MGTutoring.com. A Rational Perspective on Education.

December 18, 2009

What I Already Knew

Filed under: Education, Logic, Science — Administrator @ 12:32 pm

Writing in “Cognitive Scientists Debunk Learning-Style Theories” (Inside School Research Blog on Education Week, December 17, 2009, 9:47 AM), Debra Viaderosays:

Writing in the journal Psychological Science in the Public Interest, cognitive scientists Hal Pashler, Mark McDaniel, Doug Rohrer, and Robert Bjork argue that, of the thousands of articles published on learning styles in recent decades, few really put the theory to an adequate test.

To really determine if a theory is valid, the researchers write, a study would have to first classify students based on the theory being tested and then randomly assign them to one of several different learning methods. Students would also have to be tested before and after the instruction. If the theory is correct, the researchers said, then students would learn best when taught with the teaching methods that mesh with their individual learning styles.

Yet few studies use that or any kind of experimental method to test learning-style theory. And, among those that did, the authors found, several yielded results that contradicted the theory. The authors write:

We conclude therefore, that at present, there is no adequate evidence base to justify incorporating learning-styles assessments into general educational practice.”

That’s not to say learning-style theory would never work, the authors add. Dozens of such theories have been identified and some have never been tested at all.
What many of these theories give a name to may actually be a learning preference. And it’s a long way from preferring to be taught one way to actually learning more when taught by a compatible instructional method.

Besides which, it is we humans who must adjust to the world, to reality and all its modalities: visual, auditory, kinesthetic, etc. — it is not the world which will bend to us. Education is about preparing a child to live independently in the world and amongst other self-sovereign people; it is not about training children to stomp their feet at the world and other people in demand that their “learning styles” be pandered to.

Update (3:30 PM): (1) I should point out that, at this time, I have not yet read the article. (2) I wrote a bit about “learning styles” in my blog post Two Points of Pedagogy.

November 17, 2009

Induction, Economics and More

Filed under: Economics, Logic, Quotes, Science — Administrator @ 8:31 am

In the Introduction to A Treatise on Political Economy the author, Jean-Baptiste Say (1767-1832), makes some insightful comments on all science:

I.1
A SCIENCE only advances with certainty, when the plan of inquiry and the object of our researches have been clearly defined; otherwise a small number of truths are loosely laid hold of, without their connexion being perceived, and numerous errors, without being enabled to detect their fallacy.

I.5
The wide range taken into the field of pure politics, whilst investigating the subject of political economy, seemed to furnish a much stronger reason for including in the same inquiry agriculture, commerce and the arts, the true sources of wealth, and upon which laws have but an accidental and indirect influence. Thence what interminable digressions! If, for example, commerce constitutes a branch of political economy, all the various kinds of commerce form a part; and as a consequence, maritime commerce, navigation, geography—where shall we stop? All human knowledge is connected. Accordingly, it is necessary to ascertain the points of contact, or the articulations by which the different branches are united; by this means, a more exact knowledge will be obtained of whatever is peculiar to each, and where they run into one another.
I.6
In the science of political economy, agriculture, commerce and manufactures are considered only in relation to the increase or diminution of wealth, and not in reference to their processes of execution. This science indicates the cases in which commerce is truly productive, where whatever is gained by one is lost by another, and where it is profitable to all; it also teaches us to appreciate its several processes, but simply in their results, at which it stops. Besides this knowledge, the merchant must also understand the processes of his art. He must be acquainted with the commodities in which he deals, their qualities and defects, the countries from which they are derived, their markets, the means of their transportation, the values to be given for them in exchange, and the method of keeping accounts.
I.7
The same remark is applicable to the agriculturist, to the manufacturer, and to the practical man of business; to acquire a thorough knowledge of the causes and consequences of each phenomenon, the study of political economy is essentially necessary to them all; and to become expert in his particular pursuit, each one must add thereto a knowledge of its processes. These different subjects of investigation were not, however, confounded by Dr. Smith; but neither he, nor the writers who succeeded him, have guarded themselves against another source of confusion, here important to be noticed, inasmuch as the developments resulting from it, may not be altogether unuseful in the progress of knowledge in general, as well as in the prosecution of our own particular inquiry.

