P540 - Learning and Cognition

Unit 4: Meaningful reception learning & schema theory

Readings
Instructor notes
Learning activities
Web resources

Readings
Driscoll, Chapter 4
Optional: Gredler, Chapter 8. (This chapter does not pertain specifically to schema theory and mental models research. However, it covers research approaches that, like schema theory, attempt to account for higher forms of cognition that are not readily explained by the more mechanistic approach of CIP.)
Additional Readings: Kiewra, Kenneth A., and Mayer, Richard E. (1997) Effects of advance organizers and repeated presentations on students' learning. Journal of Experimental Education, Vol. 65 Issue 2. (Available online through Academic Search Fulltext Elite. Skim this article for a contemporary example of research on advance organizers.)
Kitao, S. Kathleen. (1990). Textual schemata and English language learning. Cross Currents, Fall90, Vol. 40, Issue 3. Available online through Academic Search FullText Elite.
Battista, Michael; Clements, Douglas H. (1998). Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, Jan98, Vol. 4, Issue 5. Available online through Academic Search FullText Elite. Skim as an example of mental models research.
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Instructor notes

Ausubel's "meaningful reception learning"

Introduction to Ausubel's theory

You probably noticed that Ausubel's theory has at least one thing in common with Gagne's: that it concerns itself primarily with intentional, or "school" learning. In that way, both theories differ from behaviorism and cognitive information processing, which attempt to explain aspects of all human learning or memory. Thus, Ausubel's theory, like Gagne's, suggests how teachers or instructional designers can best arrange the conditions that facilitate learning for students.

The overarching idea in Ausubel's theory is that knowledge is hierarchically organized; that new information is meaningful to the extent that it can be related (attached, anchored) to what is already known.

Ausubel stresses meaningful learning, as opposed to rote learning or memorization; and reception, or received knowledge, rather than discovery learning. (Ausubel did not contend that discovery learning doesn't work; but rather that it was not efficient.)

The processes of meaningful learning

Ausubel proposed four processes by which meaningful learning can occur:

Derivative subsumption. This describes the situation in which the new information you learn is an instance or example of a concept that you have already learned. So, let's suppose you have acquired a basic concept such as "tree". You know that a tree has a trunk, branches, green leaves, and may have some kind of fruit, and that, when fully grown is likely to be at least 12 feet tall. Now you learn about a kind of tree that you have never seen before, let's say a persimmon tree, that conforms to your previous understanding of tree. Your new knowledge of persimmon trees is attached to your concept of tree, without substantially altering that concept in any way. So, an Ausubelian would say that you had learned about persimmon trees through the process of derivative subsumption.

Correlative subsumption. Now, let's suppose you encounter a new kind of tree that has red leaves, rather than green. In order to accommodate this new information, you have to alter or extend your concept of tree to include the possibility of red leaves. You have learned about this new kind of tree through the process of correlative subsumption. In a sense, you might say that this is more "valuable" learning than that of derivative subsumption, since it enriches the higher-level concept.

Superordinate learning. Imagine that you were well acquainted with maples, oaks, apple trees, etc., but you did not know, until you were taught, that these were all examples of deciduous trees. In this case, you already knew a lot of examples of the concept, but you did not know the concept itself until it was taught to you. This is superordinate learning.

Combinatorial learning. The first three learning processes all involve new information that "attaches" to a hierarchy at a level that is either below or above previously acquired knowledge. Combinatorial learning is different; it describes a process by which the new idea is derived from another idea that is neither higher nor lower in the hierarchy, but at the same level (in a different, but related, "branch"). You could think of this as learning by analogy. For example, to teach someone about pollination in plants, you might relate it to previously acquired knowledge of how fish eggs are fertilized.

Instructional implications of Ausubel's theory

Ausubel's theory is not particularly in vogue today, perhaps because he seems to advocate a fairly passive role for the learner, who receives mainly verbal instruction that has been arranged so as to require a minimal amount of "struggle". Nevertheless, there are some aspects of his theory that you might find interesting.

