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.

Thank You - DonorsChoose - Robots

The following thank you also outlines how a DonorsChoose grant can morph.

Dear Lisa, Michael, Joel, Vicki, Duane, Terry, Christine, Arnie, Maria, Mike, Kristian, George, Shelly, Sy and anonymous donors,

Finding the right level of robotics with programming for continuation students poses challenges. Without your support, the sweet spot wouldn't have been found. Furthermore, your commitment help makes our robot curriculum transferable to conventional schools which may enhance their students's destinations such as First Robotics or VEX. In the future, this effort may lead to summer internships in university labs; where masters of Python, Labview, Matlab, and JMP/Minitab software are in demand.

It would have been easy to start with LEGO Mindstorm robots which use a simplified Labview language. Our continuation students are familiar with LEGO's, but that's about it. None have assembled models or wired electronics. Our school's solar panel installation program would benefit from students who know the difference between open and closed circuits. Parallax Sumobots and BOE-bots provide the needed mechanical and electrical background at low cost. These robots have built-in breadboards that force students to install LED's and speakers, for example.

The tradeoff is that their BASIC software doesn't employ graphics, just text. Students would have to start by puzzling over code, which was an open question before the DonorsChoose grant was submitted. To mitigate this concern, a cardboard robot and several plastic analog robots, OWI Sumobots, "programmed" with variable resistors, were included in the grant. The cardboard robot died a quick death and the analog robots were inconsistent. Students didn't learn much. However the Parallax robots were simple to build and actually easy-to-program: students merely copied other programs and tweaked them to see how robots would respond to modified software. Fun and learning resulted. Showing off robot battles and robot travels impressed friends and teachers.

In the future, two or four students per math lab (3-5 per day) will work on a robotics/software/wiring curriculum. They will start with MIT's Scratch and Microsoft's Small Basic. Next they will work with MIT's Picocricket and inexpensive Parallax microcontroller breadboards. Finally, they will program and fight with the Parallax robots. As an option, they can either venture into greater depth with sensors on the Arrick Arobot platform or move into VEX robots.

None of this would have been possible without your help. You encouraged a few students today and many more at the start of next year. If you have questions, please contact me. Thank you for assisting DonorsChoose in its efforts to assist teachers directly. You made a difference.

With gratitude,
Mr. A

Math Software @ NCTM

Math software needs to be placed in perspective. One size does not fit all. Various objectives, including cost, must be considered. Please refer to this diagram for areas of concern.  At NCTM, several programs were on display. Comments on them and others follow. Text in Bold means that I will attempt to vet the products in 2010-2011.

Please realize that there are many free supplements.  Making them work cohesively with a curriculum, not just as an occasional time-filler, is the challenge.  It may be wiser to use Heymath, which is designed for teaching. On the other hand, through Lesson Study, combining Wolfram Demonstrations, Gizmos, Wolfram Alpha, VirtualNerd, Brightstorm, Autograph, and Geogebra with an online assessment system; such as Daskala, could yield remarkable results.

General Purpose
Check out thinklinkr! Create and share outlines online.

Elementary

• ST Math: K-5 had large crowds.  However, it should be noted that neither ALEKS nor Johns Hopkins nor Ascend offer software for K-2.
• ThinkFun Education has many math games.
• First in Math for K-8.
• Thinkport is developing math games.
• I Play Math Games has games for k-12 under an unusual format.
• Johns Hopkins has furthered development of CTY Online for gifted students.
• Guaranteach offers 20,000 video lessons and assessment for K-12 at $15/student.
• KendallHunt offers online lessons for K-5: Aha!Math and for the gifted as Project M3.
• Math-Whizz sells online tutoring with lessons for 5-13 year-olds.
• Tadell sells online assessments in Spanish without text for English Learners in K-8.

Secondary Free Usage

• Wolfram Mathematica Demonstrations
• Wolfram Alpha
• ConceptuaMath has extensive interactives for fractions in the effort to instill number sense for Algebra as the NMAP suggested.
• WebMathTutor is a free middle school supplemental program based on Carnegie Tutor.
• Brightstorm offers 1800 free online videos for Algebra 1 through Calculus.
• Absorb offers numerous free online manipulatives.
• VirtualNerd has a basic library of free math videos and a premium, but low cost, extensive library. 
• MathTV offers online presentations from more than one teacher.
• Annenberg Media continues to offer the 20-year-old videos Algebra: In Simplest Terms and Inside Statistics series for instruction, which complements the non-profit's many professional development courses.
• STEMCollaborative has several free online games for middle school. They complement other thinkport games such as Labyrinth.

Secondary Paid Usage

• ST Math: Secondary Intervention is the software component of Mind Research's Algebra Readiness program
• RevolutionK12 offers integrated programs of detailed instruction with assessment for Algebra Readiness, Algebra 1, CAHSEE, and SAT/ACT. Newport-Mesa has used this for CAHSEE and some SAT prep.
• CatchupMath, from Hotmath, is an integrated online program with assessment for Algebra only.  It has an extremely low cost.  It could be considered an homework component for classes without mandatory homework.
• Adaptive Math offers a strong, coherent online curriculum. 
• InternetMath offers an integrated instruction system for K-8 math with random numbers in problems.
• DimensionM continues to advertise online math video games.  These should be evaluated.
• Buzzword created the most buzz at NCTM. It had a strong focus on Middle School math, and is highly compatible with how teachers and students work.  It must be evaluated in 2010-2011.  While not quite as good as ALEKS.  It has more instructional support.
• Tutor.com offers online, at home tutoring for students.
• Autograph 3.3 graphing software is designed for education: animations can run in slow mode so that students can see change better.
• AscendEDU offers online courses through Algebra 1 (116 lessons) that can work in a classroom.
• ThinkWell offers Algebra through College Algebra courses.

Programming

• Small Basic is a great starting point for 5th grade+.
• Depending on the STEM robotics program chosen, variations of Basic and C are learned.
• Python is the language of science that would enable students to work in laboratories.
• Mathematica and Matlab focus easier on mathematics than Python and are reasonably priced.
• Statistics doesn't have a standard.  Free R isn't appropriate for high school, but low cost Minitab (Windows only) and JMP are and they can be transferred to college lab environments.
• 3DVinci offers 3D geometric shapes to enhance Google Sketchup for Math.  The Pro version of Sketchup can be purchased at Ed sites for $50.