I.8
In political economy, as in natural philosophy, and in every other study, systems have been formed before facts have been established; the place of the latter being supplied by purely gratuitous assertions. More recently, the inductive method of philosophizing, which, since the time of Bacon, has so much contributed to the advancement of every other science, has been applied to the conduct of our researches in this. The excellence of this method consists in only admitting facts carefully observed, and the consequences rigorously deduced from them; thereby effectually excluding those prejudices and authorities which, in every department of literature and science, have so often been interposed between man and truth. But, is the whole extent of the meaning of the term, facts, so often made use of, perfectly understood?
I.9
It appears to me, that this word at once designates objects that exist, and events that take place; thus presenting two classes of facts: it is, for example, one fact, that such an object exists; another fact, that such an event takes place in such a manner. Objects that exist, in order to serve as the basis of certain reasoning, must be seen exactly as they are, under every point of view, with all their qualities. Otherwise, whilst supposing ourselves to be reasoning respecting the same thing, we may, under the same name, be treating of two different things.
I.10
The second class of facts, namely, events that take place, consists of the phenomena exhibited, when we observe the manner in which things take place. It is, for instance, a fact, that metals, when exposed to a certain degree of heat, become fluid.
I.11
The manner in which things exist and take place, constitutes what is called the nature of things; and a careful observation of the nature of things is the sole foundation of all truth.

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November 9, 2009

Finding Libraries At Which To Study: It’s Easy

Filed under: Logic, MGTutoring, Mathematics, Physics — Administrator @ 11:53 am

Thank goodness for the Internet — and the mathematics, physics, and reasoning that made it possible, and that continue to refine and improve it. How easy it is to find places to go to study; besides Paneras and Starbucks and home, there are nice, quiet libraries all over the place. We can see all the branch libraries in Texas at the click of a mouse.

October 2, 2009

Introducing Ardi, Ancestor of Lucy

Filed under: Biology, Logic, Mathematics, Science — Administrator @ 8:12 am

In “Before Lucy came Ardi, new earliest hominid found” (Yahoo News, Thu Oct 1, 6:33 pm ET), Randolph E. Schmid says:

The story of humankind is reaching back another million years as scientists learn more about “Ardi,” a hominid who lived 4.4 million years ago in what is now Ethiopia. The 110-pound, 4-foot female roamed forests a million years before the famous Lucy, long studied as the earliest skeleton of a human ancestor.

This older skeleton reverses the common wisdom of human evolution, said anthropologist C. Owen Lovejoy of Kent State University.

Rather than humans evolving from an ancient chimp-like creature, the new find provides evidence that chimps and humans evolved from some long-ago common ancestor — but each evolved and changed separately along the way.

“This is not that common ancestor, but it’s the closest we have ever been able to come,” said Tim White, director of the Human Evolution Research Center at the University of California, Berkeley.

Copyright © 2009 The Associated Press.

Copyright © 2009 Yahoo! Inc. A

There are articles regarding Ardi in TimeNational Geographic,  the New York Timesand more.

Science Magazine has made available the 11 articles for free; you can download them in pdf format.

You can also listen to a 45-minute audio interview with Dr. Tim White on the Website of the American Association for the Advancement of Science, which links to other goodies on their page announcing Ardi.

The hierarchy of knowledge behind understanding Ardi is amazing. In terms of discoveries in history, it reaches back hundreds of years…

October 1, 2009

The Power of Concepts

Filed under: Biology, Logic, Mathematics, Science — Administrator @ 9:00 am

In “Tiny parasite may have done in mighty T. rex” (Chicago Tribune, September 30, 2009), William Mullen writes:

CHICAGO – Sue – the biggest, meanest, meat-eating dinosaur known to history – probably was killed not by some other monster killer battling with her 65 million years ago, but by a tiny, one-celled parasite that gave her a sore throat.

That is the conclusion drawn by an international team of scientists who studied holes in the jaw of Sue, the biggest, most complete Tyrannosaurus rex fossil ever found and one of the star attractions at Chicago’s Field Museum.

The holes in Sue’s mandible bones at one time were thought to be bite marks by another T. rex during a fight sometime during her life. A paper published Tuesday in the online science journal PLoS says instead that the holes were made by a parasitic infection called trichomonosis, which continues to cause fatal disease in modern-day carnivorous birds known as raptors – hawks, eagles and osprey.

(c) 2009, Chicago Tribune.

