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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.
Wednesday, March 10, 2010
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.
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.
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 perspective! Other 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.
"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 perspective! Other 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.
Saturday, January 16, 2010
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.
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.
Tuesday, December 22, 2009
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.
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.
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