The present first lady of the U.S., Michelle Obama, has a piece in which she brings out the usual assumptive bromides of education–its overwhelming importance to economic development–the importance of teacher credentials–the steps being taken by her husband’s government–and, etc..
The Obamas, great supporters of the public school system, send their children to a private school and always have, but you can’t ignore the appetite of teacher unions for leftist politicians and the support they give you and paradoxes never bother politicians because consistency doesn’t get votes.
One quote, "And good teachers aren’t just critical for the success of our students. They are the key to the success of our economy." You can read the rest by clicking on “piece” above.
For a less polemic, and a more data based reply see "Does Education Matter" by Alison Wolf.
Wolf, A. (2002) Does Education Matter? Myths about education and economic growth . London: Penguin Books.
from the book: Shadow Dancing on the Grave of Hope:
This worked so well with Whole Language, we thought we’d have the same success with mathematics
The National Council of Teachers of Mathematics (NCTM) decided that too many students were abandoning mathematics as soon as they could. Their answer, of course, was not in methods which taught mathematics in the most effective and positive way, but from "experience" and a good hard think about what should be done from the viewpoint of "social justice", child-free theories of learning and political considerations.
The problem with relying on experience, is that it is a poor teacher, especially in teaching, where many students learn in spite of the teaching methods. The problem with having a good hard think, especially when using a committee, is that group consensus takes over and produces the fad du jour as NCTM has done twice before. So it was with the 1989 Standards produced by the NCTM, which have had a large impact on elementary and high school mathematics teaching throughout North America. An additional problem with the NCTM Standards is that they were written by elementary and high school teachers and the mathematics is murky and often incorrect, according to many mathematicians. The wondrous paradox in mathematics teaching is that, in spite of the precision of mathematics, the NCTM analysis of the subskills required is of the same poor quality as teacher produced documents in other academic areas. As one critic said, "’Explore’, ‘develop’, and ‘understand’, and their variants, are much more prominent in the text than ‘know’,'prove’, and ‘remember’." If that were not enough, the NCTM Standards are based on a mistaken notion of the nature of committees and co-operation in the workplace. The framers of the Standards seem to believe that "training workshops" for civil servants, where everyone enjoys a catered lunch and spends hours solving problems "with input from everyone" is the workplace norm. As faithful descendants of John Dewey, they regard individualism with suspicion and collectivism with favor. As civil servants, of course, it is their notion of productive work which is suspect. In spite of its obvious failings, the NCTM standards have been adopted by almost every state and province as the criteria by which textbooks are judged.
The California State Mathematics Framework, based on the NCTM Standards, was published in 1992. It stated, "It is a myth that children must master lower-order skills before they master higher ones." Mathematics, apparently, is the only pursuit for which this is true. California repudiated these Standards in 1997 after poor results and complaints of parents. Large scale polgrams are easier to refute because the bad results are apparent to so many people and result in many complaints.
The NCTM Standards used the same faulty construction process as the California Whole Language fiasco. This included:
1. Creation by committee.
2. Ignoring research. As usual, in state-protected monopolies, political correctness and fads predominated. One NCTM gem on this is, "The question, "Is Curriculum A better than Curriculum B?" is not a good research question because it is not really answerable." As usual, all curricula are the same, therefore, they must all be treated with respect. Then, ignoring this operating assumption, the NCTM goes on to make very strong recommendations about what a mathematics curriculum should be, including the fact that mathematics subskills should be de-emphasized.
This appeared in a net-based journal on mathematics: "Starting in 1968, the government funded a huge study called Project Follow-Through. It cost a billion dollars and ran almost thirty years. The purpose was to examine how different teaching methods or philosophies affected student performance. What they found was that the traditional "direct instruction" method was the most effective. Are you familiar with this study?"
Gail Burrill, President of the National Council of Teachers of Mathematics replied, "I have never heard of it." This is one of the clearest examples of the title of this section. When people rely on their own experience, they ignore the research done by hundreds of people. Ms. Burrill has written a series of teaching programs for mathematics obviously not based on the largest research project on teaching.
Subsequently, research has shown many instances in which texts based on NCTM principles have: a), lowered scores on standardized tests, or, b), produced much worse results than Direct Instruction. This has been ignored by the apologists of the Standards who, like all others in these instances, are more interested in defending their philosophy than dealing with the data because their jobs are guaranteed.
3. Domination by layman-based theory vaguely based on psychological and educational theorizing without data support.
4. Faith in teachers to apply concepts guided only by the underlying philosophy. In this case; however, training may have made matters worse by training teachers to carefully do something which does not work.
5. Accolades from those who don’t know anything about teaching mathematics but like the underlying assumptions about how children learn to do mathematics.
6. Lots of money made by those who teach the "new philosophy" or, for the more academically inclined, the new paradigm.
The only entertaining debate in education I have been able to find is whether these techniques are more detrimental to teaching reading or mathematics. There is no definitive answer to this intriguing question. Many students give up on mathematics. This is because it has been taught so poorly, with so little emphasis on fluency, not because of the intrinsic difficulty of the subject although, mathematics, of all subjects, is easiest to present as an extended IQ test with mathematical puzzles and tests.