Perceptually, all Sue would have been to us was pieces of rock. Conceptually — with science, mathematics, and measurement — the individual pieces of rock become classifiable as old bones based on their shape (i.e., their geometry); they can then be compared and contrasted (based on geometric shape, size, density, structure, etc.) with the bones of living (or recently deceased) animals to grasp that the rocks make up a whole, a skeleton; and with more knowledge (biology, zoology, botany, evolution, chemistry, physics, mathematics) they can be used to grasp what kind of animal had the bones, how the animal lived and moved, what it ate, and when it lived. All we know about dinosaurs is based on our ability to conceptualize, and therefore, ultimately, on measurement and mathematics.

September 30, 2009

Rejecting the Non-Existent

Filed under: Education, Logic, Mathematics, Quotes — Administrator @ 7:54 am

There is a great deal one can learn about logic and objectivity from mathematics. It is a very important subject to study. In Elementary Mathematical Analysis, Colin Clark says:

Suppose we wish to prove: “1 is the largest positive integer.”

Let x denote the largest positive integer. Then x>= 1, so that x^2 >= x. But x^2 is also a positive integer. Therefore x^2 = x. Dividing by x, we obtain x = 1.

What is the error in this “proof”? The moral of this example is that if we refer to nonexistent objects as if they existed, we may be led into foolish errors. Mathematicians seem to have learned this moral; politicians probably never will.

p. 107, Elementary Mathematical Analysis by Colin Clark, Wadsworth Publishers of Canada, Ltd., (c) 1982. ISBN 0-534-98018-X.

As Parmenides said: ‘What is not, neither is nor can be thought.’ A is A; A is Not Non-A.

Poetry of Parmenides

Filed under: History, Logic, Philosophy — Administrator @ 7:53 am

The Stanford Encyclopedia of Philosophy has some fragments of the (philosophic) poetry of Parmenides, with philosophic commentary. They say about Parmenides:

Parmenides of Elea, active in the earlier part of the 5th c. BCE., authored a difficult metaphysical poem that has earned him a reputation as early Greek philosophy’s most profound and challenging thinker. His philosophical stance has typically been understood as at once extremely paradoxical and yet crucial for the broader development of Greek natural philosophy and metaphysics. He has been seen as a metaphysical monist (of one stripe or another) who so challenged the naïve cosmological theories of his predecessors that his major successors among the Presocratics were all driven to develop more sophisticated physical theories in response to his arguments.

Copyright © 2008 by John Palmer

© Metaphysics Research Lab, CSLI, Stanford University

Here are some lines of his poetry:

And the goddess received me kindly, and in her hand she took/ my right hand, and she spoke and addressed me thus:/ “O young man, accompanied by immortal charioteers/ [25] and mares who bear you as you arrive at our abode,/ welcome, since a fate by no means ill sent you ahead to travel/ this way (for surely it is far from the track of humans),/ but Right and Justice did.” (Fr. 1.1-28a)

You must needs learn all things,/ both the unshaken heart of well-rounded reality/ [30] and the notions of mortals, in which there is no genuine conviction./ Nonetheless these things too will you learn, how what they resolved/ had actually to be, all through all pervading. (Fr. 1.28b-32)

Come now, I shall tell—and convey home the tale once you have heard—/just which ways of inquiry alone there are for thinking:/ the one, that [it] is and that [it] is not not to be,/ is the path of conviction, for it attends upon true reality,/ [5] but the other, that [it] is not and that [it] must not be,/ this, I tell you, is a path wholly without report:/ for neither could you apprehend what is not, for it is not to be accomplished,/ nor could you indicate it. (Fr. 2)

It is necessary to say and to think that What Is is; for it is to be,/ but nothing it is not. These things I bid you ponder./ For I shall begin for you from this first way of inquiry,/ then yet again from that along which mortals who know nothing/ [5] wander two-headed: for haplessness in their/ breasts directs wandering thought. They are borne along/ deaf and blind at once, bedazzled, undiscriminating hordes,/ who have supposed that it is and is not the same/ and not the same; but the path of all these turns back on itself. (Fr. 6, supplementing the lacuna at the end of fr. 6.3 with arxô and taking s’ earlier in the line as an elision of soi, as per Nehamas 1981, 103-5; cf. the similar proposal at Cordero 1984, ch. 3, expanding parts of Cordero 1979.)

