Module 6: Understanding

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Basic Methods of Instruction

Module 6: Understanding

  • What is understanding?

  • Why is understanding important?

  • Principles for Learning Meaningful Knowledge

  • Principles for Teaching Understanding

  • Development procedure

  • Team Activities

  • Skill Builder

  • Comments

What is understanding?

Understanding is meaningful learning. It is usually contrasted with rote learning (memorization), although it is also distinct from skill application and generic skill application. So, what is the difference between applying concepts and understanding concepts? We saw in Module 3 that concept classification is a mental skill which requires us to classify instances as being examples or nonexamples of a concept. But for many concepts, classification is not important, or not even possible. The concept of an atom is a case in point. We will probably never need (or be able) to classify actual instances as examples, but we certainly can acquire an understanding of what an atom is.

We saw in Module 3 that there are two major kinds of change relationships: procedures, which are actions performed to achieve a goal, and principles, which are natural changes, including natural processes and cause-effect relationships. Procedures can be learned rotely. You can learn to follow steps successfully without having any understanding of why you are doing what you are doing, nor why what you are doing works. In fact, it is principles which give one that understanding. Behind every procedure there is at least one principle which explains why it works (although we may not have discovered the principle yet). Hence, it is not procedures which are directly understood—they are only understood by understanding the principles which underlie them.
Let's consider a principle like the law of supply and demand. To understand the relationship between price and the quantity of a good supplied (by producers) and demanded (by consumers) is to form a mental model which integrates it with what you already know. Each such mental model, or cluster of interrelated knowledge, is referred to as a schema.
Understanding is probably the least studied and least understood type of learning within the cognitive domain. Fortunately, it is the area which is currently receiving the most attention by learning psychologists.

Why is understanding important?

When something is meaningfully understood, it is retained much longer, can be built upon to acquire further understanding, is usually very versatile in the situations and ways it can be used, and facilitates creativity. For example, the law of supply and demand (understanding that a higher price for something will reduce the amount demanded and increase the amount supplied) is something which one is not likely to forget once it is meaningfully understood. It is important for acquiring an understanding of consumption theory. It can be applied in a broad range of ways, including deciding how much to charge for cutting someone's lawn and deciding whom to vote for. And it helps one to be creative in finding ways to maximize your income. Similarly, once you understand what an atom is, you are not likely to forget it; it is essential for understanding the chemical behavior of matter (atomic theory); it is a broadly useful concept in chemistry; and it greatly facilitates a chemist's ability to develop creative ideas and products.

Principles for Learning Meaningful Knowledge

How does understanding occur?
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 -- it doesn't fit right. Then there is a restructuring of knowledge Ausubel calls "integrative reconciliation".
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).
Understanding is like a light bulb—it changes suddenly from darkness to light—in 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.

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.
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"—that 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 7.

Principles for Teaching Understanding

Case Study
Imagine your friend, Jennifer, has just found out that her student, Sam, needs to learn what a revolution is (as in a revolutionary war). She knows that it is important for him and that he does not already know what it is. She realizes that the methods she used to teach the names of the Presidents of the United States won't work very well here, but she doesn't know what to do. So she has come to you for more advice.
You, of course, know that a revolution is an armed uprising against a ruling authority; that to be a revolution rather than a rebellion, it must be widespread; and that to be a revolution rather than an invasion, it must be waged by people within the territory of the ruling authority (government). You can see right away that this is the conceptual understanding type of learning.
Based on what you now know about how this kind of learning occurs, what do you think you should advise Jennifer to do first? Think about it, and jot your answer below.
1. _________________________________________________________
Given the importance of relating the new knowledge to relevant prior knowledge, Jennifer must figure out what the important prior knowledge is and whether or not Sam has already acquired it. If he hasn't, then she must remediate -- teach that missing knowledge -- before she teaches what a revolution is. Certainly, Sam must know what fighting is and, more specifically, an armed fight. He also must know what a ruling authority is and what the territory of a ruling authority is. Of course, these labels do not need to be learned -- it is the ideas behind them which must be understood. These ideas are prerequisites in the sense that they must be understood before it is possible for one to understand what a revolution is.
First, Jennifer assessed Sam's needs and found out that he should be taught what a revolution is. Next, we have seen that she must assure mastery of relevant prior understandings. But then what should she do? Remember that Bloom identified learner participation as perhaps the most important determinant of the quality of instruction. Also remember that presentation, practice, and feedback have proven to be routine components for both memorization and skill application, although the nature of each routine component is quite different for each kind of learning. Given all of this, what are the most important recommendations you could give to Jennifer for teaching what a revolution is? Think about it, and jot your answer below.
1. _________________________________________________________

