Book Review - A Certain Ambiguity

A Certain Ambiguity was disappointing and bordering on the trivial, sadly.  In 1919, a fictional, yet exceptional Indian mathematician, worthy of being invited to a US university after living in Great Britain, believes like a child, that Euclid wrote about truth, and of course, rigid Christians jailed him.  The only thing missing from the test is an angry mob at night with pitchforks ready for a lynching.  However, good leadership by the New Jersey governor saved the day.  Thank God for educated elites!

In 1919, Riemann, Poincare, were evidently not known to all expert mathematicians as the conceit of this book.  OK.   A few physicists still believed in the ether also.  To be fair, Riemann's 1854 lecture may not have been well known, but Poincare was pretty famous at the turn of the century.  By the time of the setting of this story, topology, not geometry, was the focus of study, because formalism was well understood as the refuge for mathematics.  See the fifth paragraph below.

Still, the first person narration by an intelligent Stanford grad student, who evidently didn't know anything about series from high school math, but is worthy of a full scholarship to graduate school in mathematics, was far more improbable.  Maybe he took Calculus in summer school after being accepted.

The conclusion that happiness and contentment are found by knowing that absolute certainty cannot be proven may be a mantra for some, maybe a majority, of intelligent people, but patting oneself on the back, which seems to be the point of the book, is fairly self-serving at the very least.  Cool people don't believe in truth, just games, evidently.

A more honest and useful book would have stressed that before Riemann, Western thought, buttressed by Kant, believed that "a priori synthetic" systems existed: that our mind by itself (a priori) could obtain real knowledge (synthetic) of the world.  Euclidean geometry was the prime example of this.  As a result, a proof of God, while not rigorously found, could reasonably exist.  The main counter to this belief was found in "personal idealism," which Bishop Berkeley, along with many, many others lectured.  At it's extreme, everything is in one's mind and it is difficult, if not impossible to truly know anything about the real world (if it even exists!).  This is very unsatisfying.  "A priori synthetic" was important psychologically to many people.  Other philosophies, such as positivism in 1919 in Great Britain, arose to try to bridge the gap with dubious success.

However, the authors, Suri and Bal, could have taken another, less well known, but perhaps, more valuable interpretation of Godel's work and resolved the issue better; although not as correct politically. Godel proved that every logical system would have at least one truthful statement that could not be proved by the axioms of the system.  In short, any system is not complete by axioms alone.  This is supposed to destroy full certainty of knowledge.  Maybe, but it provides one GREAT and AWESOME question: from where do the unprovable truthful statements arise?  They have to come from something outside of the system!  In other words, the real world isn't found in "a priori synthetic," but in "synthetic a priori!"  There is something out there so to speak.  What it is - is the unanswerable question!  God may exist, or at least a reality, for that is now certain! 

The greatest problems with the book are the two horrible math errors made by the authors that invalidate so much of what they wrote.  Most critically, curved space doesn’t invalidate Euclid at all.  Maybe Gauss initially thought so; but Riemann in 1854 showed that planar geometry was merely a special case of when a triangle had 180 degrees in space.  Other spaces had either less or more than 180 degree triangles (like those on a sphere).  There is NO CONTRADICTION of Geometry by validating Einstein, if anything, it increases Geometry’s validity.  Duh!  Second, and not critically, the fifth postulate is not evidence of a statement that’s true but unprovable after Godel as the authors claim.  This is obvious since more than one fifth postulate is possible, not just one.  Duh!

A Certain Ambiguity is novel on math written by poseurs without ambiguity - an embarrassment on many levels.

The Outliers - William Gladwell - Review

The Outliers was presented to teachers at Estancia High School.  It has lessons that apply to education from both student success and organizational perspectives.   While motivational and entertaining, it's problems are many.  It's reviews are spotty.  The New Republic spent several pages on it.  

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The Outliers delivers one incredibly strong lesson in its first chapter: beware of the effect of arbitrary decisions on people's lives.  Beware cut-off dates on ages for example.  This is admirably shown in William Gladwell's first chapter.  Hockey players in Canada are chosen on teams based on their talent, but also based on their age on January first.  Those born on December 31 are effectively one year younger than those born on January second.  Obviously many younger players won't be as adept as older ones, but so it goes.  This means it may be advantageous to have two start dates for Kindergarten in schools.

A second strong lesson of the book is that timing, out of one's control, matters.  People born in the middle 1830's in history were the most successful people in history.  Cute stuff, but not too usable.

