General Principles of Informal Computation   Almost everyone is faced with situations in daily life where there is a need for quick calculations, often in the absence of paper and pencil and without a calculator. Being able to calculate mentally, and especially to make quick mental estimations, is an important goal of mathematics teaching. The phrase "informal computation" includes mental computation (done without pencil and paper or calculator) and computation where short term memory is supported by quick jottings etc, but where a formal algorithm, such as those taught at school, is not used.   Points for teachers to note: The methods used for informal computation are often quite different to the paper-and-pencil algorithms taught at school. Informal methods are often varied to take advantage of known properties of the actual numbers in the problem. For example, informal methods use facts such as 8 is close to 10, 25 is one quarter of 100 or 6 and 4 add to 10. Favourite number combinations are often used as a basis of computation. People good at mental computation use a wide variety of methods. Most informal methods are not taught. People work them out from their good understanding of place value and their number sense and their understanding of the meaning of the operations. A good knowledge of number facts is essential. Many informal methods follow unconventional patterns like subtracting or multiplying from left to right so that the big quantities are dealt with first (e,g, hundreds before ones). It is common to modify the question and then compensate later (eg. by rounding, doubling, halving etc) Informal methods are often based on using round numbers (e.g. 600, 1400, 30). In contrast, formal algorithms are often hard to carry out with round numbers (think about 1000 - 657 done by a formal subtraction algorithm). Children make many mistakes dealing with zero in formal written algorithms. For many people, the types of numbers that can be dealt with by informal computation is limited. For example, many people can calculate with 1/2 but not with other fractions. Informal computation is often step-by-step, rather than dealing with all the relationships in the problem simultaneously. Informal computation sometimes uses a primitive version of an operation. For example, addition may be done by counting on, multiplication may be done by repeated addition. In real life, estimation is as important a skill as exact calculation. It is an essential skill to complement calculator use.   Back to Main Menu