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October 10, 2006
Letter from John Dewey # 5
Many thanks to all of you who wished me speedy recovery from my stomach flu. I assure you I am fine. A momentary lapse and now I’m all the stronger for it. In the meantime, the world has become a more interesting place, what with NCTM announcing its new “focal points”, and the Wall Street Journal and the New York Times reporting that NCTM has at long last come to its senses and is going to a “back to basics” approach in its math standards. NCTM vigorously denies that the focal points represent such change and has stated that the focal points are merely a continuation of the 1989 standards, which in the view of many parents, mathematicians and (shh) teachers, ensured that computational algorithms, manipulation of symbolic expressions, and paper and pencil drill did not play a leading role in any school’s math curriculum.
Both the New York Times and Wall Street Journal suggested that perhaps the focal points represented the approach that Singapore has used in its math program which has been held responsible for propelling that island nation’s 4th and 8th graders to the number 1 spot in international math testing for the last decade. Singapore does not apologize for having students memorize the number facts. NCTM, however, finds the word “memorization” offensive, which may explain the wording of one of the “focal points” for second grade: "Children use their understanding of addition to develop quick recall of basic addition facts and related subtraction facts.” There. Every addition and subtraction fact must be understood before committing to—forgive the word—memory, sort of like Thomas touching the wounds of the great Savior. So maybe NCTM has a point when they vigorously deny that the focal points represent a change, and say this is the way they’ve always done things. Time will tell; if states change their standards and school districts start dropping Everyday Math, Investigations and other atrocities and start adopting Singapore Math, or Saxon Math, we’ll know something happened.
Meanwhile, here in ed school, all is well. Our instructor, Mr. NCTM, assured us the focal points were just a clarification, and that nothing was different. Then we set about watching some videos of teachers using the discovery method in class. One video showed a teacher engaging her students in an activity in order to teach them about slopes. I tell you, these kids were busy. She had them measuring the volumes of two mystery liquids, weighing them, filling out a chart with the values, computing the ratios of mass to volume, and all the time, she asked questions. They plotted the ratios of mass to volume of liquids and obtained two slopes, checked their results with a graphing calculator, and she questioned them about what the graphs told them about the liquids. Luckily we saw that video on two occasions, because the first time I lost track of what these kids were supposed to be doing. I almost lost track the second time, but it finally sunk in. “Oh, she’s teaching them how to interpret what the slope represents.” I came to the following conclusion about her technique: If I had had a class like that in school, I would have grown up hating math.
Another video showed a teacher with his students standing around a table in the center of the room while he explained that day’s assignment. (We were to take note of the fact that this standing-around-the-table approach was very effective because it ensured that all students were attentive and no one was asleep at their desk. And, of course, you can do this if you have a class with only 12 students as was the case in this video.)
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. And when you see teachers like these who are very good at what they do, if you didn’t know any better you would try to emulate having students spend an entire class period bending pipe cleaners into parabolas and gluing them on poster boards.
After the videos we voiced our observations to the teacher. One woman said she thought the lab approach was a good way for students to absorb the lesson—more so than a lecture. “I disagree,” I said. “Good!” said Mr. NCTM in a disagreement-is-healthy tone of voice. 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.
With unending questions and colored pipe cleaners, I remain faithfully yours,
John Dewey
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» Pipe cleaners and parabolas from joannejacobs.com
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... [Read More]
Tracked on October 10, 2006 10:54 PM
Comments
I can understand why the "John Dewey" posting was send anonymously. An ugly distortion by someone without the guts to identify him/herself.
Posted by: Michael Paul Goldenberg | October 10, 2006 08:57 PM
Mr. Goldenberg -
Saying it's an ugly distortion without going into why it's a distortion reveals the real reason "John Dewey" does not identify himself. It also makes me suspect you have no good response to the points brought up. Is this the case, or would you care to enlighten us?
Posted by: Quincy | October 11, 2006 12:28 AM
To bad you don't realize that you're the type of person that makes anonymity necessary.
