The Science of Cognitive Rigor in Education

by Ben S. Jones

I spent some time over the holidays reading papers and such related to cognition.  Seems that in the early 1990's, a group of psychologists formed a mathematical psychology subfield.

This subfield was expressly dedicated to modeling human thinking and in particular decision making. It drew some notable attention then limped along in the shadows.  The primary problem being that decisions often fall outside of traditional probability models.

At this point, some of the more mathematically-inclined people along with some physicists adopted  probability models from quantum mechanics.

Disagreement Arises

This quantum models solved a number of issues in predicting outcomes and accounted for uncertainty. This change gave rise to quantum cognition studies and split the group into two basic camps:

• The first camp adheres to the idea that at the neuron level, there is an actual physical quantum effect occurring which affects thinking.  
• The second camp adheres to the idea that brain functionality (the interplay between neocortex and cortex) creates quantum like conditions with regard to outcomes.

This is where it becomes interesting. The quantum-like modeling accepts the premise that context matters greatly and outcomes are created at the moment of request (measurement for us science types) instead of being neatly archived somewhere and simply retrieved.

The Meaning of Memory

This means that memories are in fact constructions based on context and other factors at the time of request, not static archives. This echos my thoughts on the importance of context as well as the significance that those aspects of learning which I trot out every so often.  From a cognitive rigor perspective, the quantum models are extremely intriguing.

Recall/Remembering is at its foundation a parametrized process creating an outcome from the weighted effect of its inputs, not an all or nothing retrieval of a static fact. We see from work being done in other domains like computer science and informatics that storing parameters to create the objects you need is extremely efficient when compared to storing the actual objects themselves.

Additionally, the storage of parameters opens up greater avenues for meta processing, filtering, and assimilation than the objects themselves could ever afford.

Impact on Cognitive Rigor

Given all this, the idea of Depth of Knowledge (DOK) becomes even more interesting because it encapsulates classes of hierarchical processes that generate consistent context in the learning experience.

Bloom's Taxonomy then becomes a type of "at the moment" filtering system for the selection of parameters which are greatly affected by current context, time, and other factors all contributing toward a set of potential outcomes and their accompanying uncertainties.

Further Reading

Those interested in this issue are urged to consult the following resources:

• Busemeyer, J. R. & Bruza, P. D. (2012) Quantum models of cognition and decision. Cambridge.
• Trueblood, J. S., & Busemeyer, J. R. (2011). A quantum probability account for order effects on inference. Cognitive Science, 35, 1518-1552 
• Quantum Information Processing Theory: Jennifer S. Trueblood and Jerome R. Busemeyer, Indiana University - Bloomington, Springer Press (year?)
• Busemeyer, J. R., Wang, Z., & Lambert-Mogiliansky, A. (2009). Empirical comparisons of markov and quantum models of decision making. Journal of Mathematical Psychology, 53, 423-433.