A Growth-Model facilitates a student analysis approach based upon principles used in the study of complex systems. Empirical and data-driven conclusions are reliant upon an ability to appropriately classify and quantify characteristics of dominant operational functions, providing values to facilitate numerically objective outcomes. As early as 1500 AD, it was determined that the laws of the material universe could only be understood by expressing all properties as quantified measurements. Termed “Dynamical Laws,” it is the ability to apply numerical values for functional outcomes at a given time compared to their values at a later or earlier time. This may include measures of speed, volume, density, direction, occurrences, quantity, quality, effectiveness, efficiency, frequency, timeliness, accuracy, etc. of all functional aspects of a structured and quantified Outcome.
The study of Dynamical Laws must also include an analysis of the strength and direction of any external force. One of the powerful ways of probing the behavior of students is observing how the student responds when external forces are applied. Of special concern are the "indirect" effects that take place at different places or at other times than when the force is applied. This is a measure of the relationship of cause and effect, the basis of our psychological study. Indirect-in-Space is how a student transfers the effect of external forces from the place where the force is applied, (e.g. home) to other places (e.g. school). Indirect-in-Time is how a student’s reaction may be delayed from when the force is applied, (e.g. trauma). It is essential that our study analyze the impact of dynamical forces to understand how a myriad of external forces may influence student achievement.