The third lesson is somewhat unremarkable; although vital: social background and elite status matter in success.  Children of dedicated, usually wealthy, parents who are flexible in their own accomplishments do better than those from rigid, poor families.  Duh.

The point of the three lessons is that people don't succeed by themselves, but their location in time and place determines the limits on their success.    This point is told in very engaging ways by Gladwell.  It is worth the time to read his text, but there are some caveats.
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Isaac Chotiner's valid question (The New Republic, February 04, 2009) on why the chapter on airlines and culture was included in The Outliers can be answered with these three related points.

First, Mr. Gladwell did not want his book to justify racism. If wonderful family and social support is necessary for success, then a variation of William Shockley's argument that affirmative action is of no practical value to people doomed to failure would be true: why help a poor black student with a single parent, when he or she could never be a great success like Bill Gates or Bill Joy.

Second, the Korean chapter suggests that a few tweaks to culture can fix a problem and allow reasonable success.  Similarly, affirmative action for law students seems to work out OK, as long as IQ is above 120.  Please note that this is questionable research.

Third, Gladwell above can be seen as differentiating great success, ability combined with wonderful circumstances and timing, from "good enough" success, which society can support at certain intervals such as during schooling.

Unfortunately, Gladwell made three choices that undermine his likability and discernment.  He's simply not self-reflective in his editing.  Gladwell seems so full of himself and has simple politics.

First, his excessive demeaning of Langan was coarse, bordering on mean. Langan is such a buffoon that he doesn't know there is no "thumb right on you (p. 96)" at Harvard.  However, readers of TNR's article on Zeke, Rahm's brother, may have noticed his words "But it was Harvard that was most oppressive (The New Republic, July 1, 2009, p. 27)."  Maybe Langan, wasn't all that wrong.  Furthermore, Reed College and Montana State should have been slapped by Gladwell.  They failed disgustingly; almost inexcusably.  Instead, Gladwell blesses their bureaucratic ineptness and laziness in dealing with Langan, because liberal Reed doesn't have a rigid (i.e. bad) bureaucracy.  Reed, a small liberal college, simply let go one of its most promising students. As a student at Stanford, with parents having limitations, at the same time as Langan, I struggled to get my financial paperwork delivered months after it was due each year.  I was never shown the exit - I was given emergency loans to pull me through.  One of the 'red state' arguments against affirmative action is that it's affirmative only for preferred (i.e. liberal) people.  Langan's situation makes ones wonder: is social support reliable as policy to help all people succeed?

Second, the most beautiful chapter in the book concerned how Gladwell's mother didn't claim racist discrimination in England after realizing that she and her ancestors had enjoyed generations of success because of the light tone of their skin.  Sweet.  Her blessed son disparages an abused man Langan (who has overcome a great deal) in print and left a pointless sentence in his book "Kiddo, when you leave New York, every place is Bridgeport. (p. 138)"  Yes, Mr. Gladwell may be on the A-list of the chattering class and power clique at Harvard, but his framework is immature.

Third, Gladwell acts like a 'fellow traveller.' The chapter on KIPP read like a propaganda piece by Shaw when visiting Stalin in the 1930's, where his railroad car attendants had read his work!  Yeah, sure.  My high school junior read the chapter and asked "Is KIPP for stupid people?  They work so hard, but only 83% are proficient."  Gladwell may be smart, but you could sell him some swampland near Forrest Gump.

Ten Commandments for Teachers - George Polya

I. Be interested in your subject. II. Know your subject. III. Know about the ways of learning: the best way to learn anything is to discover it by yourself. IV. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place. V. Give them not only information, but "know-how," attitudes of mind, the habit of methodical work. VI. Let them learn guessing. VII. Let them learn proving. VIII. Look out for such features of the problem at hand as may be useful in solving the problems to come -- try to disclose the general pattern that lies behind the present concrete situation. IX. Do not give away your whole secret at once -- let the students guess before you tell it -- let them find out for themselves as much as feasible. X. Suggest it; do not force it down their throats.

PLC - Extensions to Education Central Office - Comparison to JiT Quality Circles

Prior Background

Starting in the early 1980's, US manufacturers implemented Just-in-Time (JiT) and Six Sigma data-driven strategies. One of methods employed was named Quality Circles. Professional Learning Communities, PLC's, can be considered variations of Quality Circles. Analogously to a Quality Circle, a PLC focuses a school on identifying problems and responding to (student) needs quickly by using data and teams. Furthermore, the twin overarching goals of JiT are reducing cost and increasing responsiveness by eliminating waste - waste of time, waste of effort, and the waste of resources and materials. In short, distractions and disruptions kill profit and responsiveness. The overarching goal for schools is student learning. All activities that detract from this goal are waste.

