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.

Sunday, June 13, 2010

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.

Saturday, June 12, 2010

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

Wednesday, May 26, 2010

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.

  • 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
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.
  • 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.

    Sunday, May 23, 2010

    Book Review - Mathematicians by Mariana Cook

    Each mathematician, accomplished, perhaps famous, has a full page photograph and a facing page containing a brief autobiography or statement.  It can be read in a few hours.

    Brandon Fradd, a Princeton math major, thought a photo book of Mathematicians would be well-received after seeing Scientists by Mariana Cook.  Good idea.  Her photographs are striking in black and white.  Most of the people were from Princeton (not a big surprise), but individuals from Oxford, Cambridge, Harvard, and a few New York and California schools also made the list - 92 professors in total.

    Each reader/viewer will respond differently to the brief personal essays.  Timothy Gowers (I have two of his works.) tries to relate his methods to research strategies, the practical rationality of his words shows a cool balance of thought, but Harold Kuhn's reference to all of his teachers by name and the sacrifices made by his parents and the role of chance in meeting people was too easy in which to relate. I cried while reading about him.  Of course, Andrew Wiles was photographed.  His humility, considering that he proved Fermat's Last Theorem - his childhood dream, was considerable.  William Thurston's text may have been the most important.  He stressed the pain of everyday public school instruction in math for himself, but he didn't allow it to kill his imagination.  He related how internal vision and analysis worked together: paragraphs suggesting the joyful magic in doing mathematics.

    And yes, the correlation between mathematicians and the love of music is highly positively correlated.

    Thursday, May 13, 2010

    Two Year Algebra - Reboot

    Struggling students can succeed in Algebra and complete high school.

    • Organize a voluntary PLC of math teachers to pursue the pre-selected approach 
    • Consider looping for ninth-tenth grade.
    • Use a reform math text - dramatically different from the district's standard text
    • Grade Summative Assessments on a curve of highest eighth = A, offset quartiles = B,  C,  D.  If this is too drastic, then the PLC-advocated college grading scale of 75-100 is an A, 50-75 is a B, and 25-50 is a C may be appropriate.
    • Bottom eighth can earn a grade or pass by teachers's judgment or completion of alternative work such as ALEKS or StudyIsland or Algebra games like Dimension X/U or re-exam; even if semester has ended.
    • Bottom eighth cannot be determined until final for student motivation
    • Course starts with Assessment: Students scoring low that ALEKS Algebra Prep for Six Weeks
    • "Homework" completed in class as PRACTICE - careful attention paid to technique
    • Calculators used for most problems (some no calculator to mimic CST)
    • Supplements such as online formative assessment and/or Gizmos and/or Wolfram|Alpha or Akron.
    • Cultivate student growth mindset by using Brainology
    • Experiment with DimensionU online math video game.
    Possible Texts
    • Its About Time's Math Connections - not enough state standards may be an issue.
    • CPM - After 20 years, it now has state approval after changes - 1993 attack
    • Contract with Heymath! - other districts may have done this already.
    • Kinetic Books or NROC's new program, when available
    • Supplement current practice with a sequence of online manipulatives (eg Mathematica and Gizmos) coordinated with professional development and a PLC to determine sequence.
    Suggested Calculators
     Texts Review Status
    • More than one text can be selected depending on the number of teachers that volunteer and their interests.
    • CPM is used by 2-year Algebra programs where students alternate days of doing "homework" in class.  CPM claims that no supplementary materials are needed.  CPM, a non-profit, has an exceptionally low cost program:
      • August 2-6 - teacher training in Irvine at No Charge
      • Teacher text is $95 and each paperback, 3-hole punched, re-usable student text is $18
      • Classroom set of Algebra tiles is $97
      • 2" loose-leaf binder for text and notes: $1 in volume
    •  CPM has been used at Irvine's Northwood for six years.  In one-year classes, CST proficiency has increased from 30% to 80%.  In two-year classes, CST proficiency has increased from 6% to 24% and may be higher this year.  The main reason Irvine adopted CPM was to give their students a different look at Algebra from the standard texts.  CPM is also used by Northwood for Honors Geometry and Honors Algebra 2. I used CPM Geometry briefly at University High as a substitute.  The question quality was quite high.
    • Heymath! has asked us to proceed.  We would want to send them the Algebra AB pacing plan.  The Massachusetts and Connecticut experiences show this can be fruitful.
    • For Kinetic Books: To track student progress through the Algebra text and do online homework, you will want copies for the individual students. This would be the Class Set License, which is $49.95 per student.
    • Putting a Computer Lab License on some of the computers at school would allow them to do online homework while at school, but you wouldn’t be able to track their progress through the book itself.
    • Online homework is $10.00 per student. Given your situation, I’m not sure you would be doing that on a regular basis.
    • Given the above you have a few choices:
    1. If the Computer Lab License only, the students can use the text, but you don’t get any scoring information for them. 
    2. Use the Computer Lab License with online homework. With this you can track what the students do for homework that you assign. 
    3. Get Class Set Licenses for each of the students. This allows you to track their progress through the book and they can work at home. 
    4. The Class Set License plus online homework gives you the functionality tracking progress through the text as well as any homework you assign from the online homework system.

