Saturday, March 31, 2007

Critical thinking and creativity watch

It's been said that if fascism comes, it will come in the name of anti-fascism.

I am reminded of that aper├žu every time an educationist, business-type or politician sings the praises of critical thinking, higher-order thinking skills, creativity and innovation.

These are all lofty aspirations. What bothers me is that the advocacy of these worthy goals is frequently accompanied by a disparagement of subject matter knowledge. These advocates seem to believe that these qualities can be taught in a vacuum. It's questionable whether they can be taught at all. More likely they develop incidentally through a struggle with subject matter. They are certainly not free-floating entities without moorings. So to get back to the fascism case, in edland anti-intellectualism comes in the name of "critical thinking" and "creativity".

I found new evidence for this phenomenon in a fight over educational legislation in Colorado as presented by the blog Mount Virtus:

On a party line vote today, the Senate Education Committee passed a bill sponsored by Senator Sue Windels (D-Arvada) to mandate standards on Colorado schools that teach sex education. Three committee members, all Democrats - Windels, Bob Bacon, and Ron Tupa - voted to support the House Bill 1292 mandate six weeks after voting against a mandate setting higher state graduation requirements for math and science (Senate Bill 131), and eight weeks after voting against a requirement that high school graduates have basic competency in English (Senate Bill 73). Suzanne Williams (D-Aurora) was the only committee member to cast votes for all three measures.

Last week the House Education Committee, chaired by Mike “Give ‘Em Hell” Merrifield, shot down the math and science requirements after hearing support from a Jefferson County teacher, a university president (could have been two if Merrifield hadn’t rescheduled the hearing at the last minute so CU’s Hank Brown couldn’t testify), and a Lockheed engineer. Said Merrifield:
And here is the kicker:

“My contention is by forcing every child into this narrow curriculum, we are not making them more innovative, we are not making them more creative,” the Colorado Springs Democrat said, citing a national report that calls a well-rounded education the “passport to a job in which creativity and innovation are the key to a good life.”

The Witwer plan, Merrifield said, would make students “more regimented and more lock-step (with) less ability to think outside the box.”
(Hat tip to Myrtle Hocklemeier commenting at KTM II.)

The twisted thinking exhibited by this chairman of the House Education Committee (of all things!) frankly leaves me speechless. It's easy to utter a stupidity. It takes considerable effort to describe the nature of a stupidity. For example, would I have to brandish logical notions like denying the antecedent or affirming the consequent to tackle this inanity?

Another juicy example comes via D-EDRECKONING. Highly prolific blogger Ken deRosa cites a Daily Mail article in which some Association of Teachers and Lecturers suffers paroxysms of anti-intellectualism:

Schools should teach children the key skills they need for life - like walking and thinking - not set subjects such as history or French, teachers' leaders have said.

The Association of Teachers and Lecturers called for the National Curriculum to be torn up and the testing system abolished.

The union said teachers in local schools should be able to adapt lessons to fit a new framework focusing on important skills for life, rather than academic subjects.

Martin Johnson, ATL's acting deputy general secretary, said prioritising academic education over other types of knowledge was "totalitarian".

"A curriculum is a selection from the total sum of knowledge, which is exploding," he said.

"For the state to suggest that some knowledge should be privileged over other knowledge is a bit totalitarian in a 21st century environment. We are arguing that knowledge which traditionally has high status should not be privileged over other kinds of knowledge.

Schools should teach children the key skills they need for life - like walking and thinking?


Now I am waiting for an educationist to point out breathlessly that walking is an important 21th century skill.

In the meantime, Rory has left a comment at D-ED RECKONING in which he reviews the massive amount of research confirming the importance of walking:

I am finally glad someone has finally decided to address the walking achievement gap.

Study after study has confirmed that the ability to walk is a critical aspect of employment.

Our new information based society heavily depends on consumption of coffee. A recent study by a leading University determined it is much more economical to provide centralized coffee pots in office environments. Without the ability to "walk" to these coffee pots, employees will soon suffer from coffee withdrawal causing severe detrimental effects on worker productivity.

