Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 7
LA UREN B. RESNICK
7
quantitative skills needed to apply various tools of production and
management, the ability to read complex material, and the ability
to build and evaluate arguments. These abilities go well beyond the
routinized skills of the old mass curriculum. In fact, they are much
like the abilities demanded for college-bound students in the College
Board's book, Academic Preparation for College (College Entrance
Examination Board, 1983~. Yet teaching such competencies to the
mass of students remains a considerable challenge.
This, then, is part of what is new about the current drive for
teaching higher order skills. The goals of increasing thinking and
reasoning ability are old ones for educators. Such abilities have
been the goals of some schools at least since the time of Plato.
But these goals were part of the high literacy tradition; they did
not, by and large, apply to the more recent schools for the masses.
Although it is not new to include thinking, problem solving, and
reasoning in Bomeone's school curriculum, it is new to include it
in everyone's curriculum. It is new to take seriously the aspiration
of making thinking and problem solving a regular part of a school
program for all of the population, even minorities, even non-English
speakers, even the poor. It is a new challenge to develop educational
programs that assume that all individuals, not just an elite, can
become competent thinkers.
THE NATURE OF THINKING AND LEARNING:
GOING BEYOND THE ROUTINE
This challenge comes at a time when we also have new knowledge
about the nature of thinking and strong hints about how thinking
abilities are learned. In the last decade or two, cognitive science
research has allowed us to look into the thinking mind, figuratively
at least, and to specify more precisely the reasoning processes of
both successful and less successful thinkers (Newell and Estes, 1983~.
More recently, researchers have begun to investigate how the ability
and the propensity to think well are acquired and maintainecl. These
two bodies of research the nature of human thinking and on the
acquisition of thinking and learning skills are beginning to make
explicit what we mean by higher order skills and what means of
cultivating such skills are most likely to be successful. This process
of making explicit the abilities formerly left to the intuitions of gifted
learners and teachers is precisely what we need to establish a scientific
OCR for page 8
8
ED UCATION AND LEARNING TO THINK
foundation for the new agenda of extending thinking and reasoning
abilities to all segments of the population.
The most important single message of modern research on the
nature of thinking is that the kinds of activities traditionally associ-
ated with thinking are not limited to advanced levels of development.
Instead, these activities are an intimate part of even elementary lev-
els of reading, mathematics, and other branches of learning when
learning is proceeding well. In fact, the term Higher order" skills is
probably itself fundamentally misleading, for it suggests that another
set of skills, presumably called "lower order," needs to come first.
This assumption that there is a sequence from Tower level activities
that do not require much independent thinking or judgment to higher
level ones that do-colors much educational theory and practice. Im-
plicitly at least, it justifies long years of drill on the "basics" before
thinking and problem solving are demanded. Cognitive research on
the nature of basic skills such as reading and mathematics provides a
fundamental challenge to this assumption. Indeed, research suggests
that failure to cultivate aspects of thinking such as those listed in our
working definition of higher order skills may be the source of major
learning difficulties even in elementary school.
Reading as a Higher Order Skill
The process of understanding a written text, as it emerges in
current psychological and artificial intelligence accounts, is one in
which a reader uses a combination of what is written, what he or she
already knows, axed various general processes (e.g., making inferences,
noting connections, checking and organizing) to construct a plausible
representation of what the author presumably had in mind (e.g., Just
and Carpenter, 1980; Perfetti, 1985; vanDijk and Kintsch, 1983~.
The mental representation constructed by the reader does not match
the text itself, nor does the reader even try to match it, except
under special circumstances. Instead, the reader tries to represent
the situation the author had in mind or the argument the author
hoped to build. The reader's representation omits details that do
not seem central to the message. It also adds information needed
to make the message coherent and sensible. The written text, then,
is a vehicle that permits a partially common representation of some
situation or argument to be constructed by two separate minds-the
writer's and the reader's.
