Comparing public and private high schools

Whenever I am with parents of middle school children, one of the topics that invariably dominates the discussion is about the choice of high school and which one is better and why. Although the actual selection often gets determined by where one lives, there is some amount of decision making involved as people do plan their home purchases or rentals based on choice of available schools. Sometimes the choice is between sending the child to a private school at a considerable annual expense, versus going to the home school, with zero or minimal tuition fee.

Admittedly, the notion of a good school is a very subjective one. Some people look at the campus, the courses offered, proximity to home, opinion of their friends, reputation for good or bad things and other such considerations. However, for majority, goodness simply means emphasis on academic excellence. But how to quantify this in an objective and reliable manner?

California schools are annually evaluated and assigned a performance index called Academic Performance Index or API, which is supposed to be an indicator of academic excellence, among other things. The chart below shows the Growth API of 5 different public high schools for last 3 years, 2010, 2009 and 2008. Two of the schools, Wilcox High and Santa Clara High, are in Santa Clara Unified School District, my home school district. Two high schools, Monta Vista High and Mission High, are other bay area high schools known for academic excellence. I also included Gretchen Whitney High, the school with highest API score in California, for comparison purposes.


This does give a fairly good idea of relative academic performance of these schools making it somewhat easy to compare them. But what about private schools? How do you compare a private school with another private school or even a public school?

Turns out that there is another metric that can be used for comparison purposes: Combined Average SAT scores, ie; the average of the sum of critical reading, math and writing scores of all the students who took SAT. These scores for public schools, along with API and other academic metrics, can be found at California Department of Education DataQuest website. I wasn't able to find an equivalent database for private schools but most do publish their scores for the latest available year at their websites and this is how I was able to get the scores for Archbishop Mitty, St. Francis, Bellarmine, Notre Dame and Harker, five well known private high schools in the area where I live.

Llet us look at the average SAT scores of these schools:


What this shows is a ranking of both public and private high schools based on average SAT scores. Not surprisingly, the ranking of public schools based on average SAT score is not much different from the one based on API. However, what did surprise me is that the good public schools compare quite favorably with private schools.

A key difference between the API and the average SAT score is that the former is based on performance of all the students whereas the later is based on scores of only those who take the SAT test. This percentage can vary widely. For example, only 45% students of Santa Clara High took SAT in 2008-9 whereas this percentage for Gretchen Whitney was 100%. This is true in general -- low performing schools have lower percentage of students taking the SAT. As only academically inclined students are likely to take SAT, it can be argued that the low performing schools will have even lower average SAT score if all the students took the test.

At this point, a natural question to ask would be: how well the API correlate with the average SAT score? Let us look at a chart that plots both these metrics on the same chart for all the five public schools. Note that I have adjusted the intervals for API (left vertical axis) and Average SAT Score (right vertical axis) a bit to compensate for different ranges.


Not surprisingly, the correlation seems to be pretty high, validating our choice of Average SAT score as a predictor of academics and also a metric to use for comparison purposes.

I should add that the choice of schools in this post is somewhat arbitrary, and though meaningful to me, is likely to be completely meaningless for your purposes. In that sense the actual ranking is not as useful as the general idea of using average SAT score to rank a collection of private and public schools.

Other thing to keep in mind that an academic ranking can only be just one input to your selection process. Only you can decide what other aspects, such as sports, extra-curricular activities, tuition fee, proximity to residence, friends, special facilities etc. are important to you.

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: $x^2$