Before implementing solutions to a problem, it is wise to understand what the issues are.
In 1957, our government and business leaders began to recognize that high-level Science and Technology were essential to our economy and national security, requiring a large number of people trained in Mathematics, the language of Science. It also became apparent, and more so over the next 60 years, that the performance of US students in the subject averaged mediocre at best, when compared with other industrialized nations.
The conclusion that the experts came to was that there was too much rote memorization in US education, and not enough understanding. Interestingly, the many groups of Mathematics education reformers rarely include actual mathematicians. When they do, it is most often ones whose work does not require the use of tools such as the Calculus and Trigonometry.
The implemented solution was the 'New Math', and was a disaster, in large part because the teachers didn't understand what they were doing.
Later, when the situation stubbornly refused to improve, the new reformers introduced ideas such as 'lean and lively' Calculus (i.e. teach less) and taught students to use calculators and computer systems to do the rote calculations.
The end result has been that the percentage of students who have learnt the bare required facts and can do the basic computations has shrunk. Of the remainder, many have decayed their skills so far that they cannot correctly input expressions to their computing devices, and cannot understand the resulting outputs. God forbid if you ask them to do anything with fractions or percentages.
The underlying problem was that the 'expert' reformers did not understand that Mathematics is both a language and a mode of thinking. Except for the savants, its learning requires repetition of operations, by hand. After all, we don't expect people to learn instruments by listening to music, do we?
In years past, I had classes prepare a study sheet for first semester Calculus. Most could fit every definition, theorem and rule required on less than one sheet of paper. For how many subjects could one say that?
However, when I awarded 20% of the grade on the final (announced beforehand) to reproduce 3-4 of the definitions and statements of theorems, no more than 1 in 20 of the students could get them correct.
So much for 'rote learning'.
2 comments:
I like the music analogy.
Some years ago I came across a similar problem, a young chap with a chemistry degree who did not understand how to balance fairly simple chemical equations.
It is a basic aspect of understanding chemical reactions, one which I covered at school, but this chap had no idea. As far as I could see, he hadn't even been taught that simple chemical reactions occur in certain fixed proportions.
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