Page 26 - Professorial Lecture - Prof Kasanda

students are taught the mechanics of obtaining the correct answer at the
expense of understanding relationships among these facts. Backhouse,
Haggarty, Pirie, & Stratton (1992, p. 36) note that “…there are a good
many teachers who teach rules without the reasons for them.” We should
not take this to mean that there is no place for mechanical learning or
memorization of facts in the mathematics classrooms. There is. It will be a
waste of time and effort for a teacher to always show division of whole
numbers using long division when shorter and more efficient mechanical
methods could be used. Backhouse et al. (1992, p. 37) note “…for short-
term learning, the rewards of instrumental understanding are immediate
and can be seen in correct answers…” Nonetheless instrumental or
mechanical teaching and learning may prove detrimental to learners’
grasp of advanced mathematics content later in their studies. In fact
content instrumentally learned is soon forgotten. What type of teaching
takes place in our classrooms and lecture rooms? Are we teaching “rules”
for learners and students to memorize and pass our subjects? Sadly given
the evidence in both Tables 1 and 2, one is forced to conclude that
mechanical or surface teaching (Skemp, 1976; Johnes, 2006) is taking
place in our schools and by extension in our lecture rooms. Indeed, given
the large numbers of students especially in the first year of study at UNAM
often in excess of 1000 students, the lecturer has probably no other
alternative than to use the lecture method that often is associated with
memorization and regurgitation of content to enable him or her to
present large quantities of facts and information (Johnes, 2006) to the
students, often with little understanding being achieved, hence the large
number of failures in the first year mathematics courses evidenced at
UNAM.

What is the possible solution or suggestion to improving performance in
mathematics in our schools and at our University? The answer may lie in
teaching mathematics for understanding (Amoonga, 2008; Amoonga and
Kasanda, 2010) rather than teaching for regurgitation. The use of

24 |