Last summer, I asked one of my students if he was interested in spending some of his free time to study mathematics. The student looked at me and said 'I could forget what I learn now so I will wait until I come back to school then". At that time, in my mind, I would say to him 'If you understand the concept of mathematics then you won't forget' but I was quiet. I can not blame my student for his conception of studying mathematics. There have been more than one occasion, as his tutor, I have been required from the parents to teach him how to memorize formulas, different techniques of how to find answers quickly during multiple choice exams. Procedural efficiency and techniques of quick recall mathematical facts appear to play an effective role in this situation The student’s marks has been improved and he passed all his math exams last year
Instrumental understanding in mathematical learning has been wide spread in Canada due to mechanism of school testing and high entrance academic requirements from a number of well known universities. This conception of learning and teaching mathematics would carry various potential levels of difficulties for the students in the future when they try to apply their knowledge in research environment. Even though relational understanding in mathematics is a complexity process that would take time and a lot of effort from both perspective of learning and teaching. We can not ignore the fact that the degree of understanding will decide the degree of academic achievement of a student in the future.
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