OCR for page 9
LA UREN B. RESNICK
9
By their nature, normal, well-written texts are incomplete ex-
pressions of the author's mental representation. They leave out some
things essential to the representation on the assumption that read-
ers will fill them in. If this assumption is not met, comprehension
fails even if every word and every sentence has been individually
understood. Usually, this process of filling in is so automatic that
skilled readers are quite unaware they are doing it. Only when the
flow of comprehension breaks down do competent readers become
aware of their inferential and interpretive processes. Yet our mod-
els of skilled comprehension suggest that inferences are being drawn
and interpretations are being made throughout. And studies of eye
movements during silent reading, of pause patterns as texts are read
aloud, and of disruptions in comprehension caused by minor modifi-
cations at key points in the text provide convincing evidence of the
reader's inferential work even for quite simple texts.
Four kinds of knowledge are called upon as readers construct
meanings for texts. The first is linguistic knowledge: knowledge
about how sentences are formed, rules of forward and backward
reference, and the like. This knowledge is often only implicit, but
readers depend on it to find common referents, to link agent to action
to object, and to otherwise construct a representation of a coherent
set of events and relationships. The second kind of knowledge is
topical knowledge, that is, knowledge about the text's subject mat-
ter. Like linguistic knowledge, topical knowledge is often used so
automatically that readers are unaware of its contribution. Third,
readers invoke knowledge about rules of inference. This knowledge,
too, is likely to be implicit for the skilled reader. Finally, knowledge
of conventional rhetorical structures often aids the process of text
interpretation.
An example drawn from the work of Walter Kintsch (1979)
demonstrates the role of the first three kinds of knowledge in reading
comprehension and shows how interactive they are:
The Swazi tribe was at war with a neighboring tribe because of a
dispute over some cattle. Among the warriors were two unmarried
men named Kakra and his younger brother Gum. Kakra was killed in
battle. According to tribal custom, Kakra was married subsequently
to the woman Ami.
The first three sentences of this short passage are un(lerstood so
effortlessly that the reader does not notice the special linguistic work
required to build a coherent representation. Yet some inference is re-
quired. Note that the term "warriors in the second sentence has not
OCR for page 10
10
EDUCATION AND LEARNING TO THINK
appeared before. However, the definite article ~the" that precedes
the term implies that warriors have been referred to previously. The
skilled individual knows this linguistic rule, even if only implicitly.
What Is more, such a reader infers the required referent by using
topical knowledge: namely, that a war (which is referred to in the
preceding sentence) is likely to involve warriors.
Greater difficulty is encountered when the fourth sentence is
reached. The sentence is puzzling. It seems anomalous, and even
contradictory, in the context of the preceding sentences. To know
that the final sentence is anomalous, the reacler must bring topical
knowledge and rules of inference to bear. The reader knows, for ex-
ample, that someone killed in battle is no longer alive. In addition, he
or she is likely to assume that marriage requires a living bridegroom.
This leads to the inference that it is impossible for Kakra to be mar-
ried after the battle. Topical knowledge and rules of inference thus
lead to the sense that the passage is incomprehensible. Yet topical
knowledge can also provide the basis for resolving the comprehension
problem. The knowledge needed relates to ghost marriage, a tribal
custorr in which, when the oldest son of a family dies without heirs,
his spirit is nevertheless married as planned, and his younger brother
takes his place in the marriage bed until an heir is produced.
In longer texts, knowledge about rhetorical structures also inter-
acts with linguistic, topical, and inference rule knowledge. Narrative
stories, for example, frequently conform to a prototypical structure
in which, after a setting is described, an initiating event sets up a
situation in which a character responds by setting a goal. In succes-
sive episodes the character attempts to attain the goal, each attempt
producing an outcome and a response to the outcome. Extensive
research on story ~grammars" (see Stein and basso, 1982) has
shown that people depend on this prototypical structure to under-
stand and interpret stories. Readers are sensitive to the order in
which categories of information are presented. They have difficulty
recalling stories when information is given in an order other than
that specified in the idealized story schema, and most important as
evidence that this story schema plays a key role in understanding-
people tend to recall story information in the order predictecl by the
schema even if the version of the story they read or heard uses a
nonstandard order. Expository texts, too, follow certain stanciard
rhetorical forms. Structures such as compare/contrast, cause/effect,
or problem/solution provide frameworks that support and sustain
communication between author and reacler. When an author uses
OCR for page 11
LA UREN B. RESNICK
11
a familiar text structure, it serves as a kind of scaffolding for the
reader's interpretive work. For example, structural markers like "on
the other hand" and ~furthermore" are used to signal rhetorical
functions.
