Sunday, October 30, 2005

Heterodoxy lives!

Willful indifference

In Why Reading Teachers Are Not Trained to Use a Research-Based Pedagogy: Is Institutional Reform Possible? Sandra Stotsky argues that enough is now known (and has been known for decades) about how to teach reading effectively. The obstacles to teaching reading effectively are ideological. There is also a need to pretend that more research is needed to keep folks in academia artificially busy. Otherwise they might have to drive a cab.

Abstract: Reading instruction is one of the very few areas where it is not the case that “more research is needed.” Educational policy makers already have the theory and the evidence supporting it to guide the implementation of effective reading programs from K-12. In fact, they have had the theory and the evidence for decades. The central problem they face in providing effective reading instruction and a sound reading curriculum stems not from an absence of a research base but from willful indifference to what the research has consistently shown and to a theory that has been repeatedly confirmed. Using Jeanne Chall’s The Academic Achievement Challenge as a point of departure, I suggest why our education schools, through their influence on teachers, administrators, textbook publishers, and state and national assessments of students and teachers, have come to be the major obstacle to closing the “gap” in student achievement.

11th graders write

What are the ethics of posting samples of atrocious writing by students on weblogs? Should there be ethical concerns if the names of the producers of the hideous writing samples are not disclosed and the samples are otherwise slightly redacted to make identification difficult?

One of the sharpest education writers in the edusphere has done just that and now has convinced herself that posting such samples is unethical and will take down her post.

Here is a tiny snippet from these samples from 11th graders:

"in [title]. will has to deal with alot of racism bieng that she is a nigga during slavery. she sees her father get killed and then have to go home and find out that her mother is tooken buy the british. then will y goes to her aunt besty house and captian ivers try to put her back into slavery."
My view is that any lingering ethical concerns are far outweighed by the public service rendered by exposing this appalling state of affairs.

Read the rest of the samples before they disappear into electronic heaven.

Thursday, October 27, 2005

Science attempt

Something is brewing in the dismal area of science education. Not only will the NCLB science requirement kick in belatedly at some point, the fabled "nation's report card" body is stirring and drafting a "framework" for science education.

But all is not well. The good folks at the Fordham Foundation have assembled a
crack team to take a closer look at what the NAEP drafters are up to. The signs are not encouraging. Apparently, the discovering drafters are smitten by the fashionable but absurd educationist creed according to which barely literate pupils can "discover" the vast knowledge contributed by giants of science and accumulated over thousands of years on their own. Ignis fatuus is their guiding light.

Our basic position is that every child in America should receive a rich and rigorous science education in the primary and secondary grades, one that provides a broad understanding of key scientific concepts and ways of thinking. We reject the trendy notion that children, unaided, can “discover” key scientific concepts. Most of science must be taught if it is to be learned.

In these ways we demur from the “consensus” represented by several professional organizations that have offered national guidelines for science education (the National Science Education Standards of the National Research Council and Benchmarks for Science Literacy of the American Association for the Advancement of Science [AAAS]). Unfortunately, the NAEP Science Assessment Steering Committee encouraged the Framework’s authors to rely upon those very documents as their guide stars. This was a mistake. Just as the National Council for the Teaching of Mathematics (NCTM) is a partisan in the “math wars,” so, too, do these organizations represent one pole of the debate over science education and instruction. To follow their guidance is to “take one side” in an important debate rather than to strive for balance.

Let's not allow the reinvent-the-wheel crowd to follow the will-o'-the-wisp unhindered.

Wednesday, October 26, 2005

The Carnival is here

Make sure to check out this week's Carnival at the
Education Wonks. Lot's of math-related stuff. See especially the Alice entry at Kitchen Table Math and a lot more.

Sunday, October 23, 2005

Math disaster

A friend of mine teaches chemistry at a community college in South Carolina and is pulling out his remaining hair. It appears that in his introductory chemistry and remedial classes the vast majority of students (recent high school graduates) is unable to do simple calculations involving percentages. Forget about dimensional analysis.