2. _________________________________________________________

3. _________________________________________________________

4. _________________________________________________________
Certainly the knowledge needs to be presented in some form to Sam. Learner participation of some kind also makes sense. But how should the knowledge be presented? And what form should the participation take?
Let's start by thinking about what needs to be presented. Remember the principles of learning. According to Ausubel, Sam must have a good "subsumer", a broader and more inclusive idea which is closely related. In other words, Jennifer should provide a meaningful context for understanding "revolution". What would such a subsumer be in this case? Well, a revolution is a kind of war, and a kind of fighting. But war is a closer concept to revolution, because there are many other kinds of fighting besides wars. Therefore, "war" will make it easier to understand what a revolution is. This makes it a more appropriate subsumer.
But for sure Sam knows what a war is, so what does all this have to do with the presentation? Well, Jennifer should start by activating the meaningful context: "Sam, you know what a war is." Then she should relate the new knowledge to it (superordinate knowledge): "A revolution is a kind of war." Next, she can describe what a revolution is, using terms that are familiar to Sam. This entails analyzing it as to its critical attributes (subordinate parts). She can describe an example or two (experiential knowledge). She can compare and contrast it to other kinds of wars (coordinate knowledge). And if Sam was already familiar with any kinds of revolutions (subordinate knowledge), she could relate it to them. (For example, in teaching what a vertebrate is, she could relate vertebrates to dogs, people, horses, fish, and so on.) She could even come up with an analogy, like convicts revolting in a prison. And she could infer the causes of revolutions, or trace the implications if a certain revolution had never occurred.
But what about learner participation? Well, as far as practice is concerned, Jennifer can ask Sam to explain in his own words what a revolution is. Or she can ask him to explain in his own words the differences between a revolution and an invasion (which was already explained to him). But such "regurgitation" questions don't require much depth of processing. How do you think Jennifer could help cause greater depth and breadth of processing? Think about it, and jot your answer below.
1. _________________________________________________________

2. _________________________________________________________
Practice isn't the only kind of learner participation. As was discussed in Module 7, discovery learning is a form of learner participation. What are the differences between inductive and deductive participation?
Deduction could take a number of forms. Breadth of processing can be increased by creating links with other meaningful knowledge the learner already possesses. Asking the learner to paraphrase what has already been presented (which we identified as shallow questioning above) does not usually create any additional links; it usually just strengthens those which already exist. Hence, it is a relatively superficial form of deduction -- that is, it does not cause broader processing. On the other hand, elaboration does create additional links. Elaboration is the process of relating additional knowledge to what one has already learned. This is done deductively when the relationships are told to the learner.
Induction is a bit different for understanding than it is for application of principles. It is basically discovery learning, as it is for application. But its role for understanding is to get the learner to process the knowledge fairly deeply. If Jennifer compares and contrasts revolution with coordinate concepts for Sam, he is not likely to process it as deeply as if she asks him to do it: "What do you think is the difference between a revolution and an invasion?" and "What do you think is the difference between an uprising and a revolution?" and "In what ways is a prison revolt similar to a revolution, and in what ways is it different?" Naturally, feedback is very important here. This form of guided discovery should not take much longer than telling the relationships to the learner. On the other hand, pure discovery would certainly take much longer and might not result in the learner learning anything new at all. Hence, it does not seem likely that pure discovery would present any advantages over this form of guided discovery, or "figure-out" approach to instruction.


The following is a summary of what you should do to design instruction for facilitating understanding:

1. Decide what to teach.

Assess the need.

Analyze the goals.

Analyze the learner's current knowledge.

Determine type of understanding (conceptual or causal).

The following tactics are for facilitating conceptual understanding.

2. Assure important prior knowledge has been acquired

(e.g., prerequisite understandings, meaningful context).

Assess with a pretest.

Remediate if necessary.

3. Give the presentation (context, information, relationship).

Activate a meaningful context.

Relate the new knowledge to it.

Describe the new knowledge.

Provide enrichment, if needed (see #6 below).
4. Provide practice.


Paraphrasing the knowledge.

Elaborating the knowledge.

