Islands of superficial knowledge without a canoe to get from one end to the other: the nature of college mathematics / Parmjit Singh and Teoh Sian Hoon

Successful mathematics students do indeed construct a fairly large number and variety of algorithms in order to continue to achieve good results in college mathematics courses. However, what is the quality of this mathematical knowledge ‘accumulated’ from the courses taken? How well do the college examination grades in mathematics courses reflect the student’s mathematical thinking? Utilizing both quantitative and qualitative approaches, the findings indicate that the sixty-four college students involved in this study have learnt how to do numerical computation at the expense of learning how to think mathematically. The findings poignantly revealed that the accumulation of mathematics courses taken and the grades obtained in their end of semester examination do not correlate with their mathematical knowledge. The clinical interviews findings indicate that these students have an instrumental understanding rather than a relational understanding due to their emphasis on procedure rather than the process of learning. They ignore things like context, structure and situation as being crucial for constructing mathematical knowledge. Unfortunately, the development of mathematical thinking in their learning is overshadowed by an instructional focus on decontextualized content and the imparting of facts necessary to pass end semester examinations. They end up with islands of superficial knowledge without a canoe to get from one end to the other.