The advance organizer. This seems to be the most enduring Ausubelian idea, even though it can be tricky to implement. There is a fair amount of intuitive appeal to the notion of epitomizing an idea before trying to teach the details. We've all had the experience of needing to understand the "big picture" before we can make sense of the details. You could think of the advance organizer as Ausubel's notion of how to provide this.

The comparative organizer. How do we remember concepts and keep them from fading or being lost into higher-level ideas? Ausubel proposed the comparative organizer as a way of enhancing the discriminability of ideas; i.e., permitting one to discriminate a concept from other closely related ones. A comparative organizer allows you to easily see the similarities and differences in a set of related ideas.

Progressive differentiation. According to Ausubel, the purpose of progressive differentiation is to increase the stability and clarity of anchoring ideas. The basic idea here is that, if you're teaching three related topics A, B, and C, rather than teaching all of topic A, then going on to B, etc., you would take a spiral approach. That is, in your first pass through the material, you would teach the "big" ideas (i.e., those highest in the hierarchy) in all three topics, then on successive passes you would begin to elaborate the details. Along the way you would point out principles that the three topics had in common, and things that differentiated them.

Schema theory

Why do we need schema theory?

Suppose you overheard the following conversation between two college-age apartment-mates:

A: Did you order it?
B: Yeah, it will be here in about 45 minutes.
A: Oh... Well, I've got to leave before then. But save me a couple of slices, okay? And a beer or two to wash them down with?

Do you know what the roommates are talking about? Chances are, you're pretty sure they are discussing a pizza they have ordered. But how can you know this? You've never heard this exact conversation, so you're not recalling it from memory. And none of the defining qualities of pizza are represented here, except that it is usually served in slices, which is also true of many other things.

The other theories we've looked at in this course would have a difficult time explaining how we can comprehend this conversation. Schema theory would suggest that we understand this because we have activated our schema for pizza (or perhaps our schema for "ordering pizza for delivery") and used that schema to comprehend this scenario.

In our discussions of CIP and Ausubel, it may have seemed as if the learner was relatively passive. New knowledge gets "slotted" somewhere in the brain, but neither theory seems to emphasize how that knowledge gets used. Schema theory, on the other hand, attempts to address specifically how we actively make meaning of information.

What is a schema?
A schema (plural schemata) is a hypothetical mental structure for representing generic concepts stored in memory. It's a sort of framework, or plan, or script. According to Stein and Trabasso (1982), schemata are thought to have these features:

Schemata are composed of generic or abstract knowledge; used to guide encoding, organization, and retrieval of information.
Schemata reflect prototypical properties of experiences encountered by an individual, integrated over many instances.
A schema may be formed and used without the individual's conscious awareness.
Although schemata are assumed to reflect an individual's experience, they are also assumed to be shared across individuals (at least within a culture).
Once formed, schemata are thought to be relatively stable over time.
We know more about how schemata are used than we do about how they are acquired.
Driscoll suggests that a schema is analogous to:

A play, in that it has a basic script, but each time it's performed, the details will differ.
A theory, in that it enables us to make predictions from incomplete information, by filling in the missing details with "default values." (Of course, this can be a problem when it causes us to remember things we never actually saw...)
A computer program, in that it enables us to actively evaluate and parse incoming information.
We all have a schema for going to a sit-down restaurant. We are usually greeted by a hostess and seated. A server comes and take our order for drinks and food. The food is delivered, we eat, we pay and we leave. Every time we go into a restaurant, we invoke that schema and it helps us to know what comes next.
Unfortunately, it doesn't always work.
My husband and I were in Atlanta some years ago to see Shakespeare in the Park. They had never been in this particular part of Atlanta before but saw a building with a bright red and white striped awning and a surmised correctly that they could eat there before moving on to Oglethorpe University. They were greeted and seated. The server came to take their drink order, dropped them off and then never came back! After some time had elapsed, they flagged him down.
"Ooooh! You've never eaten here before!!?"
"No."
"Well, you see those refrigerators back there? You pick your cut of beef and grill it on the indoor grill."
Obviously schema can both facilitate and not facilitate learning.
How are schemata created and modified?