This broad analysis of comprehension as a meaning-imposing
process that depends on the reader's knowledge of text structure as
well as linguistic, topical, and inferential knowledge is common to
all current cognitive theories of reading. Furthermore, when studies
compare successful and less successful readers, the former always
turn out both to possess more of these kinds of knowledge and to be
more likely to use that knowledge spontaneously. Although there are
important differences among theories with respect to specific aspects
of these processes their timing, the kinds of cues that set them in
motion, the ways in which knowledge is organized there are no clis-
agreements regarding the general characterization of comprehension.
Research still does not provide a clear answer about the extent
to which meaning imposition proceeds strategically, in a deliberate,
self-conscious fashion rather than automatically and unconsciously.
Much evidence suggests that, for a skilled reader not totally new
to the text's topic, most of the work to build a text representation
proceeds quite unconsciously through processes of automatic acti-
vation. The process slows down, requires deliberate attention, and
becomes accessible to conscious awareness under special conditions:
when there is an anomaly in the text or some unusual linguistic con-
struction; when the topical domain is so unfamiliar that the reader
lacks necessary prior knowledge for interpretation; when a particu-
larly complicated chain of reasoning is presented; or when the reacler
wants to study and remember the text rather than just understand] it
(see chapters in Mand! et al., 1984, for a discussion of many of these
issues). Some psychologists (e.g., Collins and Smith, 1982) believe
that the same processes of self-questioning, summarizing, and the
like go on in highly skilled reading as in more self-conscious reacting,
but at a much faster rate. Other research (e.g., Neves anti Ar~derson,
1981; Newell and Rosenbloom, 1981) suggests that as readers develop
automatic skills the nature of the process actually changes and cer-
ta~n steps drop out. In any case, it is evident that educators ought to
aim to produce both kinds of reading comprehension abilities among
students: the ability to understand written texts automatically and
with little effort, and the capacity to apply deliberate strategies for
interpreting and remembering when the need arises.
It is striking that the processes identified In cognitive research on
OCR for page 12
12
EDUCATION AND LEARNING TO THINK
reading comprehension are related to the techniques of textual exege-
sis and analysis cornrnonly taught in high-level courses in literature,
philosophy, and other disciplines in which multiple interpretations of
texts are discussed as part of instruction. Cognitive theory, in other
words, suggests that processes traditionally reserved for advanced
students that is, for a minority who have developed skill and taste
for interpretive mental work-might be taught to all readers, includ-
ing young children and, perhaps especially, those who learn with
difficulty. Cognitive research suggests that these processes are what
we mean by reading comprehension. Not to teach them is to ignore
the most important aspects of reading. This convergence of cogni-
tive research on reading with traditional high literacy concerns offers
some promise that the goal of extending high literacy standards to
the mass educational system can be achieved.
Meaning Construction in Mathematics
A higher order interpretation of the basic mathematics curricu-
lum is less straightforward than we have been able to propose for
reading. Nevertheless, a close consideration of recent research on
mathematical cognition suggests that in mathematics, as in reading,
successful learners understand the task to be one of constructing
meaning, of doing interpretive work rather than routine manipu-
lations. In mathematics, the problem of imposing meaning takes a
special form: making sense of formal symbols and rules that are often
taught as if they were arbitrary conventions rather than expressions
of fundamental regularities and relationships among quantities and
physical entities.
Recent research on mathematics learning points to an apparent
paradox. We have abundant evidence that young children-even
before attending school develop rather robust, although simple,
mathematical concepts and that they are able to apply these con-
cepts in a variety of practical situations. Yet school mathematics is
decidedly difficult to learn for many children. Children's first and
best-developed mathematical competence is counting (German and
Gallistel, 1978~. Several investigations have shown that young chil-
dren are able to use counting to solve informally a wide variety of
arithmetic problems, including problems that they have difficulty
solving in school (Carraher et al., 1985; Ginsburg, 1977). F`urther-
more, an examination of shortcut procedures invented by children
OCR for page 13
LAUREN B. RESNICK
13
suggests an implicit understanding of several basic arithmetic prin-
ciples. For example, the min procedure (first clocumented by Groen
and Parkman, 1972) is an addition strategy that involves setting
a mental ~counter" at the larger of the two addends, regardless
of whether it is the first or second, and then incrementing by the
smaller. The child's use of such a procedure requires acknowledg-
ment, at least implicitly, of the commutativity principle of addition.
