Analytic And Synthetic Method

Assignment Name Aneela Majeed Department Education Dated 2nd November, 2009

Contents 1. Why and when teachers use Analytic and Synthetic Method? • Why teachers use Analytic Method • When teachers use Analytic Method • Why teachers use Synthetic Method • When teachers use Synthetic Method • Conclusion

Why & when teachers use Analytical and Synthetical Methods: These two methods are applicable in combination. To conclude anything about them, one has to understand them separately first.

Why teachers use Analytic Method: It proceeds from unknown to known, ’Analysis’ means ‘breaking up’ of the problem in hand so that it ultimately gets connected with something obvious or already known. It is the process of unfolding of the problem or of conducting its operation to know its hidden aspects. Start with what is to be found out. Then think of further steps and possibilities which may connect the unknown with the known and find out the desired result. In its original sense the verb ‘to analyze’ means to loosen or separate things that are together about analysis, Thorndike says that all the highest intellectual performance of the mind is analysis. It is logical method. It leaves to doubts and convinces the learner. It facilitates understanding. It also strengthens the urge to discover facts. The steps in its procedure are developed in a general manner. No cramming of a fixed steps and a ser pattern is necessitated. Each step has its reason and justification. The student is throughout faced with such questions as “how to prove the equality of two angles?” “What are the possible ways of resolving a statement into simpler elements etc?” thus the student grapples with the problem confidently and intelligently. He gains in comprehension and skill.

When teachers use Analytic Method: Example:

Why teachers use Synthetic Method: It is the opposite of the analytic method. Here one proceeds from known to unknown. In practice, synthesis is the complement of analysis. To synthesis is to place together things that are apart. It starts with something already known and connects that with the unknown part of the statement. It starts with the data available or known and connects the same with the conclusion. It is the process of putting together known bits of information to reach the point where unknown information becomes obvious and true. It is a short and elegant method. It glorifies memory. It is logical.

When teachers use Synthetic Method: Synthetic division is a shortcut for polynomial division when the divisor is of the form x – a. Only coefficients are used when dividing with synthetic division. Example:

The answer is

To do the problem using synthetic division, follow this procedure: 1. Write the polynomial being divided in descending order. Then write only its coefficients, using 0 for any missing terms.

2. Write the constant, a, of the divisor, x – a, to the left. In this problem, a = 3.

3. Bring down the first coefficient as shown.

4. Multiply the first coefficient by a. Then write this product under the second coefficient

5. Add the second coefficient with the product and write the sum as shown.

6. Continue this process of multiplying and adding until there is a sum for the last column.

The numbers along the bottom row are the coefficients of the quotients with the powers of x in descending order. The last coefficient is the remainder. The first power is one less than the highest power of the polynomial that was being divided. The division answer is

Conclusion: The pupil taught by the method of synthesis is just like a man led blind-fold to the desired goal. Since analysis is a lengthy method, it needs the help of synthesis for the removal of this defect. It will not be useful if it is not followed by synthesis. Synthesis is the complement of analysis; and, in the teaching of mathematics, the two should always go together. Analysis leads to synthesis-analyze in order to synthesis, i.e., facts or things are separated in order to find out how these can be knit together to form one whole, Analysis forms the beginning and synthesis forms the follow up work. The two are interdependent. Teacher should realize that he may offer help two the

analytic form of the solution and that synthetic work should be left to the pupils.