        Friday, May 7, 2010

        Why ALEKS Provides "the Best" Math Software

        Many different online programs for math instruction/assessment exist.  ALEKS stands out.  If teachers or administrators misunderstand its design, their choice of other programs will be arbitrary.  They will be merely victims of marketing, not arbiters of what's best for student learning.

        The internal research conducted by ALEKS on its software appears to be extensive.  Every topic network is constantly and automatically checked.  If less than 90% of students pass any topic, then the network to the question is re-verified.  In other words, after a decade of iteration, the learning progression in ALEKS is second-to-none.  However, to satisfy the various state standards, additional topics are introduced into standard curricula like Algebra 1 for coverage.  These additional standards add redundancy to the network at a price of increased time (more topics) to master a course.

        ALEKS uses time more efficiently than any other math program.  This is easy to show.  First, ALEKS uses constructed responses only, not multiple choice. Fewer correct answers are needed to show mastery; since multiple choice inherently requires more questions to cope with  false positives due to random guessing.  Second, the ALEKS web of topics and intentional time delay in verifying mastery drive efficiency.  No topic is offered until the student has a 90% chance of "passing it" due to completing a network of prerequisites.  Also, while usually only four correct answers are necessary to complete a topic, one more topic question is presented days or weeks later to verify mastery.  A wrong answer brings the topic back.  Third, its artificial intelligence engine further separates ALEKS from most other programs.  It appears to use the time-to-answer a sequence of questions correctly to determine how many questions are needed.  Sometimes a student only needs to answer two questions to complete a topic (Mastery verification is later.). In short, there is no faster method than ALEKS to develop procedural math mastery.

        As part of its interface design, ALEKS doesn't display information that the student doesn't need.  For example, neither the time on the question nor the menus of topics is displayed; although ALEKS does record time, when the student is working on a problem.  ALEKS wants students focused on the question without distraction.  There is research behind this decision. Additionally, ALEKS chose to use Java extensions to provide online protractors, rulers, etc to produce its online manipulatives.  This standard software can either be automatically retrieved (www.aleks.com/plugin) or installed.  Most other companies use Flash for interactions.  These work well, but are losing their position of being an Internet standard.  In addition, ALEKS uses natural display of answers and allows for variations in the answer of questions.  These features relax students and minimize their frustration - not a small issue.

        The last two paragraphs covered Assessment & Interface Design. of the six main aspects of online math software.

        ALEKS receives the most criticism on its Instructional Design.  In general, the criticisms are ill-considered. First, instruction is offered only when students request it.  There are no hints, and students know that they will have to do more work, if they ask for instruction.  This motivates students to try to solve problems first and, if unsuccessful, to pay close attention to solutions because they don't want to learn more than once.  Second, the instruction is simply text with graphics, no videos. While unappealing initially, they fit how most students actually do math.  For example, few students read math textbooks.  They attempt problems, then look for examples on how to do them as quickly as possible. ALEKS's instructions quickly suffice.  From another perspective, video with sound appears wonderful, but it can distract and requires computers with headphones. ALEKS works quickly and quietly even in dial-up environments.  More importantly, videos frequently waste time.  Students just look at them in a daze. The low density of information in a video is rarely worth the time to most students.  One exception exists.  Buzzmath has annotated videos, which allows students to skip sections they don't want to see so that they can go to what they want quickly.  ALEKS could offer such a service as an upgrade. 

