# Absolute Zeroes for Reading and Mathematics Abilities: Ability and Age

The molecular motion theory of heat hypothesizes absolute zero temperature at -273 Celsius. A supposed advantage of physical over social science measurement is the unique possibility of absolute zeroes. But a conceptual absolute zero is available for any variable that is successfully measured, whatever the subject matter. Indeed, some working zero must be specified before any measurement scale can be useful.

Rasch item banks for Reading and Mathematics that link test items from 1st to 8th grade were constructed so that the eight non-linear, distribution-dependent grade equivalents (GE) from 1st through 8th grade of 30,000 Chicago Public School students could be transformed into linear measures of longitudinal growth. A random sample of 248 of these 8-year growth curves were used to regress individual ability on transformations of age. Separate analyses were done for Reading and Mathematics.

The results show that:
1. Reading and Math growth slows as age increases.
2. Both growth curves are linear with loge(Age + C).
3. The integer C values minimizing residual error for these 248 students were C = 1 year for Reading but C = 2 years for Math.

The Reading plot shows the regression of Reading ability on loge(Age + 1 year). The minimum useful value for loge(Age + 1) on this line is zero. This corresponds to a Reading measure intercept of -15.3 logits, a value which could be thought of as the minimum measure. If absolute zero Reading ability is at loge(Age + 1) = 0 making Age = 0, then "absolute zero" reading ability is estimated to be at birth.

The Mathematics plot shows the regression of Mathematics ability on loge(Age + 2 years). The minimum useful value for loge(Age + 2) on this line is zero. This corresponds to a measure intercept of -22.6 logits, a value which could be thought of as the minimum measure. If absolute zero Math ability is at loge(Age + 2) = 0 making Age = -1, then "absolute zero" mathematics ability is estimated to be, not at birth, but at conception!

There are neurological, child development and archeological data which agree with these unexpected results. Foetal neurology finds that brain maturation necessary for counting is available by six months before birth. Hearing the words on which reading builds is impossible until after birth. Child psychologists find that infants demonstrate the rudiments of counting before they talk. Archaeologists find notational systems of counting and accounting preceding writing and reading by centuries.

Thus we cannot escape interest in these absolute zeroes for the social science variables of Reading and Mathematics. These zeroes imply that mathematics begins when the foetal brain is born (before birth), but that reading does not begin until ears hear words. Continual refinement of absolute zeroes is an essential component of progress in the physical sciences. We can look forward to the same kind of progress in the social sciences.

Ong Kim Lee

Absolute Zeroes for Reading and Mathematics Abilities: Ability and Age, O K Lee … Rasch Measurement Transactions, 1993, 6:4 p. 245-6

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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