Several studies (e.g., Svenson and Hedenborg, 1979; Woods et al.,
1975) have shown that children, starting at about age seven, solve
subtraction problems by either counting down from the larger num-
ber or counting up from the smaller number, whichever will require
the fewest counts. This procedure reveals implicit knowledge of the
complementarily of addition and subtraction, which in turn depends
on thinking of the minuend (top number) as a whole, with a de-
composition into the subtrahend and the difference. These examples
and many others suggest that an intuitive understanding of many
basic mathematical principles develops early and finds expression in
various kinds of practical problem-solving tasks.
There is substantial evidence that children's difficulty in learning
school mathematics derives in large part from their failure to recog-
nize and apply the relations between formal rules taught in school and
their own independently developed mathematical intuitions. Part of
the evidence lies in close analysis of the kinds of errors that children
typically make in the course of learning arithmetic and, eventually,
algebra. To an important degree, calculation errors derive not from
random or careless ~slips" but from systematically applying incorrect
procedures. These incorrect rules, of course, are not taught. Chil-
dren invent them, as they do the shortcut strategies. By analyzing
their incorrect rules we can understand what children are and are
not attending to as they learn arithmetic. The most carefully stud-
ied domain of arithmetic errors is subtraction. The kinds of errors
(called "bugs" from their similarity to minicomputer programs with
bugs in them) that children make have been carefully documented;
these bugs serve as the basis for an artificial intelligence program
(Brown and Van Lehn, 1980) that invents the same subtraction bugs
children invent but does not invent the many other logically possible
bugs not observed in children. Because the program's performance
largely matches children's performance, its processes and knowledge
base provide a theory of what children probably know and do that
leads them to buggy inventions.
According to the Brown and Van Lehn theory, children invent
OCR for page 14
14
EDUCATIONANDLEARNINGTO THINK
buggy procedures when they encounter problems for which they have
no complete algorithm available. This may occur because they have
not yet been taught what to do in special cases (for example, how
does one borrow from a zero?) or because they have forgotten certain
steps in procedures already taught. To respond, children engage in a
form of problem solving: generating possible actions and testing them
against a list of constraints. Although this is an intelligent problem-
solving process, it produces errors because certain key constraints
are missing from the test list. The missing constraints have to do
with the meaning of the symbols; constraints regarding how the
symbols ought to look on the page (e.g., only one digit per column,
borrow marks in appropriate places) are largely obeyed. What is
more, the program has no representation at all of the quantities
that are involved; it only has rules for manipulating symbols. This
suggests that children, like the program, solve arithmetic problerr~s by
manipulating symbols while ignoring their meaning (Resnick, 1987~.
We can reach the same conclusion from an analysis of the charac-
teristic errors made by students learning decimal fractions (Hiebert
and Wearne, 1985) and algebra (Matz, 1982; Resnick et al., 1987;
Sleeman, 1983~. Research on algebra learning shows that when think-
ing about transformation rules, students rarely refer either to quanti-
tative relationships or to problem situations that could give meaning
to algebra expressions. Not surprisingly, students are not very skillful
at the process of ~mathematizing," that is, at constructing links be-
tween formal algebraic expressions and the actual situations to which
they refer (e.g., Clement, 1982~. All of this points to a conclusion that
current mathematics education does not adequately engage students'
interpretive and meaning-construction capacities. This conclusion is
supported by data from national assessments (e.g., National Assess-
ment of Educational Progress, 1983) showing declines in students'
mathematics problem-solving skills even as calculation abilities rise.
In short, most students learn mathematics as a routine skill; they do
not develop higher order capacities for organizing and interpreting
information.
It seems likely that a less routinized approach to mathematics
could produce substantial improvements in learning. Although the
evidence is limited, it suggests that successful math learners engage
in more metacognitive behaviors (e.g., checking their own under-
standing of procedures, monitoring for consistency, trying to relate
new material to prior knowledge) during math learning; they are also
less likely to practice symbol manipulation rules without reference
Representative terms from entire chapter:
reading comprehension
