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:

ï Learn that their intuitive methods are valid and that mathematics makes sense.

ï Become more proficient with mental arithmetic.

ï Are motivated because they understand their own methods, as opposed to learning

by rote.

ï Become skilled at representing ideas with objects, words, pictures, and symbols.

ï 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 :

â¢ Standard algorithms are powerful in solving classes of problems, particularly where the computation involves many numbers, where memory may be overloaded.

â¢ Standard algorithms contracted, summarizing several lines of equation involving distributivity and associativity.

â¢ 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.

â¢ Standard algorithms are fast, with a direct route to the answer.

â¢ Standard algorithms provide the written record of computation, enabling teachers and students to locate any errors in the algorithm.

â¢ Standard algorithms can be instructive.

â¢ 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 :

â¢ They do not correspond to the ways in which people tend to think about numbers.

â¢ They encourage children to give up their own thinking and creativity, leading to loss of âownership of ideasâ.

â¢ The traditionally-taught (standard) algorithm may no longer be the most efficient and easily learned.

â¢ 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.

â¢ 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.

**...(download the rest of the essay above)**