It should be realized that Quality Circles have a exceptionally high failure rate in business. They need a sustained level of support and guidance. PLC's are no different.

Lack of Real Support is a Reason for Failure

While most Quality Circles fail because the teams don't function well; others fail because they need real support, in the change of administrative functions, from superiors. Real Support can be unpleasant. Consider a manager getting a request from a Quality Circle: "Your policy is stupid... Do it this way... Now!" Consider pilots, graduates of military academies, listening to poorly educated soldiers: "you missed again" or "you just targeted us, you @#$@##@$@." Support means many things, including a change in methods by the boss. Letting Quality Circles die can be pleasant!

As long as PLC's don't ask the central or district office for bureaucratic change, PLC's can be very popular with central offices. This can be seen by the paucity of research and boilerplate statements on what district offices do in increasing student learning. District offices can easily forget that their role in increasing student learning must include eliminating their waste: waste of time, waste of money, and waste of focus on bureaucratic impulses.

Typical PLC-Generated Concerns for a District Office

• Instead of tracking cuts in attendance; track and act on absences; since an absence is an absence (lost time) to student learning.
• The same course number used for two different classes violates the most basic data organization rules. A year long class with the same course number where each semsester is graded independently confuses everyone in remedial course assignments, credit issuance, and transcript analysis.
• Combining district data-analysis software with mandatory test-design software may actually inhibit collecting local data. Integrated databases are a priority, but its the responses to the questions, that require analysis and tight integration. Flexibility in question design (not just multiple-choice) and the student front-end are separate concerns that are about ease-of-use. Neglecting these limits data collection.
• Separating a district SIS from an external grade book, when both are frequently integrated, is the denial of necessary database integration. The structure of PLC's and the routines of RTI coexist poorly with a whimsical district-centered approach to student data.
• Keeping outdated student software, such as six-year-old web browsers, as standard inhibits technology implementations. Stating that this is for security, when the district office uses newer software, creates distrust and signifies that PLC is merely a sideshow at the district level.
• Standardizing textbooks across the district for all skill levels and expecting differentiated instruction to compensate is actually a non-PLC focus. Standardization within a school or school zone takes priority. District driven standardization is a distraction from the main goal of student learning. Student learning for all does not mean the same modified teaching for all. The stereotypical assembly line became obsolete 50 years ago. It serves poorly as a metaphor for education today. Claiming that a court settlement forces this is not true and lessons respect for the district.

Literature

2008's Revisiting Professional Learning Communities at Work dedicates 40 of its 519 pages to the role of a district. Key points include:

• Remove competing programs and requirements.
• Do not leave school improvement to the schools alone.
• Install systems to ensure priorities are addressed in schools.
• Focus on improvement, not on rankings.

However, there is no mention of how the district should be manage itself. This lack of requiring self-reflection in organizations contradicts the need for continuous self-reflection in the schools and the teaching staff.

Conclusions

• It's important for district personnel to be seen as working intelligently toward the goal of student learning, not going through bureaucratic motions. This isn't just for PLC morale, but for enhanced student learning.
• From a PLC perspective, the units of interest are the individual child, the school, and for vertical articulation, the school zone. Surprisingly, other school zones in a district really are no different than school zones in other districts. Districts are legacy agencies, LEA's-only, in a world of state standards and state money.
  
• Districts need to be lean and mean. Delays in providing services, due to only internal district issues, are truly unacceptable. Any district usage of funds denies funds needed for student learning; unless spent carefully. Expending money on schools is the default.

Living By Chemistry - Key Curriculum Press - Ninth or Tenth Grade Chemistry for Everyone

Background

The University of California/Lawrence Hall of Science/NSF ESI-9730634 generated curriculum Living by Chemistry, with Dr. Angelica M. Stacey as the lead writer raises inquiry-based, high school Chemistry to an incredibly accessible level. It simply allows more students with different backgrounds time to practice being a scientist while learning standards. Obviously, it can be adopted as an alternative text at many schools, but its greatest impact could be felt by convincing many students to take Chemistry in ninth or tenth grade, and, possibly, reducing the number of dropouts.