The kind of mathematics based on the NCTM Standards can be called: arithmetic-free math, skill-free math, social math, random discovery math, answer-free math, theoretical math, mathematics-free math, mathematics without numbers and so on. One book inspired by it and emphasizing all the things the progressivists think they know was called "Rain Forest Algebra". Reading these Standards is a strange experience because they give pride of place to every educational misconception currently in favor with those to whom philosophy of education is more important than results. A widely used "reform" text has this in the teacher’s guide for the 2nd grade. "…there is no such thing as a number fact. There are only relationships and these relationships are created inside the child’s head." This post-modern jargon, which holds that reality is "socially constructed", is at the heart of many of the problems with modern education. One of the critics of this philosophy offered to allow those who believe that gravity is a socially constructed concept to refute gravity’s reality by launching themselves from the balcony of his high-rise apartment. I’d pay money to see it and would be willing to bet the splat would be the same as that made by those who believe that gravity is a law of physics, independent of people’s perception of its validity.
A similar pseudo debate as that in reading has been going on in teaching mathematics. The debate is between teaching facts and teaching understanding. A good program, of course, teaches both. The "reform" movement, based on the same non-data notions from the same non-teachers we have already seen, says that it is teaching understanding and ends up teaching neither problem-solving nor basic facts. In California, for example, the mathematics standards based on reform mathematics, did not expect students to do long division with divisors larger than one digit–ever. The students do, however, have to write about their feelings while doing their math projects. At this point, California’s fourth grade students were better than Louisiana and Mississippi and worse than 36 of the other 39 states tested. The rationalizations about this are just as fascinating as those about the failure of Whole Language. A generation of students has been condemned to a "revolutionary" teaching method which has never been demonstrated to work. Fifty-four percent of the freshmen entering California State University needed remedial mathematics. Programs based on NCTM mathematics have the distinction of being inferior to traditional mathematical methods. It is difficult to believe that anything could be worse than traditional methods. In the exotic world of education, the NCTM Standards were designed to help lower-scoring groups. Naturally, they did the opposite. The supporters of NCTM believe that since the new "approach" would teach mathematics more effectively, and stated that critics of the Standards believed that, "…the Standards could be seen as a threat to the current social order." Instead, the Standards produced poorer learning in the groups the Standards were supposed to "serve".
In one experiment pitting Direct Instruction against a program based on NCTM, the lower half of the Direct Instruction group performed better than the NCTM group. In addition, the Direct Instruction teacher assigned little homework and needed very little preparation time. Direct Instruction was much more effective and efficient.
Two programs have been demonstrated to be vastly superior to NCTM dogma. The Direct Instruction methods of Engelmann and his associates consistently outperformed other methods with young children in Project Follow Through and have done so in many other experiments and demonstrations since then. John Saxon, who was unsatisfied with mathematics textbooks, developed a series of texts based on careful increases in the skill set and cumulative review to produce fluency. The Saxon curricula regularly outperform standard texts by a wide margin. Many states rejected them, with South Carolina’s textbook adoption committee giving them a score of 20 out of 100, the lowest score possible. In many states where pilot projects had shown large increases in test scores and in the number of students taking advanced courses, textbook adoption committees rejected Saxon books because they did not reflect the NCTM methods. In the upper grades, exposure to the Saxon methods dramatically increases the likelihood that students take advanced mathematics. The poignancy of the Saxon story is that he regularly offered free textbooks nationwide to any school which would use them properly. His offer was accepted infrequently, indicating, once again, that the education system is more interested in form than function. The arrogance of the NCTM is an example of what happens when a state-supported organization must defend its power base. The defense of the power base becomes more important than producing results. As Saxon says, "A mathematician will say ‘prove it’ when you state a premise. An NCTMer will say, ‘Who are you?’" (Education week, December 6, 1996).
The success of Saxon and Direct Instruction shows that the NCTM process is flawed beyond repair. For Saxon and Direct Instruction, the sequence of teaching is produced by field testing over many years. For the NCTM, a committee builds a consensus. Naturally, students only respond to what works and not to a consensus of what should work according to current theory. The NCTM is not interested in this kind of development as witnessed by the comment of a president of NCTM about the results of Project Follow Through quoted above, "I have never heard of it." A surgeon hears about this new device called a scalpel and is asked what he thinks of it. "I’ve never heard of it.", he replies.
The debate on mathematics is based on a failure to separate curriculum from teaching methods. In the "old days", mathematics teaching used methods based on the notion of, "Many will be called, but few chosen". If a student did not succeed in learning mathematics, the student was inferior. The conclusion was, that many students hated math because it wasn’t interesting enough. If the teaching methods outlined in this chapter are used, almost all students can learn mathematics without pain and frustration although natural aptitude forces a ceiling as always. The reason the drill needed to learn mathematical facts is usually so boring is that it does not use goals, encouragement, reinforcement and proper sequencing and moving on when an aim is met. Students will hate math until the component skills are taught to the level of fluency required to proceed successfully to the next set of skills. If given a task for which they are not prepared, most will give up and curse the frustration brought by vain attempts. Mathematics is not unique in this.
Proponents of NCTM mathematics and Whole Language have maintained that neither has been refuted because neither has been "really tried". This illustrates Karl Popper’s contention which applies to many other areas in the social sciences: "If something is so vague that it cannot be disconfirmed, it is scientifically useless."
Cheers and ttfn,
Grant Coulson