The
three prominent researchers of cognitive theories that is related to
the learning and teaching of mathematics
are Robert Gagne, Jerome Bruner and David Ausubel, they all put forward their ideas
initially in the 1960s , at that time,
all three were established in their carriers and recognized as authorities in their
own right. All the three attempted to define
cognitive theories of instruction; this coincided with periods of tremendous growth in scientific knowledge and expansion of,
what was now in these Western Countries Universal Secondary Education
Bruner advocated discovery learning and
gained very wide acceptance at least in schools.
The three stages of Bruner’s theory
of intellectual development are;
i.
enactive where a person learns about the world
through actions or objects
ii.
Iconic
where learning occurs through using models and pictures
iii.
Symbolic
which describes the capacity to think in abstract terms. The underlying principle
for teaching and learning at least mathematics is that a combination of concrete,
pictorial, then symbolic activities will leads to more effective learning.
Mathematics teachers should apply the burner’s theory in the following progression:
start with a concrete experience then move to pictures and finally use symbolic
representation. Students should equally be encouraged by their teachers to use
discovery learning techniques since anything discovered by the students themselves
tends to be retained for a longer period of time.
David Ausubel’s notable contribution
to the subject matter was the notion of the “advanced organizer” the advance organizer simply means a device or a mental learning
aid to help students “get a grip
“ on the new information. Put in more difficult language,
according to David Ausubel, the advance organizer is a means of preparing the
learners cognitive structure for the learning experience about to take place.
It is a device to activate the relevant schema or conceptual pattern so that
new information would be more readily ‘subsumed’ into the learners existing
cognitive structure or mental depiction. The implication of Ausubel’s theory of advance organizer in teaching and learning of mathematics is that the teacher
should always ignite and sustain the
attention and interest of his students while delivering his lessons
In the other hand, Robert Gagne was
concerned with the problem of determining just what skills and knowledge are
required for someone to be an effective performer at a given task.
He suggested that a task would be best learnt by following specific sequence of nine events
namely: gaining attention, informing the
learner of the objectives, stimulating
recall of prerequisite learning, presenting new materials, providing guidance, eliciting performances, providing
feedback about correctness, assessing performance, and enhance retention and
recall. These notions of task analysis and the importance of the correct
sequencing of instruction are followed by most mathematics teachers when designing
their progrmames.
Again the concept of Gagne’s
knowledge hierarchy leads to the
assumption that it is important to present all the necessary lower level facts before
proceeding to teach at higher level, related to this is the concept that people
can reason with higher – level concepts
if they have learned all the prerequisites lower -level information