MATHCOUNTS Stats

Got the stats on MATHCOUNTS Chapter competition participation and score from Chapter co-coordinator today. This may not make much sense to those unfamiliar with the the MATHCOUNTS competitions, so let me give a backgrounder and summaries some of the results.

MATHCOUNTS coaches hold school competitions to select 4 winners to participate in chapter competitions. These winners make a team and represent the school in chapter competition. Chapters send winning teams to state level and the states send their winning teams to national competition. The actual number of teams selected at each level depends on the size of the school, chapter or the sate.

The school where I coach is part of the Silicon Valley Chapter.

Coming back to stats:

• The number of boys participating in Silicon Valley Chapter (my school's chapter) is more than twice the number of boys and this ratio has been fairly constant over the years. National level report stopped reporting this ratio after 2007.
• Average scores of Silicon Valley Chapter is way better than the average national score for Sprint Target and Team rounds. This is also consistent over the years.
• The ratio of sixth graders participating in the contest is much more in the Silicon Valley Chapter than at the national level.

None of these are surprising, but still seeing the actual numbers is kind of a revelation.

Waiting For Superman

Watched the Waiting For Superman Netflix CD yesterday -- well made documentary with lots of stats and cogent arguments on current state of public schools in US. Much more convincing than the rival, and somewhat antithetical Race To Nowhere.

Waiting for Superman makes following points:

• The current state of public schools is not good -- decades of increased spending per student (inflation adjusted) hasn't caused average scores to move up in any significant way. A large number of public schools are failing in their basic job of preparing students for college.
• The primary reason for this state is the current structure of the school system and the teachers union. There are no systemic incentives for teachers to improve themselves or work harder.
• The causal relationship between rich neighborhoods and better performing schools is overrated. Some of the charter schools have demonstrated consistently good results in poor neighborhoods.
• The single most important factor in quality of education is the quality of teachers.
• Longer school hours (or more time with academics) improves results.

Of course, this is just a few of the points I recall from an hour and half documentary.

A Matter of Parenting Style

Why Chinese Mothers Are Superior, a WSJ excerpt from Yale Law Professor Amy Chua's new book Battle Hymn of the Tiger Mom, has generated a heated online discussion on various forms of parenting style. Most comments, at WSJ Comments tab for the article and elsewhere, are very critical of the stereotypical Chinese parenting style for its strictness and single mindedness in pursuit of excellence. However, after reading a review of the book, it seems to me that the book itself is much more nuanced and and is more about the author's personal experience of raising two daughters and learning what works and what doesn't along the way. The same is evident from her responses to readers questions where she doesn't come out as the hated mom one would imagine by just reading the title or even the whole excerpt. I believe she isn't really trying to justify or promote the style described in the excerpt but just telling the story of how she was. Perhaps later parts of the book talk about what worked and what didn't.

Stereotypical Chinese style of parenting, as defined in the article, by the way, is not without its merits, especially when practiced within limits and coupled with genuine love and understanding. Of course, not everyone is going to agree with this. But one thing is clear -- emotions run strong among believers and non-believers. The positive-negative online comments on the excerpt and the 50-50 split between 5 and 1 starred Amazon reviews indicate as much.

Leaving aside the controversy and apparent clash with western values and parenting style, I think this discussion does bring the idea of parenting and its relationship with education to a society much obsessed with its education system alone. Parents play a very critical role in development of their children, either directly by approving or disapproving specific behavior or by being a role model and creating a learning environment at home. This is equally, if not more, important in raising children who are going to better prepared to face the world and compete with the best.

Updated on Jan. 18, 2011: The WSJ published another article last Saturday titled In Defense of the Guilty, Ambivalent, Preoccupied Western Mom by Ms. Ayelet Waldman, reflecting the intense interest generated by Amy Chua's book excerpt, and talking about a more relaxed and carefree parenting style. Ms. Waldman is author of book Bad Mother: A Chronicle of Maternal Crimes, Minor Calamities, and Occasional Moments of Grace. I think most parents, even the Indian and Chinese ones, are more like Ms. Waldman than Ms. Chua, but could easily wear a different hat. In fact, here is the excerpt that I liked most from Ms. Waldman's article:

Roaring like a tiger turns some children into pianists who debut at Carnegie Hall but only crushes others. Coddling gives some the excuse to fail and others the chance to succeed. Amy Chua and I both understand that our job as mothers is to be the type of tigress that each of our different cubs needs.

My Thoughts on "Race To Nowhere"

Last Thursday I got the opportunity to watch Race To Nowhere, a documentary on increasing level of academic pressure and stress in American schools made by producer Vicki Abeles, a lawyer and a mother of three school going children. The screening followed a question answer session with a panel consisting of the producer herself and a few other advisors. The main points made in the documentary have been summarized, praised and critiqued in many excellent online reviews, including one at NY Times, another one at The Huffington Post, a level headed post by a blogger that I particularly liked and a CNN news report, so I would limit this post to my own thoughts.

