Theories of Learning and Teaching What Do They Mean for

Theories of Learning and Teaching

What Do They Mean for Educators?

Suzanne M. Wilson

Michigan State University

and

Penelope L. Peterson

Northwestern University

July 2006

WORKING

PAPER

BEST

PRACTICES

NEA RESEARCH

Theories of Learning and Teaching

What Do They Mean for Educators?

Suzanne M. Wilson

Michigan State University

and

Penelope L. Peterson

Northwestern University

July 2006

WORKING

PAPER

BEST

PRACTICES

NEA RESEARCH

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iii

The Authors

Suzanne M. Wilson is a professor of education and director of the Center for the Scholarship

of Teaching at Michigan State University. Her research interests include teacher learning,

teacher knowledge, and connections between education reform and practice.

Penelope L. Peterson is the dean of the School of Education and Social Policy and Eleanor R.

Baldwin Professor of Education at Northwestern University. Her research encompasses many

aspects of learning and teaching as well as the relationships between educational research,

policy, and practice.

Contents

Contemporary Ideas about Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Learning as a Process of Active Engagement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Learning as a Social Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Learner Differences as Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Knowing What, How, and Why . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Implications for Teaching and Teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Teaching as Intellectual Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Teaching as Varied Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Teaching as Shared Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Teaching Challenging Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Teaching as Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

NEA Appendix: Tools for Instructional Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

Doing so requires a solid understanding of the foundation-

al theories that drive teaching, including ideas about how

nts lear

hat they should learn, and how teachers

can enable student learning. This paper’s charge is to lay

out the central ideas about learning and teaching that run

throughout contemporary educational discourse. A hand-

ful of significant ideas underlie most reforms of the last 20

years. Our frame includes three contemporary ideas about

lear

ning: that learning is a process of active construction;

that lear

ning is a so

cial phenomenon, as well as an individ-

ual experience; and that learner differences are resources,

not obstacles. In addition, we discuss one critical idea

about what counts as knowledge and what students should

learn: that students need to develop flexible understanding,

including both basic factual and conceptual knowledge,

and must know how to use that knowledge critically. Our

frame is not a dichotomous one, holding that students have

ithe

r c

or p

ess kno

ledge, that students are

either passive

or active agents in their own learning. Rather,

we argue that there are shifts in emphasis, moving from

more traditional notions of learning and knowledge to

conceptions that are broader and more nuanced.

In light of those shifting ideas, we then briefly examine

the implicat

ions for teaching. Again, we focus on a few key

eas:

that teaching is intellectual work; that teachers have

a range of roles, including information deliverer and team

h; that effective teachers strategically distribute (or

share) work with students; and that teachers focus on

challenging content. The “big ideas” of the paper can then

be summarized as shown in Table 1.

ducation has always been awash with new ideas about learning and teaching. Teachers and

administrators are regularly bombarded with suggestions for reform. They are asked to use new

curricula, new teaching strategies, and new assessments. They are directed to prepare students for the

new state standardized test or to document and assess students’ work through portfolios and perform-

ance assessments. They are urged to use research-based methods to teach reading and mathematics.

Among educators, there is a certain cynicism that comes with these waves of reformist exhortations.

Veteran teachers often smile wryly when told to do this or that, whispering asides about another

faddish pendulum swing, closing their classroom doors, quietly going about their business. How are

educators to sort the proverbial wheat from the chaff as they encounter these reform proposals?

Contemporary Ideas about Learning

Scouring the shelves of any library or bookstore leaves one

swimming is a sea of “isms”—behaviorism, constructivism,

social constructivism—as well as lists of learning theories:

multiple intelligences, right- and left-brain learning, activ-

y the

ory, learning styles, Piaget, and communities of

learners. Here we do not propose a comprehensive list of all

contemporary ideas about learning. Instead, we focus on

thr

e b

ig id

eas that und

rlie most of current scholarship

and practice: learning as a process of active engagement;

learning as individual and social; and learner differences as

resources to be used, not obstacles to be confronted.

Learning as a Process of Active Engagement

erhaps the most critical shift in education in the past 20

ear

s has been a move away from a conception of “learner

as sponge” toward an image of “learner as active construc-

tor of meaning.”Although Plato and Socrates (not to men-

tion Dewey) reminded us long ago that learners were not

empty vessels, blank slates, or passive observers, much of

U.S. schooling has been based on this premise. Teachers

have talked; students have been directed to listen (Cuban

1993). The assumption has been that if teachers speak

clearly and students are motivated, learning will occur. If

students do not learn, the logic goes, it is because they are

not paying attention or they do not care.

hese id

eas were grounded in a theory of learning that

focused on behavior. One behavior leads to another,

behavioral-learning theorists argued, and so if teachers act

in a c

tain wa

students will likewise act in a certain way.

Central to behaviorism was the idea of conditioning—that

is, training the individual to respond to stimuli. The mind

was a “black box” of little concern. But behavioral theorists

had to make way for the “cognitive revolution” in psychol-

ogy, which involved putting the mind back into the learn-

ing e

quation. As Lesh and Lamon (1992, p. 18) put it,

“B

havioral psychology (based on factual and procedural

rules) has given way to cognitive psychology (based on

ls f

or making sense of real life experiences.” In this

shift, several fields of learning theory emerged.

Neuroscientists, for example, learned that the brain active-

ly seeks new stimuli in the environment from which to

2 Theories of Learning and Teaching

able 1. Benchmarks for Learning and Teaching

Benchmarks for…

Learning

Knowledge

Teaching

Moving from…

Passive absorption of information

ndividual activity

Individual differences among

students seen as problems

What: facts and procedures of a

discipline

Simple, straightforward work

Teachers in information-deliverer

role

Teachers do most of the work

Lessons contain low-level con-

tent, concepts mentioned; les-

sons not coherently organized

Teachers as founts of knowledge

Moving toward…

Active engagement with information

oth individual activity and collective work

Individual differences among students seen as

resources

What, how, and why: central ideas, concepts, facts,

processes of inquiry, and argument of a discipline

Complex, intellectual work

Varied teacher roles, from information deliverer

to architect of educative experiences

Teachers structure classrooms for individual and

shared work

Lessons focus on high-level and basic content,

concepts developed and elaborated; lessons

coherently organized

Teachers know a lot, are inclined to improve their

practice continually

earn (Greenough, Black, and Wallace 1987; Kandel and

Hawkins 1992) and that the mind changes through use;

hat is, learning changes the structure of the brain

(Bransford, Brown, and Cocking 2000). However, it is still

too early to claim that neuroscience can definitely explain

how people learn.

The work of other cognitive theorists helps here. For

example, research suggests that learners—from a very

young age—make sense of the world, actively creating

meaning while reading texts, interacting with the environ-

ment, or talking with others. Even if students are quietly

watching a teacher speak, they can be actively engaged in a

process of comprehension, or “minds on” work, as many

teachers describe it. As Bransford, Brown, and Cocking

(2000) wrote, “It is now known that very young children

are competent, active agents of their own conceptual devel-

opment. In short, the mind of the young child has come to

life” (pp. 79–80). This cognitive turn in psychology is often

referred to as a

constructivist approach to learning.

Understanding that students construct meaning has led

to increased attention to students’ interpretations of what

they witness in class. Recall the game of “telephone”: A

phrase, whispered from person to person, is followed by

hilarit

y when the last person announces something quite

different from what the first said. This game exemplifies

the role of interpretation in any human endeavor. At the

basest level, what we “hear” is filtered through our

assumptions and values, attention, and knowledge. Some

students interpret

Moby Dick differently from the way oth-

ers do. Some students interpret the film

The Patriot differ-

ently from they way their friends do. All of us, in school

and out, shape and sculpt the information we encounter,

“constructing” our understanding. Although two students

mig

ht e

ncounter exactly the same information, as active

participants in their own knowledge building, students

develop understandings that can be qualitatively different.