        Intermixed with Assessment Design is Database Design.  ALEKS satisfies the main math problem criterion:  whether through randomization or question quantity, the number of questions per topic is far more than what can be shared between students.  In short, cheating by having shared question/answer lists is squelched by ALEKS and several other programs.  Another subtle feature is the speed of the database when reports are being generated.  ALEKS is so fast, that the browser refresh rate appears slower.  Other programs, such as APEX, have slow to generate reports. From a teacher usage perspective, fast reports are critical.

        The bars and circle charts in ALEKS's reports are easy to understand.  Many have hyperlinks to other reports which greatly saves time.  The only program with better reports may be Daskala, which is limited to simple sequences of multiple choice questions.  ALEKS reporting could be improved by an all student-class report. This is a small issue, but teachers who have students spread between many classes, have to remember what class a student is in to find the student's status.  It would be valuable to have a list report of students and their classes with hyperlinks to the student's report.

        The one area in which ALEKS can improve, or at least freshen, is account management.  ALEKS works with active licenses, which is the best method, but ALEKS lacks ease in both enrolling students and also in identifying unenrolled users.  The information is there, but it is tedious to use.  On the other hand, unlike many other active license software vendors, it doesn't lose data on previous students. A simple list with fields would resolve the enrollment issue.

        The great issue with ALEKS is that it intentionally rejects rich problems - problems that require strong student insight and drawing from multiple sources to find solutions.  This is contentious.  Research by ALEKS probably shows what I see in the classroom: many, perhaps the majority, of independent students simply stall out when confronted with problems that stretch them too much.  This is sad, but it may just indicate that the desire for math software to do everything - no classroom needed - is a false dream, not research-based.  The 90% rule really means a great deal to ALEKS's programmers.  Mastery of procedural skills is the goal. The subtleties of applications are left to classroom instruction.

        A superb product with richer problems is Carnegie Tutor, CT.  Since questions are rich, each question has many objectives built into it.  When student cannot solve a problem, the instructional help to get through it; including the teacher, requires considerable time, and is inherently different for each student!  CT does have underlying artificial intelligence, but it is results are still linear.  If a student is stuck, they must stop.  This is a prescription for failure in many computer environments, but CT offers  appealing instruction. Another program with rich questions is StudyIsland. Good students are attracted to it. If a student struggles, StudyIsland, like ALEKS, allows students to work on other topics.  In short, students stay working - the great benefit of student choice.  StudyIsland even incorporates some simple AI to give students easier questions in a topic, if the grade level questions are causing failure.  This appears wise, but the ALEKS approach of moving the student through a network of topics, not a flow of topics within the same top-level topic shows far more sophistication in improving the transferable skills of each student.

        The more problems that students complete as practice, not experience, each hour, the better!  In my observations, only SmartMath and IXL, have higher problem completion rates, with SmartMath having more concentrated practice, but these are K-6 programs!  Student choice - for whatever reason, like fatigue or boredom - should be allowed.  It keeps students working.  Also, in years of ALEKS and SmartMath usage, not one question mistake has been found by me.  APEX is riddled with errors, iPass has problems, and StudyIsland has a software link to report mistakes, to which StudyIsland responds promptly.  IXL only has a few errors.  This issue is missed in software evaluations.  Maintaining confidence in the software is an important issue in the value of the software.

        In summary, ALEKS does its jobs exceptionally well on three of six categories: Assessment, Interface, and Database.  On the two categories Account Management and Reports, ALEKS is very good.  Yet, strangely, in Instructional Design, ALEKS is either the best or inadequate, depending on a reviewer's knowledge and/or desires.  ALEKS Corporation has decided to focus its software on what they believe works best in software, from a research basis.  Others want a full, rich instructional system which is a desirable goal.  This may be an example of the best being the enemy of the better.  More may be desired in instructional capabilities and in rich problems, but it is not clear whether or not this is valid with more than a few students.  ALEKS thinks not; and ALEKS could easily deliver additional features.  In the years I've used ALEKS, the company has grown from 20 to 120 employees.  More importantly, ALEKS retains its earnings and pours it into development.  It is not a cash cow. ALEKS provides the fastest pathway to procedural fluency.  Asking software to do more may be unwise or self-delusional.

