Jim teaches mathematics, but not at community college level, so his background is university education. Studies below are more [...]]]> Because the book that I was reading in my last post mentioned stark differences between Japanese and American instruction. I decided to watch this talk given by Jim Stigler earlier this year, and took some notes:

Jim teaches mathematics, but not at community college level, so his background is university education. Studies below are more remedial level, outside his core experience.

1. Focus on cross-cultural work, and culture differences
   • K-12 TIMMS, study teaching, do video survey, 8th grade math class
   • random sample, get data on average teaching
   • teaching is a cultural activity. Huge differences across culture, small difference within culture. Very pervasive, and constraining. Even with autonomy, they choose to teach with same technique.
   • American teacher demonstrates how to solve problem, then students practice. Japanese present class with problem that students don’t know how to solve. Students are confused, challenged, agonized. Then students share approaches, and discuss.
     1. Teachers don’t goto teaching school, so they repeat how their own teachers did it.
     2. Culture diff: We think it is unfair to expect students to do something they haven’t been shown before. We are very, very uncomfortable to watch someone struggle or be challenged.
     3. Very hard to change cultural activity. Students/parents will go on strike. Have to break the ‘natural order of things’.
2. devolpmental mathematics
   • Japanese do better on international tests, because of their instruction. Not innate abilities.
   • But there is no one way, because other countries do very well too, but employ different techniques.
   • not even focus on ‘real-world’ problems increase understanding. Same with ‘group-work’.
   • Something else at issue: quality and enthusiasm. Techer creates effective learning environment regardless of teaching methodology.
   • Japanese teach area of triangle: give students sheets of many different kinds of triangles, no measurements or dotted-lines for height. Ask: come up with a way to get the area that will work for all of these triangles. Can cut, fold, rotate, etc.
   • No real pattern in these learning approaches. Amer teacher gets uncomfortable, and gives the formula away. Cultural change difficult.
   • In US. no teachers that presented a making connection problem followed through, always turned it into a procedure problem.
   • two features connected with higher performance
     1. struggle. have to actually work at it. desirable difficulties.
     2. making connections: explicit relationship between problem (real-world) and procudure (math concepts).
     1. fast, fun, exciting: think you understand, but bad when measured.
     2. hard, sticky, no fun: hate the experience, but good when measured.
   • Hong Kong has many procedure problems. So it’s not the quantity of making connections lessons that counts. Just need some.
   • We handle variability across schools: low-achieving students in different school than high-achieving. Japan, large school, variability occurs within classroom. Don’t track ability.
   • To measure all the angles in a pentagon, and notice you always get same answer, is not a struggle approach. Instead measure, 3, 4, 5, predict 6-sided. then try derive the formula. explain why the formula works. Can you always divide polygon into triangles?
   • Watch the TIMSS videos
   • Interviews at community college (students that failed a placement test)
     1. students view math as whole bunch of rules to be memorized. Don’t think that it’s something that can be figured with analysis, or that there are reasons behind the rules.
     2. When asking conceptual (non-standard) questions, got remarkably low correct answers. Regardless of student placement (even the better placed students didn’t get it, at the same rate) Don’t know what it means to multiply by a fraction.
3. clear principles to develop instruction
   • Don’t get to high achieveing, but starting with procedure. Must integrate concepts all the way.
   • Try stats class, in case these students auto-shutdown in normal math class.
   • Add 3rd bullet to learning strategy: Practice. but not repitition. deliberate practice, something differs with each problem instance, so have to refigure, reinforce neural paths.
   • stat and math proficiency, flexible and stable knowledge understand concepts, procedure stragegies, productive disposition (belief can figure out answer).
   • primary drivers: struggle, make connection, practice.
   • need instructional resources to create these learning opportunities. need students that are prepared to engage (esp if have history of failure). need teachers that can implement, flexible, creative.
   • lesson design: try to implement struggle by starting with rich problems. helps to start with struggle. try to change cultural routine.
   • conception flow: figure out how to ask questions. see polygon example above. Why does this work? is assumption always valid?
   • practice not repitive. It’s analysis.
4. questions, comments.
   • Feels like disservice to directly challenge and watch students struggle. unfair to ask students to solve problem they’ve never seen before. Teachers supposed to dispense knowledge. Image of newton and apple: understanding supposed to happen quickly; easy to fake: “Oh! I get it.” Teacher has to have resolve not to continue unless students actually gets it. Must require engagement.
   • clear about struggle: have clear problem. it must be useful interesting question. problem directed by goal, struggle must be making direct progress toward solution. must believe that the struggle will pay off.
   • Japan: socialize students to understand that learning is about suffering. vs America: engagement is entertainment. Students: Jap 90% think study hard is way to success, America 90% think getting good teacher.
   • Are there materials that will prevent teacher from regressing to old behavior/technique. Have exams that are really tough on concepts, integrative of procedures. Test must be aligned with the goal of instruction.
   • One teacher allowed students to bring in sheet of whatever they wanted: then they stopped complaining about it being memorization.
5. Summary:
   1. Struggle to learn. But it pays off.
   2. Make conceptual connections. The procedure/formula comes from analysis.
   3. Practice, but not repetition.

