Teaching for understanding

[Dean-Smith]

Here are six priorities for teachers who teach for understanding:

1. Make learning a long-term, thinking-centered process.

From the standpoint of the teacher, the message about performances of
understanding boils down to this: Teaching is less about what the
teacher does than about what the teacher gets the students to do. The
teacher must arrange for the students to think with and about the
ideas they are learning for an extended period of time, so that they
learn their way around a topic. unless students are thinking with and
about the ideas they are learning for a while, they are not likely to
build up a flexible repertoire of performances of understanding.
Imagine, if you will, a period of weeks or even months committed to
some rich theme--the nature of life, the origin of revolutions, the
art of mathematical modeling. Imagine a group of students engaged over
time in a variety of understanding performances focused on that topic
and a few chosen goals. The students face progressively more subtle
but still accessible challenges. At the end there may be some
culminating understanding performance such as an essay or an
exhibition as in Theodore Sizer's ( 1984) concept of "essential
schools." Such a long term, thinking-centered process seems central to
building students' understanding.

2. Provide for rich ongoing assessment.
I emphasized earlier that students need criteria, feedback, and
opportunities for reflection in order to learn performances of
understanding well. Traditionally, assessment comes at the end of a
topic and focuses on grading and accountability. These are important
functions that need to be honored in many contexts. But they do not
serve students' immediate learning needs very well. To learn
effectively, students need criteria, feedback, and opportunities for
reflection from the beginning of any sequence of instruction (cf.
Baron, 1990; Gifford and O'Connor, 1991; Perrone, 1991b).
This means that occasions of assessment should occur throughout the
learning process from beginning to end Sometimes they may involve
feedback from the teacher, sometimes from peers, sometimes from
students' self evaluation. Sometimes the teacher may give criteria,
sometimes engage students in defining their own criteria. While there
are many reasonable approaches to ongoing assessment, the constant
factor is the frequent focus on criteria, feedback, and reflection
throughout the learning process.

3. Support learning with powerful representations.
Research shows that how information is represented can influence
enormously how well that information supports understanding
performances. For instance Richard Mayer (1989) has demonstrated
repeatedly that what he terms "conceptual models"--usually in the form
of diagrams with accompanying story lines carefully crafted according
to several principles--can help students to solve nonroutine problems
that ask them to apply new ideas in unexpected ways. For another
example, computer environments that show objects moving in
frictionless Newtonian ways we rarely encounter in the world can help
students understand what Newton's laws really say about the way
objects move (White, 1984). For yet another example, well-chosen
analogies often serve to illuminate concepts in science, history,
English, and other domains (e.g. Brown, 1989; Clement, 1991; Royer and
Cable, 1976).
Many of the conventional representations employed in schooling--for
instance, formal dictionary definitions of concepts or formal
notational representations as in Ohm's law, I = E/R--in themselves
leave students confused or only narrowly informed (Perkins and Unger,
in press). The teacher teaching for understanding needs to add more
imagistic, intuitive, and evocative representations to support
students' understanding performances. Besides supplying powerful
representations, teachers can often ask students to construct their
own representations, an understanding performance in itself.

4. Pay heed to developmental factors.
The theory devised by the seminal developmental psychologist Jean
Piaget averred that children's understanding was limited by the
general schemata they had evolved. For instance, children who had not
attained "formal operations" would find certain concepts inaccessible--
notions of control of variables and formal proof, for example
(Inhelder and Piaget, 1958). Many student teachers today still learn
this scheme and come to believe that fundamental aspects of reasoning
and understanding are lost on children until late adolescence. They
are unaware that 30 years of research have forced fundamental
revisions in the Piagetian conception. Again and again, studies have
shown that, under supportive conditions, children can understand much
more than was thought much earlier than was thought.
The "neo-Piagetian" theories of Robbie Case (1985), Kurt Fischer
(1980), and others offer a better picture of intellectual development.
Understanding complex concepts may often depend on what Case calls a
"central conceptual structure," i.e., certain patterns of quantitative
organization, narrative structure, and more that cut across
disciplines (Case, 1992). The right kind of instruction can help
learners to attain these central conceptual structures. More broadly,
considerable developmental research shows that complexity is a
critical variable. For several reasons, younger children cannot
readily understand concepts that involve two or three sources of
variation at once, as in concepts such as balance, density, or
pressure (Case, 1985, 1992; Fischer, 1980).
The picture of intellectual development emerging today is less
constrained, more nuanced, and ultimately more optimistic regarding
the prospects of education.
Teachers teaching for understanding do well to bear in mind factors
like complexity, but without rigid conceptions of what students can
and cannot learn at certain ages.

5. Induct students into the discipline.
Analyses of understanding emphasize that concepts and principles in a
discipline are not understood in isolation (Perkins, 1992; Perkins and
Simmons, 1988; Schwab, 1978). Grasping what a concept or principle
means depends in considerable part on recognizing how it functions
within the discipline. And this in turn requires developing a sense of
how the discipline works as a system of thought. For example, all
disciplines have ways of testing claims and mustering proof--but the
way that's done is often quite different from discipline to
discipline. In science, experiments can be conducted, but in history
evidence must be mined from the historical record. In literature, we
look to the text for evidence of an interpretation, but in mathematics
we justify a theorem by formal deduction from the givens.
Conventional teaching introduces students to plenty of facts,
concepts, and routines from a discipline such as mathematics, English,
or history. But it typically does much less to awaken students to the
way the discipline works--how one justifies, explains, solves
problems, and manages inquiry within the discipline. Yet in just such
patterns of thinking lie the performances of understanding that make
up what it is to understand those facts, concepts, and routines in a
rich and generative way. Accordingly, the teacher teaching for
understanding needs to undertake an extended mission of explicit
consciousness raising about the structure and logic of the disciplines
taught.

