Driscoll, Chapter 4
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.)
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
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.
Ausubel's "meaningful reception
Introduction to Ausubel's
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.
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.
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
four processes by which meaningful learning can occur:
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.
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.
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.
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.
of 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
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.
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.
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
Why do we need schema theory?
Suppose you overheard
the following conversation between two college-age apartment-mates:
A: Did you order
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:
Driscoll suggests that
a schema is analogous to:
- 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.
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
- A play, in that
it has a basic script, but each time it's performed, the details will
- 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
- A computer program,
in that it enables us to actively evaluate and parse incoming information.
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!!?"
"Well, you see those
refrigerators back there? You pick your cut of beef and grill it on
the indoor grill."
can both facilitate and not facilitate learning.
How are schemata created
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.
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:
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.)
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
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
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
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
- 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:
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
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
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?
Mental models (particularly
from mathematics and science):
- 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?
- 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
- Explicitly teach
- 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.
for a whole list of misconceptions in teaching physics (click on "Facets
of thinking in physics" or "What are facets and facet clusters?".
4.2 Thought activity
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
Remember that I am your audience for the papers. While 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.
There are two schema theory links on the Web