The concept of God is, for most believers, [...]]]> Ordinarily I wouldn’t post up a bunch of stuff that I encountered on YouTube, but this collection of one persons account of his deconversion from Christianity to Atheism is so thoughtfully considered and carefully presented that I was absolutely captivated, and would like to share it.

The concept of God is, for most believers, an aggregate of other beliefs. There is no silver bullet, single argument, that will disavow a believer of the God concept. For the author, his belief was built upon

1. logical arguments (exemplified by Schroeder’s The Science of God).
2. answered prayers.
3. God as the source of morality.
4. Life as a testament to the creator.
5. The Bible as the divine word, full of wisdom.
6. The supporting testimony of other Christians.
7. The personal relationship with God, and personal experiences of God.

The big issue with prayer is that the likelihood of having a prayer answered is proportional to the likelihood of that event occurring even without supernatural intercession. Prayer, in a sense, puts a person in the driving seat with respect to an omniscient God. It should be better to figure out what God’s will is directly, rather than plead for what we’d like to have happen. Scientific evidence points out that prayer has no positive effect on patients recovery. [Study of the Therapeutic Effects of Intercessory Prayer (STEP) in cardiac bypass patients: A multicenter randomized trial of uncertainty and certainty of receiving intercessory prayer American Heart Journal, Volume 151, Issue 4, Pages 934-942 H. Benson, J. Dusek, J. Sherwood, P. Lam, C. Bethea, W. Carpenter, S. Levitsky, P. Hill, D. Clem, Jr., M. Jain] The traditional dichotomy of “yes”, “no” and “wait” responses that can be received from God in answer to prayer, is entirely psychological.

How can the Bible contain all of God’s Possible Knowledge, if it can’t answer very specific questions such as those regarding dating or personal life objectives. The Holy Spirit, helps by stepping in and filling those gaps. A university class in Professional Ethics, however, completely changed his mind. A text for the class included Being Good, by Simon Blackburn. The professor focused more on ‘how do we make good decisions’, and didn’t reveal his biases during the presentation of dilemmas. In regards to God, he raised the Euthyphro Dilemma, taking the position that Divine Command Theory is bankrupt, because it would allow obviously bad things (rape, murder, pillaging) to ‘become’ good by God’s command. Thus, morality is separate from God, and not a derivative of His command. Do you do good things because you want to be good, or to get into heaven? If you want to be good for its own sake, then you must do the moral footwork, and not delegate this responsibility to God, be threatened by eternal punishment in Hell, or bribed by eternal salvation in Heaven.

There is a discord between the Bible and Science. Genesis is debunked by Big Bang Theory, age of the Earth, Theory of Evolution, Rainbows after the Flood, etc. Schroeder initially offered a reasonable time-frame that allowed compatibility between these magisteria. A post about the book on Amazon was responded to by a professor, claiming that none of the scientific evidences above, are solved by a relativistic time shift. The professor had changed his own mind about God after using the personal library of Ramon Menendez Pidal to vet that the Bible was the result of construction of several previous sources. [Who Wrote the New Testament: The Making of the Christian Myth by Burton L. Mack, and A History of God by Karen Armstrong both provide good layman references to this fact.] Schroeder’s book is an example of extrallusory intelligence.

The professor alerts our author to the tactic of reverse terminology, and shows that “The doctrinal underpinnings of the Bible have been known to be mythological for centuries.” (as shown by Some Mistakes of Moses by Robert Ingersoll, who recounts the conflict between historical linguistics and the Tower of Babel). This conversation evolves, and the professor moves to remove himself from the conversation to avoid inevitable disenchantment, advising not to worry about religious details too much. The author reflects that many of his congregation are not on the path to Truth, and likely fear the dark waters and questions in which he travels, turning their backs on Truth (but he has nevertheless learned spiritual lessons from them).

The Bible clearly offers explanations for why educated people reject god (Romans 1:22). He kept many verses as guidance through his life, but hadn’t actually read the Book from cover to cover. In Genesis, he encountered stories with immoral behavior by God’s characters, and inconsistent punishment for such actions. Hardening Pharaoh’s heart and killing all the firstborn sons violates both freedom and justice. Exodus and Leviticus are found to be full of incredibly detailed rules about sacrifice and offerings, no longer necessary since Jesus’s death. Numbers and Deuteronomy are also full of tedious details, and legalistic jumbo, that Christians with the Holy Spirit don’t need. Some details are fond to be inconsistent: in particular, God’s wrath concerning Judas in Acts is now an account of remorseful self-infliction in Matt). Apologetics is found to be somewhat contorted logic to rescue these inconsistencies.

Our author is now well on his way to using secular learnings as his moral and ethical guide, rather than lessons from the Bible. The Amazon professor, holds the position that many of these stories are incredibly preposterous (Order of Creation, Two different accounts, Noah’s Ark vs actual number of species, God’s command to kill children (Deut 20:16)) Questioning God’s word is still very uncomfortable for our author, as the Bible was communicated directly from God, and comes to us, unedited. But translation is not the problem, for the Bible was written by various authors each with political aims to reconstruct (edit) history. This is the Documentary Hypothesis (The Bible with Sources Revealed by Richard Friedman). The Bible is now no longer an infallible source of Truth.

