Sunday, February 6, 2011

Book Review - The Death and Life of the Great American School System - Ravitch

Diane Ravitch, Bill Gate’s number one enemy in his words, doesn’t stoop to blogger-style comments. She is an educational historian! Her critique of education reformers and their emphasis on tests may not rise to Susan Sontage levels, but it is devastating nonetheless.  My review that follows tries to supplement her kind words

Perhaps it’s best to read The Death and Life of the Great American School System in reverse order.  The last chapter stresses what can be done to improve our schools in ways that are achievable and positive.

The penultimate chapter discusses the non-criticized roles of Gates, Broad, and Walton family (Wal-mart). These foundations have contributed to almost all “elite” ed institutions: dissent has been minimized.
Dr. Ravitch doesn’t discuss particular silencings, but my favorite group, Core Knowledge, which pressures for improved curriculum has become very quiet over test, test, test. The organization merely presses for more integrated content from curriculum to test.  Again, she doesn’t stoop to my levels of writing things like why don’t they preach what they practiced: Gates went to a wonderful, liberal high school that allowed him time to work on projects, why does he stress accountability now.  He’s like G. Canada of the Harlem Charter School who brags about reading constantly while growing up, but now presses for accountability.

The third to the last chapter focuses on the limitations of testing. No legitimate organization and no country has adopted testing of students as the way to target teachers. Yet we say that we are research-based.  Of course, here Dr. Ravitch agrees, but she still pulls back. She shreds the VAT people, because they also advocate for no licensing, no advanced education etc of teachers because it doesn’t correlate to higher test scores.  Dr. Ravitch doesn’t state the obvious conclusion: If VAT results don’t correlate to anything, then they are worthless.  The key fact that Dr. Ravitch leaves out is that TIMSS scores correlate with the number of demographic questions answered.  This implies, or I infer, that test results are a cultural issue, not a teaching issue!  The only strange omission in her text is that the unreliability of VAT results is due to “regression to the mean.” She left out that well-know term.

The funniest chapter is the one on “choice.” Who can be against choice? She points out that Schools of Choice were the standard to keep white schools white after 1954 in the South. Choice means segregation. Of course, it will mean the same thing now, but it will be seen differently.  Of high importance is that even schools that try to be random in student selection are not in practice. Low achievers are dismissed.  This can be seen in my school district Newport-Mesa. Early College High School is meant to have 100 students per class. Only 34 graduated! The other students returned to different schools. The good news was that the test scores of this school were equal to those of a high-SES school for everyone. Are congratulations in order?

In other words, Dr. Ravitch presents evidence quietly and the reader brings the heat to this work.  This is clear in that she doesn’t argue, as I would, that all of the attacks on public education are to reap its cash in privatization. This is obvious to me because Gates, Broad, and company refuse to put any money into Catholic schools; even though they have excellent track records in educating poor students. They are in decline because of subsidized competition from charters, which most of whom deliver weak results.

This is the book to read if you value the value of local community schools, see the value in local democracy, and worry about the unchecked power of reformers.  If you just think the market should decide things, while ignoring the impact of regulations and foundation money on the market, don’t bother.

Tuesday, December 28, 2010

Math Games & Competitions @ NCTM 2010

While the focus at NCTM is on policy and instruction, the vendors displayed some interesting items.

Board/Box Games
Math Competitions
Math Compatible Alternatives

The American Contract Bridge League provides a Youth4Bridge afterschool program.  Bridge, chess and go are the three most difficult to play games.  They take focus and practice.  While a bridge club may not succeed by itself, a game club where all three available may be. The club could also offer simpler logic games, both table and construction, such as the Games listed above.

Saturday, December 4, 2010

Book Review - Innumeracy - Paulos

Innumeracy, at a mere 135 pages, jumps in with easy math play. Paulos didn't want a mathematical Cultural Literacy with lists, but an immersion in what being math literate means in attitude and application. Clearly, he sees mental math as fun and the prerequisite to mastering what's necessary; since without some joy, there is little interest in learning enough math to protect one's mind from deception and to gain the tools necessary for interacting with the modern world.

Intermixed with play are quick comments on what should be taught such as Discrete Mathematics (not the conventional push for Calculus), and the very real need for Probability and its Applied Mathematics cousin, Statistics. Paulos, like others such as Mlodinow, realizes the danger in humans seeing patterns where there is only randomness. We need Statistics to detect error within ourselves; not just to detect errors in arguments by others. To put this differently, a mathematical mind isn't about tricks or computation, but how see, how to obtain the heuristics needed for problem solving or merely seeing problems where others have no vision.

