The Establishment of a Functional Relation Among Several Variables: Distance Travelled, Wheel Size and Rotational Frequency

Abstract

Our object has been to understand how the child constructs a functional relation from among several variables. In Experiment III we dealt with the coordination of two series of variables: wheel size and distances travelled. In the present experiment we will add a third, rotational frequency. We use the term frequency because the object of the task is the composition of the relative speed of two wheels during the same time period and not the estimation of their absolute speeds. Let W be the size of the wheel, D the distance travelled and F the rotational frequency; we thus have three linked variables, i.e. whether the yellow car A goes faster or farther than the green car B is a function of W, D and F. We will attempt to find out how the child establishes: (1) compositions of qualitative relations when one of the variables is kept constant, for example: D₁>D₂ and W₁ = W₂ ⇒ F₁ >F₂ (D₁ is the distance travelled by the first car A, and D₂ that travelled by B); (2) reciprocal compensations such as when D₁>D₂ and W₁ > W₂ and the subject is asked to find the relationships of rotational frequency between 1 and 2; and (3) the quantification of these relationships.