Esp

cial

y imp

rtant has been the growing revelation of

the powerful role of prior knowledge and experience in

learning new information (e.g., Bauersfeld 1988; Brown

1994; Cobb 1994, 1995). Students enter school with ideas,

and those ideas are a significant force to be reckoned with.

Researchers have shown that students’ beliefs that the

ear

th is flat last well after teachers and others have told

hem otherwise (Vosniadou and Brewer 1989). Elemen-

tary-age children have been found to hold naive theories

f prejudice and discrimination that resonate with the

theories of social scientists who have grappled with simi-

lar questions about why people dislike or discriminate

against those who are different (Rose 2000). Similarly,

Byrnes and Torney-Purta (1995) found that adolescents

use naive social, economic, and political theories in iden-

tifying causes of social issues. Many young children cannot

understand why 1/4 is larger than 1/8 because 8 is bigger

than 4 (Gelman and Gallistel 1978). Researchers are con-

tinuing to uncover how students’ preconceptions, nonsci-

entific beliefs, conceptual misunderstandings, vernacular

misunderstandings, and factual misconceptions act as

powerful filters in what and how they learn.

When we acknowledge that students interpret—and do

not automatically absorb—the information and ideas they

encounter in the world through the experiences and theo-

ries they bring to school, the links between learning and

teaching become more complicated. Rather than appear-

ing as a natural result of teaching, learning is seen as inher-

ently “problematic.” Teachers might create opportunities

for students to learn, but teachers cannot control students’

interpretations. Teachers become responsible for diagnos-

ing students’ interpretations and helping them alter, edit,

and enric

h them. But we get ahead of ourselves. Each of the

shifts in learning theories that we discuss here has implica-

tions for teachers’ roles and responsibilities. We discuss

these concomitant shifts in the second half of this paper.

One unfortunate consequence of the increased interest in

constructivist learning theories has been the wholesale

rejection of behaviorist theories of learning by some enthu-

siasts. This “throwing the baby out with the bathwater” phe-

non is neither new nor productive. Students can learn

while they absorb new information (indeed, just because

children are sitting still and quiet does not mean that their

minds ar

e not r

cing),

ust as the

y can learn through being

more active. Similarly, activity does not mean that learning

is taking place. Any and all theories are based on limited

information; they are conjectures and assertions based on

empirical research, and all scientists, including learning sci-

entists—are constantly interrogating their theories.

oreover, there are times when one needs multiple theories.

ust as p

hysicists can think of light as both wave and parti-

cle, teachers can theorize about learning in both cognitive

What Do They Mean for Educators? 3

or other examples of this work, see Confrey (1990), Erlwanger (1975),

Roth, Anderson, and Smith (1987), Smith (1993), Toulmin (1995), and von

Glasersfeld (1987).

As in all fields of scholarship, there is considerable debate between differ-

ent theories and versions of theories. Theories of constructivism are no

exception. For an overview of the theories of constructivism, see Greeno,

Collins, and Resnick (1996); for a critical perspective, see Hirsch (1996) and

Phillips (1995).

nd behavioral terms (Wilson 2003). Sfard (1998) argued, in

fact, that we need multiple metaphors for learning and that

o throw one out in favor of another is dangerous.

Because theories vary in their quality and rigor, it seems

imperative that teachers be well-informed, skeptical con-

sumers of “new” educational ideas or reigning theories

(Hirsch 1996; Phillips 1995, 2000; Sfard 1998). They inter-

pret, adapt, and combine those theories as they use them in

practice. Indeed, current thought suggests that a “balanced”

view of learning and teaching is crucial (e.g., Kilpatrick,

Swafford, and Findell 2002). Students need opportunities to

learn in multiple ways, and teachers need to have a peda-

gogical repertoire that draws from myriad learning theo-

rists. Recent reviews of the state of the art in learning theo-

ry, especially

How People Learn (Bransford, Brown, and

Cocking 2000) and

How Students Learn (Donovan and

Bransford 2005), are particularly helpful resources in

culling the major findings from learning research.

Lear

ning as a Social Phenomenon

A second significant shift has involved a growing awareness

among learning theorists of the social aspects of learning.

Previous generations of psychologists have focused on

individuals’ learning. Current work has placed more

emphasis on the critical role of social groups in the devel-

opme

nt of understanding. Although solitude and peaceful

silence provide good opportunities for learning, the social

occasions of conversation, discussion, joint work, and

debate also play a critical role in learning. Think of small

children when they are first learning to identify dogs.

Initially, everything with four legs may be pointed to as

“dog”: a neighborhood cat, a cow in a field passed while on

a drive through the countryside, the gerbil next door.

hildr

en learn to distinguish between cat and dog, cow

and dog, and rodent and dog by making public their claims

and having parents gently amend their pronouncements.

Lik

ise,

mathe

mat

icians may hunch over their work

alone in an attic study for months, perhaps years, learn-

ing—reading books and others’ papers, playing with num-

bers, scratching out alternative solutions. When they think

they have it right, they deliver a paper at a conference or

submit an article for publication. In so doing, they put

the

ir “knowledge” to a public test, where is shaped, edited,

and so

times rejected by conversation, debate, and dis-

course.

Even though Andrew Wiles preferred to work in

solitude on the sol

ution to Fermat’s last theorem, it was

not until he presented his work to multiple and public

juries of his peers that his solution was eventually

strengthened and accepted (Singh 1997).

his cluster of theories dealing with the social aspects

of learning is known by varying labels, including

social

onstructivism, sociocultural theory,

ctivity theory.

Many theorists identified with these traditions trace their

ideas back to Vygotsky (1978, 1981; see also Wertsch 1981,

1985), a psychologist who theorized about the influence of

the social world on an individual’s development.

Although these theories are not all identical—indeed,

there are some considerable differences—they share some

concerns and beliefs. First is the point that knowledge is

inseparable from practice: we know by doing. This means

that we need to look at people while they are doing some-

thing meaningful—that is, working on authentic prob-

lems—if we want to “see” what they know. Let us consid-

er an example. Many students have difficulty when they

encounter fraction problems in school. Lacking real

understanding of the concepts involved and experience in

finding solutions, they are confused about which proce-

dure to apply or why it is relevant. Yet researchers have

observed children and adults demonstrating competencies

in solving fraction problems in other, real-world contexts.

Lave (1988), for example, observed a Weight Watchers

class in which participants demonstrated their knowledge

of mathematics through the measuring involved in learn-

ing about appropriate eating habits. Being on Weight

Watchers means learning to reason proportionally and

reducing serving sizes to control caloric intake. At this

meeting, the problem the group was working on entailed

figuring out what three-fourths of a recommended serv-

ing (two-thirds of a cup) would be:

In this case they were to fix a serving of cot-

tage cheese, supposing the amount laid out for

the meal was thr

e-quarters of the two-thirds

cup the program allowed. The problem solver

in this example began the task muttering that

4 Theories of Learning and Teaching

One way to learn more about the social aspects of disciplinary communi-

ies in

es reading biographies and autobiographies of scientists, histori-

ans,

iters, mathematicians, and so on. See, for example, Collingwood

(1946/1956) or Hexter (1971) on history, Hardy (1940/1969) or Wiener

(1956) on mathematics, Latour and Woolgar (1986) on science, or any num-

ber of stories—such as Dava Sobel’s

Longitude (1995) about the intellectual

and political history of an idea. For a more abstract discussion of disciplines

as c

ommunities, see King and Brownell (1966), Kuhn (1962), or Popper

(1958).