Something must have gone awfully wrong with these students' math instruction in high school and probably even earlier in elementary school. I am on the case investigating.

I teach math to eighth graders and know that teaching math successfully need not be rocket science. Most of my students can now convert fractions to decimals and percents (and vice-versa) in their sleep. They can also solve the three different types of percent word problems (unkown rate, whole and part) in their sleep.

The following is an aspect of how I teach percentages after teaching the concept that a percentage is an equivalent fraction with a denominator of one hundred.

I have my students create a table with three columns. Each column is labeled fraction, decimal, percent. This visualizes the operations and helps reduce confusion. They can go from left to right to start with fractions and end up with percents, or from right to left to start with percents and end up with fractions.

Converting percents to fractions generally poses no problems when the percent is a whole number, e.g. 47% --> .47 --> 47/100. A special problem arises when the percent is a fraction like 5-1/4 %. This is where the students need to realize that an additional step is required. Many students want to enter 5.25 in the decimal column. The task of the teacher is to focus on this problem and to show that the students must first convert to 5.25%, then to the decimal .0525 and on to the fraction.

A good way to drive home this point is to contrast the conversion of 5-1/4 (without %) and 5-1/4% to decimals and writing 5-1/4% and 5.25% in the percent column. Only now can 5.25% leave the percent column and move to the decimal column to become .0525. Bingo!

I also have my students solve percent problems as proportions and equations. I drill them in identifying the rate (percent), part and whole in any percent problem. For equations I have them use the rb=a formula. r=rate (percent), b=base (whole) and a=amount (part). This is also a nice algebra exercise since they need to solve for a, b or r as the case may be.

I once again have them make a table with three columns and several rows. The columns are labeled r, b and a.

Then I have them look at various percent problems and ask them to identify what's known and unknown. If the percent is unknown, a question mark goes into the box of the r-column and what's known (whole and part) goes into the respective boxes of the b-column and a-column.

If a (the part) or b (the whole) is unknown, the procedure is repeated accordingly. This works amazingly well and the visualization once again helps to minimize confusion.

An added advantage is that the students learn how to solve for the various variables and how to manipulate the rb=a formula, e.g. r=a/b, b=a/r.

It is amazing, though, how many of these 8th graders find this manipulation of variables difficult. Adults might consider this manipulation child's play. But it really represents a huge jump to this age group to go from the concreteness of numbers to the abstractness of variables (letters).

This concludes the lesson on how to teach percents for understanding. Instructivist will give other lessons on how to teach math successfully to middle graders as he sees fit.

Sunday, October 16, 2005

Quantifying instruction

What is good teaching? Can it be quantified as educational researchers are trying to do. I, for one, am glad I am nowhere near a coding sheet and instead rely on observation, common sense and intuition.

Good teaching is far more than directly observable and measurable behavior. Good teachers possess traits and qualities that either cannot be quantified or are hard to quantify. I would even go so far as to claim that trying to quantity these traits and qualities is a case of scientism, which I idiosyncratically define as an attempt to quantify qualities that are ill-suited for quantification.

How, for example, do you go about quantifying an inspiring, radiating personality? How do you quantify a sense of humor, wit, a capability for empathy, a developed sensitivity to the zone of proximal development? How do you quantify imagination, creativity and a capacity to teach for understanding? How do you distinguish numerically between genuine and phony sentiment and what numbers would you assign to a story-telling capability?

I think education would be much better served if we approached the question of what makes a good teacher from a humanistic-philosophical perspective. But then, of course, we would first have to have a notion of desirable educational goals because "good" does not exist in a vacuum.

