who got involved became leaders of California’s traditional math movement.

    That sums up the failure of the New Math program. New Math was technically superior to Old Math, and it demanded greater technical ability from the teachers. Very few of the teachers had such ability. It would have been better if the New Math curriculum was offered only to those students who would have benefitted the most from it, and taught by the handful of teachers (and flown-in professors) capable of teaching it.

  5. Indigo Warrior: If you mean the 60’s new math, that is correct, though the emphasis in the lower grades was on a set theoretical approach to teaching basic number and math skills which was deemed by many mathematicians and educators to be inappropriate. Good teachers were able to teach the basic skills the kids needed and supplement this with the theory. Teachers who were not so skilled relied on the presentation in the textbooks and students did not obtain the basic facts and skills they needed. Compounding the problem was that the textbooks written by the School Mathematics Study Group (SMSG), which were primarily authored by mathematicians, were placed in public domain. Publishers then grabbed the material without understanding what it was and hijacked it into textbooks so they could ride the new math wave and make money. As a result, many of the commercial textbooks were very bad.

    Some good texts did come out of that era, but mostly for the high school level. Dolciani was part of SMSG and authored an excellent algebra text that is still used today. The SMSG geometry text became commercial via Moise/Downs “Geometry” (Moise and Downs were two of the authors of the SMSG text). That text is still used by some high schools.

    The “new new math” that Joanne is speaking of followed the lead of the NCTM 1989 (and later 2000) standards, which resulted in a de-emphasis of basic facts and skills in favor of teaching students “critical thinking” and “higher order thinking” skills in the context of so called “real world” problems. NSF embraced this concept and awarded over $100 million in grants for the writing of math programs/texts such as Everyday Math, Investigations in Number, Data and Space; Connected Math Program; Core Plus; IMP; Math Thematics: the list goes on. These have done damage equal to if not more than the 60’s new math which at least had some mathematicians working on it. The new new math texts and programs were written mostly by educators.

  6. Indigo Warrior says:

    Barry: Yes, I meant the old New Math from the 1960s.


  1. The pedagogical is political

    Joanne Jacobs provides much material on the glories of current American educational practice