Schemata are created through experience with people, objects, and events in the world. When we encounter something repeatedly, such as a restaurant, we begin to generalize across our restaurant experiences to develop an abstracted, generic set of expectations about what we will encounter in a restaurant. This is useful, because if someone tells you a story about eating in a restaurant, they don't have to provide all of the details about being seated, giving their order to the server, leaving a tip at the end, etc., because your schema for the restaurant experience can fill in these missing details.

Sometimes, details get filled in incorrectly. For example, Elizabeth Loftus did some research examining people's recall for details after watching films of car accidents. Two groups of people saw exactly the same tape of a car accident. Both groups were asked a series of factual questions after the accident with only one difference - one of the groups was asked "How fast were the cars going when they bumped into each other?" the other was asked "How fast were the cars going when they crashed into one another?" The group who got the "crashed" question was twice as likely to recall broken class at a later session (when indeed there had been none) than the group with the bumped question. Thus, our schemas help us fill in details which may never have been present in the original situation.

Not all of the information we have about an experience necessarily gets added to our schema. For example, there's a restaurant in Indianapolis where the seating booths are little jail cells. After you're seated, the server closes your cell doors. (Of course, you can escape any time you want, as long as you've paid your bill.) Even though you may go to this restaurant several times, your restaurant schema may still not include tables as miniature jail cells. This information is simply an outlier; it may be too unlike your experience at other restaurants.
Three processes are proposed to account for the modification of schemata:

Accretion: New information is remembered in the context of an existing schema, without altering that schema. For example, suppose you go to a bookstore, and everything you experience there is consistent with your expectations for a bookstore "experience." You can remember the details of your visit, but since they match your existing schema, they don't really alter that schema in any significant way. (Note that this is analogous to Ausubel's derivative subsumption.)
Tuning: New information or experience cannot be fully accommodated under an existing schema, so the schema evolves to become more consistent with experience. For example, when you first encountered a bookstore with a coffee bar, you probably had to modify your bookstore schema to accommodate this experience. (Note that this is analogous to Ausubel's correlative subsumption.)
Restructuring: When new information cannot be accommodated merely by tuning an existing schema, it results in the creation of new schema. For example, your experience with World Wide Web-based bookstores may be so different from your experience with conventional ones that you are forced to create a new schema. (Note that this may be similar to Ausubel's superordinate learning, or combinatorial learning, depending on the situation.)

What are mental models?
Mental models goes beyond schema theory to include perceptions of task demands and task performances. Mental models researchers are interested in how people perform tasks and solve problems in school settings and in the real world. (You can think of problem-solving as including both knowledge of schemata and knowledge of procedures.) This kind of research has been most prevalent in the sciences and mathematics.
Why are schema theory and mental models important in teaching and learning?
It's important to understand that schemata are powerful forces in learning. In an article on the role of schemata in story comprehension, Stein and Trabasso (1982) noted that:

Schematic knowledge has a significant effect on organization of ambiguous or disorganized stories.
Narrative schemata specify expected components of a story, such as the time sequence of events, and causal relations that should connect the events; during encoding or retrieval of a story, missing events may be inferred to fill in omitted information, and events may be reordered to correspond to a real-time sequence.
Many studies have shown that the use of schematic knowledge is so powerful that listeners have little control over the retrieval strategies used during recall of narrative information; even when listeners are instructed to reproduce texts verbatim, they cannot do so when the text contains certain types of omissions or certain sequences of events.

For example, consider the following excerpt from a story:

The girl sat looking at her piggy bank. "Old friend," she thought, "this hurts me." A tear rolled down her cheek. She hesitated, then picked up her tap shoe by the toe and raised her arm. Crash! Pieces of Piggo--that was its name--rained in all directions. She closed her eyes for a moment to block out the sight. Then she began to do what she had to do.

If you have a well-developed schema for "piggy banks", this story should be readily comprehensible. You would understand that traditional piggy banks were usually made of some fragile, brittle material, that they contained a slot for inserting and saving coins, and that the money could only be removed by breaking them.

