AXIOMATIC-GENERAL SYSTEMS
BEHAVIORAL THEORY (A-GSBT)
Developed by: Kenneth R. Thompson
An A-GSBT for Education Analysis on the Impact of
“Standards” and “Assessments” on Education Systems
No Child Left Behind and the P-16 Initiative have focused on the necessity of introducing Standards and Assessments in school evaluations in order to evaluate both student progress and teacher effectiveness.
The intent is well founded as a means of assuring that students are learning what they should and teachers are effective in their instruction. But, there has been little assurance that either will produce the expected results. Both have been proposed as an “obvious” solution.
However, what is the impact of the Standard and Assessment Programs on our schools, teachers and students?
A-GSBT for Education may be able to assist in providing this answer.
There are several theory axioms that may be of value in this research, and they may help to direct the empirical research required to arrive at a reasonable answer.
Relevant
Properties
The first relevant property that describes the nature of both Standards and Assessments is system environmental change, since both are frequently imposed from outside the school system.
Three additional properties that are relevant, although they may not be directly so, are toput, feedin, and input. Certainly any Standards or Assessments will result in a system change that came about as the result of these three properties.
Another interesting property that will affect Standards and Assessments is filtration. This property can be viewed as one that indicates the school system’s resistance, or filtering, of the effort to impose outside change on the school system.
Openness is a property that may affect how a school system responds to the imposition of Standards and Assessments.
The properties that help to measure the effectiveness of Standards and Assessments are fromput, feedout, and output.
An analysis of the effect of Standards and Assessments on a school system can be initiated with the preceding properties. Additional properties and their associated axioms may need to be considered as the research develops. However, these initial properties and their associated axioms will provide a substantial initial analysis.
Having determined some of the properties that define the scope of the research, the associated axioms must be determined, and are given below.
The Associated Axioms are those in which one or more of the above properties are cited.
As is seen, there are a great number of axioms that will result in literally thousands of theorems. For that reason, the research must proceed in a careful manner so as not to become too cumbersome and so that the more important results are most likely to be obtained during the initial phase of the research.
Relevance for
Research on
Standards and Assessments
In view of the apparent fruitfulness of this research, it appears as though it will be very helpful in understanding the impact of current Standard and Assessment Programs on our schools, teachers and students.
The axiom numbers that are preceded with an asterisk are ones that have not been fully developed and defined previously. The affect relations specified in these axioms will need definitions prepared. However, it is apparent that some of these new axioms may be very important in determining the outcome of this research.
Associated
Axioms
1. If educational system environmental change increases, then change in educational system input is greater than some value.
2. If educational system environmental change increases, then change in fromput is greater than some value.
3. If educational system environmental change increases, then change in feedback is greater than some value.
4. If educational system environmental change increases, then change in filtration is greater than some value.
5. If educational system toput increases, then input increases to some value and then decreases.
6. If educational system toput greater than some value increases, then fromput increases.
7. If educational system toput is close to minimum, then fromput increases.
8. If educational system toput increases, then filtration decreases to some value and then increases.
9. If educational system toput increases, then regulation less than some value increases.
10. If educational system input decreases, then fromput decreases.
11. If educational system input decreases, then storeput decreases.
12. If educational system input increases, then filtration decreases.
13. If educational system input decreases, then filtration increases.
14. If educational system input is greater than some value, then regulation is greater than some value.
15. If educational system output increases, then fromput increases.
16. If educational system storeput decreases, then feedout decreases.
19. If educational system feedin increases, then fromput increases to some value and then decreases.
20. If educational system feedin increases, then spillage increases.
22. If educational system feedthrough is less than some value, then filtration is greater than some value or spillage is greater than some value.
23. If change in educational system feedback is greater than some value, then system environmental change increases.
26. If educational system filtration is greater than some value, then compatibility is greater than some value.
27. If educational system is filtration less than some value, then compatibility is less than some value.
28. If educational system filtration increases, then adaptability increases.
29. If educational system openness increases, then efficiency decreases.
30. If educational system environmental change increases and fromput increases, then change in feedout is greater than some value.
31. If educational system environmental change increases and fromput increases, then change in feedthrough is greater than some value.
32. If educational system environmental change is greater than some value and feedthrough is greater than some value, then stability is greater than some value.
33. If educational system toput increases and fromput increases, then feedthrough increases.
34. If educational system toput is constant and efficiency is greater than some value, then regulation is less than some value.
35. If educational system input is constant and fromput is constant, then output is constant.
36. If educational system input increases and storeput is constant, then feedout increases.
37. If educational system input increases and storeput is less than some value, then change in input equals change in storeput.