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September 15, 2009

An Anecdote on Science and the Importance of Context

Filed under: Education, Logic, Science — Administrator @ 10:03 am

In “Why Raindrops Fall in Different Sizes” (Live Science, 23 July 2009, 09:56 am ET), Senior Writer Andrea Thompson says:

Instead, by analyzing high-speed movies of falling water droplets, Villermaux and Bossa found that the drops go through a series of shape-shifting moves and finally burst apart into a spray of multi-sized drops. [At this point, there is a video illustrating the process. -- MG]

First, the falling spherical drop gradually flattens out into a pancake shape. As it gets wider and thinner, it eventually captures the air ahead of it and deforms into a shape something like an upturned plastic grocery bag, the study shows.

When the inflated “bag” reaches a certain size, it breaks apart into many smaller droplets, which fall to the ground and get you wet. The distribution of droplets that result from the burst matches the variation seen in natural rainfall, the team reported.

This model of droplet burst was known in other contexts, such as diesel engines and liquid propellant combustion, but had never been applied to rain.

“The atmospheric science community simply had another scenario in mind, and didn’t make the connection,” Villermaux told LiveScience in an email.

© Imaginova Corp. All rights reserved.

Fascinating…

What’s more, the story shows that knowledge goes to he who appeals, not to authority and tradition, but, like Aristotle, to reason, logic, and the evidence of the senses.

August 28, 2009

Fats, Rats, and People

Filed under: Biology, Exercise, Health & Nutrition, Logic — Administrator @ 7:04 am

In “High-Fat Diets Are Bad For You? I Smell A Rat” (“Fat Head” Blog, August 20, 2009), Tom Naughton writes about a recent pseudo-scientific study:

The point is, a high-fat diet isn’t natural for rats.  I looked it up, and rats are listed as omnivores who will eat pretty much whatever is available, but prefer cereal grains.  (They probably like looking at that American Heart Association seal of approval on the box.)  When you feed an animal – or a human – an unnatural diet, you’re going to get negative results.

The Lipid Hypothesis became accepted partly because when researchers fed rabbits lard and cholesterol, the rabbits rapidly developed heart disease.  Well, go figure … rabbits rarely attack pigs and eat them.  When other researchers tried the same experiment on dogs, they couldn’t induce heart disease, no matter how much lard they fed them.  So they concluded that dogs don’t get heart disease.  But they do – if you feed them grains.

If rats eat a lot of fat and then become lethargic and stupid, that says nothing about how a high-fat diet affects humans.  We’ve been eating fatty diets for hundreds of thousands of years.  We didn’t become fat until we started eating grains.  (And we didn’t become stupid until we started feeding fat to rats and thinking the results mean anything.)

In another rat study that hit the news this week, researchers suggested that high-fat, high-protein diet leads to insulin resistance.  Once again, we’re looking at animals that aren’t eating anything close to their natural diet.  If a high-fat, high-protein diet had the same effect on humans, the Inuits and the buffalo-hunting tribes should’ve been plagued by diabetes.  They weren’t.  But after Native Americans were herded onto reservations and forced to live on flour and sugar, they became one of the most diabetic populations on the planet – more than 50% in some tribes.

August 6, 2009

How Not to Teach Science — And the Only Antidote

Filed under: Education, Logic, Science — Administrator @ 7:21 am

Teresa Bondora, owner of How to Teach Science (HT2S), says:

Science is not like math, which is progressive. In math we teach the simple concepts and then progress through simple operations, fractions, etc. We expect that very young children will learn to memorize their multiplication tables but cannot learn simple rules of chemistry or physics. When they have grasped these basic math concepts, we can begin the ideas of algebra. But in science, there is no linear progression. Science is web-like. All parts are interconnected. To answer one question in biology, we must use chemistry. To understand why in chemistry, we can use biology. Physics is dependent on the biology of the body to explain motion in humans.

Then why did physics develop historically as it did? Why are some concepts and principles more abstract than others, and hence dependent logically on those others? And why did geometry and Euclid’s Elements have such a profound, formative effect on modern physics? And why is math such a big part of science?

She also says:

I have since learned that there is a very wrong way to teach science. The way we were taught, with Chemistry saved for High School, with the elitist attitude toward the “harder” sciences, books that stress content, it is very damaging and not at all the way to show our children how science works.

If you don’t stress content, then what do you stress? (For one thing, method makes no sense without content. For another, the subject(s), i.e., content, of a science is one thing that determines the methods needed to understand and investigate the subject — we cannot do psychology with the methods of physics, and we cannot do physics with the methods of psychology or biology.)

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