        Lastly, pricing matters.  It's easy to forget that software providers are businesses that pay not only for programmers, but also for salespeople, customer service representatives, clerks, brochures, trade shows, etc.  Years ago, in a private conversation with an ALEKS executive, I was told that to go below $42 average per user would kill R&D over time.  Obviously, large school districts could bargain for a better price and home users, with their many customer service interactions, would have to pay more, but to maintain the average was vital. I never forget this when purchasing other software at 5 -10$ per user, which I frequently do.  These programs may not be able to keep improving without venture investments, and programs that cost over $100 per year - many do - may not maintain steady users.  ALEKS's pricing allows sustainability and improvement year after year.


        Dennis Ashendorf has extensively used the following:
        • ALEKS
        • APEX
        • iPass
        • IXL
        • RevolutionPrep
        • SmartMath
        • XLPrep
        Dennis Ashendorf has lightly used
        • Carnegie Tutor
        • STMath

        Sunday, May 2, 2010

        Threats to Public Education

        The attached chart serves as a starting point for discussing the locus of school criticisms.  While not exhaustive; it nonetheless covers the motivations and subsequent grounds for attacks.

        APEX Learning Workshop Report - Pomona - 28 April 2010

        From other users:
        • Add senior summer school with real summer grad ceremony (major life event)
        • Two week CAHSEE prep @ 2 hours per day yields great improvement in test skills
        • Develop student flow chart to keep students on track
        • Due dates must be added for email coach reports
        • APEX must allow different color code triggers (future component)
        • Individual school sites and teachers must be allowed to modify rules
        • Print out math appendix for student use
        • Use gaggle.net for student email
        • Alt Ed students don't progress unless pushed continuously
        • Apex can be used within a Blackboard environment for essays
        • Locke (a Green Dot school) uses APEX 8-12 & 1-5 daily
        • Since APEX courses are grade level, one school uses NWEA 8th grade to qualify English
        • One school moved all study sheets onto online question progra.
        • APEX changed software for one school so that all inactive licenses after 30 days were archived
        • Study is available during Quizzes
        • Use Student Session report
        July 1st is the new release date - what's included has not been released to Sales
        CAHSEE diagnostic allegedly works well.
        APEX suggests "Literacy Advantage" for EL's
        AP courses can be offered to small classes using online AP APEX instructors

        Thursday, April 29, 2010

        Calculators @ NCTM

        Graphing Calculators

        TI MathForward is a solid way to use graphing calculators in block schedules.  Also, the latest revision to TI-84 software allows pretty print display.  All TI-84's should be upgraded.

        The TI NSpire has been upgraded.  Each teacher can send only one to TI to be swapped with a new one by Dec 31, 2010.  IMHO, the nine (ten) or more NSpires at Estancia should be sent to TI, one at a time, with a different teachers name; so that the whole small set can be upgraded.  Other schools should act similarly.

        HP doesn't make new calculators anymore.  The division was sold off to a reseller.

        Low Cost Classroom Sets

        The Sharp EL-W535 ($10) and EL-W516 ($13) deliver the natural display features of the Casio fx-300ES (HP 300s) and Casio fx-115ES, respectively at lower prices with, most importantly, faster input/output of fractions.  However, initially the Casio is chosen by students because it's display is the most natural.  After showing the faster Sharp output, they switch.  The Casio fx-300ES does have a list feature, that the EL-535 doesn't and it's battery may last longer because of a solar panel for power.  With the list feature, the W516 can serve a student from Middle School through Statistics.  TI's two line calculators aren't as fast or useful sadly.

        Only AP Calc and AP Stats require facility with a graphing calculator.

        In short, the Sharp W535 would serve well for class sets in middle school.  In high school, the 516 would work.  These calculators can be used in a variety of STEM classes, where students would/could understand how to use them.  Letting everyone use different calculators is similar, but not as big a problem, as letting everyone use a different text.  The current standard practice of anything goes with calculators is and has been incorrect.

        Tuesday, April 27, 2010

        Primary Curriculum Advances @ NCTM

        The three major vendors and the many NSF spinoffs displayed their wares.  For example, the ThinkMath! program seemed relatively balanced between reform and traditional approaches.  Also, it uses the number line as its unifying theme - just as the Mind Research Institute does with its Algebra Readiness.  It should be noted that several vendors stated 'the math wars were over long ago; except in California.  Remember, Everyday Math is the largest selling curriculum in the county.'