Saturday, October 08, 2005

Arrested development

Constructivism reigns supreme in ed schools. It is the unquestioned doctrine that guides all aspects of teacher preparation. It should therefore be of some interest to find out what it is all about, if there is an empirical core that can be discerned from the thick fog that envelops hapless teacher candidates. The prospects are not good. Von Glaserfeld calls constructivism "a vast and woolly area in contemporary psychology, epistemology, and education."

Trying to pin down constructivism -- to see if it can be defined in a meaningful way and whether there is any sense that can be separated from nonsense -- is like searching for the unicorn.

At this point of my search, the best I can do is conclude that constructivists display a case of arrested development. Constructivists are stuck in the Piagetian sensorimotor or, at best, pre-operational stage. This infantilism that manifests itself in constructivists goes a long way in explaining educationist hostility to knowledge and educationist anti-intellectualism. But this infantilism is golden compared to the denial of objective reality by radical constructivist gurus like von Glaserfeld.

Let me elaborate a bit.

Constructivists cite Piaget and Vygotsky as their progenitors. Piaget did groundbreaking work on how toddlers develop intellectually and came up with different stages (really a continuum divided into stages to get a better handle on this development). For example, a toddler might recognize at some point that an object that is moved behind another object and disappears from sight does not cease to exist (permanence). Or a toddler might discover on his own that an object falls when released or that bumping into a wall is not a good idea or that a flame is hot.

The constructivists' fallacy is to carry this notion of discovery and individual experience to absurd lengths and apply it to later years -- to adolescence and even adulthood. Learning then becomes solely a matter of discovery and individual experience from which one constructs one's own knowledge and meaning. But you cannot "construct" broader knowledge ex nihilo and keep reinventing the wheel endlessly. You need external input. You need to benefit from the knowledge accumulated over thousands of years. This is where constructivism breaks down. Constructivism presents itself as a theory of learning based solely on experience. But personal experience is limited. Broader learning also needs to tap into an existing body of knowledge that constructivists disparage.

This otherwise imcomprehensible educationist hostility to knowledge and especially imparting knowledge becomes clearer when one considers the views of leading radical constructivist gurus like von Glaserfeld who seem to come straight out of the loony bin:

Von Glaserfeld is one of the leading apostles of radical constructivism. Radical constructivism rejects the traditional philosophical position of realism and adopts a relativist position. The traditional view of realism sees knowledge as a representation of an absolute reality - a world "out there" prior to having been experienced. The radical constructivists sees knowledge as "something that is personally constructed by individuals, in an active way, as they try to give meaning to socially accepted and shared notions." As von Glaserfeld himself says "knowledge is the result of an individual subject's constructive activity, not a commodity that somehow resides outside the knower and can be conveyed or distilled by diligent perception or linguistic communication"

This explains why educationists don't believe in an external body of academic knowledge that should be communicated to students. It explains why teachers are not allowed to teach, i.e. give explicit instruction.

On the other hand, how constructivists can claim Vygotsky as one of their own still remains a mystery to me. His notions of the zone of proximal development and scaffolding are sensible and don't rule out explicit instruction (despised by constructivists). His emphasis on socio-cultural factors doesn't fit in with "constructing one's own knowledge" either.

I wish someone could explain all these mysteries to me.

UPDATE #1: In the meantime, reader Rob has helpfully directed me to a scholarly article called Does No One Read Vygotsky’s Words? Commentary on Glassman that exposes attempts to Deweyize Vygotsky through omissions, distortions and inventions.

From the abstract:

In the May 2001 issue of Educational Researcher, Michael Glassman proposed several commonalities in the thinking of John Dewey and Lev Vygotsky. However, in addition to general problems in the article (misstatements about scholars’ writings and a reliance on unsupported inferences), the discussion misconstrues major concepts and topics addressed by Vygotsky’s theory of cognitive development—psychological tools, the role of the cross-cultural study, the zone of proximal development, and the nature of conceptual thinking. In addition, Glassman attempted to force Vygotsky’s goals into a Deweyan framework. The result is a misportrayal of Vygotsky’s work.
UPDATE #2: I dug out my ed psych text (Anita Woolfolk) we used in grad school to see what it says about Piaget and constructivism. From it I learn that knowledge is "constructed by transforming, organizing, and reorganizing previous knowledge. Knowledge is not a mirror of the external world, even though experience influences thinking and thinking influences knowledge. Exploration and discovery are more important than teaching." The quote is Woolfolk speaking and giving a summary of Piaget's purported views under the heading "Assumptions about Learning and Knowledge."

