Essay: ALGORITHM – MEANING

In the most basic sense, an algorithm is a process- a set of detailed instruction that must be carried out in a particular order and follows logic to attain a given result. An algorithm is a well-defined procedure or set of rules guaranteed to achieve a certain objective.
You use an algorithm every time you follow the directions to put together a new toy, use a recipe to make cookies, or defrost something in the microwave (personal algorithms).
When the term algorithm used in math, it typically refers to a set of steps or procedures used to solve a mathematical computation. In mathematics, an algorithm is a specific series of steps that will give you the correct answer every time. For example, in grade school, you and your classmates probably learned and memorized a certain finite steps or procedures for addition, subtraction and multiplying etc. (standard algorithms).
Algorithm are of two type: informal (personal) and formal (standard) algorithm.
An informal algorithm is a procedure that the student him/herself figured out while a formal algorithm is a process and procedure that has been taught to them. It may or may not be similar to a conventional algorithms (formal algorithms).
Examples on Informal Algorithms Examples on Formal Algorithms
1. ADD the given numbers
109 + 207
Jimmy did like this. David did like this.
=100+9+200+7 109-9=100
=300+16 207-7=200
=316 200+100=300
9+7=16
300+16=316
2. Multiply the given number
25×13
25(20+5)
x13(10+3)
————–
15
60
50
+ 200
—————
325
1. ADD the given numbers
109+207
1
109
+ 207
——–
316
——–
2. Multiply the given number
25×13
1
25
x13
————
75
+25x
————
325
MERITS OF INFORMAL ALGORITHMS
They learn to think and use their common sense, as well as new skills and knowledge. Students who invent their own procedures:
 Learn that their intuitive methods are valid and that mathematics makes sense.
 Become more proficient with mental arithmetic.
 Are motivated because they understand their own methods, as opposed to learning
by rote.
 Become skilled at representing ideas with objects, words, pictures, and symbols.
 Develop persistence and confidence in dealing with challenging problems.
ADVANTAGES OF THE FORMAL ALGORITHMS
Plunkett (1979), Thompson (1997), Usiskin (1998) and other writers offered several reasons for this. These included :
• Standard algorithms are powerful in solving classes of problems, particularly where the computation involves many numbers, where memory may be overloaded.
• Standard algorithms contracted, summarizing several lines of equation involving distributivity and associativity.
• Standard algorithms are automatic, being able to be taught to, and carried out by, someone without having to analyze the underlying basis of the algorithm.
• Standard algorithms are fast, with a direct route to the answer.
• Standard algorithms provide the written record of computation, enabling teachers and students to locate any errors in the algorithm.
• Standard algorithms can be instructive.
• For teachers these are easy to manage and assess.
DISADVANTAGES OF THE FORMAL ALGORITHMS
Kamii and Dominick (1998), McIntosh (1998), and Northcote & McIntosh (1999) have potential dangers that can be summarized as follows :
• They do not correspond to the ways in which people tend to think about numbers.
• They encourage children to give up their own thinking and creativity, leading to loss of ‘ownership of ideas’.
• The traditionally-taught (standard) algorithm may no longer be the most efficient and easily learned.
• They tend to lead to blind acceptance of results and over-zealous applications. Given the focus on procedures that require little thinking, children often use an standard algorithms when it is not at all necessary.
• There is a high probability that the students will lose conceptual knowledge in the process of gaining procedural knowledge.
There is also the use of relevance. Students use standard algorithms for only a small proportion of their calculation.