Math Games & Competitions @ NCTM 2010

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


Board/Box Games

• Foxmind offers many shape/placement strategy games.  Of high interest for symmetry in action is the four game sequence:
• Equilibrio
• Tangramino
• Architecto
• Clicko
• Arithmo - paper-based
• Khet - laser-mirror table-top game
• ISeeCards - simple card games
• Delta Education - various math games
• Hexagonoes

Math Competitions

• MathCounts (Middle School)
• American Mathematics Competitions
• AMC 8 (14.5 years old and younger)
• AMC 10 (grades 9-10)
• AMC 12 (high school)
• American Regions Math League - also lists all national/state competitions
• Power Contest
• Local Competions
• Mathematical Olympiads (4-6 and 6-8)
• Mathathon - fundraiser for St. Jude Hospital (K-8)
• Pomona (high school)

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.

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.

Quick Clip - Online Education

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.

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.

Costa Mesa High School Ranks in Top 6% of US Schools

Costa Mesa has joined Corona del Mar and Newport Harbor in the top 6% of US high schools according to Newsweek's easy-to-understand 2010 list based on Summer 2009 data.  CdM ranks in the top 1% and Harbor ranks in the top 3%.

For reference, Irvine's exceptional University High School is included in the chart below.  The lower the score, the better.  Only 1,600 schools out of 27,000 made the cut.

Jay Mathews, an education reporter for the Washington Post and Newsweek, developed the structure of the data.  However, the Newport-Mesa Summary, source of the chart above, is solely the responsibility of Dennis Ashendorf.