        A full, rich curriculum from Korea has personalization for problem sets/homework.  After a teacher enters formative assessment data into the software, a customized worksheet is printed for each student.  Students can progress at their own speed.  Numino is an elaborate curriculum in English that should be examined; although the website is 99% in Korean.

        However, Singapore Math had the strongest attendance both at its booth and presentations. Furthermore, other Asian countries, particularly South Korea, displayed approaches that varied with conventional (Reform or Traditional) US approaches.  Certainly, the emphasis on mental math (common in Europe also) versus the algorithmic approach of US instruction is the most important difference between the cultures.

        In brief, Singapore Math blends Number Sense, Word Problem Models, and Mental Math.  These areas may be separated to form either an extensive intervention or an American spin.  For example, Math With Meaning offers small Word Model texts that can be used for daily instruction for each grade level 1-6.  Also, Jongsoo Bae has developed a very rigorous yearly program for mental math.  Interestingly, Jongsoo Bae has also developed an exceptional program for home workbooks which trigger video instructions with the voice pen.  Combining the products of both vendors with the current prevalence of manipulatives and math software would generate a strong curriculum that would rival Singapore Math and be more accessible to parents.

        While the 1995 curriculum has been approved for California, the 2002 revised curriculum has not.  While some claim that the newer curriculum hasn't shown success in TIMSS; it is now available from a major US publisher (Harcourt's Great Source imprint): Math in Focus.  It now includes "non-Singapore" aspects; such as reteaching.

        For more info on Singapore Math:  www.singaporemath.com, www.marshallcavendishonline.com, www.singaporemathtraining.com, and www.the-pi-project.com.  Professor Ban-Har Yeap, a Singapore leader, spoke three times at NCTM.

        Singapore Math people often make fun of elaborate US manipulatives.  For example, the beautiful Digi-blocks system is compared with beans glued to popsicle sticks poorly.  IMHO Digi-blocks are beautiful things.  They cover 0.01 through 1000 and truly do make magnitudes interesting also.

        Game vendors were present.  Arithmo provided newsprint puzzles that reinforce operational and number sense skills and FoxMind's sequence of 3D games stood out.

        Secondary Curriculum Advances @ NCTM

        While elementary school math remains in a quiet turmoil; approaches to high school curriculum are fairly stable.

        "Research-based" Curriculum

        The Collegeboard has fully released it's pre-AP English/Math curriculum named Springboard.  This is researched-based in a different way.  It tries to embed not just the math knowledge, but also the communication knowledge that colleges expect students to have.  By the time a student starts AP, he or she may not have enough time to develop appropriate academic skills for college.  Springboard appears to be considered a hard curriculum that allows a greater chance of college success.  It starts in sixth grade and offers either Algebra 1 or "Middle School 3" in eighth grade.

        IMHO, Springboard should be carefully examined.  Even if there would remain the need to continue using the current texts for students who cannot keep up even with interventions.  The effort to use just one text for math courses, while making "Williams" easier, is misguided from an instructional perspective.  One size does not fit all.  ACT provides a test-based approach to rigorous content called QualityCore that covers more areas and works with current texts.

        Furthermore, the Kucera Sequence for eighth graders passing Geometry should be strongly considered:
        • Accelerated Algebra 2 + Trig in ninth grade
        • AP Stats in tenth
        • Accelerated Pre-Calc, followed by Calculus A in eleventh
        • Calculus BC in twelfth.
        Algebra Readiness

        UCLA has split its coherent Introduction to Algebra program into packets called Math Links.  This helps schools, who don't teach the course for the full year, focus on specific needs in short times.

        Its-About-Time offers Aim for Algebra which competes with the coherent Introduction to Algebra.  I thought it was better, but the teacher delivery quality to students matters far more.

        The Mind Research Institute now offers the software for its Blueprint for Algebra separately.  The complete Blueprint program takes about 1 1/2 years to complete - not good.  It's possible that the software alone may help enough as a supplement to an eighth grade math course.

        High School Preparation for Algebra 1 is a unique ALEKS program.  ALEKS suggests that after an assessment at the start of Algebra 1, students who score of 7% or less should be pulled into this program for 6 weeks approximately, 1 hour per day to catch up.  This is very rapid.

        10th Grade CAHSEE Prep Approaches

        Since CAHSEE results strongly affect 10th grade API, it would be wise to offer a deliberate, year-long, not short term preparation approach.  Revolution Prep offers a solution online for Math and English; in addition to its Algebra Readiness software.  This software could be combined with a tenth grade Business Math course.


