David Ausubel, a pioneer in studying this type of learning, pointed out that two things are necessary for understanding to occur: (1) the content must be potentially meaningful, and (2) the learner must relate it in a meaningful way to his or her prior knowledge. For potentially meaningful knowledge to become meaningful knowledge to a learner, it is usually, according to Ausubel, subsumed under a broader, more inclusive piece of meaningful knowledge closely related to it. Understanding of the concept "sonnet" is enhanced when we learn that it is a kind of poem (assuming we understand what a poem is). The more distinct the new knowledge is from the relevant subsumer, the harder it is to understand. The key to understanding, it appears, is relating it to appropriate prior knowledge. But sometimes, particularly when one's understanding is incorrect, subsumption does not come easily ó it doesn't fit right. Then there is a restructuring of knowledge Ausubel calls "integrative reconciliation".Ý 

Schema theory extends Ausubel's theory of meaningful learning by identifying other types of relationships which help lend meaning to new knowledge. But the same two processes remain, only with different names: what Don Norman refers to as "accretion" (plugging new ideas into a schema) and "restructuring" (making important changes to a schema). He has also identified an intermediate process, which he calls "tuning" (making smaller changes to a schema), which shows that there is a continuum between these two extreme forms of understanding. Assimilation occurs when you plug new knowledge into an existing schema, whereas restructuring occurs when the new knowledge results in your reconceptualizing (significantly modifying a schema) in order to understand (reconcile conflicts with your prior knowledge).Ý 

Understanding is like a light bulbóit changes suddenly from darkness to lightóin contrast to the gradual process by which rote memorization and skill application occur (see Fig. 6.1 below). Small steps are taken when accretion occurs; medium steps when tuning occurs; and large steps (momentous insights) when restructuring occurs. 

Figure 6.1. An important difference between understanding and skill application.

The issue of what is understanding is a difficult one. One view is that there are two major kinds of understanding: understanding things (concepts), and understanding how things change (principles, or causal models). 
 

Conceptual understanding

Concepts are understood by establishing relationships with prior knowledge. But what are the kinds of relationships which help lend meaning to new concepts? Norman identified the "isa", "hasa", "cause", "act", "iswhen", "location", and "object" relationships, among others. Therefore, it appears that meaningful learning of some kind can occur when appropriate links are made to any of a variety of kinds of relevant prior knowledge, including: 

Superordinate knowledge, which is broader and more inclusive. For example, for teaching the concept of erosion, you might relate it to the superordinate concept of movement of material, if the learners already learned what that is. 

Coordinate knowledge, which is on the same level of breadth and inclusiveness. For example, erosion might be related to the opposite kind of movement of material, the coordinate concept of sedimentation (the depositing of material in layers), if the learners already learned what that is. 

Subordinate knowledge, which is narrower and less inclusive. For example, erosion might be related to the subordinate concept of wind erosion, if the learners already learned what that is. 

Experiential knowledge, which is specific cases of the new knowledge. For example, erosion might be related to the little gully that was formed in the dirt outside the school in the last big rain storm, if the learners were already familiar with that. 

Analogic knowledge, which is similar but outside the content area of interest. For example, erosion might be related to sanding down some wood, if the learners were already familiar with that. 

Causal knowledge, which indicates how something influences or is influenced. For example, erosion might be related to its effects on transportation (e.g., washing out dirt roads), if the learners were already familiar with that.Ý 

Procedural knowledge, which indicates how something is used. For example, erosion might be related to methods of contour plowing for preventing water erosion on farmland, if the learners were already familiar with that. 

It is important to note that superordinate, coordinate, and subordinate knowledge can be of two types: kinds or parts. Any concept can be a kind of something or a part of something; it and a coordinate concept are both kinds of the same superordinate concept, or parts of the same superordinate concept; and it has both kinds and parts of itself. A circulatory system is a part of an organism and a kind of body system. Its parts include a heart and arteries and veins; and its kinds include 2-chamber circulatory systems and 1-chamber systems. 

As can be seen from the above examples, each of these types of prior knowledge has a corresponding type of relationship which can contribute to one's understanding. It may be useful to think of these relationships as dimensions of understanding, many (but not all) of which will be important for any given idea that is to be understood. This is related to the notion of  "breadth of understanding". 
 

Causal understanding

Principles, or interrelated sets of principles called causal models, are a very different kind of understanding. The water cycle is a causal model in which various changes (evaporation, condensation, and precipitation) occur, and a variety of other changes (events) influence them (temperature, humidity, wind, convection currents, and so forth). Causal models are understood primarily by: (1) establishing relationships between the real events that constitute a causal model and the generalities (principles or causal models) that represent them, and (2) learning about the network of causal relationships among those events (changes). This type of understanding will not be further discussed in this module, but you will have an in-class exercise to invent some instructional tactics for teaching it.Ý 
 

What are the obstacles to conceptual understanding?

It is helpful to think in terms of obstacles to initial acquisition of conceptual understanding and obstacles to retention of that understanding. Understanding is quite the opposite of memorization in that acquisition is what is difficult; retention is relatively easy. Since acquisition is mainly a matter of relating the new knowledge to appropriate prior knowledge, there are three major obstacles. First, the appropriate prior knowledge must indeed have been acquired already. Second, the appropriate prior knowledge must be "activated"óthat is, it must be brought to mind. And third, the proper relationship between the new knowledge and the prior knowledge must be learned. The more links which are created with relevant prior knowledge, the greater the depth and/or breadth of understanding. 

Once conceptual understanding has occurred, retrieval problems are relatively rare. However, if some piece of meaningful knowledge is not used for a long time, it can undergo what David Ausubel calls "obliterative subsumption" (I love that term!). To the extent that conceptual knowledge is subsumed under a broader, more inclusive representation of it, lack of use can result in the more detailed refinement being merged back into the subsumer from which it sprang, becoming indistinguishable from it. The more similar it is to its subsumer, the more quickly it is learned, but the more quickly it can also be forgotten. 

How can you tell if someone understands? It is a lot more difficult to measure (or test for) understanding than to measure rote memorization. This is because understanding cannot be directly observed. It can only be inferred from various observable behaviors. There are observable behaviors for each of the kinds of relationships. They include contextualizing, comparing and contrasting, analyzing, instantiating, analogizing. and so forth. For causal understanding, they include such things as explanation (making an inference), prediction (describing an implication), and solution (solving a problem), which were described in Module 5.