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On the 30th September, 1999, Nigeria government launched the universal Basic Education (BE). One of its aims and objectives is to ensure the acquisition of the appropriate levels of literacy, innumeracy, manipulative and life skills, need for laying the foundation for lifelong learning (FRR, 2004). In order to achieve this laudable objective, there is need for effective teaching and learning of Mathematics which is one of the core subjects in both Primary and Secondary schools. Mathematics as a discipline has great input in the scientific and technological development of any Nation.
Attuned (2003) emphasized that Mathematics is a great heritage of human cultures and civilizations. A nation that is eager to develop needs the services of economists, technicians, engineers, technologists, environmentalists and so on. All these must be well trained in Mathematics. The primary school is a very crucial and sensitive period in the life of the child. Children at this level are entering the concrete operational stage of Pigged, a stage at which children could learn concepts if systematically, methodically and appropriately presented.
At this stage, children are introduced to the basics of education. Learning at this stage serves as foundation for future and whatever learns at this level becomes indelible in the memory of the children. The primary school education is a foundation stone and bedrock for later education. For pupils to enjoy learning of Mathematics at this level, there is need to make the environment conducive. Sunder, Dares and Panky (2009) defined the environment as the aggregate of all external conditions as well as influences on life and development of an organism, human behavior and society.
Hence, there are lots of works on the part fetchers to make teaching and learning of mathematics more interesting in our primary schools. Apart from heredity, environment we live in affects our performance Flying and Sorrel, 1994) Salaam (2005) considered poor method of teaching Mathematics at the primary school level as one of the major factors contributing to student’ poor performance in the subject in later life in secondary school level. Thus, there is need for teachers to acquire deep knowledge of the content of the mathematics so as to be able to pass same to the pupils and develop in them a good foundation.
Kola (2006) affirmed that teachers instructional strategies especially at the foundation level of teaching and learning is a vital aspect of the nation’s productive independence. Competency in the teaching methods, skills and techniques are all needed for effective curriculum development. It is necessary for teachers to adopt methods that allow for peer interaction, inquiry, independent discoveries which is necessary for the problem-solving in mathematics. In this paper, attempts are made on the general principles of handling the topics in primary schools syllabus and brief strategies for the teaching some the elementary topics.
SOME METHODS AND TECHNIQUES OF TEACHING MATHEMATICS The life of children could be made or marred depending on how teacher handle the teaching/learning process. This is particularly relevant in the case of mathematics in which topics are in chains. The teacher may acquire mastery of the contents but lack skills in the appropriate methods. This may affect the students understanding of the subjects. There are many approaches to teaching of mathematics. These include: Problem solving * Discovery Approach * Expository * Laboratory * Questioning skills * Individualizing group work * Demonstration, etc. Johnson & Rising, 1972) All these methods are good but no teaching method could be regarded as superior to the other. In application, combination of these methods will be ascribable. It all depends on the content, objectives and the nature of the learners. BASIC PRINCIPLES OF EFFECTIVE TEACHING OF MATHEMATICS 1. Basic stages fetching and learning Facade (1981) identified three significant stages of learning topics in mathematics. These are: * Concrete materials and demonstration of real life situation stage * Semi-concrete or pictorial studies stage * Abstraction stage Pupils in the primary schools have the age ranges between 5 and 12.
This is the age period that coincides approximately with the Piglet’s concrete operational stage. This is a transitional stage between the pre-operational erred (a period when the child cannot yet perform any serious operation, a period of intuition when the child’s reasoning is not yet quite logical) and the formal operational stage (a period when the child thought process now becomes systematic and reasonably well integrated). At the concrete operational stage, the child is able to learn the operations more effectively when the Operations are Concrete because the child’s actions are based on the objects that can be seen.
Thus teachers of mathematics at this stage need to use instructional materials to facilitate thorough grasping of concepts and reminisces. 2. Activity-Based lea ring Technique Learning is more effective when is activity-based. According to Fletcher (1 980), pupils remember easily concepts built by them than concept just passed onto them. Hence, teaching and learning of mathematics should not be teacher and chalkboard interaction alone. Pupils should be actively involved. Thus mathematics lessons should be more interactive and assignment on every concept taught is very important. 3.