        Texas A&M has an online Statistics program for Teachers to prepare them for AP. Best if visiting A&M.

        The second edition of Statistics through Applications is now available.

        Monday, April 26, 2010

        Four Year Math + Financial Algebra @ NCTM

        Several states have four year math requirements.  While California only requires two, the first three years of math applies to the API and the fourth year is needed for smooth transfer to college.  In short, four years of math are needed by students from a school viewpoint.

        In four-year states, a subtle issue is whether or not passing is required in the fourth year!  Also, standards-based math courses are expected. Jokes about arithmetic/formula-based Business Math for students having completed Geometry/Algebra 2 are frequently made.  As an alternative, a soon-to-be a-g approved Financial Algebra course (Textbook is available for review) has Algebra 1, Geometry, and Algebra 2 problems.  It would work well as a junior course in support of Summative Math.

        While many pathways exist, sensible high school pathways would breakdown into the following (yes, my understanding of Business Math is appropriately different than Harbor/Mesa):
        • Algebra ABCD - Done or advise student to take Geometry, then Algebra
        • Algebra CD or Algebra 1/Business Math - Done
        • Algebra CD or Algebra 1/Geometry => Algebra 2, then PreCalc/Stats(AP)/Financial Algebra
        • Geometry/Algebra 2 => PreCalc/AP Calc or Financial Algebra/Statistics(AP)

        Sunday, April 25, 2010

        Statistics @ NCTM

        AP Statistics 2009 results and rubrics were reviewed and the new lead reader introduced.

        AP Stats is now the 8th most popular AP test with an 8% increase after three years of double digit growth.

        The main concern in grading to students is that they must be very "communicative" in their answers.  For example: if a question says that the "the following values are drawn from a normal distribution," then answers to the question must state that the probability calculated was based on a normal distribution, not just the numeric answer.  Otherwise, zip.

        Lee Kucera of Capo High mentioned that her school has four sections of AP Stats for tenth graders!  120 students that complete Algebra 1 in 7th grade, Geometry in 8th grade, Accelerated Algebra 2 + Trig in 9th grade, AP Stats in tenth, Accelerated Pre-Calc, followed by Calculus A in eleventh, and Calculus BC in twelfth.

        Interpret Capo's approach.  Stats is needed more than Calc, but "we" expect top students to take Calc; therefore Capo does both!

        Monday, April 19, 2010

        TEDxNYED - Dan Meyer - 03/06/10

        Starts out conventionally, but when he gives a real problem, the strength of his approach (Reform Math!) lays the groundwork for people to learn Traditional Math.

        Saturday, March 13, 2010

        The Road to Success

        The TED video of the Director of Disney's Imagineering indirectly relates to Education.  It takes off after the "Candle Problem" is played out.  This is a must see video that WILL CHANGE YOUR LIFE

        IMHO the dumbing down of education is actually the realignment of topics for simple grading systems. It may be that the increased use of multiple-choice tests drives away the type of problems that really matter.  Furthermore, the debates about group work and, perhaps, the Math Wars, were and are distorted by inappropriate, simply false, evaluation methods.

        Wednesday, March 10, 2010

        EL's Must Pass Math

        Slide show runs at seven seconds per slide

        Comments on Slides

        2.  Arne Duncan has repeatedly stated that the achievement gap and access are civil rights issues.  This will open up school districts to civil rights suits, which will hurt and cost.  Yes, it will happen, and there will be a lot less money for teaching.

        3.  Professor Dweck of Stanford stresses that people who think "Smartness" is just genetic, don't work hard for several simple reasons.  She stresses that intelligence is developed and that "learn, learn, learn" can be a normal way for students to think also.  This effort to defeat the "internal" squelcher, may also help defeat the "external" squelcher of peer pressure.  IMHO this is far more important to get students to understand than ALL other activities.  The professor's research is exceptionally strong.

        4.  Really knowing the vocabulary to pass math tests (not just math vocabulary) must be explicitly taught in context.  This is not about posters.  This is about seeking "multiplication tables" level of knowledge.  Pressing forward with SDAIE strategies in math must be reinforced.