Relating it to superordinate knowledge with ... context.

Relating it to coordinate knowledge with . . . comparison / contrast.

Relating it to subordinate knowledge with . . . analysis.

Relating it to experiential knowledge with . . . instantiation.

Relating it to analogical knowledge with . . . analogy.

Relating it to causal knowledge with . . . inference.

Relating it to procedural knowledge with . . . function.

Identifying roles with . . . roles.
Note: The types of relationships (dimensions of understanding) that are important for a given concept should be included in the test, practice, and (if enrichment is required) presentation. However, the object of each of these types of relationships (i.e. what the new knowledge is being related to) should be different in the test, practice, and presentation.
5. Provide feedback.

Confirm or correct.

6. Provide enrichment as needed.

For the presentation:

Use a guided discovery approach.

Use elaboration techniques:

Relating it to superordinate knowledge with ... context.

Relating it to coordinate knowledge with . . . comparison / contrast.

Relating it to subordinate knowledge with . . . analysis.

Relating it to experiential knowledge with . . . instantiation.

Relating it to analogical knowledge with . . . analogy.

Relating it to causal knowledge with . . . inference.

Relating it to procedural knowledge with . . . function.

Identifying logical relationships with . . . implication.

Identifying roles with . . . roles.

For the practice:

Use hints (prompting).

For the feedback:

For a wrong answer, use hints in question form.
7. Provide systematic review.

Require the learner to use the knowledge at several evenly spaced points in time over the remainder of the course.

A Development Procedure

1. Pick a concept that needs to be understood (needs analysis and content analysis).

2. Pick which relationships constitute the important dimensions of understanding for that concept (needs analysis and content analysis).

3. Identify which of those relationships have not already been acquired by the learners, and list them as new relationships to be taught (learner analysis).

4. Pick the best "objects" (ideas which are related to the idea of interest by each relationship) for each new relationship (e.g. what you compare and contrast the main concept with).

5. Identify which of those objects have not already been acquired by the learners, and list them as new objects to be taught (learner analysis).

6. Design a sequence for teaching the new objects and relationships.

7. Design a strategy (or approach) for teaching the whole understanding.

8. Design the tactics (e.g. comparison/contrast, analogy) for teaching each dimension of understanding.

Team Activity:
Invent Some Instructional Tactics for Teaching Causal Understanding

Your task is to work in pairs to invent some instructional tactics for teaching causal understanding. Invent your tactics inductively by figuring out how you would teach a particular causal model that you should be pretty familiar with: the water cycle.

First, take about five minutes to analyze the causal model for the water cycle. Think of several additional causes and/or effects to elaborate the following causal flow diagram:

The Water Cycle
Second, spend the rest of the time figuring out how to best teach an understanding of it (not ability to apply it). Figure out what it means to understand these causal relationships, and how you can best help that understanding to occur. Then analyze your ideas to identify tactics that you could use to design instruction on any causal model.
Finally, be prepared to share your tactics with the class.

Skill Builder

Go to the HyperCard Program for this.

Group Activities:

Practice with Feedback

Synthesis: Sample Lesson


by Brandt, Hammer, & Holtzman

The following is a sample lesson that shows the use of the strategies and tactics you have just studied. It is for a fairly difficult lesson, so it includes rich instruction (the use of many enrichment tactics).
The lesson is preceded by a blueprint, which provides the specs (specifications) for the lesson. Once you become experienced with lesson design using these instructional strategies and tactics, you will create this kind of blueprint in your head whenever you set out to design a lesson. Until then, it is helpful to write it out. You will find the following activities very beneficial to your understanding! Please do them.
1. With your team, study the blueprint carefully and see if you can envision from it what the lesson will be like. See if you can spot any weaknesses before you even look at the lesson itself, and discuss them. Also try to identify what you think will contribute most to the effectiveness and appeal of the lesson.
2. Look at the lesson, together as a team. For each tactic used, think up a different way that tactic could have been implemented, and discuss it.
3. Look at the test and compare it to the practice. Are the two sets of items interchange-able. Were all the appropriate kinds of relationships used (super-/co-/subordinate, experiential, analogical, etc.)? Were appropriate objects chosen for each relationship? Try to reach consensus on these questions.
4. Discuss what instructional tactics could be deleted if the difficulty level were a 1 instead of a 4 (i.e., if the students' prior knowledge and ability were such that the concept was very easy for them to learn).
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