Students friendly/ real life Situation Approach Mathematics is a practical subject. Hence a teacher of Mathematics must be friendly and humorous. Students understand a concept very well when it is related to their previous experiences. 4. Teach principles and concepts Inasmuch (2002) suggested that mathematics teacher should depart from the traditional system of instruction which is already endemic in the teaching system. A system where teacher writes topic on the chalkboard, put up the formula and apply is now obsolete. There is need to work from principle and understanding underline concepts.
For example, in a typical primary five lesson where a teacher is to teach ‘Volume of a Cuboids”, he writes the topic on the chalkboard and proceed as follows: Volume of a cuboids = length x breadth x height Example 1 Let the length 1 CM, breadth CM and height 1 Com, find the volume Solution Volvo =lax = economic = comma In the above example, the teacher would not explain the principle behind the formula Volvo. = x box h and reason behind the com unit. By this approach, classroom instructions have been reduced to rote learning in mathematics.
Hence, every mathematics topic is seen as abstract by the pupils. 5. Consideration of Students entry Behaviors Eagan (1985) states that the super ordinate knowledge cannot be learnt unless the subordinate knowledge has been fully understood. Teacher must ensure treatment of pre-requisite knowledge to given topic before attempting to teach the topic. The general syllabus may not be properly arranged. It is the duty of the teacher to make sure that the pupils have sufficient entry behavior before a topic is taught. 6. Graduation and spreading of Examples Classrooms examples must be graduated and well spread.
Classroom examples should cover various categories of problems on a given topic and should be graduated for simplest to presumed difficult topics. 7. Effective Evaluation Approach Evaluation is concerned with acquisition and processing information needed o improve pupils’ learning , a teacher teaching as well as to refine the intrinsic goodness of materials and methods used in the teaching-learning process(Lowell ; Mamas, 2009). This means that in for effective learning to have taken place, teacher must evaluate himself, the pupils, the materials used and strategies applied in the teaching learning process.
Continuous evaluation is necessary at every stage of teaching and learning of mathematics. There is need to select progressive books set out for effective evaluation at every stage of learning process. It important that teachers should give students plenty of graduated home assignment, mark assignment and take time to work out corrections with emphasis on the pupils difficult areas. ILLUSTRATIVE EXAMPLES ON THE TEACHING OF SOME SPECIFIC TOPICS Time and space will not allow consideration of many topics here neither would the treatment be elaborate.
However, guides provided here will show some application of the principles listed. Illustration on the teaching of L. C. M. And H. C. F. 1. Lowest Common Multiples L. C. M. The popular approach among teachers is to write out the prime factors of given numbers and then use them to obtain the L. C. M. It is not that the approach is mathematically wrong. It is one of the good approaches but it is like climbing the tree from the top. The following procedure is however suggested: Entry Behavior: This is the previous knowledge of the students relevant to the topic to be taught.
In this case, teacher should ensure that pupils are familiar with multiples and factors of given numbers. This can be ascertained under the introduction to the topic. Step 1 : Discuss the concept of Common Multiples of two given numbers and use this to identify the common multiple. Step 2: Let the pupils identify the smallest number among the common multiples as the required L C. M. Example Multiples off are 3, 6, 9, 12, 15, 18, 21, 24, . Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, . Common multiples of 3 and 4 are 12, 24, 36, Least Common Multiple (L. C. M. Is 12 More examples should be discussed using the above approach before proceeding to the popular prime factors approach. Step 3: Let the pupils see the prime factors approach as a good method most importantly when multiples are higher numbers. Example: 9 = 3 x 3 12-xx L. C. VI. =2X2X3X3 = 36 Alternatively, We may solve as follows: 12 6 3 L. C. M. =2X2X3X3 The teacher needs to give sufficient graduated exercises on both methods for pupils to practice both in the class and as home assignments. 2. Highest Common Factors H. C. F Like the procedure discussed above for L. C. M. , H. C. F. Would also be treated from the basis. Here, the entry behavior of pupils should include identification of factors of given numbers and the L. C. M. To obtain the H. C. F. Of two or more numbers, the factors of the numbers must be identified first. This should be followed by their common factors and then the highest common factors. For example, Factors of 12 are 1, 2, 3, 4, 12 Factors of 18 are 1, 2, 3, 6, 9, 18 Common factors are 1, 2, 3, 6. In terms of prime factors, the H. C. F. Can be obtained as follows: 24=2x2x2x3 30=2 x 5 Alternatively 2 24 30 2 12 15 15 5 of 24 and 30 TEACHING OF PERIMETER AND AREA OF A RECTANGLE 3.