L.B. Ral from Progressive University cautions against a biased approach to walking instruction though. He notes that different cultures have different styles of walking.

Meanwhile, disabled activists have called the new emphasis on walking instruction discriminatory. They point out that thousands of wheelchair bound people across the country are able to get around quite well without walking. They recommend "walking" classes be replaced with inclusive instruction on "moving".

Thursday, March 29, 2007

Segregate non-students

A New York City teacher writes about the horrendous discipline problems she faces every day:

Most recently, a student threatened a student and a teacher in the same day, yet is still sitting in class. Not even a suspension! Rumor has it that the principal feels we have too many suspensions and is using shady means to cover up that fact. Either our school totally lacks the infrastrucutre to handle unruly students, or there is major corruption going on at the administrative levels. Last semester, there was a fight in my classroom. As per protocol, I called security. The line was busy. One of the two security guards in the building (yes, we only have to for two whole schools) sits on the phone all day, making personal calls. Another time, a teacher called for a student making threats, and the guard told her she simply wasn't coming! In any case, we all know students must feel safe to be able to learn. Students should not feel safer outside the school than within. How can I protect my students when I have no recourse to discpline students effectively? How can I protect my students when I myself don't even feel safe?


The one thing I know for sure is that I am totally burned out. Battling disruptive and extremely disrespectful students every single day, being totally taken advantage of in terms of the contract, and walking on eggshells with administrators so as to remain on their "good side" has really been an exhausting experience. As a result, I have lost my belief that I am actually making a difference. The problems that plague NYC schools are so beyond the scope of one person to fix. It is really overwhelming.
There is something fundamentally wrong with a culture that produces so many disrespectful, unruly students. Nevertheless, no matter how bad the school, there are always well-behaved students willing to learn. We owe it to them to create a propitious learning environment. That means we have to get serious about segregating dysfunctional non-students. This is a first step toward achieving quality education. It runs counter to entrenched dogma, but it needs to be done.

Sunday, March 25, 2007

How should reading be taught?

A little gem of an article that appeared in Scientific American called HOW

A scientific consensus should be nigh. But then there are those fans of the psychotic guessing game who think that learning how to read is as natural as learning how to speak. A pervasive misconception. See also how whole language hurts the disadvantaged.

Whole language raises the question whether a theory that is largely grounded in crackpottery can be said to be upsetting the scientific consensus. I say it does not.

Boxed-in creativity

When educationists don't want to impart knowledge (which they don't by definition), they mumble something about "critical thinking" and "creativity".

In the Comments section of Education Week and in response to an article in Education Week, writer SteveH argues persuasively that you cannot think outside the box if you don't know what's inside the box:

Creativity is even more poorly defined, but many toss it out like everyone knows what it means. What is creativity in math? It's something that is only possible when it is built on mastery of a whole lot of basic skills. It is not something learned top-down. You have to know what is inside the box before you can think outside of the box. There is nothing worse in the scientific world than a technical report whose authors do not cite (or even know about) other work in their field.

Here is a problem that I had to solve a number of years ago. Find, as fast as possible, the intersection line segment of two triangles. The triangles are each defined by three [X,Y,Z] points and you have to be able to eliminate triangles that are not close very quickly.

Employers do not want "creative" employees who want to rediscover the wheel. They want employees who know the literature and can look it up. When they have to look it up, they need to know where to go and they need to implicitly know the difference between a dot product and a cross product. They need to know what a box check is; not creatively discover it. Only after reviewing the literature and finding no solution that meets the need, do you begin to get creative. But creativity takes knowledge and mastery of the basics. Real creativity is only possible by standing on the shoulders of those who have gone before you. Creativity is not sheer dumb luck. Knowledge and mastery do not reduce creativity, they enhance it.
With a fine touch for the comical, Education Week encourages readers to comment on the effect of "school reform."

What do you think? Does the current approach to school reform favor the regurgitation of random facts over the development of critical and creative thinking?
It doesn't say which school reform but I am assuming Education Week is referring to NCLB's accountability schemes. If holding educationists accountable for educating kids is likely to result only in a "regurgitation of random facts," then the state of education is in even worse shape than I had previously assumed. The conclusion I reach is that educationists simply don't know how to educate, if holding them accountable for minimal standards results in a regurgitation of random facts. I suggest they vacate the field and leave education to others.

