Variation in first year college students’ understanding on their conceptions of and approaches to solving mathematical problems / Parmjit Singh

A primary goal of mathematics learning and teaching in secondary school is to develop student’s ability to solve a wide variety of complex mathematical problems as a preparatory stage for college. complex mathematical problems as a preparatory stage for college.
In view of this, the objective of this paper is to investigate the mastery
of content level that first year college students bring with them to
the mathematics classroom with reference to their national
examination grades (Sijil Pelajaran Malaysia). The study
investigated the conceptions of 127 student and their heuristic
actions in mathematical problem solving. Among these students
98.5% had obtained an A grade in the national examination for
mathematics. Both quantitative and qualitative approaches, namely
written assessment (five mathematical problems) and interviews were
utilized in assessing student’s relational understanding of
mathematical concepts in problem solving. The percentage of correct
responses from these students, who can be considered as the cream
of the crop of the nation, for the five items in the written test were
74.8%, 72.4%, 67.7%, 52.8% and 18.9 %.The data indicates that
the grades obtained in the national examination did not reflect their
mathematical knowledge in mathematical problem solving. The study
concludes that capable mathematics students (the ones who obtained
an A grade in the national examination) when placed in the context
of non-routine problems have difficulty solving what may be considered elementary mathematics for their level of task
achievement. This evidence seemingly indicates that many students
from high schools are not acquiring the mathematical skills expected
of college level mathematics.