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Solving problems is an everyday requirement starting from how

to get a meal.
To solve a problem one must consider 
strategies necessary to 
arrive at the solution
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When given a problem one is supposed to follow the procedure of problem solving,which involves
  1. Reading the problem to understand what  is required 
  2. Listing the information given in the  problem 
  3. Identify the required formula or a number relationship which will help solve the problem. 
  4. Substitute the relevant information in the formula or the number relationship. 
  5. Perform the necessary calculations 
  6. Answer the question asked in the problem.
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Teaching Mathematics Effectively At

Primary Teacher Training Colleges
There is an urgent need to sensitize  mathematics tutors on when to teach 
aspects of PTE paper 2 to our trainees.
We teach our trainees on how to make  the scheme of work and how to lesson plan yet we spend very little time to teach them how to teach mathematics to the pupils. 
We do not spend enough time on  methods of teaching mathematics to pupils.
We mention and even sometimes  describe what the methods are but we 
rarely illustrate to them on how to teach  given concepts by those methods. 
We rarely teach our trainees by those  methods ourselves.

The methods of teaching mathematics are.
  1. Discussion
  2. Demonstration/ observation/Illustration
  3. Q/A method
  4. Role play
  5. Field work
  6. Project work
  7. Discovery method
  8. Problem solving method
The one we have neglected most yet crucial  to life is problem solving. This method holds the solutions to almost all our paper  2 problems. 

Solving problems is an everyday  requirement starting from how to get a meal , build a house for the family……..etc 
To solve problems one must consider  strategies necessary to arrive at the solution. 
Mathematics problems are meant to  be samples of problems in every day life. 

The solutions of these are meant to equip pupils with the various skills which 
they can apply when faced with similar  problems.

For every mathematics concept to  be taught let us start by stressing the 
meaning of the concept.
Then all new concepts be introduced by  the corresponding practical activities and particularly at given development stages. 
Lets us go to class with the  teaching aid, then name it and spend time 
on how to make it.then finally how to use  it. This includes calibrated instruments of mathematics. 

I also advice the following ;
  1. Have a programme of giving particularly  1st years the paper 1 revision papers and let it have a continuous feedback system. 
  2. Before a tutor begins this weeks work  let him /her spend time working out the difficult problems they encountered in the  course of last week s calculations, but at the same time point out on how the  markes are awarded by scoring in method s(M)shown and the skills such as B, P ,L  and accuracy marks(A) etc. 
Success in mathematics depends wholly on having a positive attitude. Lets aim at competency based education in which we nature the capabilities and innovative of our children, by production of good primary school mathematics teachers.
  • To help us prepare activities that lead children to understand and master concepts in mathematics it is important look at the objectives of teaching primary mathematics as stipulated in the primary mathematics syllabus
  • To acquire an understanding of numbers  and numeration  Specifically the learner.
  • To develop ability to perform the four  basic operations  Why? In order to identify and use relevant operations in everyday life.
  • To develop skills in measurements,  approximation and estimation Why? In order to be able to estimate measures in real life.
  • To develop spatial concepts and ability  to use them  Why? To be able to apply spatial concepts in everyday life.
  • To acquire techniques of collecting, recording, representing and interpreting data Why? In order to be able to use information from tables and graphs to decide on the course of action. 
  • To develop positive attitude towards  mathematics and make good use of leisure time Why? In order to relate mathematics to  desirable experiences in everyday life.
  • To develop techniques for investigation  and problem solving strategies Children develop concepts through observation and by doing different  activities. Children learn mathematics better if their abilities, needs and interests are taken into account. 
All new mathematical concepts should  be introduced by a practical activity.
It is important for a teacher to know all the mathematical concepts and formulas  across the syllabus and how they come about. 
All new mathematical concepts should be  taught by discovery method. 
During the teaching the learners must be  involved and engaged. This is the only way  we can develop the competencies in the pupils.