Showing how math play leads to value, Paulos proposes models on what having numeracy can exhibit: for example, a logarithmic safety index for rating everyday risk, but he never says "model this." He treats the reader with respect.

Each chapter of the book (1988) presents an area where innumeracy leads to error in different aspects of modern life. This isn't a must read. Those who know, know. Those that don't, probably wouldn't pick it up - sadly.

Monday, August 16, 2010

Book Review - The Drunkard's Walk - Leonard Mlodinow

Another book trying to escape a book. Mlodinow desperately wants to push the theme: humans make errors because they are not only not wired to incorporate random outcomes in their analysis, but also are wired to impart patterns to outcomes that are actually random. The law of small numbers is an example of this. This is the double wammy that makes us dumber than rats in some behavioral studies. Unfortunately, the author barely comes close.  Instead, 80% of the book covers the history of probabilistic thinking through statistics through the mathematics of error which culminates into the useful math of statistical mechanics.

The stories and anecdotes, Dr. Mlodinow (who has collaborated twice with Hawking!) relates are wonderful and well-told. The progression is thoughtful and coherent and interesting. Yet, the text stops well short of the math of "decision analysis,"which makes the chit-chat on poor human thinking beneath many other authors from both breezy and mathematical perspectives.

The modern editorial decision to exclude even one mathematical expression from a book on mathematics or even an illustration limits the work. While the book might read well on a Kindle(tm), books on this topic should be on an iPad/web with hyperlinks. The irony of an exceptionally intelligent author writing about the limits of human action, using weak tools that he emasculates even further, doesn't bring a smile to my face.

While this review sounds negative, it should be noted that The Drunkard's Walk is better than the average pop science/math book.  Learning about Cardano's development of outcomes in a sample space was inspiring and the restatement of the importance of Bayes, without putting him down, was uplifting. This helped counter the exasperation of reading about Bernoulli's golden theorem four times without being told what it was. De Moivre was mentioned and more could have been said of Polya's role in fully proving De Moivre's Central Limit Theorem, but 20th century math doesn't exist in the book!

In summary, Mlodinow's book joins other pop books in providing one very important value: it is a quick read that provides scaffolding for a reader, not to go further intentionally, but to allow advanced work a home in the brain later. For example, decades ago, if I had known of Riemann's great contribution to geometry, I would have realized in the years ahead why I was being taught particular items and they would have stuck better.

Friday, June 18, 2010

More Support for AP and Indirectly Newsweek's Rankings

Online cheating on graded school work is a real problem.  Sites like answers work very well for many assessments taken at home and at school.  Even math problems are solved online.  My more open students love to take an online class, they claim "[they] finish in a day, get an A.  What are friends for?"  With more and more students taking online courses, the irregularities in grading remain unresolved.

AP, IB, and Cambridge tests are proctored and are identical to all takers.  Their results have integrity, if not validity.  As a teacher who has offered courses from many online curriculum providers, I deeply know how believable an A or B is from an online course completed at home.  Zip.  It is what it is.

Taking an AP test is far, far better than taking an online assessment.  Newsweek and Jay Mathews have it right from the standpoint of a beneficiary of a school's rigor, which is what really matters.

Wolfram|Alpha and Online Math - A Wonderfully Unfortunate Fit

Wolfram|Alpha brings much of Mathematica to everyone.  It is a wonder of the 21st century, and it greatly helps doing math homework in Algebra, Algebra 2, Trig and more.  As a result, grades must be determined by classroom testing and work alone.  Online, distance learning in mathematics is more than compromised - it's obliterated, if grading with credit is an outcome.

Consider StudyIsland, one of the best online programs.  One student completed the entire course with an A in a matter of a few class periods by placing each question into WolframAlpha - every possible problem.  It takes far longer to type a problem such as Solve 3/(x+6) + 2/(x+1) = x/(x^2+7x+6) than to get the answer.  Copy the problem yourself, paste it into Wolfram|Alpha and see.  The plot is a bit funny, but the answer is clear.  Obviously, this would be grand for instruction, but not evaluation.

In short, teach online, but grade in class.  Perhaps regional centers for proctored exam taking with video cameras on students and their computer screens will be the next growth industry.