Making Mathematics RelevantAuthor(s): Ian ThompsonSource: Mathematics in School, Vol. 17, No. 4 (Sep., 1988), pp. 36-38Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214517 .

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Making Math Relevan

lan Thompson, School of Education, University of Newcastle upon Tyne

In a recent document' summarising many HMI reports on individual primary and secondary schools the following observation is made:

"Mathematics is over-concerned with the practice of com- putational skills, much of which is unrelated to any context that would confer meaning and importance on the work being done"

The necessity of ensuring that mathematics is perceived by children as being useful to their needs has been stressed in many publications over the last two decades. Most people would agree that children need to appreciate that mathema- tics can often help them to solve the problems that they meet in everyday life, but research, and the personal experience of many teachers, suggests that there are a great many children and adults who see little or no connection between what takes place in mathematics lessons and their personal activities in the world outside the classroom. The ACACE (1981)' research report mentions the feelings of anxiety and stress experienced by adults when being inter- viewed about the subject of mathematics, and includes amongst the reasons offered for their inhibitions about

using mathematics "the seeming lack of relevance of math- ematics to everyday contexts."

In a publication' which considers various aspects of secondary education HMI (1978) made the following observation:

"... it was common for the schemes of work ... to refer to the need to relate the mathematics taught to the problems of everyday life, but the convincing realisation of this aim was much more rare."

Teachers only appear to pay lip-service to the idea of illustrating the usefulness of mathematics, and generally fail to portray the subject as one that possesses such wide applicability.

Mellin-Olsen (1981)4 postulates a theory concerning two different rationales that pupils adopt for the learning of mathematics: the I-rationale which leads to the study of mathematics because of its potential for being instrumental in enabling the pupil to obtain a job, and the S-rationale which involves participation in mathematical activities because they are seen to be significant to the individual learner in some way or another. This conception of what is

36 Mathematics in School, September 1988

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significant knowledge will vary from pupil to pupil, but it seems likely that any mathematics which is used in a context that the pupil finds meaningful; which develops her aware- ness of the uses of mathematics in the world beyond the classroom; which stimulates aesthetic appreciation, or which awakens an interest in mathematics as a fascinating subject in its own right is more likely to contribute to the adoption of an S-rationale rather than an I-rationale for the

learning of mathematics. There would therefore appear to be a need for teachers to provide the children they teach with a variety of experiences which might help them

develop an appropriate rationale for learning. One such activity with the potential to provide such an

experience involves an item of computer software which

actually obliges children to use mathematics in a realistic context. This program is "Cars - Maths in Motion"'' a realistic simulation of Grand Prix motor racing. Computer simulations are used by some primary teachers as a focus for thematic or topic work spanning several cur- riculum areas, and by some secondary History or Science

departments, but little use appears to have been made of this type of program in the mathematics classroom.

A brief description of the program in action should provide a good idea of the mathematical skills and concepts involved in its use. Children work in teams of two or three to prepare their racing cars for the big race at one of ten world-famous racing tracks. Using a copy of the circuit

maps provided the children have to make some preliminary calculations about the course features. They have to measure the length of the straights and use the scale and information provided on the circuit plan to classify them as short, medium, or long. Using a protractor they then measure the angle of the bends, and decide whether they are

long, medium or tight bends. These activities are done away from the computer, and the information gathered enables the children to enter a maximum safe speed for each of the

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twenty circuit features on to their team worksheet. Once at the computer each team has to enter its team

number, driver's name and temperament, and has to make a

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Mathematics in School, September 1988 37

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note of the weather forecast for the day. Next come the crucial workshop adjustments which have to be made to the car in order to prepare it for the idiosyncracies of the particular circuit being used. This is done by selecting a number from 1 to 10 for each of the following aspects: engine tuning, where a high number improves performance on straights; aerodynamic downforce, where a high number produces a better performance on bends; suspension adjust- ment, which is modified to suit the roughness of the track, and gearbox ratio, where a high ratio improves acceleration at lower speeds but gives a slower top speed. This activity involves a great deal of necessary discussion in order to decide the optimum adjustments to cope with the different features of the circuit. It also provides an excellent oppor- tunity for cross-curricular work in the primary classroom or liaison with the Science department in the secondary school.

As a result of these adjustments the computer provides each team with a "performance percentage" for each of the

38

six types of feature (long straight, tight bend, etc). The original maximum speeds have to be multiplied by these percentages to give a safe speed for each feature. These speeds are then entered as the race plan. A practice lap report provides information on performance at each race feature, with feedback ranging from "Satisfactory" to "Engine Blowout". Teams are allowed as many opportun- ities as the teacher decides in order to adjust their cars and race speeds. Each team is told its lap time and can ascertain its current position on the starting grid.

The final pre-race activity is the all-important Pit Team Briefing where various tactical decisions have to be made. From five tyre types - ranging from fast dry to wet - teams have to select their starting type and decide whether to make a time-consuming pit stop to change their tyre type part way through the race. The final decision concerns fuel. Teams are told the length of the race - 10 laps is a reasonable length for beginners - the maximum fuel capacity and the fixed fuel consumption rate. They have to measure the total length of the circuit and then decide how much fuel they need to carry.

When all the teams have entered their race plans the Grand Prix race takes place. In addition to reporting the incidents that occur and the positions at the end of each lap the computer provides lap and lag times for each team. The children become very involved and excited during the race urging their drivers on, and can experience for themselves the results of their detailed planning and hard work as their drivers fight it out on the track.

As the children gain in experience the teacher can modify the circuit details by making the race up to 99 laps long. This necessitates the drivers making pit stops to fill up and to change tyres to match the changing weather. Calculations have to be made concerning the number of laps covered by the time the weather changes, the minimum amount of fuel needed to cover the required distance, and the optimum number and timing of pit stops.

"Cars" provides a stimulating focus for the use of mathematics for a specific purpose. It forces pupils to work in groups, to involve themselves in group discussion, and to experience corporate decision-making in a mathematical context. It can encourage the making and testing of conjec- tures, and can provide an environment where pupils can ask "What if..." questions in a non-threatening situation. The program has the added advantage of involving children in the use of percentages, decimals, linear and angular measurement, multiplication and division, the interpreta- tion and creation of tabulated information, strategic think- ing and general problem solving skills for a purpose that they see as exciting, important and relevant. Using the program in class can provide the necessary motivation and stimulus for children who have difficulty with some of the skills or concepts involved to want to work on these mathematical aspects in their more traditional mathematics lessons so that they might improve on their performance in the next race.

If mathematics educators are able to develop a wide variety of activities which involve the use of mathematics in other realistic and motivating situations then this should go some way towards providing the HMI's "context that would confer meaning and importance on the work being done", and could lead to more students developing and adopting an S-rationale for the learning of mathematics.

References 1. HMI (1984) "Education Observed 2" DES. 2. Sewell, B. (1981) "The Use of Mathematics by Adults in Daily Life"

ACACE. 3. HMI (1978) "Aspects of Secondary Education" HMSO. 4. Mellin-Olsen, S. (1981) "Instrumentalism as an Educational Concept"

Ed. Stud. Maths 12, 351-367. 5. "Cars - Maths in Motion" is available from Cambridge Software

House, Town Hall, St. Ives, Cambs. Price a19.

Mathematics in School, September 1988

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