Some comments on the dismal state of mathematics in today's education
Primary and secondary education is in a constant ferment both in the United States and Britain. It is easier to find out about the British state of things than the American, because in America education is atomized into tiny, uncoordinated fragments. Every local authority does its own thing there, and the results cannot be anything but uneven and, generally, poor. There are no standards except the ragged ones established by states to "assess the results of education." I have discussed the Colorado situation on another page. Here are some thoughts after reading the BBC Education website on the subject recently.
No one really knows whom to hold responsible for evident failure: teachers, pupils, administrators, parents or the entity called the "school". Schools are rated as "failing", and it is difficult to resist this classification when the results in some schools are consistently bad, and in some schools consistently good. However, wholesale changes in staff seldom make much of a difference. The same holds for teachers, with the apparent belief that a good teacher can not only make a pupil want to learn, but to learn successfully. This is true, of course, to some degree, but such people that make a real difference are so rare and unlikely to be found in a school that it cannot be the foundation of a good school.
The "best" schools seem to know how to be "best": make certain only to take on good pupils. It must certainly be the pupils that are responsible for satisfactory progress, if they are given the necessary resources, which are minimal, and cannot include superior teachers. Oddly, when they fail, it is the school that is held responsible, not the pupil. This curious fact must somehow trickle down to the pupil, with the result that all incentive disappears.
Teachers are better and better paid, but their lives must be a misery. I cannot understand why anyone would continue in the teaching "profession", which is not a "profession" but menial employment under a horde of prying supervisors, after their initial enthusiasm for teaching children is beaten out of them. Teaching cannot, and does not, generally attract people of high or average intellectual power, but makes do with those who enter the field for some other reason. Teachers are blamed for a "failing" school, not the pupils or the administrators, who are the real perpetrators.
As reported by the London Institute of Education, there is a severe shortage of teachers with any qualifications in mathematics or science, and these subjects are generally "taught" by those with no knowledge or appreciation of them. In the United States, there are no teachers with real subject qualifications at all, just various specializations and majors. It is said that many actually brag about not having any knowledge of mathematics or science, as somehow distinguishing them as literary or cultured. It distinguishes them as stupid. There needs to be no other reason to explain the disappearance of real mathematics in primary and secondary education, and for the poor performance of pupils in these subjects. In primary education, the pupil encounters no person with knowledge beyond the minimum required to function in society. The result is not surprising. However, the teachers are not to blame for this state of affairs: those who manage the schools are. Here are stupid people that ensure that the whole system is suffused with stupidity from bottom to top. This is not a new phenomenon by any means. I have observed it as a victim of the system, and as an observer. The facts are hard, but there they are.
A primary education of six to eight years is ample for transmitting the skills of reading, writing and everyday calculation. That this has been unsatisfactorily done with reading and writing is well-known, and is an absolute disgrace. It does not take much intelligence to grasp these subjects, and practically everyone is capable of it. However, I have seen American college students in which the skills are not satisfactorily developed.
What is so glibly called "maths" or "mathematics" in teacher parlance is really not that at all, but arithmetic or logistic in older terminology, or "the maths required for everyday life and work". This is simple calculation, and there is little theory behind it. Some people think that there is merit in doing addition and subtraction without a calculator, and there is, but not much. Doing it by hand does not teach anything--it is solely rote work depending on memorization of tables of addition, subtraction and multiplication. It does not even come close to mathematics in its school form. A pocket calculator is far superior to calculation on paper, especially in accuracy. In the recent revisions of the British A-level examinations in mathematics (a level somewhat above US high school graduate level) the use of calculators was recently restricted, "so that the concepts would be better understood." The concepts turn out to be the rote memorization of a list of some 40 formulas for working out certain problems. Do you see what I mean about stupid people?
It is also reported that pupils have diffculties with problem solving, fractions, decimals and percentages. They also find multiplication and division a bit hard, but are OK with addition and subtraction. This is evidence of attainment that used to be reached in the first or second grade, but now pupils struggle with it years later, apparently. Anyone who cannot learn or teach this material is unfit for anything by the most menial manual agricultural employment.
Nurses seem to occasionally have problems with decimal points, giving some child 10 grams instead of 10 milligrams of a potent chemical. This is probably more a result of carelessness than arithmetic skills, but it still shows a bad grasp of magnitudes, that is exacerbated by the decimal system, where everything depends on a modest little point. The "mathematical" skills of the whole medical profession might be doubtful, if we have people here who are proud of their stupidity. Current attempts to replace medical professionals with nurses is ill-advised, since nurses are not expected to have analytical or problem-solving capabilities, but to carry out prescribed procedures conscientiously and accurately.
I believe that language is the key to education. Someone with "mathematics" but no letters can only be a kind of idiot-savant. An intelligent person can be ignorant of mathematics, because interest has been absent, but is still capable of it. A person not capable of mathematics--without the quotes--is not intelligent. Language is part of our mental inheritance. Through writing, it can be extended magnificently by the active intelligence, and furnishes the universe of thought. Mathematics is created by man through logic; it is a completely human creation, and can be intensely interesting and fascinating. It has also been of great practical power, a power unknown to the non-mathematical. It comes at levels suitable for all degrees of intelligence as well.
Simple numeracy is both entertaining and useful, and available to nearly everyone. It is much more than the ability to perform mental arithmetic, a rote skill that is so much admired by educators. However, educators do not seem to know how to develop numeracy beyond this modest skill, because they are not numerate themselves, and because they are not, actively despise it to cover their own inadequacies.
I know a university professor who teaches electric circuits to engineering students. This professor has never once used what he teaches for any purpose whatsoever. He makes up examination questions and evaluates the students' responses, but he has had no experience with the application of the subject to real problems. He is one of a great number about which similar things could be said. Most teaching is in this spirit today, at all levels. Teachers, indeed, are not encouraged to add application and breadth to their knowledge, but just to teach. Mere teaching skills must be subordinated to intellectual skills; they are useless by themselves. In primary and seconday schools, mathematics is not taught, because there is no one there who understands mathematics, or likes mathematics, and this situation is not likely to change. The rare exception makes the papers.
Composed by J. B. Calvert
Created 3 October 2000