Woolfolk goes on to helpfully explain how knowledge is constructed citing Moshman (1982). Knowledge construction is directed by internal processes like Piaget's organization, assimilation and accommodation. This means that new knowledge is "abstracted from old knowledge." It turns out that "[k]nowledge is not a mirror of reality, but rather an abstraction that grows and develops with cognitivie activity. Knowledge is not true or false; it just grows more internally consistent and organized with development."

Talk about being self-referential. Where is the external input?

I don't know what to make of this. I can understand that we might have to readjust our thinking when we learn new things that might conflict with or supplement our previous knowledge. But apparently there is no input of new knowledge from an external source. Saying that knowledge is constructed by transforming, organizing, and reorganizing previous knowledge is purely self-referential. Previous knowledge is simply remixed and stirred the way you might mix the ingredients of a cake. Nothing new is added. How relevant is all this to teaching reading and writing skills, math, science, history, geography, literature or languages?

Neither relevant nor helpful. It's all nonsense -- nonsense on stilts that has managed to become the dominant creed of the ed establishment. Constructivism is to education what creationism is to science. Both lack an empirical basis and rely on some unfathomable, ineffable, magical, supernatural thing said to "construct" something out of nothing.

How refreshing, then, to have someone like Prof. Plum rip the mask off this pretentious drivel:

What is Constructivism?

Constructivism is big word that makes education perfessers think they are intelligent.

Constructivism is an invention that makes education perfessers think they know something that everyone else doesn't.

Constructivism is a set of statements about learning that are quite simpleminded and generally false.

"Knowledge can't be transmitted from one person to another. 'Learners' have to construct knowledge." [This very statement shows that constructivists don't believe what they say. Isn't the statement an effort to transmit knowledge?]

"Therefore, teachers should not teach directly by telling or showing (e.g., how to solve math problems). Instead, they should guide students as STUDENTS figure out concepts (what granite is) and strategies (how to sound out words, how to solve math problems)." [Constructing knowledge means NOTHING more than comparing and contrasting, identifying sameness and difference, making inductions and deductions. This is all OLD news. There is NO reason why teachers can't teach in a direct and focused fashion. In fact, students "construct knowledge" (figure things out) better--faster and with fewer errors--when they ARE taught directly, rather than expected to "discover" knowledge--which makes no sense, anyway. If knowledge is constructed, what IS there to discover?]

"How each person constructs knowledge is unique. Therefore, teachers should not arrange instruction in sequences. Instead, students should select learning tasks. Don't worry. They will select what they are ready for." [Unique in the DETAILS but not in the general logical operations by which human beings learn. If each person is unique, I guess physicians should not take their blood pressure.]

"Drill (distributed practice) is bad. It is boring. It is not needed." [Baloney!]

"Tasks should be 'authentic.' Holistic. Teach the fundamentals of chemistry in the CONTEXT of chemistry experiments. Teach phonics skills in the context of reading." [This is the prescription for keeping kids ignorant and unskilled and for leaving them demoralized.]

"Since each student's learning is unique and INTERNAL, you cannot use quantitative and standardized methods of assessment. It should be qualitative--how students feel and think about what they are learning." [This makes no sense. Body temperature is also "internal," but you can measure it quantitatively and with a standard instrument. Likewise, you can easily count how many math problems kids do correctly. This is a cop-out to protect constructivists from data that would ruin them.]