        5.  The reasonable goal of 9th grade Algebra doesn't make it mandatory for ill-prepared students.  Delaying Algebra with different elective math courses until they are ready is wise and doesn't punish them with F's (zero credits) or pointless D's.  Naming the courses Math Topics or Algebra Support or General Math helps.  The course codes are already present.  These courses are really all the same:  support Algebra Readiness.

        A district could use "grant" money to support special groups, outside or inside of RandR, to entice teachers in this area to use alternative methods and to press for results.  This would serve as a model PLC for both school and district and justifies the use of "special" money.

        Of course, the state direction must be satisfied with all deliberate effort.  There is no reason that bonuses to 7th/8th grade math teachers couldn't be offered for making students Algebra Ready or Algebra Readiness Ready. Teachers could bid for these positions; which would give Management some flexibility.  A 9th grade bonus for Algebra Ready for 10th grade may also be wise.  

        6.   Adjusting courses and course titles so that students always earn credit in math would be wise.  Failing Algebra 1A may allow Algebra A credit or Algebra Support Credit or General Math.  If each math area had one shared computer, for online math; then this adjustment could be handled with minimal scheduling support.

        Grading can be done as completion of work and quizzes or Final Test.  It may be best to offer Incompletes; instead of F's.  Students can use Credit Recovery to earn a grade.  Failure is not an option.

        7.  There are many aspects to motivating students.  First, tell them that they can be done with math in 10th grade.  It's OK.  If they are succeeding, they will stay, and getting them to care about finishing Algebra in 9th or 10th is a big deal.  It may motivate them to master Algebra Readiness.  Second, tell them that they can "graduate" after 10th grade if they pass the CHSPE which requires Algebra.  It's OK. Very, very few will leave school, if they are succeeding.

        Monday, March 1, 2010

        A Very Short Introduction to Math (Review)

        Professor Timothy Gowers starts with the need for models and ends with the usefulness and necessity of estimation.  The body of the book gives the flavor, the value and the connectedness of Proofs, the calm resolutions of infinity and the impact of changes in dimension and Geometry.

        No.  Not a problem-based course.  Not a history lesson.  No sexy examples.  Little mention of the titans.  Yet the point of doing math, its constraints and pathways, would strike anyone who reads the book.  Whether high school students would get it.  I'm not sure.  The maturity in the words and the totality of the immersion within its few pages is sublime.  In knowing that exact answers are rarely found, but knowing the boundaries of the answers and their closeness to actual mimics our own lives.

        This would be a must read in a non-ADHD world.

        Gowers also wrote the Princeton book on Math.  The professor is a Fields medal winner.

        Monday, February 22, 2010

        The Black Hole War

        Leonard Susskind's book is not just a popularization: it's a chronicle of discovery and of the people involved.  It echos Watson's Double Helix with Hawking playing the role of Pauling, but it's far more fair, yet unsettling.  Scientists stand on the shoulders of previous great scientists, and it's clear that Susskind and the many other scientists he describes stand on the shoulders of Hawking, but also they have surpassed him, and they know it.  At times, it is like reading words of physicists who arrived after Einstein like Heisenberg, Dirac, ..., in real time.  These are greats who in many ways moved passed Einstein.  Susskind and friends are the greats who have moved passed Hawking.  If only for this reason, this book allows the reader to be a fly on the wall of science history, and it's fun the read.

        But it is much more.

        My knowledge of nuclear physics, while not deep, is not trivial.  In the 1970's I worked in the Stanford Physics department and was well aware of the whys and hows of the linear accelerator and PEP.  Now, I might as well be a worthless witch doctor at Johns Hopkins.

        Be ready to be dazzled.  Alice in Wonderland doesn't come close to the reality of the Holographic Principle - yes, Virginia, you're a hologram.  The wild woollies of string theory or the math of strings (spinning elementary particles) amazes and Susskind makes it fairly clear without any equations.  Smart guy holding the endowed Felix Block chair of Physics at Stanford.  He is no lightweight.  He does briefly state one or two objections to this "Plank Area" world. Basically, string theory has not been proven - it simply works better than anything else.  More subtly, it hasn't been shown to be unique.  Another mathematical approach may be more "true."  Even more importantly, the emphasis on dualism between elementary particles and protons/neutrons etc is questionable.  Physicists believe in dualism; perhaps too much.

