ALGORITHM - MEANING

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 25Ãâ€"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 25Ãâ€"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.