38. If change in educational system input is greater than change in feedthrough, then spillage increases.
39. If educational system input is greater than some value and spillage is less than some value, then storeput increases.
40. If educational system input is less than some value and spillage is less than some value, then storeput decreases.
41. If educational system input is constant and efficiency at a given time is less than some value, then efficiency increases.
42. If the ratio of maximum educational system selective information to input decreases, then feedout decreases.
43. If educational system fromput increases and output is less than some value, then feedout decreases.
44. If change in educational system fromput is less than some value and change in storeput is less than zero and change in fromput is greater than zero and the negative of change in storeput is greater than some value, then efficiency decreases.
45. If educational system output increases and feedback is greater than some value, then input increases.
46. If educational system storeput increases and (filtration decreases or spillage decreases), then information growth increases.
48. If educational system (feedin increases and feedout is constant and compatibility is constant) or (feedin is constant and feedout increases and compatibility is constant) or (feedin is constant and feedout is constant and compatibility decreases), then openness increases.
49. If educational system (feedin decreases and feedout is constant and compatibility is constant) or (feedin is constant and feedout decreases and compatibility is constant) or (feedin is constant and feedout is constant and compatibility increases), then openness decreases.
50. Change in educational system input is greater than change in fromput.
51. Change in educational system feedin is greater than change in feedout.
52. Educational system efficiency is equal to the maximum efficiency if and only if feedin is equivalent to feedout.
90. If educational system toput increases, then centrality decreases.
91. If educational system feedin decreases, then unilateralness decreases.
92. If educational system feedin less than some value decreases, then hierarchical order decreases.
93. If educational system feedin decreases, then complexity degeneration increases.
94. If educational system feedout is less than some value, then complexity degeneration increases.
96. If educational system toput is close to minimum and fromput increases, then disconnectivity increases.
97. If educational system feedin increases and compatibility is nearly minimum, then disconnectivity increases.
98. If educational system storeput increases and (filtration decreases or spillage decreases), then integration increases.
*99. If input increases, and storeput is greater than some value; then segregation with respect to referent affect relations.
100. If educational system complete connectivity increases, then feedin increases.
102. If educational system interdependence increases, then feedin increases.
105. If educational system centrality increases, then toput decreases.
106. If educational system complete connectivity increases or strongness increases, then toput increases.
107. If educational system complete connectivity increases or strongness increases, then input increases.
108. If educational system complete connectivity increases or strongness increases, then filtration decreases.
110. If educational system complete connectivity increases or strongness increases, then openness is less than change in fromput, and change in fromput is less than change in input.
111. If educational system complete connectivity increases or strongness increases, then change in storeput is greater than change in fromput.
115. If educational system unilateralness, or weakness increases, or disconnectivity increases, then input decreases and fromput decreases.
*116. If passive dependence with respect to reward affect relations increases, then feedout decreases.
*118. If independence with respect to Leadership Subsystem affect relations increases, then fromput increases.
*119. If independence with respect to Leadership Subsystem affect relations increases, then output is less than some value.
*120. If independence with respect to Leadership Subsystem affect relations increases, then feedout decreases.
*121. If wholeness with respect to referent affect relations is greater than some value, then the absolute value of the difference of fromput from maximum fromput is greater than some value.
*122. If wholeness with respect to referent affect relations is greater than some value, then openness is close to minimum.
*123. If hierarchical order with respect to Leadership Subsystem affect relations increases, then filtration increases.
*126. If passive dependence with respect to inquiry and legitimate affect relations increases, then feedout increases and spillage increases and maximum selective information is greater than some value.
*127. If passive dependence with respect to inquiry and expert affect relations increases, then feedout decreases and spillage greater than some value increases and maximum selective information is less than some value.
*129. If wholeness with respect to inquiry and referent affect relations increases, then the ratio of maximum selective information to input increases.
*130. If disconnectivity with respect to instructional and referent affect relations is greater than some value, and complete connectivity with respect to instructional and referent affect relations increases, and wholeness with respect to instructional and referent affect relations increases; then input increases, and fromput increases, and feedout decreases, and regulation increases.
*131. If disconnectivity with respect to instructional and expert affect relations is greater than some value, and complete connectivity with respect to instructional and expert affect relations increases, and wholeness with respect to instructional and expert affect relations increases; then input increases, and storeput increases, and feedout increases, and filtration increases.
*132. If disconnectivity with respect to instructional and referent affect relations is greater than some value, and passive dependence with respect to instructional and referent affect relations increases, and wholeness with respect to instructional and referent affect relations increases; then input decreases, and fromput decreases, and feedout decreases, and regulation decreases.