        Consider that recently the Poincare Conjecture was proven - so 19th century!  The proof required dealing with scale, getting close to a surface requires different math than being far away.  Physicists don't seem to know this issue may actually apply to them in subtle ways that their hubris may preclude.  And that's the rub.  All talk, no experiments, but for good reason:  to test out their theories would a take a linear accelerator the size of the milky way.  Oh yeah, one of the ideas of really modern physics is that small things are heavier than big things.  When this starts making sense, you become self-aware of your sanity: alt world is the world.

        In short, Susskind delivers an accessible tour de force of science today from the view of giants.  If you're serious about knowing how the world really works, not in the simple political sense, read this.

        Monday, February 1, 2010

        Defense of Newsweek's Challenge Index

        Criticism of Newsweek's Challenge Index is misplaced and misdirected. This is due to the limited background of critics who show no knowledge of a valuable analog: evolutionary theory.  Consider two of stronger critics of Jay Mathew's work: Sara Mead and Andrew Rotherham.  They succinctly write:

        "A successful high school should show high levels of student achievement, graduate almost all of its students and not let any demographic subgroup suffer at the expense of others. Most national and local experts and policymakers share these values. To be sure, graduation rates and student achievement are hardly the only indicators of a school's quality. At a minimum, however, America's best high schools should be expected to meet these basic criteria. 

        "Yet our analysis shows that many schools on Newsweek's list do not meet these minimum standards."
        Mead's and Rotherham's words appear well-chosen and difficult with which to disagree, but they are actually irrelevant and misleading for the simple reason that education is an individual achievement. Bureaucratic measures are not only meaningless, but often distorting to individual students. The efforts in education are simply those of multiple single individuals seeking the necessary trade-offs and efficiencies in teaching the many; and there are many types of many.  Education is hard, but education is not policy.  Forcing education to fit policy is a fool's game. There are many fools. 
        In 1966, simple Darwinism, which holds that evolution functions primarily at the level of the individual organism, was threatened by opposing concepts such as group selection, a popular idea stating that evolution acts to select entire species rather than individuals. George Williams's famous argument in favor of the Darwinists delivered the decisive response to those in opposing camps. His Adaptation and Natural Selection, now a classic of science literature, is a thorough and convincing essay in defense of Darwinism; its suggestions for developing effective principles for dealing with the evolution debate and its relevance to many fields outside biology ensure the timelessness of this critical work.  Almost all Ed wonks ignore this.  For example, they think that subgroup success and small "achievement gaps" on tests matter.  Well it does for them and it sounds compassionate, but what does it matter to an individual student?  Is it realistic to think that someone picks the a school because it has a small achievement gap, without asking "how much achievement or why does that matter to me?"  Do Hispanic parents chose a school for their children because the Native-American subgroup did OK, without asking "what's OK or what does that matter to me?"  Saying "meeting proficiency in state standards" truly begs many questions.  People want a safe school with solid academics to maximize the chances of their children becoming successful.  Everything else, outside of athletic considerations, is silly fluff for irrelevant-to-learning, but not to concerned bureaucrats in the education business.  This can be nasty sounding.  For example, a school with a high dropout rate isn't really an issue to successful students.  It may actually be a plus: get rid of low-performing riffraff.  This is what sport teams on campuses know also.
        The Challenge Index simply and effectively helps parents and students pick schools from their perspectiveOther measures may have some utility for education bureaucrats, but not for families.  Bureaucratic measures shouldn't be mentioned in public because they lead to confusion like those from advocates of social group selection in the early 1960's.

        Friday, January 1, 2010

        Games Played by Len Fisher

        The subtitle of the book is a variation on its "real" title: Game Theory in the Everyday Life of Len Fisher. While pleasant, and somewhat helpful as an introduction, a better book is struggling to get out.

        Rock, Paper, Scissors is best read by reading the chapters in reverse order. Fisher really wants to write about trust and how to gain it, by realizing that game theory not only describes situations (the seven dilemmas identified by Nash equilibriums), but also identifies methods for breakthroughs. Various problems in everyday life (mainly Fisher's!) and some business/political ones can be identified, then addressed. This is good stuff. Knowing the Ultimatum and Centipede games provide value.

        A reader upon completion will most likely believe that while the book was worth the time and effort, a better book should be available with more interesting examples, that would have been MORE worth the time and effort. It's as if Fisher "mailed" it in. He couldn't have spent more than a few weeks (if that long) writing it. It's merely a money-maker that doesn't show great depth of knowledge or effort by the writer, but it is understandable.