Conceptions of functions among first degree and diploma students / Siti Aishah Sheikh Abdullah

The concept of functions is one of the most important topics in mathematics
learning. However many studies have indicated various difficulties students
exhibited in learning the concept of functions. Tall & Vinner used the term
concept images to describe how students think about concepts. A person S
concept image can differ greatly from the formal mathematical definitions of
the concept. This study explores an aspect of understanding the concept of
functions related to this theme. One hundred and ninety university students
from two different universities and with a different academic background
participated in the study. The first group of students were diploma students in
their second semester of engineering programme. The second group were first
year students enroll in science based degree in another higher institutions.
Data were gathered from questionnaires which asked students to identify
functions in graphic and algebraic forms. They were also requested to give
reasons for their choices. A large number of students indicated a strong
tendency to observe function only as a formula between x and y. Their
justification for rejecting or accepting representations of functions showed a
rather rigid and limited understanding of the concept. Many were unable to
give clear reasoning explaining their choices according to the formal definition
from their previous learning.