ACT research clearly shows that taking Physics, Chemistry, and Biology in high school correlates well with graduating college. Leon Lederman has convincingly argued that a sequence beginning with Physics First works best. However, with Biology being the 10th grade NCLB test in California, a sequence of Chemistry - Biology could serve students and that state adequately. From an opportunity-cost standpoint, the current practice of ordinary students taking ninth grade Earth Science or Integrated Science does not correlate with college graduation. In effect, ninth grade non-core science requires that students complete four years of science. Yeah, that happens. Bluntly, students in non-core ninth or tenth grade courses do not graduate college from a statistical basis. However, the core science alternative is beset with problems; since many students have weak backgrounds that preclude success using conventional Chemistry texts. Living by Chemistry offers light, engaging paperbacks with numerous experiments to drive students into classes. It helps solves the rigor/engagement problem.

Goal

Keeping students in school with interesting academics and supporting teachers with easy-to-use materials are the purposes behind the Living in Chemistry curriculum. Typical students and science teachers can thrive on the small texts, detailed teacher guides, and exercise kits. More interestingly, practicing Chemistry is real and different from other courses. It gives students a flavor of real academic work. It's risk entices. More students in Chemistry may correlate with the holy grail of increased rigor concommitant with a higher graduation rate.

Implementation

Designate one teacher to offer one to two sections of Chemistry with ninth graders having priority. Make sure texts are approved for full year piloting or satisfy whatever rules are necessary. Try not to issue a new course number - Chemistry standards are Chemistry standards. The next Chemistry class to students would be AP Chemistry anyway.

Debug the course over the year. If successful, add additional sections as more teachers and classrooms become capable of teaching the course. In California, an Earth Science teacher has to pass on Chemistry CSET, but this isn't about eliminating Earth Science, but increasing the number of students taking the core science courses. Remember, ninth grade Biology was rendered obsolete with the advent of molecular Biology 50 years ago. It's time to change. The world has. Taking Chemistry before Biology enriches the curriculum for all.

Why Singapore Math

In 1983, Singapore ranked 17/26 in TIMSS.  Singapore then adopted a new national curriculum for all schools.  In 1995, Singapore ranked 1/41.  Singapore has remained in the top 1 or 2 since.  Hong Kong SAR is the main challenger with Finland close.

Singapore has recently adopted a heavily revised curriculum that is more focused on problem-solving.  The impact of the revision, particularly on calculation/number sense, isn't clear at this time. "Singapore Math" refers to the 1994 revision, with modifications for California.

Singapore Math can be seen as having these distinguishing features:

  1.  Going in depth on a few topics for mastery learning
  2.  Extreme emphasis on building Number Sense
  3.  A coherent, longitudinal approach in the use of modeling to solve word problems

Instruction follows a basic sequence of Concrete - Pictorial - Abstract - Mental Math. One hour per day with little homework is employed.

Mental Math means that students learn to add, subtract, multiply, and divide internally.  Flash cards are barely known as existing!  Calculators are unnecessary.  For example, 15 is seen as 10+5, which means that students may determine internally that 9+6 = 9+(1+5) = (9+1)+5 = 10+5 = 15 or 28-13 = (28+2)-(13+2) = (20+10)-(10+5) = (20-10)+(10-5) = 15. One way isn't mandated, but students must explain their process.  In short, place value and the use of tens are paramount to an extent that is unknown in the United States.  Abstract algorithms such as multiply and carry or long division are delayed for as long as feasible.

Developing models, as precursor for algebra, follow an orderly progression, by doing 1-3 daily word problems.

     K-1 Manipulatives
        2 Base 10 blocks
     3-4 dots/disks
     5-6 Rectangles         

Each word problem is solved following the same form:  Model - Equation(s) - Sentence answer - (scratch area).  Neatness and completeness matter in this MES system.

One implication of Singapore Math is to ask parents not to help!  Americans teach the wrong methods too early.
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The above words are edited notes of a presentation by Corrine Khoo-Lieu (Palo Alto) of the Pi Project on March 28 in Los Angeles.  Extensive demonstrations of activities were performed.  One of several small training consultancies on Singapore Math.  Richard Bisk (Massachusetts) is another highly sought after consultant.
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The SmartMath software, written in Hong Kong, used in the CRO, mimics much of Singapore Math. If a district wanted to implement Singapore Math, a rollout works best, but K2 can be done easily at one time. 3-4-5 could follow year by year or one year after K2.

Alternative Attendance Measure in Instruction

Reducing cuts is important. However, contacting parents or student for excuses after a student's return makes less sense now than in the past.

