### Abstract:

Curve-fitting essentially means the construction of a function rule (formula) that fits a given set of data. In the case of a set of data of a linear function, additional function values as well as a rule for the function can readily be found by identifying the change in function value per unit increase in the value of the independent variable. This study consists of a teaching experiment with Std 6 and Std 7 pupils, with a view to assessing the extent to which pupils can acquire aspects of the gradient concept by doing simple curve-fitting. The teaching experiment comprises a pilot study with Std 6 pupils in 1995, and a final project with Std 6 and Std 7 pupils in 1996. In the pilot study, a sequence of 20 learning tasks requiring curve-fitting was given to pupils. Most of these tasks are about linear functions, but some non-linear cases are included in order to counter narrow concept formation. Observations during the pilot study indicate that the tasks are too simple, and do not present sufficient intellectual challenges to stimulate a level of thinking which supports concept formation. In the final project, only 6 tasks, presenting a substantially higher level of intellectual challenge, are used. The typical structure of these tasks is that pupils have a rule (formula) which makes it easy to find additional function values. Most of the tasks relate to realistic contexts. It has clearly emerged that pupils, in most cases, use a recursive strategy to find additional function values. However, most pupils respond constructively to suggestions by the teacher that function values can also be found by identifying a computational (algebraic) relationship between the values of the two variables. The extent to which the sequence of tacks contributes to the construction and internalisation of the concept gradient, has been evaluated by means of three written tests, as well as by analysis of some video-recordings of pupils; work and discussions during the instructional program. The results indicate that curve-fitting tasks may indeed be useful in promoting construction of the gradient concept.