*133. If disconnectivity with respect to instructional and reward affect relations is greater than some value, and passive dependence with respect to instructional and reward affect relations increases, and wholeness with respect to instructional and reward affect relations increases; then if system environmental change is greater than some value, then adaptability is greater than some value, and input is less than some value, and storeput is less than some value, and filtration is greater than some value.
*134. If disconnectivity with respect to instructional and legitimate affect relations is greater than some value, and passive dependence with respect to instructional and legitimate affect relations increases, and wholeness with respect to instructional and legitimate affect relations increases; then feedout increases, and spillage is greater than some value, and regulation is greater than some value.
*135. If disconnectivity with respect to instructional and punishment affect relations is greater than some value, and passive dependence with respect to instructional and punishment affect relations increases, and wholeness with respect to instructional and punishment affect relations increases, and hierarchical order with respect to instructional and punishment affect relations increases; then if system environmental change is greater than some value, then adaptability is less than some value, and fromput decreases, and feedout decreases, and regulation decreases, and stability increases, and equifinality increases.
*136. If maximum active dependence with respect to development inquiry and legitimate affect relations; then fromput is less than some value, and filtration increases, and spillage increases, and regulation is less than some value, and active dependence with respect to inquiry affect relations decreases, and active dependence with respect to instructional affect relations increases.
137. If educational system feedout is greater than some value and compatibility is less than some value, then segregation is less than some value.
138. If educational system toput increases and compactness greater than some value increases then regulation increases.
139. If educational system toput increases and it is not the case that compactness greater than some value increases, then efficiency decreases.
140. If educational system (fromput is constant or fromput decreases) and complete connectivity increases and strongness increases, then feedthrough decreases.
*141. If toput increases, and independence with respect to Leadership Subsystem affect relations increases; then feedout increases.
143. If educational system feedin is constant then homeostasis is less than some value.
144. If educational system filtration decreases, then isomorphism increases.
145. If educational system filtration is greater than some value, then stability is greater than some value.
147. If educational system toput increases and feedout is close to minimum, then stress increases.
148. If educational system environmental change is greater than some value, and it is not the case that feedthrough is greater than some value, and feedback is greater than some value, then stability is less than some value.
*149. If filtration with respect to instructional affect relations increases, then isomorphism with respect to instructional affect relation increases.
150. If educational system automorphism increases, then input increases and storeput increases and fromput decreases and feedout decreases and filtration decreases and spillage decreases and efficiency decreases.
151. If educational system isomorphism increases, fromput decreases and feedout decreases.
*157. If isomorphism with respect to instructional affect relation increases; then the fromput decreases, and feedout decreases.
158. If educational system toput increases and size is constant, then feedback increases.
159. If educational system environmental change is greater than some value and compatibility is greater than some value and stability is greater than some value, then storeput is greater than some value or filtration is greater than some value or spillage is greater than some value.
160. If educational system toput increases and fromput increases and size is constant, then feedout increases.
161. If educational system output is constant and automorphism decreases and homomorphism is greater than some value, then feedout decreases.
162. If educational system toput is less than some value and feedin increases and stability is less than some value, then stability increases.
163. If educational system toput is greater than some value and feedin decreases and stability is less than some value, then stability increases.
*189. If maximum active dependence with respect to research inquiry and legitimate affect relations; then input increases, and fromput increases, and storeput increases, and filtration increases, and automorphism with respect to instructional affect relations increases.
190. If educational system homomorphism at time 2 is greater than homomorphism at time 1, then toput is nearly maximum and size degeneration is nearly maximum and complexity degeneration is nearly maximum.
194. If educational system size increases and complexity growth is constant, then toput increases.
195. If educational system size increases and complexity growth is constant, then feedin decreases.
196. If educational system size increases and complexity growth is constant, then feedout increases and change in feedout decreases.
1. DS’ É DIP > a
2. DS’ É DFP > a
3. DS’ É D¦B > a
4. DS’ É DFR > a
5. TP É s(IPa : t(1), IP¯b : t(2)) | a < b
6. (TP > a) É FP
7. TP » 0 É FP
8. TP É s(FR¯a : t(1), FRb : t(2)) | a < b
9. TP É (RR < a)
10. IP¯ É FP¯
11. IP¯ É SP¯
12. IP É FR¯
13. IP¯ É FR
14. IP > a É RR > b
15. OP É FP
16. SP¯ É ¦O¯
19. ¦I É s (FPa : t(1), FP¯b : t(2)) | a > b
20. ¦I É SR
22. ¦T < a É (FR > b Ú SR > c)
23. ¦B > a É DS’
26. FR > a É C > b
27. FR < a