Living in a Post-National Math Panel World

Barry Garelick:

The British mathematician J. E. Littlewood once began a math class for freshmen with the following statement: “I’ve been giving this lecture to first-year classes for over twenty-five years. You’d think they would begin to understand it by now.”
People involved in the debate about how math is best taught in grades K-12, must feel a bit like Littlewood in front of yet another first year class. Every year as objectionable math programs are introduced into schools, parents are alarmed at what isn’t being taught. The new “first-year class” of parents is then indoctrinated into what has come to be known as the math wars as the veterans – mathematicians, frustrated teachers, experienced parents, and pundits – start the laborious process of explanation once more.
It was therefore a watershed event when the President’s National Mathematics Advisory Panel (NMP) held its final meeting on March 13, 2008 and voted unanimously to approve its report: Foundations for Success: The Final Report of the National Mathematics Advisory Panel.

National Math Panel.

3 thoughts on “Living in a Post-National Math Panel World”

  1. The DOE runs a monthly ed news program. This month’s topic was the math panel.
    On the show, you can see footage of Vern Williams, the (black) middle-school math teacher/math panel member mentioned by Barry Garelick, teaching algebra in a delightfully traditional manner. Mr. Williams appears on the show during one of the Q&A sessions. Questioned about his teaching, he relates how he likes to start the year by introducing Cantor set theory, exploring the different types of infinity. The kids get so excited and love arguing about the concepts. No doubt they are unaware that they are not enjoying an authentic mathematics experience. No, this math is quite abstract and woefully unconnected to the students’ real world experiences. And dollars to doughnuts he doesn’t spend the class time with kids in groups trying to figure out what the different types of infinity might be and then constructing the countable and uncountable types themselves either. So current ed-school dogma says it’s just not genuine, authentic mathematical learning. But what fun anyway. His reply to the host’s question about what professional development is available in his district was revealing. Unfortunately, he says, there is too much pedagogy and not much about content.
    In the article above, Barry quotes Steven Rasmussen, publisher of Key Curriculum Press, which publishes math textbooks as saying ”This report is biased in favor of teaching arithmetic and not [modern] mathematics…and it’s biased in favor of procedures and not applied skill.” MMSD parents should be aware that Key Press publishes the texts currently used in most MMSD algebra and geometry classes- Discovering Algebra and Discovering Geometry, which are heavily skewed towards discovery and applications, algebra and geometry lite, if you will. Key Press specializes in reform math, unlike other publishers who publish several lines of textbooks, both reform and traditional, easy and rigorous.
    A comment vis-à-vis the ‘math wars’- I’ve said this before, but it bears repeating, and repeating. Many of the news reports related to the panel report caricature traditional math proponents in the usual one-dimensional way. We are all simpletons who reduce math to tables of math facts, algorithms, and procedures and are oblivious to all else mathematical. Nonsense, baloney, rot. By all means, students should present solutions at the board for the class. Definitely real world applications are important. Of course people need to know multiple ways to calculate, estimate. Naturally people need to be flexible in their thinking. Yes, it’s important to understand why algorithms work. BUT, it is also important to understand and appreciate the math removed from its real world clothing in all its naked glory and be able to turn it to any abstract or real world problem where it may prove useful. It is, as the report concludes, very important to have memorized lots and lots of basic math facts. Students need to learn to discern the most efficient method to solve a problem in a given context and use that method. Sometimes this might be a standard algorithm or procedure, sometimes not. Traditional math proponents do in fact advocate for the balanced approach. It is easiest for people to think of these things in black-and-white, casting us as totally opposite the other side. But I don’t think there are many people promoting traditional math, at least among those who really understand math, who fit this common portrayal. There, now I feel better.

  2. No doubt they are unaware that they are not enjoying an authentic mathematics experience. No, this math is quite abstract and woefully unconnected to the students’ real world experiences.
    Actually, ed school types think of “inauthentic” math experiences to be things like factoring, solving equations, etc–the stuff you need to know to automaticity in order to achieve the higher order thinking. They would probably like what Vern is teaching, but as Celeste implies, they would criticize him for “telling” too much and not letting the kids “discover” it for themselves. Funny thing; the kids Vern teaches are gifted. So wouldn’t they get bored with the traditional method that Vern uses? Apparently not. Either the ed schools or Vern has it wrong, and it isn’t Vern.

