Rasch meta-metres of growth in reading and mathematics attainment tests

Although hardly known, Georg Rasch had an approach to studying growth based on the principle of invariant comparisons, the same principle for which he is well known with his models for measurement. The approach identifies a non-linear function of time, called a meta-metre, which governs the growth of all individuals of a population. Then within the meta-metre, each individual’s rate of growth is linear and invariant, thus permitting ready comparisons of rates of growth among individuals using standard statistical procedures. This presentation illustrates the approach with the educationally important variables of reading and mathematics attainment tests from two longitudinal studies. Each of the meta-metres show early rapid, decelerating growth, with noticeably different rates of growth among sub-populations. Decelerating growth is also related to the common grade scale, showing that any grade difference between groups in the early years invariably increases in later years. This increase has implications for interventions for groups at risk in their attainments.

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