As I listened to the narratives, the main thought going around in my head was not one of complete agreement or of violent disagreement with the points made, but one of "whatever is true is also not true" about a topic as complex as education in the large and diverse body of students, teachers, parents, schools and policy makers. Yes, some students get burdened with more work and higher expectations than is healthy for them but is that true for all or even a majority of students, at all or even a majority of schools, in all or a even a majority of households? The documentary itself does not include any statistics or scientific research in this area, and relies mostly on individual testimony by parents, students and educators. I have two daughters, one in elementary schools and one in middle school, have known many parents with school going children and interact with a class of middle schoolers on a regular basis, but have never heard anyone complain about burnout or stress due to academic pressure.

There is no denying that we live in a society where success and achievement means a lot, perhaps much more than inner happiness. But that is the world we live in. Thankfully, we also live in a world where individuals can decide what they want from life and make choices accordingly. No one compels a parent to expect his or her child to get A+ in all subjects, do 3+ hours of sports practice, participate in innumerable after-school clubs and, on top, to do social work while completely ignore play, socializing with friends, experimentation and entertainment. In fact, this was the main takeaway for me: there are a lot of things to do out there but it is up to the students and parents to decide what areas and how much effort is appropriate for them.

Commentary on "Understanding Divisibility"

Divisibility, the property of an integer being a multiple of another integer, and many other related concepts such as primality, Greatest Common Divisor (GCD), Least Common Multiple (LCM) etc. are central to the learning of Number Sense and form the basis for working with fractions and many other higher level math topics. The notion of divisibility and related operations are usually introduced in elementary schools over a number of years, but are rarely presented as a collection of related ideas. Also, they tend to skip certain kind of reasoning in favor of rote memorization. For example, kids might learn that if the sum of digits of a number is divisible by 3 then the number is also divisible by 3, but may not know why this rule works.

Advanced math texts focus more on formal and structured treatment full of lemmas, theorems and formal proofs under the general subject of Number Theory.

So I planned to start this year's MATHCOUNTS club with an overview of Divisibility. As there is rarely enough time in the class to go over all the topics in sufficient detail, I thought it will be good to point them to relevant stuff on the Web. However, my search drew blank. Wikipedia articles are good but too advanced and disjointed for an average middle school student. Relevant articles at other sites also didn't stand up to my expectations.

So I resolved to roll my own tutorial: Understanding Divisibility. It takes somewhat unconventional approach to introduce ideas and provide insight on mathematical reasoning by stating them in plain English and avoiding too much use of notations that may be a put-off for the younger crowd, such as modulo arithmetic for explaining rules of divisibility.

The current version at the time of this post is still rough at edges but I plan to polish it over time based on feedback here and discussion in the class.

MathTex Test Post

square of x: $x^2$

Unjustified Criticism of The Way Math is Taught

I have come across many unjust criticisms of US education system in general and the way math is taught in particular, but this one takes the prize: the author, who himself is a math teacher, criticizes a particular problem statement as being unrealistic, the solution to be artificial and the laments that the problem doesn't teach any problem solving skill.

It is not that I see no need to improve the US education system or the way math is taught. There are many valid criticisms and many more ways to improve the system. Carefully chosen and well worded problem statements are certainly one of them. But I found the acerbic reaction to this particular problem statement to be misguided. Let me explain myself.

Let us first take a look at the problem

A youth group with 26 members is going to the beach. There will also be 5 chaperones that will each drive a van or a car. Each van seats 7 persons, including the driver. Each car seats 5 persons, including the driver. How many vans and cars will be needed?

The problem can easily be solved by representing no. of cars and vans as two variables and writing equations satisfying the constraints as stated in the problem. However, the author feels that this particular problem is not worthy of being introduced to students for following reasons:

1. "One, is the problem realistic? Would a real person need to solve this problem?
2. "Two, is the solution realistic? Would a real person solve the problem using a system of two equations?
3. "Three, in what ways does this problem help our students become better problem solvers?"

The author does elaborate on each of the points and you should read the blog post to understand his point of view. What follows is my reaction to his points:

Is the problem realistic? My answer: yes, it is as realistic as it can get. The domain of the problem statement is certainly familiar to most students and they understand the role of chapreones as drivers, the difference between cars and vans and the need to optimally use the vehicles. A real life scenario may have additional constraints in some aspects such as the need to seat friends together, availability of specific types of vehicles only and less constraints in others such as no need to fill all vehicles to their full capacity. But simplification or idealization is routinely done in scientific or engineering problems and I see no reason why it shouldn't be done in a math problem.

Is the solution realistic? Well, given the simplicity of the numbers involved, a student might be able to solve the problem by simple trial and error and I'll accept that as a valid solution. In fact, that is what I would expect from a 3rd or 4th grader. A system of equations with two variables is certainly a more generalized solution and very realistic for the problem. Historically, the system of linear equations arose in the field of transportation as a way to optimize routes and this particular problem and solution are good substitute for the more generic problem.

In what ways does this problem help our students become better problem solvers? First, students learn how to convert a real life scenario to a system of equations. Based on my own experience working with middle school children I can say that this in itself is no mean feat. Second, they are able to relate the answers back to a real life solution. If the teacher encourages alternative solutions, such as the one using trial and error or the one using a single variable, then the students also get a better understanding of the system of equations. Much better than just solving a long list of equations without relating to any situation, real or unreal.

Yes, we can come up with more real problem scenarios from different fields of Science, Engineering, Operations Research or Accounting but will the students find that more palatable? I doubt. Saying that most people don't face situations requiring solution of a system of equations and hence should not be included in curriculum misses the point about teaching maths.