Mathematics is a very human activity
Along with the tempestuous seasons of Nfld two times a year, we also are entertained by tempestuous public discussions on mathematics in high schools, every five years or so. (Please see: Why N.L.‘s math curriculum is failing students - CBC interview of Prof. Sherry Mantyka, MUN.)
After the tempest, the government take stock of the overall damage, figure out new solutions and how well to “implement” them with the help of committees of experts in the psychology of learning, believers in the relevance of calculators, experts on the educational uses of cyber paraphernalia to produce yet another set of new methods and textbooks to suit the young minds of the second decade of the 21st century — and most likely the results will turn out to be just as before!
“There is no royal road to geometry,” so replied Euclid when the ruler PtolemyI Soter asked Euclid if there was a shorter road to learning geometry than through Euclid’s Elements. When I started learning English in Grade 4 in India, I did look for the ‘royal road’ but could not. I am still learning it.
Mathematics is the same, like learning a foreign language; royal road! no dice!
Let’s look at the overall picture (re: high school mathematics). The “discovery method” (discovering math concepts) has not worked for the past 20 years or so. It did not work for Columbus. He tried to discover India without learning any concrete facts about it, and ended up bumping into North America at the nick of time. (The crew were planning to murder him the next morning as they were getting tired of his merry-goose-chase.)
The discovery-textbooks on mathematics don’t seem to make any sense either to teachers or to students. They don’t explain the techniques, explicitly write out the formulae, give examples, and THEN let the students make further discoveries. The math teachers themselves that I talked to told me that they don’t use the textbooks, but only the workbooks where problems and formulae are.
When I ask my first-year college/university math students, most of them are not even aware of a textbook.
Power-points, Smart-boards, DL etc. are another story. So what is wrog?
I have taught math and physics for more than 25 years, and have had great discussions with my friends and colleagues who were successful teachers. What I am convinced of, for successful math learning, is: 1. More humans and less machines to teach; 2. Smaller classes (less than 15) so that students can develop a friendly relationship with the teacher. We all know that teacher-student friendship is important for learning. Fifteen students seems to be a magic number;
3. Mathematics can be learned only by doing problems, just like language can be learned only by using words. With smaller classes, the teacher will have time to help students individually with their solutions and writing style.
4. There are excellent textbooks in the market, with many real-life questions involving biology, ethnology, ecology, psychology, and even linguistics. There is no need to write any methodology-based new books, particularly books that even teachers find hard to make “discoveries” with;
5. Numerical fluency should be constantly developed through mental arithmetic. Calculators should not be allowed, excepting in problems with large decimal numbers;
6. If possible, there should be more lectures and/or tutorial classes for mathematics assigned in the normal timetable, even if it requires reducing the total number of subjects.
The reader and the government may feel let down — the above suggestions don’t seem to involve our advanced technology, but only mere human beings. But mathematics is a very human activity.
K.S. Ramadurai writes from Carbonear. He is an instructor of mathematics and physics at the College of the North Atlantic in Carbonear.