For examples of various theories of social constructivism, sociocultural

theory, and activity theory, see Bakhurst (1995), Cobb (1994), Dewey (1988),

n (1994,

1995), Harre (1986), Lave and Wenger (1991), Newman and

olzman (1993), Rogoff (1994), Tharp and Gallimore (1988), Vygotsky

(1978,

1981),

and

tsc

h (1985).

e had taken a calculus course in college....

Then after a pause he suddenly announced

hat he had “got it!” From then on he appeared

certain he was correct, even before carrying

out the procedure. He filled a measuring-cup

two-thirds full of cottage cheese, dumped it

out on the cutting board, patted it into a cir-

cle, marked a cross on it, scooped away one

quadrant, and served the rest.

Thus,“take three-quarters of two-thirds of

a cup of cottage cheese” was not just the

problem statement but also the solution to

the problem and the procedure for solving it.

The setting was part of the calculating

process and the solution was simply the

problem statement, enacted with the setting.

At no time did the Weight Watcher check his

procedure against a pencil-and-paper algo-

rithm, which would have produced 3/4 cup

2/3 cup = 1/2 cup

. Instead, the coincidence of

the problem, setting, and enactment was the

means by which checking took place. (p. 165)

Thus, although the sort of problem the man in the

Weight Watchers group encountered (i.e., “What is two-

thirds of three-quarters?”) may throw both children and

adults f

or a loop when they confront it as an abstract

“school” problem, it proves far more tractable when indi-

viduals learn by “doing”; that is, when they are solving

authentic problems situated in meaningful contexts.

A second principle of sociocultural theory is that learn-

ing is fundamentally a social phenomenon that takes place

within the communities we belong to (including class-

om communities). These two beliefs lead to the idea that

knowledge and learning exist in the interactions between

individuals and the contexts in which they live, in the

ies we participate in. Thus, “communities of prac-

tice” or “learning communities” become critical to learn-

ing. We learn, these theorists argue, by participating in

groups—first by observing others do the work and then by

gradually becoming a member and full participant of the

group. Lave and Wenger (1991) illustrated their theory

ith examples of different apprenticeships (midwives, tai-

s, U. S. Navy quartermasters, butchers, and nondrinking

alcoholics). Initially, people join these communities and

watch, as the the

orists suggest, from the sidelines (they call

this

peripheral participation). Over time, and as the newer

members become more competent, they move closer to

the center of the community:

“

Legitimate peripheral participation” pro-

vides a way to speak about the relations

etween newcomers and old-timers, and

about activities, identities, artifacts, and com-

munities of knowledge and practice. A per-

son’s intentions to learn are engaged and the

meaning of learning is configured through

the process of becoming a full participant in

a socio-cultural practice. This social process,

includes, indeed it subsumes, the learning of

knowledgeable skills. (Lave and Wenger 1991,

p. 29)

A third feature of these theories is that it is within those

communities that standards lie. The norms for testing the

quality of a performance are determined by groups, not

individuals, and one’s performance is assessed through

genuine participation. In all areas of knowledge, groups of

mathematicians and scientists, historians and writers

together determine—through criticism, debate, proof, val-

idation, and so on—their shared standards. Similarly,

these social entities co-construct the language used in

those debates, for the discussions cannot proceed absent a

common language (Bakhtin 1981; Bruner 1986; Kozulin

1990; Lave and Wenger 1991; Vygotsky 1978; Wertsch

1985; Wertsch and Rupert 1993).

Although so

cial groups have always played an impor-

tant role in an individual’s learning—parents edit their

children’s talk, doctors argue over the latest issues raised in

the

American Journal of Medicine—U.S. schools have tra-

ditionally focused on the individual aspects of learning.

Students have worked quietly at their desks, writing

papers, filling out worksheets, taking tests, and reading

xtbooks. Ideas have not been submitted to public debate.

In part this is because teachers must manage groups of

children who are not there voluntarily (see Cusick 1992).

and othe

rs (2003) described the typical form of

learning in U.S. schools as assembly-line learning, and

they contrasted it with learning through participation.

Assembly-line instruction is hierarchical; teachers and stu-

dents have fixed roles; motivation is through extrinsic

rewards; and learning is done through lessons that are

renched from any meaningful context. In contrast,

lear

ning thr

ough participation is collaborative; roles are

flexible; motivation is intrinsic; and the purpose of the

vity is clear and meaningful to all participants.

A final feature of these theories is that they highlight

the situated nature of learning, that is, that we learn in

particular situations and contexts. This might help explain

What Do They Mean for Educators? 5

hy transfer—being able to take what one has learned in

one situation and apply it to another—is not a given.

tudents do not necessarily transfer their learning from

one problem to the next. Recognizing the important role

that contexts play in shaping when and what we learn, psy-

chologists and learning scientists have begun to under-

stand what it takes to help students transfer their learning

to new situations. For example, if the initial learning was

not robust, students cannot transfer what they learned. As

Bransford, Brown, and Cocking (2000) noted:

Time spent learning for understanding has

different consequences for transfer than time

spent simply memorizing facts or procedures

from textbooks or lectures. In order for

learners to gain insight into their learning

and their understanding, frequent feedback is

critical: students need to monitor their learn-

ing and actively evaluate their strategies and

the

ir current levels of understanding.

(pp. 77–78)

Scholars have also discovered that learners who under-

stand more about their own learning—researchers call

this a

metacognitive awareness—have greater capacity to

transf

er their learning to new problems and contexts.

These insights int

o transfer allow us to understand more

about

what students need to know (a topic we return to

shortly) if their knowledge is to be generative—that is,

transferable to new contexts.

Theories about shared knowledge and the effects of the

community on one’s learning have become increasingly

important in education (e.g., Cobb 1994, 1998; Salomon

and P

rkins 1998; Tharp and others 2000; Tobin and

Tippins 1993). This interest in sociocultural and activity

theory has led some educators and reformers to argue for

a w

r ar

y of organizational structures in U.S. schools,

including cooperative groups, classroom discussions, and

student performances. In so doing, teachers are asked to

focus not only on individual students but also on the

development of “communities of learners.” Thus, teachers

need to keep their eyes both on the individual learners in

the

ir classrooms and on the classroom community creat-

d b

y teacher and students.

Learner Differ

ences as Resour

ces

Another significant shift has occurred in the value that we

place on individual and group differences. One of the self-

evident truths of schooling is that learners come with

ifferent experiences, capacities, understandings, and

backgrounds. As the United States has made progress in

oving toward its goal to provide a high-quality universal

education for all citizens, those differences have increased.

When only the sons of ministers and lawyers attended

schools in order to follow in the footsteps of their fathers,

teachers did not have to deal with many differences,

because their students were much like them.

As schools became more democratic, that changed.

Teachers had to learn to deal with the inevitable differ-

ences that students bring to school. For a long time, how-

ever, we spoke of differences as static abilities that deter-

mine how much or how fast a learner can learn (often

because we believed that there was a single way to learn or

think.) Teachers, in fact, often used tests as a way of

screening children. Differences were considered deficits. If

a child came to school with a background different from

that of someone else, teachers often talked about what the

different student did not know or had not done. But as our

country and our schools learn more about what it means

to be multicultural, we have been legitimately chastised for

this “deficit model” of students (especially students who

are different from us) and urged to think of differences as

resour

ces to use, not as obstacles to overcome.

Yet it is not only out of some set of ideological or polit-

ical commit

ments that this emphasis on what learners

bring has g

ained popularity. Instead, it is a logical out-

growth of the shift toward a constructivist stance toward

learning. If learners construct their own meaning, teachers

must know something about where learners start. One

cannot build a bridge without a clear sense of the location

of both shores. Likewise, teachers cannot create a bridge

between subject matter and student without having a clear

nse o

f what students know, care about, can do, and want

to do. Rather than treating learners’ starting places as

“gaps,” teachers need to assume that students start in sen-

sib

le pla

es.

chers need to “give learners reason” by

respecting and understanding learners’ prior experiences

and understandings, assuming that these can serve as a

foundation on which to build bridges to new understand-

ings (Duckworth 1987; Lampert 1984, 2001). In support

of this perspective is the fact that psychologists have failed

o find a singular theory of learning that would justify a

ficit explanation for student differences.