Saturday, March 10, 2007

A tale of three math books

This is a hoot!

Here is an example from the fabulously encyclopedic old Kitchen Table Math of the quality of different textbooks. The first two problems are from Singapore Math and Saxon, respectively. The last "problem" is from the egregious and execrable fuzzy math text Trailblazers. Compare and contrast indeed!

Posted on May 26, 2005 @ 20:05 by CatherineJohnson

problems in three grade 5 textbooks

from the last page of Primary Mathematics 5B (U.S. Edition):

18. A fish tank is 2/5 full after Sara poured 14 gal of water into it. What is the full capacity of the tank in gallons?

final problem in Saxon Homeschool Math 6/5 3rd Edition:

Change each of these base 10 numbers to base 5:
a. 31
b. 51
c. 10
d. 100
e. 38
f. 86

from the last page of Math Trailblazers Grade 5:

4. Write a paragraph comparing two pieces of work in your portfolio that are alike in some way. For example, you can compare two labs or your solutions to two problems you solved. One piece should be new and one should be from the beginning of the year. Use these questions to help you write your paragraph:

Which two pieces did you choose to compare?

How are they alike? How are they different?

Do you see any improvement in the newest piece of work as compared to the older work? Explain.

If you could redo the older piece of work, how would you improve it?

How could you improve the newer piece of work?
With "math" instruction like that, the U.S. is sure going to remain competitive with the rest of the world.

Parents, don't let educationists ruin your child's opportunities in life. Fight the fuzzy math plague!

Sunday, March 04, 2007

Educationist misconceptions

Good discussion at KTM II on constructivism. ("Constructivism attacks the immune system that saves us from silliness")

I even managed to deliver myself of an opinion that then accidentally turned into a brief statement of my teaching philosophy:

I cannot understand for the life of me how construction and discovery can be compatible. If knowledge is just lying around the kitchen table or on the floor to be discovered, then why does it need to be constructed? If it is to be constructed, why does it need to be discovered?

I can understand construction in the banal sense that we must somehow integrate external input (from observations, books, sage on the stage, etc.) into our knowledge apparatus, but the external input must still be there. This type of integration is necessarily always active, contrary to educationist palaver. So-called "constructivists" militate against this external input and disparage textbooks, explicit and expository instruction, etc. [All based on a misconception of constructivism. See below.]

My own favored teaching/learning model is one I dubbed the Optimal Electrode Gap model [spark gap might be better], or OEG model (somehow I feel I must turn this into an acronym. Acronyms lend legitimacy even to screwball ideas. Not that I consider the OEG model to be a screwball idea).

The analogy is taken from physics. When relatively high voltage is applied to electrodes, three things can occur depending on the electrode gap:

a) no sparks fly if the electrodes are too far apart

b) a short-circuit is created if the electrodes touch each other

and c) sparks begin flying if the gap is just right.

This technical bit lends itself beautifully as an analogy and even metaphor for education where it has major implications for teaching and learning. The flying sparks are a metaphor for true learning and understanding. The electrode gap stands for the kind of pupil/teacher interaction. Finding the right gap is at the heart of a teacher's teaching ability and skill.

If a teacher talks above the head of the pupil without connecting with the pupil's prior knowledge, then the gap is set too wide and no sparks fly. If the teacher tells the student (who may not be paying attention as is most often the case) everything without allowing for creative tension and some student struggle, then we have a short-circuit (the electrodes touch each other) and the voltage is for nought.

On the other hand, finding the right gap prevents pupil frustration on the one hand and wasted energy on the other, and can lead to student excitement and enthusiasm, and a real sense of accomplishment. [I presume Vygotsky's zone of proximal development is something along those lines, but note below how educationists manage to turn a good idea into an absurdity].

