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Methods/ Mathematics


             Implications.
             Dienes' theory, like Piaget's emphasized the importance of an active learning environment where children are actively involved or engaged with concrete mathematical representations.
             Dienes' work makes somewhat more explicit the need for teachers to be aware of individual learning rates and styles.
             Van Hieles.
             Dutch educators who taught math for a number of years and discovered students had difficulty understanding geometry. They saw there are five levels a student must past through. .
             5 levels.
             Visualization.
             Their global appearance and not their property recognize shapes.
             Analysis .
             Here students observe the component parts of figures but are unable to explain relationships.
             Informal dedication.
             Here they are able to deduce the properties of figures and express inter relationships, both within and between figures.
             Formal deduction.
             At this level formal deductive proofs can be created.
             Rigor.
             Different axiomatic systems can be compared rigorously.
             Expository Method.
             1. Good expository teaching involves a clear or orderly sequencing of information to be taught.
             2. There is usually some teacher-pupil questioning with this approach so that he broad development of the lesson depends on the pupil's responses.
             3. Exposition in the Primary classroom seems most effective when the pupils are organized into interest groups.
             4. Careful planning is required. Each stage should be understood before moving on to another.
             5. Concrete teaching aids are often used in the initial stages. All teachers' can find useful ideas.
             6. It is essential that questions and answers constitute a dialogue; a pupil's answer should be carefully analyzed.
             7. Even when the answers appear incorrect, exploration initiated by the teacher can lead to decision and proves fruitful to both teacher and student.
             An example of this is the addition of sing digit numbers.
             Step1.
             Teacher presents problem of 3 + 4 after suitable motivation introduction.
             Step 2.


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