Cross-cultural research on teaching also supports the

not

n that indi

idual differences among students can be

resources. In contrast to the deficit model often seen in the

United States, Japanese teachers view individual differ-

ences as a natural and beneficial characteristic of the

6 Theories of Learning and Teaching

roup. They believe that individual differences produce a

range of ideas and problem-solving strategies for students’

iscussion and reflection. Based on their experience,

Japanese teachers can predict the likely responses of stu-

dents to a topic and use this knowledge of student think-

ing and the nature of the discussion that is likely to occur

to plan their lessons more completely (Stigler and Hiebert

1999).

The differences of which we speak are myriad. Students

bring differences in intelligence and interest, in ethnicity

and race, in culture and gender. Gardner’s (1983) work on

multiple intelligences is probably the most well known,

although it is part of a stream of scholarship that contin-

ues to explore questions of innate and developed ability

and capacity. Delpit (1995; Delpit and Kilgour 2002) and

Ladson-Billings (1994, 2001) have written eloquently

about the complexity of teaching African American stu-

dents in racially aware ways, and the literature in this field

continues to grow, as researchers learn more about the

experiences of children who come from different cultures.

Critical to teachers’ conceptualizing their students as

resources is knowledge of the homes and cultures of stu-

dents (e.g., Knapp and Shields 1991). Moll (1990; Moll

and Greenberg 1990), for example, discovered that

Mexican American households are clustered according to

kinship ties and exchange relationships. Further, these

household clusters develop rich “funds of knowledge”—

information about practices and resources useful in ensur-

ing the well-being of all households. Each household in

the cluster has expertise needed by the entire cluster—car

repair, appliance upkeep, plumbing, education, herbal

medicine, first aid, and so on. Together, the households

form a cluster for the exchange of information and

esour

ces. In this conception of community life, all indi-

viduals are not expected to have the same expertise.

Instead, knowledge is distributed and communally shared.

standing these cult

al differences, many scholars

argue, would help teachers draw on students’ experiences

within classrooms, enabling teachers to make more explic-

it and meaningful connections to students’ communities.

For example, in Moll and others (1992), teachers in Tucson

chose two or three students and conducted interviews with

those st

udents and their families so that they might learn

e about their community. Working together with the

researchers, teachers then began exploring ways to inte-

grate what they were learning about these networks into

their classrooms. One teacher used her awareness of a stu-

dent’s experiences with selling candy from Mexico in the

United States to create interdisciplinary lessons about

andy production. Students studied mathematics, science,

and health; one parent came to class and taught the stu-

ents how to make Mexican candy.

Similarly, teachers might also draw on the work of Rose

(1989, 1995) on the Hispanic and Chicano experience and

of Au (1981) on the Hawaiian experience, as well as that of

Ogbu (1992) on the relationship between cultural diversity,

learning, and schooling in rethinking how to tailor instruc-

tion to take advantage of student differences. But race and

culture are not the only significant differences among our

students. With the rise of feminism in academic circles,

questions about gender differences have also come to the

forefront of American education (see, e.g., Belenky and

others 1986; Gilligan, Lyons, and Hanmer 1990; Pipher

1994). Class is also important (although not studied as

directly or as often), as are issues of second-language learn-

ing. Although it would be impossible for teachers to take

into account all of the possible relevant differences among

their students, continuing to learn about these differences

and a

dapting one’s instruction accordingly is one of the

permanent challenges teachers face.

As we mentioned earlier, there are multiple theories of

learning for teachers to consider. Here we have neither

considered the comprehensive list of those theories nor

discussed each in detail. However, we have noted that there

are three themes that run across many theories: that stu-

dents ar

e active constructors of their own knowledge; that

learning is both individual and social; and that students

are resources to be tapped, not obstacles to be overcome.

We now turn to one additional shift in foundational theo-

ries, one that concerns not so much

how students learn as

what they learn.

Knowing What, How

, and Why

The fourth and final significant shift concerns assumptions

about knowledge:

what students should learn. It is no

r e

noug

h that st

udents quietly master only the facts

and rules of a discipline. Contemporary educational

reform demands that students have a more flexible under-

standing of mathematics and language arts, biology and

physics, and geography and history. They must know the

basics, but they must also know how to use those basics to

entify and solve nontraditional problems. Alternatively

escr

ibed as

itical thinking, teaching for understanding,

mathematical power,

and so on, this theory has the under-

ing ass

ump

tion that to know a field one must master its

central ideas, concepts, and facts

and its processes of

inquiry and argument. Biologists do not sit in lonely labs

regurgitating their knowledge of cells. They search out new

What Do They Mean for Educators? 7

roblems and use research methods to solve those prob-

lems, all the while using their knowledge of the “basics.”

fter those same biologists have solved a new problem,

they present it for public critique, submitting their work

for critical review by colleagues. If the work is not defensi-

ble in this public domain, they return to their laboratories

to reexamine their evidence and revise their thinking.

Similarly, if students are to leave school armed with the

knowledge and skill necessary to participate as citizens

and thinkers, they need to know many things. They need

to learn about the ideas, theories, facts, and procedures of

a discipline. They need to become fluent with the linguis-

tic systems of a field, developing the skill and knowledge

associated with inquiry in that field, which includes both

individual methods and the social context of the intellec-

tual discourse. Thus, they need extensive experience with

the ways in which ideas are argued and proved in discipli-

nary fields as well as a deep and thorough understanding

of the facts and concepts in each field. Children need to

write, the reformers argue, so that they can read critically

and not be persuaded by spurious text. Students need to

do statistical analyses of problems that they themselves

identify so that they might be better consumers of statis-

tics use

d daily by the press. Students need to read primary

sources and work on their own historical interpretations

so that they are better able to critique the ones they read

(Brune

r 1960/1977; Dewey 1902/1956; Schwab 1978a).

Clearly, we run the risk of oversimplification with such

a brief tour through very complicated ideas. We do not

want to suggest that these ideas about learners, learning,

and knowing are either mutually exclusive or monolithic.

In fact, their compatibility is one reason for their popular-

ity in the last 20 years. Because disciplinary knowledge is

veloped in communities, such as those of mathemati-

cians and physicists, the emphasis in these theories on

inquiry, discourse, community, and social construction of

kno

e s

port one another. Because we assume that

teachers must know what their students know and think,

treating students’ differences as resources rather than

obstacles makes sense. Because contemporary theories of

knowledge emphasize individuals and their interpreta-

tions, constructivist theories of learning seem reasonable.

ut in the last 20 years we have also witnessed consid-

able debates about which ideas about learning, learners,

teaching, and knowledge deserve pride of place. Critics of

some standards ha

e rightfully noted that it is problemat-

ic to mix images of what students should be learning

(knowledge) with how they should be learning (teaching),

because teachers ought to have latitude to make their own

ecisions about appropriate pedagogy. Critics also have

worried about the tendency of some educators to adopt

rthodoxies that are either limiting or not based on

empirical evidence (e.g., Hirsch 1996; Ravitch 2000).

Discussions concerning race and culture have raised ques-

tions about an oppressive, monolithic “politically correct,”

“social justice” stance. Further, within the disciplines, con-

siderable debate has taken place about the nature of

knowledge, the role of interpretation, and an apparent

slide into a frightening relativism.