This is my teaching philosophy in a nutshell. I am not sure how all of this ties in with prevailing theories, but I suspect it incorporates elements from a variety of philosophies.
In the Comments section of the post, Barry Garelick cites a quote that addresses one of the major misconceptions under which educationists are laboring, namely that the constructing pupil needs no external input:

I was referring to a paper by Anderson, Reder and Simon called "Radical Constructivism and Cognitive Psychology" which appeared in a collection published by Brookings Institute in 1998. In the paper, they state:

“A consensus exists within cognitive psychology that people do not record experience passively but interpret new information with the help of prior knowledge and experience. The term “constructivism” is used in this sense in psychology, and we have been appropriately referred to as constructivists (in this sense) by mathematics educators. However, (AND THIS IS A BIG ‘HOWEVER’ FOLKS) denying that information is recorded passively does not imply that students must discover their knowledge by themselves without explicit instruction, as claimed by radical constructivists. In modern cognitive theories, all acquisition of knowledge, whether by instruction or discover, requires active interpretation by the learner. The processing of instruction can be elaborate, its extent growing with the amount of relevant knowledge the learner brings to the task.”
Catherine Johnson of KTM I and KTM II fame contributes a terrific quote that further elaborates on this enormously damaging and widespread educationist misconception:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.
Barry Garelick points out that my spark gap analogy fits in nicely with Vygotsky's ZPD:

Yes, the spark gap analogy is quite good. It fits in with the Vygotsky theory of Zone of Proximal Development or ZPD. You want to teach children in that zone (i.e., the spark gap is not too wide) and provide the scaffolding or guidance to help bridge that gap.
BeckyC cautions that constructivists go off the deep end when it comes to defining the pivotal term "scaffolding". Scaffolds are usually high up next to a building and I am speculating that educationists begin to suffer from a case of vertigo when they are on a scaffold and fall off. How else to explain this educationist fall into the abyss of absurdity?

It's in trying to define what constitutes scaffolding that the constructivist mischief begins again in earnest.

Constructivists deny the possibility of scaffolding by directly instructing or directly telling the child how to bridge the gap between what he knows and what we know he could know next. They allow indirect methods only, and they are even uncomfortable with presuming to know what the child should know next. They wait patiently, and they wait and wait. After all, it's not their child, and the child goes away at the end of the school year.
Let's hope that through repeated exposure one or the other educationist will come to recognize the terrible misconception under which they have been laboring.

Friday, March 02, 2007

More parents fighting fuzzy math

Another parent group has formed to fight the fuzzy math plague. This time in Plainfield, NY.

Among the complaints:
Kids don't have basic skills.
Homework is unrecognizable.
Oodles spent on tutors.

Hat tip to Linda Moran.

Thursday, March 01, 2007

Teaching fractions

There is more to knowing and teaching fractions than meets the eye. Paper by H. Wu.

1 Definition of a Fraction . . . . . . . . . . . . . . . . . . . . . . 4
2 Equal Division of a Segment by Ruler and Compass . . . . . . 20
3 Equivalent Fractions (Cancellation Law) . . . . . . . . . . . . 22
4 Fraction as Division . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Ordering Fractions (the Cross-Multiplication Algorithm) . . . 38
6 Addition and Subtraction of Fractions . . . . . . . . . . . . . 46
7 Multiplication of Fractions . . . . . . . . . . . . . . . . . . . . 62
7.1 Formula for the product, and first consequences . . . . . . . . 64
7.2 The first alternative approach . . . . . . . . . . . . . . . . . . 74
7.3 The second alternative approach . . . . . . . . . . . . . . . . . 78
8 Division of Fractions . . . . . . . . . . . . . . . . . . . . . . . 80
9 Complex Fractions . . . . . . . . . . . . . . . . . . . . . . . . 88
10 “Of” and Percent . . . . . . . . . . . . . . . . . . . . . . . . . 93
11 Ratio, Rates, and the Fundamental Assumption of School
Mathematics (FASM) . . . . . . . . . . . . . . . . . . . . . . . 99
12 Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 108
13 APPENDIX: Some Remarks on the Teaching of Fractions in
Elementary School . . . . . . . . . . . . . . . . . . . . . . . . 117