And from this set of sophomoric beliefs, you get whole language, fuzziest math, inquiry science, literature without literacy, and history without moral and political lessons.


Constructivist "theory" is a mishmash of overlapping platitudes and absurdities--"empty words and poetic metaphors" (Aristotle, Metaphysics). Taken separately, constructivist "propositions" are merely simpleminded. Taken together, they are indistinguishable from the verbal behavior of a person suffering from chronic schizophrenia.

"Reality is a construction."
"Knowledge is a construction."
"Experience is a construction."
"Experience is constructed with constructs."
"Constructs are constructed out of experience."
"Reality is knowledge."
"Knowledge is reality."
"Experience is reality."
"There is no knowable reality external to the knowing subject (the constructor)."
"Individuals and groups construct meaning as they interact with environments."
"Therefore, no statement can be more than relatively true."
"A current body of knowledge ('reality') is a context that shapes the construction of knowledge."
"Therefore, environment, knowledge, experience, meaning and reality are the same thing."
What does progressive/constructivist education actually look like in practice. Here we have a smartly written account from someone who is experiencing it first hand:

In my lesson during the first block, we read a lot of the primary source documents out loud together, and then I led a discussion about them and we took notes together. This was roundly condemned as the wrong approach, and so the next period I had to let them read and interpret in groups. As usual, they wasted a lot of time and I don't really think they understood it. Not that I'm sure they had totally understood it in the first block, since they didn't have the proper historical background and I can't give them quizzes, but at least I got some reasonable answers out of the class discussion. In the second block, everyone got something different, depending on their group. It was so frustrating. I don't want to learn to teach like this because I don't think it's right. But I can't contradict the teacher. But I need the practice. It's an education grad school moral dilemma. The best kind.
This is just the last paragraph of a fairly long post. Read the whole thing.

UPDATE #3: Here are more sources on constructivism:

What is Constructivism?

"Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to 'transfer' mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept." [Emphasis added].
- Calculus, Concepts, Computers, and Cooperative Learning (C4L)
These prescriptions would explain the surfeit of math cripples. I know from my own experience teaching math that students thrive when having things explained to them combined with guided practice and independent homework in the form of distributed practice and overlearning.

Sunday, October 02, 2005

Non-instruction (rev.)

Of all the educational lunacies dreamed up by educationists, non-instruction must be among the looniest.

Here is an account from the frontlines of what is not happening in a high school math class. The account relates the experiences of a student in a math class in which the teacher won't teach. It was posted at Kitchen Table Math, a lively math site that has been called "the hippest online math ed community in the known universe."

Hello, my name is Colin Johnston and in this post I will describe the horrors of high school algebra.

On the first day of my junior year, I stepped into my math class. I will leave names out so as not to offend anyone. I had heard mixed reviews about the math teacher that I would have this year, but people generally said he was a pretty good teahcer. As the bell rang, the class sat down and waited patiently for him to enter the room. He slowly stepped into the classroom. He looked like a smart enough guy. He then passed out the textbooks and walked to the front of the classroom. He began talking about the curriculum we would cover this year, his grading scale, etc. He then said something, however, that didn't go down as easily as the other things he had mentioned. He said "You kids have been told how to do everything in your math careers. That is, up until now. This year, you are going to learn how to teach yourselves."

What? Then why don't we just take this class at home, over the internet? What is the point of having a teacher that doesn't teach? I made these same arguments to my friend after class, but he just shruged it off. "It will probably get better as the year goes on." He said. I guess I would give it a shot.

But as this year has gone on, things have gotten worse if anything. Now, the norm for the class is come in, sit down, spend an hour correcting last nights assignment (it takes so long because everyone has so many questions), get the new assignment, and puzzle over it for 10 minutes until you finally give up due to complete lack of understanding. Such is life in the new new math, Constructivism.
As Colin says, why not just take this class at home, over the internet? Maybe constructivists are on to something and this is the wave of the future. It would help save hundreds of billions spent on "education."