But recent research suggests that we cannot let political

differences obscure the fact that

all students need deep

knowledge of content. Research in cognitive science helps

us understand why it is important for students to have

both a sound basis of factual knowledge, and a flexible

understanding of how to use that knowledge in authentic

and new contexts. As Bransford, Brown, and Cocking

(2000) argued:

To develop competence in an area of inquiry,

students must: (a) have a deep foundation of

factual knowledge, (b) understand facts and

ideas in the context of a conceptual frame-

work, and (c) organize knowledge in ways

that facilitate retrieval and application…. To

develop competence…students must have

opportunities to learn with understanding.

Deep understanding of subject matter trans-

forms factual information into usable knowl-

edge. A profound difference between experts

and novices is that experts’ command of con-

cepts shapes their understanding of new

8 Theories of Learning and Teaching

hese differences were at the heart of the curriculum debates of the 1990s.

ncerned that the curricular reforms of the 1980s had swung too hard in

the direction of teaching for understanding, with too little attention paid to

the basics, legislators, parents, and educators began calling for more “bal-

ance.” California passed the ABCs legislation, mandating the teaching of

phonics and basic math facts (Wilson 2003). The NCTM 2000 Standards

paid more explicit attention to foundational ideas of mathematics, which

was heralded by a number of journalists as a move “back to the basics.” The

nat

nal hist

ory standards were roundly criticized for too much attention to

interpretation and multiculturalism (Nash, Crabtree, and Dunn 1997), and

several organizations, including the American Federation of Teachers, evalu-

ated state standards for their content, precision, clarity, and rigor.

The questions being raised about school knowledge parallel similar questions

t disciplinar

y kno

ledge. For example, there is considerable debate in

the fie

ld o

f history about the roles of fact, truth, and interpretation. When an

eminent historian, Simon Schama, wrote a piece of historical fiction entitled

ead C

taint

ies

(1991) se

al hist

ians pub

licly chastised him for toying

ith q

uest

ns o

historical truth. Similar debates characterize literature,

mathematics, and the sciences. In part, these questions arose in the wake of

deconstructivism and postmodern thought. See, for example, Fish (1980).

nformation: it allows them to see patterns,

relationships, or discrepancies that are not

pparent to novices. (pp. 16–17)

We can no longer presume that algorithmic fluency is

the same thing as conceptual understanding. Over and

again, researchers have shown that students can master

algorithms yet have little conceptual understanding. Thus,

teachers need to make sure that students know content—

facts and concepts—and know how to use that content

flexibly to solve significant problems. As we have already

seen, such knowledge is essential for the transfer of learn-

ing from one context to another—in this case, perhaps

most significantly, from learning in school to learning and

using knowledge out of school. As the National Center for

Improving Student Learning and Achievement in

Mathematics and Science (NCISLA) portrays learning

with understanding, “Understanding for life: We will meet

the future head-on if we learn with understanding: linking

eas one to another in a rich intricate web; applying what

we learn to answer new questions; reflecting on knowl-

edge; and expressing ideas in creative ways. With under-

standing, learning becomes personal. It lasts a lifetime”

(NCISLA 2005).

Implications for Teaching and Teachers

As we al

l know, the relationship between learning and

teaching is complex. Moreover, research on learning has

often been conducted independently of research on teach-

ing, leading to a gap in understanding between the two

communities of researchers who understand and work on

learning and those who understand and work on teaching.

In recent years, scholars have been trying to bridge the gap

tween these intellectual communities with some modest

success (Romberg and Carpenter 1986).

One reason the relationship remains elusive is that

lear

ning cannot b

e mandat

eachers cannot guarantee

that a particular student will learn (Jackson 1986). A

teacher may valiantly try to teach mathematics to a student,

but whether the student learns something depends on

many factors within and outside the teacher’s control: Is

the student motivated? Did the teacher use the appropriate

inst

ructional strategy? Is the student interested? Are the

lassr

oom and school conditions conducive to learning?

Are the student’s parents supportive? Is there enough time

to digest the ideas and p

ractice new skills? Is there any peer

pressure? The list goes on. Nevertheless, these four ideas

about learning, learners, and knowledge have important

implications for the work of teachers. We propose several.

eaching as Intellectual Work

Perhaps the most significant implication of these ideas

bout learning and knowledge is that they imply that

thoughtful teachers are intellectuals who think both about

subject matter and students, constructing bridges between

the two. Reformers long ago learned that curricula cannot

be teacher-proof—for teachers inevitably shape the mate-

rials they use based on their own knowledge, beliefs, and

assumptions (e.g., Clark and Peterson 1986; Cohen,

Raudenbush, and Ball 2003; Shulman 1983). Yet wide-

spread belief persists that teaching is a straightforward

enterprise. Using textbooks, teachers follow each page,

directing students in what they should read and do. If the

materials are good, and everyone behaves himself or her-

self, so the logic goes, students will learn.

That is simply not true. Resources are mediated by

teachers and students, and they are situated within con-

texts that matter (Cohen, Raudenbush, and Ball 2003).

Good teachers must think hard about what they want their

udents to learn, contemplating myriad questions: What is

interesting about this subject for my students? What ideas

and concepts are particularly difficult? Why? What are the

different means I can use to help students grapple with

these ideas?

What do my students already know that might

help? What do they believe that might get in the way? What

time of the day is it? The year? How can I use my students’

diverse backgrounds to enhance the curriculum? How can

I create a community of learners who can support the indi-

vidual and social construction of knowledge?

Notice here that answering any and all of these ques-

tions entails theories and knowledge about learners and

learning. Because the situation matters, teachers must

think of the time of year, school, classroom, and commu-

nit

y (the so

cial contexts of learning). When teachers

decide what to teach, they must find ways to emphasize

both concepts and facts and modes of inquiry (the nature

kno

e students need to acquire). When teachers

consider what students will find interesting or difficult,

they need ways to access students’ minds; they need to cre-

ate communities among their students (learners as active

constructors of knowledge). Thus, much of teachers’

thinking is informed by the ideas about learners and

lear

ning we discussed earlier.

he cur

rent emphasis on teacher thinking and decision-

making has led to a sea change in the way that we think

bserve, and evaluate teachers and their teaching.

Research on teaching now entails asking teachers why they

act as they do and what they learn from their experiences.

Administrators no longer crouch in the back of classrooms,

What Do They Mean for Educators? 9

illing out checklists of behaviors. Instead, teachers and

their colleagues (other teachers, principals, and curriculum

oordinators) are expected to talk about why they taught as

they did, answering questions about their reasons, ratio-

nales, and reflections: Why did you teach this lesson? What

did you hope to accomplish? What would you change? New

performance-based assessments—for example, the assess-

ment system of the Beginning Teacher Assessment

Program in Connecticut, teacher portfolios collected

through INTASC, and the processes and products required

by the National Board for Professional Teaching

Standards—assume that to understand teaching, we must

observe both thought and action, watching what teachers

do and asking them to defend their choices. Such assess-

ments now involve interviews and portfolios, as well as

more traditional standardized tests and observations.

The emphasis on the intellectual aspects of teaching is

not intended to override the fundamentally moral aspects

of teaching. We agree with Palmer (1997) and Schwab

(1978b),

who argued persuasively that it is problematic to

divorce discussions of mind from heart, for the intellect is

deeply personal. Rather, this attention to teachers’ ratio-

nales (including explicated theories of teaching and learn-

ing) is intended to hold teachers more accountable for

their actions, as any professional is, so that all students are

treat

ed equitably and receive comparable high-quality

instruc

tion (Ball and Wilson 1996).

The recognition that

teaching involves both intellectual and moral aspects only

adds to its complexity.