On the other hand, if you have no schema for piggy bank, the story probably makes little sense, like the one below.

The procedure is actually quite simple. First, you arrange things into different groups. Of course, one pile may be sufficient depending on how much there is to do. If you have to go somewhere else due to lack of facilities, that is the next step; otherwise, you are pretty well set. It is important not to overdo things. That is, it is better to do too few things at once than too many. In the short run this may not seem important but complications can easily arise. A mistake can be expensive as well. At first, the whole procedure will seem complicated. Soon, however, it will become just another fact of life. It is difficult to foresee any end to the necessity for this task in the immediate future, but then one can never tell. After the procedure is completed one arranges the materials into different groups again. Then they can be put into their appropriate places. Eventually they will be used once more and the whole cycle will then have the be repeated. However, that is a part of life.

Did you notice yourself looking for details which would key you to use the right schema? We feel quite disoriented when a schema cannot be activated.
What are some implications of schema theory and mental models research for instruction?
Schema theory:

Provide unifying themes for content, since information that lacks a theme can be difficult to comprehend, or, worse, the learner may "accrete" the information to the wrong schema, like the unlabeled washing machine story above. I'll bet you were waiting in anticipation for that answer. Your schema of teacher includes "will share the right answer (eventually!)".
Choose texts with "standard" arrangement so that they conform to student expectations.
Encourage students to read titles and headings.
Point out the structure of particular kinds of texts; e.g., what are the common features of published research articles?
Ask questions to determine what students' current schemata might be.
Pay attention to student answers and remarks that may give clues about how they are organizing information; i.e., what schemata are they using?
Mental models (particularly from mathematics and science):

Identify students' current "theories" or algorithms.
Use student errors as a source of information about their mental models.
Use "think aloud" activities, since these help to uncover current models.
Model real problem-solving for students. Students need to see that solving problems is not just a matter of plugging numbers into an algorithm; rather it is a matter of determining the kind of problem so that an algorithm can be successfully applied.
Explicitly teach problem-solving strategies.
Focus on processes, structures, and decisions, not answers.
Provide a mix of problem types, rather than grouping problems of one type; otherwise, students won't develop skill at determining problem type.
Confront incomplete or inaccurate schemata (particularly in science) with problems or outcomes that don't match what the learners expect to happen. Use them as a basis for discussion ensuring that tuning and restructuring are occurring to bring the schema more in line with scientific knowledge. See http://www.talariainc.com/facet for a whole list of misconceptions in teaching physics (click on "Facets of thinking in physics" or "What are facets and facet clusters?".

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Learning activities

4.2 Thought activity #1:

At the end of unit 4 and at the end of the course, a short thought paper (3-5 pages) will be required.

• The first paper may be about behaviorism, cognitive information processing, or meaningful learning/schema theory.
• In the second paper, you should choose two theories to compare/contrast in light of a problem, issue or setting of interest to you. At least one of the theories must come from Unit 5 or 6; the other can be any other theory we’ve covered that you have not yet written on. In other words, you will have written papers on at least three different theories by the end of the course.

Your task in these papers is to evaluate a theory from the perspective of a setting, issue, or problem of importance to you, and to determine how well the theory “fits” the setting or problem you have chosen.

Remember that I am your audience for the papers. Although I want you to demonstrate that you have a basic understanding of the theory, don’t take up valuable space re-stating the theory. Be sure your paper is about something (i.e. it should not just be a series of unrelated reflections or observations about the theory). Like all good papers, it should have a descriptive title, some kind of thesis statement, and some sort of conclusion after a review of your “evidence”. And, as with any paper of this kind, I will expect it to be well organized and coherent. Sample titles might include “Behaviorism and coaching basketball” or “Schema theory and mathematics education: A match made in heaven?” or “”Making sense of Bruner’s theory of cognitive development in college instruction”.

This is not intended to be a library research paper. You do not necessarily need to use any resources other than the text and class readings/discussion. You should, however, attribute ideas and citations as appropriate.

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Web resources
There are two schema theory links on the Web Resources page.
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Comments: joalexan@indiana.edu