Monthly Archives: October 2013

Nicholson Baker, Algebra II, Lurking Variables and Making Shakespeare Elective

calvinIn a recent article in Harper’s magazine, “Wrong Answer – The case against Algebra II”, author Nicholson Baker argues against having Algebra II as a required course in the high school math curriculum. He points out that when we force students to take such abstract and rarely used concepts as rational functions or Fourier analysis, we do nothing but produce thousands of students who not only hate algebra, but math in general.

Baker marshals an impressive array of witnesses, many of them mathematicians, who support the view that Algebra II should be an elective. Towards the end of his article, Baker writes: “Math-intensive education hasn’t done much for Russia, as it turns out.”  In other words, Russia is an example of an inverse correlation between math-intensive education and…what? Material benefits? Political freedom? Democracy? Let’s say the general well-being of the population.

I would argue that Baker’s statement is an example of a lurking variable.

Russia’s math prowess was originated from above, when Peter the Great modernized Russia by force. Since modernization implied a strong army, engineers were sought for armaments, fortifications and building a navy. Mathematics therefore became a prized skill/profession, one encouraged and compensated by the government. Mathematics thus became an avenue for an individual’s material progress, increased freedom and respect.

Peter’s tradition continued in Communist Russia, where engineers were needed for another round of forced industrialization, building an armaments industry, including a nuclear arsenal and a rocket force. (The hard sciences did not escape Stalinist purges, but in general mathematicians fared better under Stalin’s murderous repression than other professions).

Therefore, the “math-intensive education” variable in Russia was associated with government support, support that over the years morphed into respect for math in the general population.  If the explanatory variable is “math-intensive education” and the response variable is “the general well being of the population”, government directed activities are a lurking variable that affects both the explanatory and the response variables and hence the correlation. A certain type of actions, forced by the government through coercion or financial rewards, is the one variable that in Russia affected both the direction of the education and the well-being of the population.

The “command” style of Russian political life affected both an emphasis on math education and (negatively) the well being of the population.

Baker continues:  “But historical counterexamples don’t seem to interest the latest generation of crisis-mongers. We’ve once again gotten ourselves caught up in a strangely self-destructive statistical cold war with other high-achieving countries.”  Perhaps, but a recent report suggests that American workers are becoming less productive because they are falling behind in math skills when compared with workers from other countries. I quite agree that, as Baker mentions, carpenters and plumbers probably do not need Algebra II. However, I would venture to say that the executives who are the bosses of these carpenters and plumbers most likely have gone college and therefore through Algebra II in high school.

Baker’s solution is to “… create a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mind-stretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the infinitesimal, change-explaining powers of calculus. Throw in some scatter plots and data analysis, a touch of mathematical logic, and several representative topics in math history and math appreciation… Make it a required course…Then turn the rest of algebra, geometry, and trigonometry into elective courses, just as music and art and biology are. Pay math teachers better and — this is important — stop requiring Algebra II for admission to college.”

I have no quarrel with paying math teachers better. However, where is that line between required and elective? Shakespeare’s English is difficult to read (and sometimes understand) by today’s readers. Would Mr. Baker make Shakespeare elective?

Common Core (Geometry) – The Good, The Bad and The Ugly

GoodBadUgly3Common Core Geometry was sprung on us this year, without any kind of preparation. In addition, the State of California, in its politically-driven-wisdom (a great example of an oxymoron), is asking us to offer Geometry to all of our students who have finished Algebra 1 – even if they had “passed” it with a D. This is to create “opportunities for all”.

So how is Geometry faring in Common Core?

THE GOOD.  There is no doubt that Common Core envisions a superior Geometry course compared to what we teach now. The projects, the modeling and the writing components will require more critical thinking from the students.

In addition, the sample problems that I have seen from the two national testing consortia are better (i.e. they require more thinking) than what our current textbooks offer.  I have always believed that a math textbook can be judged by its sets of problems – by this criterion, Common Core Geometry does indeed promise to be a better course than the current one.

