Calculators
Calculators can help in the development of problem-solving skills by allowing the child to focus on the structure of a problem and possible methods of solution. The skills of estimation and trial-and-error methods of problem-solving can be developed. This allows children to look at problems from the real world, where the numbers involved might otherwise be too unwieldy for them to handle.
The child's attitude towards mathematics can also benefit from the use of the calculator by taking some of the drudgery out of complex calculations. Children can then experience success in mathematics, which is an important factor in maintaining interest and enthusiasm for the subject. By making tasks more manageable, children may gain the confidence to try new tasks and persevere with problems that cannot be solved quickly. Exploration and investigation can be encouraged and discussion promoted. Calculators can make problem-solving more accessible to low-achieving children who might otherwise never experience correct problem solution because of the frequency of computational errors.
The calculator can play a significant role in the mathematics programmefrom fourth to sixth class. However, children will need to know and use number facts to check the reasonableness of answers obtained with the calculator. They will also need to have a good understanding of number in order to make judgements about when it is appropriate to estimate, to calculate mentally or to make a quick pencil-and-paper calculation. The ability to decide when it is necessary to use a calculator is equally important.
It is recognised that some parents and teachers will be unfamiliar with the ways in which calculators can be used to develop mathematical skills and understanding. Parents will need to be reassured that their children will continue to master number facts and processes.
Choosing calculators for the classroom
Many children will have experimented with calculators at home, and many of them will own one. However, if they are to be used in the classroom, it is advisable that the children all have access to the same type of calculator.
- keys on classroom calculators should be of a reasonable size and have a positive click action to avoid keying in incorrect numbers
- the display should have at least eight digits and be large enough for two or three children to see
- a constant memory function is useful when building up number patterns.
Some calculators operate by using arithmetic logic. These allow operations to be performed in the sequence in which they are keyed in: for example 3 + 4 x 2 will give 14 as a result.
Calculators that use algebraic logic wait until the whole equation is keyed in before commencing the operation, hence 3 + 4 x 2 will give 11 as a result, as it will do the multiplication operation first. Algebraic logic uses priorities in sequences of operation which we call BOMDAS (brackets, of, multiplication, division, addition and subtraction).
Interesting experiments can be undertaken by comparing the results of both types of calculator.
Using calculators in the classroom
- children should be taught how to handle and take care of calculators
- they should be given adequate time to experiment with them
- they will need to understand the priority of operations (BOMDAS) to develop efficient and accurate use of the calculator
- it is very important that children are taught to analyse the problem in order to assess which operation is required. They should also be comfortable with estimation so that they will realise when a calculation may be incorrect.
Information and communication technology
Like the calculator, the computer is a tool that can be used by children and teachers but is not a substitute for good teaching.
Drill and practice programs can provide an attractive alternative to pen-and paper tasks and is particularly useful with younger or less-able children who may need stimulation or extra practice on a particular topic. There are many useful programs available that can be used with infants to develop pattern recognition, shape matching and early number work but such use of the computer is short-lived and must not be over-used when a child has achieved mastery.
Adventure programs often require the child to solve specific mathematical problems in order to progress through a game, and they also give experience in the area of general problem-solving. Many of these programs allow a choice of level so they can be used with different classes.
Databases are perhaps one of the most effective areas of ICT use in schools. We are constantly being presented with results of surveys, charts and forecasts in the media. Simple databases give children the opportunity to manipulate smaller amounts of data relevant to their own interests, for example height, weight or colour of eyes. The use of more sophisticated data handling programs will enable children to develop this concept in handling larger amounts of information, perhaps on a school level; for example, have all tall children blue eyes? how many children have a cat for a pet? how many boys have cats? Data handling is also important in other areas of the curriculum and can be used to investigate population trends or rainfall amounts in geography, or to collate information in a local history project.
Spreadsheets are becoming increasingly popular for exploration of number patterns and for tabulating numerical data. They are also useful for teachers in keeping numerical records that need to be updated on a regular basis, for example reading ages.
LOGO is a computer language that has been used successfully with children for many years. It is extremely valuable in work on direction, line, angles and shape. It also encourages the re-working of a problem and the concept of multiple approaches to solving a problem. LOGO requires logical thought, and this can be helpful to a child who finds it difficult to deal with large, complex word problems.
The child can plan his/her work on squared paper, discuss possible approaches and then refine them. When he/she is satisfied with the 'plan' it can be entered into the computer. It can then be tried out and further refined. The off-computer planning is an extremely important part of the process. This approach works best when children work in pairs and are encouraged to plan, discuss, record and test their plan. The emphasis will always be on the process rather than the product. When children work together like this it encourages collaboration and cooperative thinking.
Internet access. The internet can be used to access information and data that can be used by the children in problemsolving or data handling exercises. It can also be used by teachers to download materials and information relevant to their work. As with calculator use, children must become more discerning about when it is appropriate to use ICTs to solve a problem and which element of that technology will be of most use to them.