Teaching as Varied Work

Another common mistake made in this era of reform is to

presume an isomorphic relationship between approaches

o t

eaching and modes of learning. Some “radical con-

structivists” have argued that teachers must never tell stu-

dents anything, and that all knowledge must be construct-

d ind

ently of the teacher’s watchful eye. But a

teacher might believe that students are active constructors

of their own knowledge yet still choose from a broad array

of instructional strategies, ranging from drill and practice

to recitation, from cooperative groups to simulations. In

creating these educational opportunities for their students,

eachers use manipulatives and historical artifacts; they

create scientific inquiries and mathematical problems.

ecause teachers take on different roles in these differ-

ent instructional configurations, much current talk of

teaching explores the use of alternative metaphors to cap-

ture the essence of teaching; instead of teachers being

thought of as tellers, we hear about teachers being coaches,

guides and collaborators. But one metaphor alone will not

do, for there are times when teachers must and should tell,

and other times when teachers should inquire, using their

classrooms as laboratories for their own learning (as well as

that of their students). However, because coaches often uti-

lize a broad range of instructional strategies, let us consid-

er the “teacher as team coach” concept further.

The appeal of “teacher as coach” lies in the fact that

coaches support players as they learn to demonstrate mas-

tery—even excellence—as independent artisans. Coaches-

as-teachers must help players develop foundational knowl-

edge and skill, provide opportunities for practice, facilitate

classroom discourse, and keep an eye on the structure and

timing of a player’s learning. In fact, the teacher-as-coach has

been a predominant metaphor in the work of the Coalition

of Essential Schools (Muncey and McQuillan 1996; Sizer

1984). Sometimes referred to as “natural learning,” the learn-

ing involved in team play is often very different from tradi-

tional sc

hool learning. As Heath (1991) explained:

Natural learning sites shape the semantic and

situational constraints of reasoning in basic

ways. Identifying and solving problems, mov-

ing from the known to the unknown, and

creating meaning through reasoning analog-

ically mark everyday reasoning in situations

that int

grate individuals into teamwork and

depend on guided learning in mixed-age

groupings. (p. 103)

This is the kind of learning that many reformers and edu-

cators argue for. Consider the reflections of a Little Leaguer

who compares his learning on the baseball team to school:

Like I know how to do things, but not

how to,

so it

’s more fun to play baseball also because

ou ar

e active, and there’s fun to do baseball

moving around and talk all the time. Like in

10 Theories of Learning and Teaching

r an e

xample o

the r

ang

e o

f strategies used by mathematics teachers in

this country and others, see Schmidt and others (1996) and the analysis of

mathematics teaching by Stigler and Hiebert (1999) in

The Teaching Gap.

See Shulman (1986) for a discussion of the paradigmatic shifts in research

on teaching, as well as Shulman (1987) for a discussion of the role of knowl-

edge in teaching. Performance-based assessments are the heart of the work

of the National Board for Professional Teaching Standards.

For readers interested in literature on the moral aspects of teaching, see Ball

and Wilson (1996), Hansen (1995, 1996, 2001), Palmer (1997), and Tom

(1984).

chool, you’re quiet all the time. In baseball

you can talk all you want.

[

The coach] taught us to get grounders,

like, plant our feet down like this and move

down. We wouldn’t just be, like, learning; he

actually has us do that, and he actually gives

us ground balls. Like in teaching, they just tell

you how to do it. (Heath 1991, p. 107)

Just as students cannot learn baseball simply by hearing

the coach tell about it, they cannot learn history, science,

literature, and other academic disciplines only by hearing

someone tell them about it. They need to do the kind of

work that scholars in these fields do—piecing together

evidence, understanding the leaps necessary to make infer-

ences, noting when they have to rely on their own theories

of human behavior. Experiences such as these help stu-

dents develop a critical eye, enabling them to become con-

sumers and users of knowledge. Part of this process

involves testing ideas out in public with peers. But to do

so, students—like mathematicians or historians—will

need to learn how to present and discuss their ideas with

others in intellectually productive ways.

To al

low for the public testing of ideas, teachers have to

create occasions for classroom discourse and act as rudder,

keeping the collective discussion and joint work on course.

Coaches often have their players consider a hypothetical

episode, making explicit various possible responses. For

example, a baseball coach might ask the team, “What

could have happened if Rob had bunted? What about the

man on second?” Then the players might think through

various responses and consequences (Heath 1991). In the

same way, a teacher might lead a discussion in which stu-

nts speculate on alternative interpretations of a particu-

lar piece of literary or historical text (Hartoonian-Gordon

1991; Wineburg 2001). This type of discussion is but one

xample o

w t

chers might make visible to learners

not only what is to be known but also how one comes to

know it as a literary scholar or historian.

In addition to helping students learn through doing and

structuring classroom discourse, coaches must do even

more. A coach needs to know each player’s individual tal-

nts and craft team strategies that take advantage of those

tale

nts.

Central to the task is helping all players accept the

value of individual differences. As Heath noted, “A team

cannot expect to have all members at the same level of abil-

ity in the same complex skills.” In much the same way,

teachers who believe that knowledge is constructed and

that groups of students and teachers can learn more

ogether than apart must find ways to construct a commu-

nity of learners that takes full advantage of the breadth of

nowledge and experience different members bring.

According to this image of teaching and learning, the

ideal classroom will no longer be one in which 30 students

are always listening to the teacher or silently working. Part

of learning would still involve lecture, drill, and practice,

for some basic knowledge must be routinized so that it will

inform interpretation and debate. However, students

would also work in alternative arrangements—small and

large groups—talking to each other, making public their

personal knowledge and beliefs, constructing and testing

their knowledge with peers and teachers. To help them,

teachers would have to understand when and how to use

different pedagogical approaches.

To argue for a more varied, eclectic range of teaching

methods is not to say, “anything goes.” Rather, contempo-

rary learning and teaching theorists propose quite the

opposite. Teachers must systematically consider their

lear

ning goals and their students, the subject matter they

want students to learn, and select pedagogical strategies

that will enable student learning. Those strategies ought to

be selected thoughtfully, varied in their approaches, and

refined over time through reflection.

Teaching as Shared W

ork

Educators have long been interested in how students learn

from students as well as from teachers. Nearly 30 years ago,

Schwab (1976) argued for a “community of learners.”

Several models for teaching and learning presume that

teaching is shared work between students and teachers

(teachers still have responsibility for making sure that stu-

dents learn). Cooperative learning, team learning, and

ciprocal teaching are but a few examples of the many

ways classroom work can be distributed.

Cooperative learning, broadly defined as an educational

unity in which students learn from one another, has

taken numerous forms (e.g., Cohen 1994; Johnson and

Johnson 1994; Johnson, Johnson, and Stanne 2000; Kagan

1985, 1993; Slavin 1986, 1990). With roots in theories of

social interdependence, collaborative learning has been very

successful when implemented well. Slavin (1990) argues

that tw

o hallmarks of high-quality cooperative learning are

osit

ive interdependence and individual accountability.

Team learning is closely related to cooperative learning.

rding to Senge (1990) “team learning is the process of

aligning and developing the capacity of a team to create the

results its members truly desire” (p. 236). Reciprocal teach-

ing, another form of teaching as shared work, is a technique

What Do They Mean for Educators? 11

sed to develop comprehension of text in which teacher and

students take turns leading a dialogue concerning sections

f a text. Students are taught to use four strategies in work-

ing through the text: predicting, questioning, summarizing,

and clarifying misleading or complex portions of the text

(Brown and Palincsar 1989; Palincsar and Brown 1984).

Designed to improve children’s reading comprehension,

modifications of reciprocal teaching have been used to teach

poor decoders, second-language learners, and nonreaders,

including adaptations that involved other pedagogies, such

as jigsaw (Brown and Campione 1996). Reciprocal teaching

draws directly on sociocultural and activity theories of

learning that emphasize the critical role of authentic partic-

ipation in meaningful, purposeful activities.

