Hierarchy and Academic Knowledge

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What does a hierarchy, an ordered relationship among items, have to do with education? There are corporate structures and military ranks. Where does this fit into education?

In an educational setting, there is an inherent structuring of knowledge that pertains to the level of abstraction. The more abstract any topic, the more it depends on the information that precedes it. It all begins at the level of perceptions — taste, touch, smell, sight, and hearing — which serves as the base of all knowledge.

We can illustrate this with an example. Tables and chairs are visible to us but the concept furniture is abstract. We need both knowledge and experience with many different tables, chairs, couches, and bean bags to arrive at the concept of furniture. Abstract definitions — “somewhat moveable large objects in a home that are used for living” — mean little without sensorial experience. Given this ambiguous description, a child could easily mistakenly classify a refrigerator or washing machine as furniture. 

Teaching the more abstract in lieu of the perceptually obvious is an inversion of the order needed to learn. This example is exaggerated and virtually nobody would teach such a simple concept this way. However, this error presents itself in virtually all aspects of curricula throughout every level of education, which has serious implications as students advance in their academic careers.

These errors occur, for example, in horizontal learning where a 2nd grader may be taught more abstract concepts such as fractions before fully grasping addition. This child may start the school year with two weeks performing addition up to 20, then shift to do basic fractions, then learn some elementary geometry, and then 2 months later return to add up to 100. Nothing learned in each lesson can directly carry over to the next, and in a sense, the child has to cognitively “reinvent the wheel” each time they learn something new. Since no logical structure is developed and the child can’t build off of previous knowledge in any systematic way, this has the potential to create an aversion to learning as the child advances. This contrasts with a vertical learning approach, which emphasizes mastery and conceptual understanding of the material before proceeding to the next subject area. 

For another example, consider a freshman in high school learning about inflation before learning in detail about the law of supply and demand or how the government controls the money supply. There is simply no way this student could fully grasp the causes and consequences of inflation without first understanding these more fundamental concepts. The student may mimic knowledge by using aspects of pattern recognition or incorporating other heuristics to pass an exam, but this certainly does not represent true conceptual knowledge. Although this is a more complex example, this is principally the same type of error as a child being taught furniture without first learning tables and chairs.

This method of unsystematic learning stands in contrast to a more logical structure where knowledge of one topic is directly and purposefully carried over and serves as the base for the next topic. Below are two vital reasons why a proper hierarchy of knowledge is so crucial for education:

Motivational – Once a child has a full range of context for why they are learning a given topic that flows hierarchically from their earlier knowledge and experience, they will have gained real conceptual understanding. Similar to the notion of how “success breeds success” the more authentic and first-handed knowledge a student has in a specific area, the more incentivized they will be to keep learning. Aristotle recognized that there’s an inherent joy in using and developing our capacities to their fullest potential. Sequential learning facilitates such development and use.

Logic is taught through context and hierarchy– If a central goal of education is to make a student logical in their thinking, it would be unreasonable to teach a student the highly abstract formal laws of Aristotelian logic and expect them to make sense of it. The only way to teach a child to be a logical thinker is through delivering essentialized content in the proper hierarchical order required for the child to form generalizations and principles. In this context, ‘essentialized’ means the most important information that is fundamental to understanding a given subject area.

Let’s suppose a history teacher is aiming to convey to his students the principle that authoritarian governments lead to low levels of societal and economic prosperity. Assuming a relevant amount of background knowledge, this would be done by probing the student to identify the fundamental component(s) all authoritarian governments share in common that would necessarily lead to the formation of the principle.

Allowing the student to arrive at important theories and principles in this inductive manner ensures a child’s conclusions are tethered to reality by linking up previous knowledge with current knowledge. By repeatedly performing this inductive process over a period of time across multiple subject areas, the student will systematically be trained to think in principles and eventually turn into a logical, independent, and confident thinker.

It is only through proper respect for the hierarchy of knowledge that a student can achieve a proper rational education and the ability to deal with the abstract requirements of life as an adult.

Jeff Frenkel
Jeff Frenkel is a father and home-school teacher.