Posted by: allen | October 11, 2006 02:42 AM
I appreciate the use of the name "John Dewey" in the tagline because it sarcastically emphasizes how his ideas have been set up as a straw man for anything "constructive". Dewey never intended for unguided constructivism, and inquiry that doesn't guide a student to correct answers and then acknowledge the "discovery" is useless. Between the lines of this sarcasm is the truth of constructivism's success, that however it is achieved, a student hasn't learned until they associate new information within an existing framework of understanding.
Posted by: Brad Hoge | October 11, 2006 08:36 AM
"Between the lines of this sarcasm is the truth of constructivism's success, that however it is achieved, a student hasn't learned until they associate new information within an existing framework of understanding."
I find it hilarious that "constructivists" pretend that they have a monopoly on understanding. It's double funny since sound math instruction aims at undestanding on the one hand, and the "discovey" crowd denies students the foundation for undestanding on the other hand.
Posted by: instructivist | October 11, 2006 09:10 AM
What exactly is supposed to be horrible about the parabolas activity -- the fact they used pipe cleaners? The fact that no direct answers were given to students? The fact that they weren't seat-belted into a chair listening to a lecture on something they could just as easily do themselves?
"John Dewey" leaves out a crucial missing piece of information: Whether the students in the parabola activity actually learned, retained, and understood the material -- and how their understanding compares to that of students in a more traditional setting. This post is not arguing that a discovery learning approach works less well than a traditional approach. In fact it does not appear to *argue* at all, but rather paint the entire idea of constructivism with a single, broad stroke. Uncritical rejection of discovery learning is no better, and no different, than its uncritical acceptance which "Dewey" finds so abhorrent.
I've seen students struggle with the material in the parabola activity when they merely listen and read, and then finally "get it" once they do an activity, for example using Geometers Sketchpad, where the effects of changing the parameters in the formula are really visible. So perhaps I should write a post pseudonymously talking about how ridiculous lecturing is.
But instead, maybe it would be more accurate to say that lecturing and discovery learning are complementary approaches, tools to be used in certain circumstances and not used in other circumstances, like hammers and wrenches. We don't need to pick sides and fight it out.
Posted by: Robert | October 11, 2006 09:24 AM
I did not mean to suggest that the only alternative to the discovery style is pure lecture. That's not a dichotomy I believe in, and as the last commenter suggests, there is room for both discovery and lecture. I was taught in a traditional manner, but I would say that as traditional as it may have been, it contained many elements of the discovery method. Teachers did not merely stand up in front of the room and lecture, but asked many questions. The difference was that key information was transmitted directly, early in the lesson, and then such information was built upon in the form of problems that we were asked to solve, think about, or discuss. Ultimately we were put in the position of applying such information in new applications.
The video about slopes was a very confusing array of information similar to an excercise in the Connected Math Program, except that the data are provided in the book, rather than asking students to measure and weigh the liquids. In both cases, it is a convoluted approach to an application of y = mx + b, and I felt that the material could have been presented in a far more effective and efficient manner while still challenging the students to answer key questions.
I feel the same way about the parabola exercise. The teacher could have asked the same questions that they explored in groups without spending so much class time with poster boards and assessing of one another's work. He could have assigned problems in class or as homework that would allow the same amount of discovery, while ensuring that all students looked at all the constants of the equation and how they affected the shape, rather than having one group look at one particular set of constants with the hopes that everything would merge when they assessed one another's work.
It is true I do not have the data on how much that class retained compared to the traditional ones, but I have been observing classes in the local schools, which is part of our class work as well. I observed eighth grade classes in a school where the math department uses the algebra texts by Mary Dolciani from the mid-80's. The problems are challenging and much material is covered. The teachers asked many questions of the students and there was active discussion of problems presented at the board. While there was no group work that I observed, the school has a reputation of placing a large percentage of students in a prestigious magnet high school in the area. I believe there was a proper mix of discovery and lecture.
There are different degrees and methods of discovery learning or constructivism. I agree some of it is good. I also believe some of it is wretched.
Posted by: John Dewey | October 11, 2006 01:34 PM