It is important to note here that suggesting a reconcep-

tualization of teaching as including more listening to stu-

dents, sharing of work, and asking of probing questions

does not mean telling teachers to stop talking or holding

the classroom’s center stage. Some overzealous reformers

urg

e teachers to change their practice radically, implying

that lectures and direct instruction are “bad.” This is not

our intent here; the effectiveness of inquiring into students’

thinking versus direct instruction is an empirical question

yet to be thoroughly researched. Most good teachers pre-

sume that they need to use a broad array of very different

instruc

tional strategies depending on whom and what they

are trying to teach, as well as when and where. The

reformist ideas we are discussing here propose integrating

more inquiry about students’ thought into teachers’ prac-

tices, as well as strategically deciding when teaching ought

to be shared among teachers and their students. Again, our

argument is one of shifting emphasis, not wholesale rejec-

tion or acceptance of one ideology or methodology.

chers are eclectic by nature and necessity.

Teaching Challenging Content

unning thr

oug

hou

t c

ntemporary visions of teaching is

an assumption that teachers will be teaching challenging

content. International comparisons, including the work of

TIMSS researchers (e.g., Schmidt and others 1996) and Ma

(1999), suggest that students in the United States typically

get fed a diet of thin content, “a mile wide and an inch

eep,” as Schmidt is often quoted as saying (e.g., Schmidt,

night, and Raizen 1996). Both in survey and video-

tape analyses, TIMSS researchers found that U.S. students

were exposed to a curriculum that was thin and fragment-

ed. “The content appears to be less advanced and is pre-

sented in a more piecemeal and prescriptive way” (Stigler

and Hiebert 1999, p. 57). In snapshot images comparing

athematics lessons in the United States, Germany, and

Japan, these researchers found the distinguishing charac-

eristics of U.S. lessons to be “learning terms and practic-

ing procedures.” German lessons, which tended to be

teacher directed, focused on “developing advanced proce-

dures.” Japanese lessons emphasized “structured problem

solving” in which Japanese teachers mediated the relation-

ship between the students and the content.

More in-depth analyses of these images examined three

indicators of content: level of difficulty, how extensively

content was developed, and coherence. In level of difficul-

ty, U.S. eighth graders studied topics that students in the

other two countries encountered a year earlier. The nature

of the content also differed. Whereas U.S. lessons did not

go beyond the basic definitions and procedures, lessons in

the other two countries used the basics to explore the

deeper properties and relationships in mathematics.

Regarding the degree to which content was elaborated,

findings indicate that the concepts in U.S. lessons were

simpl

y mentioned or stated, whereas in Japan and

Germany concepts were usually developed and elaborated.

Finally, with respect to lesson coherence, the researchers

found that the majority of teachers in all three countries

made explicit links between one lesson and another, but

only the Japanese teachers routinely linked the parts of a

lesson (Stig

ler and Hiebert 1999).

Although the U

nited States clearly has a long way to go

to meet high national and international content standards,

an important point that is usually lost in the sometimes

heated debates over high standards versus the basics is that

even the basics are challenging if one truly understands

them. Consider, as an example, even and odd numbers.

Learning even and odd numbers is an uncontroversial part

the elementary school curriculum. In standards docu-

ments, it might be listed as “students will be able to iden-

tify even and odd numbers.” Although most of us would

l r

lat

ively confident in our ability to identify an even

number, there is much more to it than that relatively sim-

plistic statement. Consider three relevant definitions that

are mathematically equivalent:

Fair share: A number N is even if it can be

vided into two (equal) parts with nothing

ft o

ver. (Algebraically,

N = 2 x k;

i.e.,

k + k.)

air

A n

umb

N is e

n if

it can be divided

into twos (pairs) with nothing left over.

(Algebraically,

N = k x 2; i.e., 2 + 2 + 2 + ... + 2

[

k terms].)

12 Theories of Learning and Teaching

lternating:

he even and odd numbers

alternate on the (integer) number line. So,

tarting with the even number 0 (or 2, if 0

makes one uneasy), one gets the even whole

numbers from there by counting up by twos.

Note: This is often referred to as the “skip” or

“skipping” method, for children will skip

from 1 to 3 to 5 on the number line.

As they learn even numbers, children might ask ques-

tions or propose solutions to problems that involve any

one of these definitions. Children ought to have opportu-

nities to understand the mathematical operations and

concepts that they encounter in ways that go beyond the

mere recitation of rules, procedures, or algorithms. Thus,

teachers need to understand why these three definitions

are mathematically equivalent (i.e., why do they specify

exactly the same class of numbers?). Although teachers

may get by with thin content knowledge as long as they

emphasize facts, procedures, and singular right answers,

when teachers move toward inquiry and seek to build on

students’ knowledge, they need much deeper content

knowledge regardless of whether they are teaching high-

level problem solving or the basics.

To summarize, there is no one right way to teach well.

This does not mean that anything goes, for there are some

things we kno

w about teaching. Every teacher needs a

repertoire of instructional strategies that range from

methods of direct instruction to cooperative and small

group work to one-on-one work. No single method will

work for a given teacher for all students in each subject

every day. Whatever method is chosen, teachers need

strong content knowledge to make challenging content

und

rstandable and to allow for ideas to be developed

fully and coherently. Teachers needs to weigh their options

thoughtfully, making decisions about what methods and

nt b

est me

et their goals and the needs of their stu-

dents for a given unit of instruction.

Teaching as Inquiry

If students are to serve as resources and teachers are to

enhance their professional knowledge constantly, then

eaching requires much more inquiry (Duckworth 1987;

Lamp

rt 1985, 1990, 2001). We cannot expect teachers to

know everything there is to know about the 20- or 30-odd

students in each class. In many ways, teachers must act as

scientists, investigating students’ thinking, finding ways to

learn about how particular students are actively construct-

ing their understanding. Teachers must probe students’

nderstanding, sometimes even interviewing them about

their thoughts and logic. Instead of being mere founts of

nowledge, teachers will also have to become inquirers,

asking questions and testing hypotheses about what their

students know and do not know.

In addition to learning about their students, teachers

need to learn much more about their subject matter.

Shulman (1986, 1987) proposed that teachers possess a

particular kind of subject-matter knowledge—pedagogi-

cal content knowledge—that allowed them to understand

how to represent knowledge to their students. Pedagogical

content knowledge is born of practice. Although one can

learn some things about powerful instructional represen-

tations outside of teaching, most teachers acquire this

form of professional knowledge through teaching. Such

learning continues over a lifetime (Feiman-Nemser 2001).

Thus, although experienced teachers might have a wealth

of accumulated knowledge from years of work with, say,

third graders, there is still much teachers need to learn

out the specific third graders they meet each new year,

as well as new things about the subject matter they are

teaching, the pedagogies available to them, and the most

powerful ways to help students interact with that content.

Thus, the significance of inquiry. Some would argue

that teachers have always learned from their practice. Yes

and no. We have always asked students questions: “Who

wants to write the answer on the board? Who had trouble

with number 8? What’s the capital of Nebraska? Why did

Romeo kill himself?” Seldom, however, have we asked

those same students to make public their rationales. With

little time and many students, teachers typically do not ask

questions such as, “Why do you think that? What is your

rationale for solving the problem in that way? Could you

e done it another way? What do other people think of

that answer?” Eager to get on with it, students and teach-

ers alike are accustomed to short, clipped questions and

similar

y t

se r

esponses, assuming that the reasons under-

lying the responses are self-evident. Similarly, teachers

typically process student work quickly, skimming answers,

checking proper responses, scribbling red-inked com-

ments. Those same teachers seldom share a student’s work

with a colleague, asking questions such as, “What do you

think this c

hild was trying to do with this story?”

aditional forms of assessment—often taking the form

of standardized tests—have compounded the problem of

lear

ning fr

m o

ne’s students. Instead of “giving students’

reason,” such tests assume one right answer and test the

child’s thinking against that standard. New work in assess-

ment shifts the emphasis and focus away from “right and

What Do They Mean for Educators? 13

rong” answers toward the collection of data that will help

teachers know what students are thinking (Glaser and

ilver 1994). Traditional school organizations only make

the situation worse. Schools have not been organized to

support teachers’ learning from their own practice and

from one another. Reformers in the 1980s argued that to

support teacher learning, schools would need to be

redesigned so that they were equally well organized and

equipped to support student and teacher learning; hence,

the call for professional development schools.