The author reveals that God is attributed, fortuitous coincidence, beauty, numinous experience, etc, and given credit for all that is good. The Holy Spirit is recognized as a voice different from his own, providing guidance and inspiration unlike his own conscience. Religion is the metaphor through which he understands his personal experiences. Failure in daily activities guide our author to a stronger devotion to his faith, yet in college the material is now found to be unsurmountable, even with stronger devotion. Speaking with atheists becomes his new motivation, for it alone now brings feelings of God’s will.

Even if the Bible is not the word of God, having directly communicated reveals that God exists. The Amazon Professor, in respectful observance, neither denies the authors sincerity, nor agrees. Persistence leads our author to continue the the conversation. The logical arguments are battered back and forth, and the professor begins teaching: given what we know, God is just a concept, and personal interaction with Him is a simulacrum. The God concept gives the believer a surrogate parent.

Finally the author concedes that it is possible, the history/creation of the universe, the construction of religion, the lack of positive intercessory prayer, the (im)moral behavior of individuals, the independence of morality from God etc, the personal revelations, all can happed without God. The carefully considered evidence from the Professor, leads our author to see that all these things are explainable without resort to God. Occam’s Razor leads the author from “it is possible that there is no God” to “there is no God”.

It begins [...]]]> The Libertarian think tank CATO recently published a small, trite piece that attempts to establish The Case against Literary (and Software) Patents. Being a Libertarian, I actually agree with the position; I just don’t think that this article fully explored the issue. Here, I seek to provide some links to more fundamental content.

It begins with the hypothetical existence of a ‘Literature patent’. I consider such an idea to be terrible at face value, and the article actually dismisses it as much. It would be ridiculous to expect every author to carefully comb over their work making sure that it doesn’t infringe on any registered plots or (worse!) plot devices (good buy holodeck!) Acquiring knowledge of registered patents would be prohibitive for a beginning author, they’d have to rely on publishers/editors. This significantly raises the cost of creating an innovative work. Not to mention the human effort the government must spend to maintain consistency in it’s patent database, and the legal costs and liabilities for the inevitable infringement.

The article then proceeds to demonstrate what happens in patentable areas. Immediately, there is a land grab on the ‘low hanging fruit’. During this process, established market leaders tend to benefit, because the have the resources (both funds and people) to make a large number of claims and file the required paperwork (economics of scale apply to paper shuffling too). Typically only a relatively few companies will be successful in this endeavor. The initial grab might also appear to be an ‘economic stimulus’, as it will show a remarkably steep and sudden interest in the field, resulting from the underlying similarity of the tragedy of the commons. After the market settles, a few incumbents then use their patent portfolios to threaten up-start competition. As the article points out, in the world of software patents, so much of the field is so obvious, that agents without an explicit interest in software will find themselves infringing as a normal course of their business but will be without their own patent portfolio and unable to make a bargaining counter-threat.

Another economic phenomenon that happens as a result of the patent system’s existence is economic stalemate. This actually happened with the sewing machine, as recorded by Adam Mossoff in A Stitch in Time: The Rise and Fall of the Sewing Machine Patent Thicket, which was blogged about at the Volokh Conspiracy. He recounts how the marketing and distribution of the sewing machine was actually encumbered by the patent system, because the machine required the combination of several innovations, and no single agent held all patents on the functionality. History also demonstrates the practice of ‘patent trolling’, whereby a company, which doesn’t actually produce anything, seeks to profit by legal threats of infringement and licensing agreements on its patent portfolio. The resulting stalemate was finally resolved through the explicit creation of a patent-holding company, whose sole function was to share the patents and resulting profits of all involved manufacturing firms.

So we can see that for areas where copyright is already established practice, the introduction of an extension of the patent system results in litigation and paperwork and encourages the preservation of an established regime of a few powerful companies working in loose collusion, both of which tend to outweigh any potential benefits to development and innovation

Now, I’d like to go out on a limb here, and reject the very concept of ‘Intellectual Property’. Richard Stallman has spoken out against its use, and continuously advertises the fact that it’s deceptive and misleading. At the root of the issue is that ideas and physical matter behave differently. That is, copying != stealing. The reasoning behind this position is fairly simple, when an idea is copied that does not deprive the original possessor from the idea. When you tell me about your theory of X, you don’t suddenly forget after telling me. In contrast, if you give me an apple, now you no longer have that apple. Ideas are part of a different realm of existence.

Finally, I’d like to point out the slippery slope, what happens if we go too far with this property idea: we might lose The Right to Read, or watch How creativity is being strangled by the law.

I hope that through these references, you can see where, how, and why I’ve developed my position on the patent issue; I’m firmly on the side of maximum freedom (and that includes the opening up of all media: open-music, open-software, open-hardware, open-design, open-architecture, open-video, open-government, open-literature, etc…)