Perimeter of a rectangle The popular approach among teachers is to draw a rectangle and move straight to Perimeter 2(L + B). They then give one or two examples. The formula is right but rote memorization is encouraged here instead of required spiral approach which is necessary to build mathematical concepts. The following procedure is suggested: Entry Behavior: For this topic, the pre-requisite knowledge of pupils on addition, multiplication of numbers Would be ensured. Step 1 Explain thoroughly the concept of rectangle. A rectangle is a plane figure bounded by four straight lines in which adjacent sides are perpendicular.
Explain the concept of perpendicularity thoroughly by showing actual life examples such as edges Of a cuboids or the classroom or by arranging a ruler perpendicular to the other. Step 2: Show various examples of a rectangle such as surface of a textbook, surface of a table etc. Step 3: Draw rectangles of varying dimensions and facing different directions Step 4: Let the pupils recognize a rectangle as a plane shape having only two emissions Step 5: Let the pupils recognize the perimeter of a plane shape as the total distance round the shape.
Step 6: Lead the pupils to draw rectangles of varying dimensions and measure the perimeters. Step 7: Lead the pupils to derive the formula p + B) b perimeter = I + b + I + b = 21 + b = 20 + b) Step 8: Give graduated examples using formula Type (I) Given I and b as whole numbers Type (ii) Given I and b as decimal fractions Type (iii) Given perimeter with either side to obtain the other side Evaluation: Sufficient practice exercise should be given to the pupils. 4. Area off Rectangle.
With the meaning of rectangle already stated above, the entry behavior here should include addition and multiplication of numbers. The following steps are recommended: Step 1: Let the pupils understand the meaning of area as the amount of surface taking or occupied by a shape. Lead the pupils to compare area of different surface by just estimating relative bigness of the surfaces. Step 2: Lead the pupils to understand that areas are measured in terms of the number of square units (e. G. Square CM) that can be taken out of the objects.
Step 3: Lead the pupils to find by drawing the number of centimeters (I. E. He area) of the following rectangles: (I) CM Length CM, breadth CM (ii) CM CM Length CM, breadth CM (ii) CM CM (I) Area = 1 Come (ii) Area = CACM Step 4: The concept of square centimeter should be clearly illustrated. Let the pupils know that a square centimeter is shape of dimension 1 CM by 1 CM. Step 5: The pupils should be allowed to practice with sufficient examples using counting of square centimeters.
Step 6: After finding area of many rectangles using this approach, pupils should be led to see that in all cases Area ; length x breadth Step 7: Now lead the pupils to use the formula Area = Engel x breadth to find area using graduated examples as in the case of perimeter above. CONCLUSION Primary school is the foundation of a child education. It is an important and sensitive level of education. The way pupils are taught at this level could determine the future not only of the child but also of the nation.
For a country to be technological developed, there is need for efficient handling of mathematics at this and other levels since mathematics is the mother of all of sciences which are bedrock of technological growth. In this paper, we have tried to look into the conceptual way of handling Mathematics in Primary schools. In conclusion, it is necessary to summarize the three basic steps in the teaching of concepts in primary schools. These are: * The content: A teacher must begin by identifying the objectives and the content to b e taught in developing a concept. Method of presentation: The method Of instruction to be adopted should be determined. A resourceful teacher makes use of combination of methods. * Strategy: The strategy to be adopted should also be determined. In doing the teacher must bear in mind ; the mathematical accuracy, meaning to the pupils and the method conferring with psychological principles of teaching, appealing and application. If the en unrated procedures are properly followed, pupils will find learning of mathematical concepts more interesting and attractive.