Learning to inquire—both in class in the company of

one’s students and alone in personal reflection and out-

side of class in the company of one’s peers—is unnerving

and time consuming; it also requires the development of

new knowledge and skill. Knowing how to listen is a skill

to be developed, not an inherited trait granted all teachers,

therapists, lawyers, and doctors. It requires sensitivity to

better and worse questions, the capacity to read between

the lines of a student’s response, and use of alternative

forms of assessment. Such inquiry would also require that

teachers learn a pedagogy of investigation (Lampert and

Ball 1998), asking good and researchable questions about

their teaching and students’ learning; strategically docu-

ment

ing their practice through records that can be revis-

ited (e.g., student work, teacher journals, and videotapes);

invit

ing criticism and debate about one’s teaching; and

participat

ing in communities of practicing teachers (Ball

and Cohen 1999).

This stance—teaching-as-inquiry—will require sub-

stantial changes in the culture of U.S. schools. Recent

descriptions of practices in Chinese and Japanese schools,

however, provide us with images of the possible (Shulman

1983). Researchers have found that teachers in Japan and

Shang

hai,

for example, participate in study groups and les-

son-planning groups designed to improve teaching itera-

tively over time. In Shanghai, for instance, teachers regu-

lar

y c

t and write up research they have conducted

in their own classrooms. In Japan, teachers “polish” their

lessons over time (Paine 1990; Stigler and Stevenson

1991). Japanese teachers participate in “lesson study,” col-

laborative groups in which teachers plan, teach, critique,

and revise their lessons (e.g., Fernandez 2003; Fernandez,

annon, and Chokshi 2003; Lewis and Tsuchida 1998).

esso

n-study groups have begun appearing across the U.S.

public school landscape as a professional development

activity (e.g., Paterson School 2 in New Jersey; Viadero

2004). Some U.S. universities and other organizations are

studying this approach to instructional improvement and

providing information about it. [See NEA Appendix.]

ther forms of teacher inquiry are also gaining popu-

larity. Cochran-Smith and Lytle (1993, 1999), Zeichner

nd colleagues (Gore and Zeichner 1995; Zeichner and

Noffke 2001), and others (e. g., Henson 1996; Stenhouse

1983) describe the power and potential of a scholarship

created by teachers for teachers. Alternatively called

action

research, teacher research, self-study,

and a scholarship of

teaching,

these approaches reflect a growing interest in

enabling practitioners to conduct and report on inquiries

into their own and their colleagues’ practices. This interest

not only concerns K–12 schooling but has become a pop-

ular topic in higher education as well, as scholars and the

American Association for Higher Education call for a

scholarship of teaching (Boyer 1990; Shulman 1993).

Conclusion

The Scottish physicist James C. Maxwell is credited with

saying, “There is nothing as practical as a good theory.” As

experienced teachers, we believe that all teachers operate

according to theories. Our practice is driven by our “theo-

ries” about what will work for our students. Some of those

theories are explicit and are learned in school; some are

tacit and are the products of years of experience in

scho

ols—as teachers, parents, and students. The theories

we briefly explore here have enormous potential both for

helping tea

chers explain why they teach in the ways they

do and for disturbing those patterns and prompting teach-

ers to rethink their practice.

Although many people want to claim that teachers are

born, not made, we believe that good teaching requires

teachers to create and use, expand and reject, construct

and reconstruct theories of learning and teaching. Those

theories are not intuitions, or “common sense” but care-

ful

y crafted lessons learned from years of experience and

careful inquiry. We also believe that teachers have more

power over their pedagogical choices when they have

e the

ir the

ies explicit and tested them with class-

room experience, colleagues’ critiques, and knowledge of

current research.

We hope that this brief tour through predominant the-

ories of learning and their implications leads readers to

consider important questions: How do we think children

lear

n mathematics? Or history? Why do we think that

using smal

l g

roups will help students develop certain

understandings and not others? When a textbook seems

par

icular

y helpful or harmful, to what extent is the prob-

lem located in underlying assumptions about how teach-

ers ought to teach and how students learn best? When we

encounter a new curriculum, what are its theoretical

14 Theories of Learning and Teaching

nderpinnings, and how do they align with our previous

experience and with other theoretical and empirical schol-

rship? It is only through interrogating our own tacit

assumptions about the answers to questions such as these

nd through the theories produced by new generations of

education scholars that we can make progress on that life-

ong journey of becoming accomplished practitioners.

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What Do They Mean for Educators? 21

1. Teaching for Understanding:

A Guide to Video Resources

Teaching videos are potentially useful as tools for instruc-

tional improvement, especially when used in group set-

tings where teaching strategies can be discussed. The pur-

pose of this NEA publication is to make teacher profes-

sional communities, teacher educators, and individual

teachers more aware of the growing array of video

resources that depict “teaching for understanding.” It pro-

vides an overview of the types of videos available,

describes how they are being used, and includes a selected

bibliography of some major, nonprofit sources. (Available

from the NEA Professional Library; see inside front cover

for ordering information.)

2. Lesson Study Resources

Lesson study is another promising approach to instruc-

tional imp

rovement. The following are only a few of the

many organizations providing access to research,

resources, and networking opportunities for teachers

interested in lesson study. Each of these sources has links

to other organizations and additional resources.

■

The Lesson Study Group at Mills College

(htt

p://lesso

nresearch.net/).

■

The Lesson Study Research Group at Teachers College,

Columbia University (http://www.tc.edu/lessonstudy/).

■

esear

h f

r B

etter Schools (http://www.rbs.org/

lesson_study/).

3. Standards-Based Instructional Resources

The professional associations and organizations that devel-

oped national content standards have all produced

esources intended to assist teachers to implement their

standar

ds.

Because national content standards and the sup-

porting resources all drew on the same research as this

working paper, the resources tend to be consistent with the

theories described. The national content standards and

supporting resources may or may not be aligned with indi-

vidual state standards.

The quantity and quality of resources vary considerably

by subject. Much more is available in mathematics and sci-

ence than in other subject areas. Standards-based

resources in the core content areas are available from the

following sources.

A. Mathematics

■

National Council of Teachers of Mathematics

(htt

p://www.nctm.org).

B. Science

■

American Association for the Advancement of

Scienc

e/Project 2061 (http://www.project2061.org).

■

National Science Resources Center, a partnership of

the Natio

nal Academies and the Smithsonian

Instit

ution (http://www.nsrconline.org).

C. English Language Arts

■

National Council of Teachers of English

(www.ncte.org/store/books/standards).

■

International Reading Association (http://www.

ira.org/resources/tools/index.html).

D. Social Studies

■

National Council for the Social Studies

(htt

p://ncss.o

rg).

■

National Center for History in the Schools

(http://www.sscnet.ucla.edu/nchs).

■

National Council for Geographic Education

(http://www.ncge.org/standards/).

■

Center for Civic Education (http://www.civiced.org/

ds.html).

■

ional Council on Economic Education, National

Association of Economic Educators, and Foundation

r T

ching Economics (http://www.ncee.net/ea/

program).

NEA Appendix: Tools for Instructional Improvement

Research

1201 16th Street, N.W.

Washington, D.C. 20036-3290

71266 7/06 hls