1. MATH TEACHING METHODS
1. Teaching and Learning – no easy task –
complex process.
2. Each pupil is an individual with a unique
personality.
3. Pupils acquire knowledge, skills and attitudes
at different times, rates and ways.
4. 8 general teaching methods for math:
Co-operative learning Exposition
Guided discovery Games
Laboratory approach Simulations
Problem solving Investigations
5. For effective teaching use a combination of
these methods:
Co-operative groups
1. More a method of organization than a specific
teaching strategy.
2. Pupils work in small groups (4-6) – encourage
to discuss and solve problems
3. Accountable for management of time and
resources both as individuals and as a group.
4. Teacher moves from group to group giving
assistance and encouragement, ask thoughts
provoking questions as the need arises.
2. 5. Group work is visually reported to the entire
class and further discussion ensues.
6. Method allows pupils to work together as a
team fostering co-operation rather than
competition.
7. Provides for pupils – pupils discussion, social
interaction and problem solving abilities.
Implications for Teaching
1. Promotes co-operation among pupils
2. Pupils learn to accept responsibility for their
own learning (autonomy)
3. Reinforces understanding –each pupil can
explain to other group members.
4. Implies change in teachers role from leader to
facilitator and initiator
LIMITATIONS
1. Requires more careful org. and management
skills from the teacher.
2. Demands careful pre-planning and investment of
time and resources in preparing materials.
EXPOSITION METHOD
1. Good expository teaching involves a clear and
proper sequenced explanation by the teacher
of the idea or concept.
3. 2. Usually, there is some teacher-pupil
questioning (dialogue)
3. Careful planning is required – go from what
pupils know – each stage of development
should be understood before the next is begun.
4. All teachers would find useful ideas from
GAGNE – Teaching begins at the lowest level
which serves as a prerequisite for a higher
level.
BRUNER – Math is rep. in at least 3 ways –
enactive, iconic, symbolic
DIENES – (dynamic principle) play should be
incorporated in the teaching of math concepts.
IMPLICATIONS FOR TEACHING
1. Fast and efficient way of giving information
2. Relatively easy to organize and often requires
little teacher preparation.
3. It is possible for teacher to motivate with
enthusiastic and lively discussion
4. The lesson can be regulated according to the
pupils response.
4. LIMITATIONS
1. Poor expository teaching leads to passive
learners
2. Retention and transfer of learning may be
curtailed
3. Does not adequately cater to individual
differences
4. It can be, and generally is, teacher dominated
rather than child-centered
GAMES
1. A procedure which employs skills and/or chance
and has a winner
2. Predominantly used to practice and reinforce
basic skills, additionally can be used to
introduce new concepts and develop logical
thinking and P.S. strategies
IMPLICATIONS FOR TEACHING
1. Usually highly motivating
2. Pupils enjoy playing games
3. More likely to generate greater understanding
and retention
4. Games are an active approach to learning
5. Good attitudes to math are fostered through
games
5. LIMITATIONS
1. Collection and construction of materials for
game is time consuming
2. Classes engaged in playing games are likely to
be noisy
3. A game approach is not suitable to all areas of
the syllabus
GUIDED DISCOVERY
1. Usually involves the teacher presenting a series
of structured situations to the pupils. The pupils
then study these situation in order to discover
some concept or generalization
2. As opposed to exposition, the learner is not told
the rule or generalization by the teacher and then
asked to practice similar problems. Instead
pupils are asked to identify the rule or
generalization.
3. Not all pupils find it easy to ‘discover’ under all
circumstances and this may lead to frustration
and lack of interest in the activity. To avoid
this, it may be necessary to have cards available
with additional clues. These clues will assist the
pupils, through guidance, to discover the rule or
generalization.
6. LIMITATIONS
1. Time consuming for teacher to organize –
some pupils may never discover the concepts
or principles
2. It demands a fair amount of expertise from the
teacher. Requires technical expertise (i.e. how
best to organize or present the subject) and a
good knowledge of the pupils (i.e. how much
help/guidance should be given.
INVESTIGATIONS
1. The idea of an Investigation is fundamental
both to the study of math and also to the
understanding of the ways in which math can
be used to extend knowledge and to solve
problems.
2. An investigation is a form of discovery
3. At its best, pupils will define their own
problems, set procedures and try to solve
them.
4. In the end, it is crucial for the pupils to discuss
not only the outcomes of the investigation but
also the process pursued in trying to pin down
the problem and find answers to the problem
7. 5. As opposed to the guided discovery lesson
where the objectives are clear. An
investigation often covers a broad area of math
objectives and include activities which may
have more than one correct answer
IN DOING INVESTIGATIONS STUDENTS
GENERALLY FOLLOW THE FOLLOWING
FEATURES:
1. Initial problem
2. Data collection
3. Tabulate or organize the data
4. Making and testing conjectures
5. Try new concept if first conjectures are wrong
6. Attempt to prove a rule
7. Generalization of the rule
8. Suggest new or related problems
More able pupils can develop their creativity
doing investigations and can perform all of the
above 8 features.Weaker pupils may only be able
to carry out the first 3 stages.Investigations are
suitable for mixed ability groups
8. IMPLICATIONS
• Suitable for mixed ability groups
• Promotes creativeness
• Can be intrinsically satisfying to pupils
LIMITATIONS
• Require a high degree of teacher imput
• Can be difficult to fit into the conventional
math syllabus
• Can be time consuming
LABORATORY APPROACH
• Approach may be defined as “learning by doing”
• More often than not it involves children playing
and manipulating concrete objects in structured
situations
• Purpose is to build readiness for the
development of more abstract concepts – often
combined with guided discovery methods
IMPLICATIONS FOR TEACHING
• The approach has the support of theorists
• In an organized situation, pupils are able to
proceed at their own rate
9. • Pupils develop their own spirit of inquiry
• It is especially useful for younger children and
slower learners
LIMITATIONS
• Requires a good supply of materials and
suitable designed classrooms
• Demands a fair amount of teacher preparation
and creativeness
PROBLEM SOLVING
The ability to solve problems is at the heart of
mathematics. Mathematics is only ‘useful’ to the
extent to which it can be applied to particular
situation and it is the ability to apply mathematics to
a variety of situation to which we give the name
‘problem solving’
SIMULATIONS
• A simulations can be defined as a reconstruction
of a situation or a series of events which may
happen in any community.
• A simulation required each pupil to make
decisions based on previous training and
available information.
10. • After the pupils make a decision, they are
provided with opportunities to see or discuss one
or more possible consequences of this
decision—in some ways simulations are really
sophisticated games such as monopoly.
IMPLICATIONS
• It is related to pupil’s own experience and thus
motivating
• It is an active approach to learning
• It fosters retention
• It develops new roles functions for both teacher
and pupil
• It fosters cooperation among students
• It relates mathematics to ‘real-life situations’.
LIMITATIONS
• These are similar to games, that is, time
consuming to construct, not applicable to all
topics and likely to generate a fair amount of
noise.
