. Teaching and Learning – no easy task – complex process. 2. 2. Each pupil is an individual with a unique personality. 3. 3. Pupils acquire knowledge, skills and attitudes at different times, rates and ways. 4. 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. 1. More a method of organization than a specific teaching strategy. 2. 2.

Pupils work in small groups (4-6) – encourage to discuss and solve problems 3. 3. Accountable for management of time and resources both as individuals and as a group. 4. 4. Teacher moves from group to group giving assistance and encouragement, ask thoughts provoking questions as the need arises. 1. 5. Group work is visually reported to the entire class and further discussion ensues. 2. 6. Method allows pupils to work together as a team fostering co-operation rather than competition. 3. 7. Provides for pupils – pupils discussion, social interaction and problem solving abilities. Implications for Teaching . 1. Promotes co-operation among pupils 2. 2. Pupils learn to accept responsibility for their own learning (autonomy) 3. 3. Reinforces understanding –each pupil can explain to other group members. 4. 4. Implies change in teachers role from leader to facilitator and initiator LIMITATIONS 1. 1. Requires more careful org. and management skills from the teacher. 2. 2. Demands careful pre-planning and investment of time and resources in preparing materials. EXPOSITION METHOD 1. 1. Good expository teaching involves a clear and proper sequenced explanation by the teacher of the idea or concept. . 2. Usually, there is some teacher-pupil questioning (dialogue) 2. 3. Careful planning is required – go from what pupils know – each stage of development should be understood before the next is begun. 3. 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. 1. Fast and efficient way of giving information . 2. Relatively easy to organize and often requires little teacher preparation. 3. 3. It is possible for teacher to motivate with enthusiastic and lively discussion 4. 4. The lesson can be regulated according to the pupils response. LIMITATIONS 1. 1. Poor expository teaching leads to passive learners 2. 2. Retention and transfer of learning may be curtailed 3. 3. Does not adequately cater to individual differences 4. 4. It can be, and generally is, teacher dominated rather than child-centered GAMES 1. 1. A procedure which employs skills and/or chance and has a winner 2. 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. 1. Usually highly motivating 2. 2. Pupils enjoy playing games 3. 3. More likely to generate greater understanding and retention 4. 4. Games are an active approach to learning 5. 5. Good attitudes to math are fostered through games LIMITATIONS 1. 1. Collection and construction of materials for game is time consuming 2. 2. Classes engaged in playing games are likely to be noisy 3. 3. A game approach is not suitable to all areas of the syllabus

GUIDED DISCOVERY 1. 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. 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. 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. LIMITATIONS 1. 1. Time consuming for teacher to organize – some pupils may never discover the concepts or principles 2. 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. 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. 3. At its best, pupils will define their own problems, set procedures and try to solve them. 4. 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 1. 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. 2. Data collection 3. 3. Tabulate or organize the data 4. 4. Making and testing conjectures 5. 5. Try new concept if first conjectures are wrong 6. 6. Attempt to prove a rule 7. 7. Generalization of the rule 8. 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 IMPLICATIONS 1. • Suitable for mixed ability groups 2. • Promotes creativeness 3. • Can be intrinsically satisfying to pupils

LIMITATIONS 1. • Require a high degree of teacher imput 2. • Can be difficult to fit into the conventional math syllabus 3. • Can be time consuming LABORATORY APPROACH 1. • Approach may be defined as “learning by doing” 2. • More often than not it involves children playing and manipulating concrete objects in structured situations 3. • Purpose is to build readiness for the development of more abstract concepts – often combined with guided discovery methods IMPLICATIONS FOR TEACHING 1. • The approach has the support of theorists 2. • In an organized situation, pupils are able to proceed at their own rate . • Pupils develop their own spirit of inquiry 2. • It is especially useful for younger children and slower learners LIMITATIONS 1. • Requires a good supply of materials and suitable designed classrooms 2. • 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. 2. • A simulation required each pupil to make decisions based on previous training and available information. 1. • 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 2. • It is an active approach to learning 3. • It fosters retention 4. • It develops new roles functions for both teacher and pupil 5. • It fosters cooperation among students 6. • It relates mathematics to ‘real-life situations’. LIMITATIONS 1. • 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. 2.

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