Common Core Geometry also wants to be more mathematically rigorous – for example it defines congruence as the result of a sequence of rigid motions that map one object identically into another. This approach also has the advantages that it helps students “see” motions in space and deals with constructions at the very beginning – certainly a good way to draw kids in.

THE BAD. I am not aware of any Geometry textbook that is truly “Common Core”. Most textbooks labeled as Common Core are old textbooks with perhaps very few modifications. Pearson’s and Glencoe’s Geometry textbooks are good examples of this “quick-to-the-market” (but not good) products.

It took about a month into the course before I hit upon engageNY’s Module 1 for geometry. To this date, as far as I am aware, it still is the only published coherent and complete material aligned to Common Core (Geometry).

And here is where the problems begin.

It is difficult and (at least temporarily) unproductive to ask students to explain the reasoning when nobody has asked them to explain their reasoning before.  It is difficult and (at least temporarily) unproductive to ask students to do investigations, when they have not been trained in investigations. So the first two major problems with Common Gore Geometry are lack of materials that form a complete, coherent course and the fact that teachers and students have been thrown in the “critical thinking” pool without any swimming lessons.

However, with time, these difficulties will likely be resolved. More disturbing to me is the fact that I have doubts about the rigor claimed by Common Core – Geometry. Certainly, requiring explanations of one’s reasoning process does strengthen students’ critical thinking skills. Certainly the problems that I have seen in engageNY’s module are a step (or may be two) above those in our current textbook. However, these problems are not on the level of Weeks and Adkins or Moise and Downs. Why can’t we go back to the level of rigor of 1960s American textbooks? Is it because now Geometry is taught to many more students than to the “elite” few of those times and therefore many of today’s students are not as well prepared?

Another problem I see is that, besides defining  congruence as the result of mapping through rigid motions, there are no other “math-pedagogy” new ideas in Common Core Geometry. In an article titled “Teaching Geometry According to the Common Core Standards”, Professor Hung-Hsi Wu (U.C. Berkeley), one of the originators of the Common Core curriculum, states that ”…once reflections, rotations, reflections, and dilations have contributed to the proofs of the standard triangle congruence and similarity criteria (SAS, SSS, etc.), the development of plane geometry can proceed in the usual way if one so desires.”

Kind of a letdown, if you ask me.

Therefore, despite an abrupt start and a lack of materials, Common Core appears to be a step in the right direction, but it does not reach the levels of academic rigor that we asked of our students in the 1960s. We seem to have tilted the balance away from solving truly challenging math problems towards communications and investigations. One wonders if this is such a good change of emphasis.

THE UGLY. Alexander the Great is quoted as saying that “An army of sheep led by a lion is better than an army of lions led by a sheep”. Well, Alexander need not lose any sleep – at our school we have an army of sheep led by sheep.  I have never seen so much confusion, mixed and often conflicting directives.  First, we were all told to march in step, teach the same thing at the same time and give the same exams. The only concession to Common Core was to move the chapter on transformations towards the beginning of the course. (No mention however of why we were doing transformations at the beginning of the course, before congruence). Then the teachers said it was not practical to march in lockstep and the department decided that each of us will follow our own pace provided we cover the same material by the midterm so we can give a common midterm exam. Then we decided not even to give the same midterm exams.

Admin has no idea of what to do with Common Core except to tell us that Common Core is the Promised Land and to pepper their dialogue with new buzz-words such as DOK-4 (depth of knowledge – level 4). They (the administrators) however, will not provide a map of how to get to this new mathematical Zion or the resources needed to get there.

Our teachers are not better. We are supposed to have weekly meetings to exchange ideas about how to “get to Common Core”. All I hear is a bunch of old women (they are in their late 20s and early 30s actually) moaning and groaning that there is no textbook, no resources and no training. This in the age of the Internet! They are truly more comfortable with the old ways then they are trying to teach in novel ways.

And so, once more I go my own way. I dig stuff up from the Web, maintain my own pace, give my own exams and pass only the kids that deserve it. C’est la vie.