A Computer Assisted Tutorial for introducing the idea of "function" at Key Stage 3. 

Rosemary Fraser, Wellington College, Belfast.

Ken Houston, University of Ulster.

Introduction.

It is widely accepted that algebra is a difficult topic for pupils to learn and to understand. Hence it is reasonable to experiment with innovative ways of encouraging pupils to learn algebra. It is also widely recognised that children are good at, and enjoy, playing computer games and doing other things with computers. Hence it is reasonable to seek to develop computer software which children will be motivated to use and which will help them learn algebra or other topics in their curriculum. This short paper describes a software package which introduces pupils to the concept of "function" through the use of a "function machine". The idea of a function machine is used widely by algebra teachers and it is usually introduced fairly early in the algebra course they give to Year 8 pupils. (This information comes from a survey carried out in post primary schools in the Belfast area. Thirty schools were included in a sample and 24 schools returned at least one questionnaire.) The other topics most often used for the introduction of algebra are flow charts, co-ordinates and balancing numbers.

While computers are not yet available in large numbers in schools, someday soon they will be available in sufficient quantities to allow all pupils reasonable access during class time. It is therefore desirable to experiment and to invent ways of using computers to help learners learn and teachers teach. There is a need now for more teachers to find out about what is available , how to use it and how to use it in teaching. Don’t just leave it to the twenty somethings coming fresh out of college; get involved wherever you are in your career. Yes, it will take time and some effort, but why should the young ones have all the fun!

Research seems to show that when pupils use computers as learning aids their motivation and their understanding are enhanced. Computers as teachers are one-to-one, can give immediate feedback and can be reasonably personal without being overly judgmental. They don’t get tired or impatient and pupils can practice procedures and tasks as often as they wish and at the speed they like. Computer Based Tutorials are interactive and thus encourage a form of dialogue with the pupil. Furthermore, as Computing Science research advances, intelligent tutorial packages will become more commonplace and the human-computer interface will become more friendly.

The Software Developed.

Rosemary Fraser has developed a HyperCard tutorial package for use with Year 8 pupils. It is available (to Mac users only, we regret) on request, for the price of a floppy disc and postage. It is based around the idea of a function machine and it additionally encourages the recall of multiplication and addition number facts. In the first section of the tutorial, pupils have to calculate in their heads the values of ax for a given value of a, for a selection of random values (integers between 0 and 9) of x. Pupils click on a dice icon to generate the random numbers and then they enter their value of the function. They are told immediately if they are right or wrong and are given chances to redeem incorrect answers. They can then repeat the procedure or move on to the next section.

In section 2 pupils are given two inputs to the machine and the corresponding outputs and have to work out what the function does. Section 3 moves on to composite functions of the from ax+b and sections 4 and 5 introduce the idea of the inverse of (ax+b). Section 6 illustrates the difference between (ax+b) and a(x+b), while section 7, like section 2, gives pupils two inputs and the corresponding outputs to the function ax+b and requires pupils to find a and b. Finally section 8 introduces the idea of variable. The input to the machine is, literally, x. The values of a and b are given and the pupil has to enter the algebraic expression for the answer.

Evaluation.

The Year 8 pupils who experimented with the software found that the computing science aspects of the programme were good, namely that there was visual clarity, consistency and compatibility between the different screens, informative feedback from an explicit tutor, good functionality, flexibility and control and good on-screen guidance and support. All of the pupils completed the mathematical tasks successfully.

Acknowledgement.

This paper is based on Rosemary Fraser’s MSc thesis "Using the computer as an aid to the introduction of algebra at Key Stage 3", University of Ulster, 1997.