  3. Here in Madison we have the ed school at UW and it’s WCER (Wisconsin Center for Education Research) which churns out large quantities of current edthink. They also partner with our local school district in many initiatives, so much of this thinking makes it’s way verbatim into MMSD (Madison Metro School District) documents.
    Here’s a link to one example of a WCER document about authentic pedagogy:
    This paper contains detailed definitions/standards of authentic pedagogy, instruction, and assessment. From the paper-
    Assessment Tasks-
    Standard 6: Problem Connected to the World: The task asks students to address a concept, problem, or issue that is similar to one that they have encountered, or are likely to encounter, in life beyond the classroom. Unfortunately, no example is given of this standard.
    Classroom Instruction-
    Standard 4: Connections to the World Beyond the Classroom: Students make connections between substantive knowledge and either public problems or personal experiences.
    Example for Standard 4,
    Connections to the World Beyond the Classroom
    In a 4th grade math class, students were to figure the costs of running a household on a monthly budget of $2,000. The teacher gave students a list of typical categories for expenses including rent, groceries, electricity and telephone service. Students were to determine actual costs by looking through a real estate guide for rent, choosing groceries from a local store’s price list, etc. They constructed budgets by examining the materials and discussing the possibilities with one another. There was evidence that students derived personal meaning from this lesson. For example, in looking at rental guides, two boys expressed surprise to find that some buildings did not allow pets. “How about the bus line?” one asked. “Bus line? We don’t need a bus line, we have cars,” said the other. In another group, a girl chose a cheaper apartment without a dishwasher because she did not mind doing dishes by hand. In a third group, two other girls, after deciding to rent a $740 apartment, changed their minds because they felt it was too expensive. This lesson scored high on “Connections to the World Beyond the Classroom.” Students had to look at real costs and make priority choices in creating their budgets. For instance, they could lower rent by finding cheaper apartments, sharing with more people, or giving up luxuries. The activities linked mathematical content to decisions that students would need to make in life beyond school.
    I remember my daughter had a group project like this in 4th grade Everyday Math. They had to spend $100,000 on a vacation. She didn’t learn any math, but she learned that for her chosen vacation, spending $100,000 was virtually impossible. We eventually were reduced to browsing the web to find expensive gems and artwork to bring back as souvenirs. It was very frustrating because the project required basically no math, except adding a column of multidigit numbers, but did entail extensive knowledge of accurate browsing methods, which were not taught as part of the project. And they spent a LOT of time on this.
    On the other hand, she had a couple of interesting projects in 5th grade (NOT Everyday Math, but something her resourceful teacher dug up.) They constructed their own clinometers and went outside and used them to deduce tree height. So they learned how math with angles and triangles describes our world and how you do something useful with it. And the kids got to stretch their legs and get some fresh air too, the value of which cannot be overestimated. They also did shadow measurements and used similar triangles to discover heights of tall objects. It was great.
    However, it was also time-consuming, and math instruction cannot be merely a string of these fun discovery projects if one is to make one’s way through the requisite math in 13 years. Sometimes you have to buckle down and spend time mastering methods and, well, doing just plain math.
    It may be that K-12 educators are misunderstanding what comes out of the ed schools and overemphasizing the real world aspect in math when that isn’t the intent. But that is what goes on. Not that I would devalue applications. They are important and math teaching needs to incorporate plenty of that. But it’s taken to such an extreme that the curricula now in use bend over backwards to have virtually every problem set in a real world context. This requires more and more contortions as you move up through higher grades. The books become extremely long and there isn’t time to do any problems with truly difficult mathematical content because so much time is spent in the real world minutiae. I mean, imagine how hard it is to get practice in integration techniques if every HW problem is phrased as a story problem that one has to wade through before one can set up the actual integration.
    The Math Panel addresses this issue. To make math books more concise and focused, they recommend removing photographs with attendant motivational stories and also eliminating problems where most of the work is social studies and science, not math. They hold up Singapore’s math books as examples of well-designed texts. There are story problems aplenty in Singapore’s texts, but also lots of math and no time-consuming projects that don’t teach much math. Will these recommendations influence MMSD Teaching and Learning? Dump CMP, maybe?

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