Before a PLC (Professional Learning Community) emphasis, teachers would issue zeros for missing work if students cut. The reward for bad behavior was no work, followed by more poor behavior because students quickly realize that zero's force them to fail in a standard 0-100 point system, which creates more hassle and costs for the school system as a whole and dropouts. Now, students must complete their work: attendance is irrelevant for grading, but vital for learning. More subtlely, the joy of being sick goes away to the student. This approach has been used successfully in summer school for years: excuses are irrelevant. The metric that matters is attendance, not the reason. The three-days-to-change-a-cut rule remains somewhat useful for awards, but no reminders to students and parents to clear a cut need or should be made. Getting students to school is the issue, not asking them or parents for an excuse when they arrive or afterwards.

Furthermore, sadly, there is a correlation between poor attendance and disruptive behavior. Since students can be transferred at no, or little charge, to a County ACCESS High School after four full days of cuts, it actually behooves schools and the majority of students within them to have absences marked as cuts. It gives schools more flexibility in dealing with, frankly, dangerous students.  Reminding returned students or requiring excuses before students return to school is self-defeating and wasteful of everyone's time. It's merely going through the motions of improving attendance.

In short, attendance is the only issue. Excuses are irrelevant. Higher attendance does not result by administratively pressuring ourselves to reduce the number of marked cuts. The enemy to learning isn't cuts, but excused absences! Working this number down would have positive effects.

Possible Metric

a. ID the number of First Period Absences in last semester as a baseline.
b. ID the number of Full Day Absences in last semester as a baseline.
c. Record the number of First Period Absences and Full Day Absences this semester.
d. An increase in First Period, but a decrease in Full Day means a real system improvement has occurred.
e. Decrease/Increase in all absences is the obvious main statistic.
f. Trend the two numbers above and single period skips.

When Multiple Choice Becomes Continuous Assessment with Positive Reinforcement

Multiple-Choice, MC, assessments inhibit long term learning. As a rule, they may work for summative assessment, but not formative. Furthermore, in mathematics, since guessing can yield correct answers, false positives usually cloud software responses. As a result, more MC problems are needed for students to solve in online classes, which usually decelerates learning. One of the secrets of better adaptive math software, such as ALEKS and Carnegie Tutor, is that they employ only a few constructed response questions. They allow a student to show mastery faster than most multiple-choice programs which struggle to compensate for false positives; especially since quick guessing is a common strategy with low achieving students. MC programs generate unexpected student responses because they are too ready to help.  XLPrep and possibly Study Island, are examples of MC software that may frustrate student learning because their response to errors or successes don't demand that each student needs to want instruction at that moment and struggle through it! While at first counterintuitive, pretty instruction is merely a time-killer for many low-achieving students. ALEKS and SmartMath offer simple explanations only after a student, somewhat reluctantly, asks for it, knowing that he or she, will have to read to understand. This may also be a problem with the constructed-response software iPass. It's detailed instruction is beautiful, but students eyes wander during the videos, because they are forced to watched.

However, multiple-choice software doesn't have to suffer from the conventional maladies. In particular, SmartMath from Encyclopedia Brittanica (USA) and Planetii (Hong Kong) demands students answer 30 MC questions in a row without error! Random guessing is automatic test failure, not just a missed question. Students can earn stars, actually limited insurance, to save themselves from immediate failure by doing many problems correctly during earlier practice sessions. Adapting to a rapid train of MC questions seems to turn the problem of inhibited long term learning on its head. Instead of letting distractors interfere with their learning, students quickly seek them out to discard them in the search for a correct answer. Distractors seemingly concentrate thinking, not dissipate it. Finally, the active decision-making on choosing to earn zero to six stars, which allow 30 out of 30 to 30 out of 36 (a missed question generates an equally difficult question) involves the students responsibly in their own learning. They have to decide when to take the test because earning six stars takes a long time. This engagement and active self-assessment is the secret behind SmartMath, which allows issues with multiple-choice to evaporate.

After using many different brands of software in classrooms using during semester trials over the last four years, two programs have worked well together for full class coverage: SmartMath and ALEKS. The results of a quick assessment place students into SmartMath or ALEKS. While SmartMath has a rapid mastery option, students can take a Billy Madison approach: they try to spend only 1-2 weeks per level (six levels total) and start at Level One, which is a tough first grade! With cute, spinning avatars jumping for joy with correct answers, students march through the curriculum feeling their way through the inherent difficulties. As a subtle extra motivator, stressing that SmartMath was originally developed in Hong Kong also raises the importance of each individual's success. Students realize that they are being evaluated from an international perspective. Success matters more.