**ERIC Number:**EJ1001912

**Record Type:**Journal

**Publication Date:**2012

**Pages:**18

**Abstractor:**ERIC

**Reference Count:**32

**ISBN:**N/A

**ISSN:**ISSN-0146-9282

A Theory of School Achievement: A Quantum View

Phelps, James L.

Educational Considerations, v40 n1 p2-19 Fall 2012

In most school achievement research, the relationships between achievement and explanatory variables follow the Newton and Einstein concept/principle and the viewpoint of the macro-observer: Deterministic measures based on the mean value of a sufficiently large number of schools. What if the relationships between achievement and explanatory variables followed Planck's quantum concept/principle and the viewpoint of the micro-observer; that is, the nondeterministic measurement of individual schools, each with its own probability? What influence would a quantum theory of school achievement have on research, training, and practice? The author argues that there is no set of generally accepted concepts or mathematical principles underlying the multiple diverse studies estimating the relationships between school achievement and various explanatory variables; in short, there is no comprehensive theory of school achievement. In this article, the purpose of the analyses and thought experiments, culminating in a series of postulates, is to define the fundamental concepts and mathematical principles of such a theory. These issues are addressed in this article through discussion of the following: (1) Why achievement measures are quantum in nature: discrete integer values with upper- and lower-limits requiring probabilistic measurements; (2) Why normal curve statistics commonly used in achievement research are based on continuous variables with no upper- and lower-limits and implied deterministic measurements; (3) How normal curve statistics can accommodate the quantum nature of achievement by considering the relationships between achievement and explanatory variables as nonlinear, nondeterministic, and probabilistic; (4) How nonlinear relationships allow for the calculation of achievement levels and probabilities unique to each individual school (Planck's microview); (5) How the nonlinear interpretation leads to a calculation of cost-effectiveness; (6) How conceptually and statistically related variables can be combined to measure their collective influence on achievement; and (7) How normal curve statistics and combinations of explanatory variables can be used in a comprehensive theory of school achievement and mathematical model simulating how changes in individual school policies could influence the probability of improved achievement. (Contains 1 table, 10 figures, and 23 endnotes.)

Descriptors: Academic Achievement, Computation, Probability, Statistics, Mathematical Models, Fundamental Concepts, Quantum Mechanics, Experiments, Prediction, Achievement Gains, Scores, Statistical Distributions, Graphs, Data, Calculus, Effect Size

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**Publication Type:**Journal Articles; Reports - Research

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A