Math­e­mat­ics is a very hu­man ac­tiv­ity

The Compass - - OPINION -

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.

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