6. Teach for transfer.
Research shows that very often students do not carry over facts and
principles they acquire in one context into other contexts. They fail
to use in science class or at the supermarket the math they learned in
math class. They fail to apply the writing skills that they mastered
in English on a history essay. Knowledge tends to get glued to the
narrow circumstances of initial acquisition. If we want transfer of
learning from students--and we certainly do, because we want them to
be putting to work in diverse settings the understandings they
acquire--we need to teach explicitly for transfer, helping students to
make the connections they otherwise might not make, and helping them
to cultivate mental habits of connection-making (Brown, 1989; Perkins
and Salomon, 1988; Salomon and Perkins, 1989).
Teaching for transfer is an agenda closely allied to teaching for
understanding. Indeed, an understanding performance virtually by
definition requires a modicum of transfer, because it asks the learner
to go beyond the information given, tackling some task of
justification, explanation, example-finding or the like that reaches
further than anything in the textbook or the lecture. Moreover, many
understanding performances transcend the boundaries of the topic, the
discipline, or the class room--applying school math to stock market
figures or perspectives on history to casting your vote in the current
election. Teachers teaching for a full and rich understanding need to
include understanding performances that reach well beyond the obvious
and conventional boundaries of the topic.
Certainly much more can be said about the art and craft of teaching
for understanding. However, this may suffice to make the case that
plenty can be done. Teachers need not feel paralyzed for lack of
means. On the contrary, a plethora of classroom moves suggest
themselves in service of building students' understanding. The teacher
who makes learning thinking-centered, arranges for rich ongoing
assessment, supports learning with powerful representations, pays heed
to developmental factors, inducts students into the disciplines
taught, and teaches for transfer far and wide has mobilized a powerful
armamentum for building students' understanding.

WHAT IS UNDERSTANDING?
At the heart of teaching for understanding lies a very basic question:
What is understanding? Ponder this query for a moment and you will
realize that good answers are not obvious. To draw a comparison, we
all have a reasonable conception of what knowing is. When a student
knows something, the student can bring it forth upon call--tell us the
knowledge or demonstrate the skill. But understanding something is a
more subtle matter. A student might be able to regurgitate reams of
facts and demonstrate routine skills with very little understanding.
Somehow, understanding goes beyond knowing. But how?
Clues can be found in this fantasy: Imagine a snowball fight in space.
Half a dozen astronauts in free fall arrange themselves in a circle.
Each has in hand a net bag full of snowballs. At the word "go" over
their radios, each starts to fire snowballs at the other astronauts.
What will happen? What is your prediction?
If you have some understanding of Newton's theory of motion, you may
predict that this snowball fight will not go very well. As the
astronauts fire the snowballs, they will begin to move away from one
another: Firing a snowball forward pushes an astronaut backward.
Moreover, each astronaut who fires a snowball will start to spin with
the very motion of firing, because the astronaut's arm that hurls the
snowball is well away from the astronaut's center of gravity. It's
unlikely that anyone would hit anyone else even on the first shot,
because of starting to spin, and the astronauts would soon be too far
from one another to have any chance at all. So much for snowball
fights in space.
If making such predictions is a sign of understanding Newton's theory,
what is understanding in general? My colleagues and I at the Harvard
Graduate School of Education have analyzed the meaning of
understanding as a concept. We have examined views of understanding in
contemporary research and looked to the practices of teachers with a
knack for teaching for understanding. We have formulated a conception
of understanding consonant with these several sources. We call it a
"performance perspective" on understanding. This perspective reflects
the general spirit of "constructivism" prominent in contemporary
theories of learning (Duffy and Jonassen, 1992) and offers a specific
view of what learning for understanding involves. This perspective
helps to clarify what understanding is and how to teach for
understanding by making explicit what has been implicit and making
general what has been phrased in more restricted ways (Gardner, 1991;
Perkins, 1992).
In brief, this performance perspective says that understanding a topic
of study is a matter of being able to perform in a variety of thought-
demanding ways with the topic, for instance to: explain, muster
evidence, find examples, generalize, apply concepts, analogize,
represent in a new way, and so on. Suppose a student "knows" Newtonian
physics: The student can write down equations and apply them to three
or four routine types of textbook problems. In itself, this is not
convincing evidence that the student really understands the theory.
The student might simply be parroting the test and following memorized
routines for stock problems. But suppose the student can make
appropriate predictions about the snowball fight in space. This goes
beyond just knowing. Moreover, suppose the student can find new
examples of Newton's theory at work in everyday experience (Why do
football linemen need to be so big? So they will have high inertia.)
and make other extrapolations. The more thought-demanding performances
the student can display, the more confident we would be that the
student understands.
In summary, understanding something is a matter of being able to carry
out a variety of "performances" concerning the topic--performances
like making predictions about the snowball fight in space that show
one's understanding and, at the same time, advance it by encompassing
new situations. We call such performances "understanding performances"
or "performances of understanding".
Understanding performances contrast with what students spend most of
their time doing. While understanding performances can be immensely
varied, by definition they must be thought-demanding; they must take
students beyond what they already know. Most classroom activities are
too routine to be understanding performances--spelling drills, true-
and-false quizzes, arithmetic exercises, many conventional essay
questions, and so on. Such performances have their importance too, of
course. But they are not performances of understanding; hence they do
not do much to build understanding.

David Perkins
American Educator: The Professional Journal of the American Federation
of Teachers; v17 n3, pp. 8,28-35, Fall 1993.