By Alfie Kohn
Closely related to the [mostly false] notion
time yields more learning is the belief, widely held by both parents and
teachers, that homework is useful because it affords an opportunity for
students to practice the skills they’ve been taught. This, of course, is a
defense of a certain kind of assignment – namely, the kind that involves
practice. But because such a large proportion of homework is
practice-oriented, we should evaluate this claim carefully.
There’s obviously some truth to the idea that practice
is connected to proficiency. People who do something a lot often get better
at doing it. But once again we find ourselves with a proposition that turns
out to be true in a far more limited sense, with more qualifications and
caveats attached, than may have seemed to be the case.
Giving students homework that involves drill and
practice is often said to “reinforce” the skills they’ve been taught in
class. This verb is tossed around casually, as if it were sufficient to
clinch the case. But what exactly is meant here? Unless it’s assumed that
practice is reinforcing by definition, one would have to demonstrate that
good results are indeed likely to follow from mere repetition. And it’s not
at all clear that this is true, except under very limited circumstances. For
example, it wouldn’t make sense to say “Keep practicing until you understand”
because practicing doesn’t create understanding – just as giving kids a
deadline doesn’t teach time-management skills. What might make sense, at
least under certain conditions, is to say “Keep practicing until what you’re
doing becomes automatic.” But what kinds of proficiencies lend themselves to
this sort of improvement?
The answer is behavioral responses. Expertise in tennis
requires lots of practice; it’s hard to improve your swing without spending a
lot of time on the court. You learn to pull back and follow through with
just the right movement so the ball lands where you want, and eventually you can
do this without even thinking about it. But to cite an example like that to
justify homework is an example of what philosophers call begging the
question. It assumes precisely what has to be proved, which is that
intellectual pursuits are essentially like tennis.
The assumption that the two activities are analogous is
an outgrowth of a doctrine known as behaviorism, widely associated with John
B. Watson, B. F. Skinner, and their followers. On this view, all that
matters are behaviors that can be seen and measured, and “man is an animal
different from other animals only in the types of behavior he displays,” as
Watson announced on the first page of his best-known book. Thus, it makes
perfect sense that most of the principles of learning that emerge from the
work of behaviorists were developed on lab animals. Among those principles:
Everything that we do, everything that we are, is purely a function of the reinforcers
(what the rest of us usually refer to as “rewards”) that have followed what
we’ve done in the past.
When teachers and parents talk about using homework to
“reinforce” the material students have learned – or, more accurately, the
material they were taught, which they may or may not have learned – the term
isn’t being used in this technical sense. But that doesn’t matter. Whether
they realize it or not, they’re buying in to the same attenuated view of
learning that emphasizes drill and practice because their focus is on producing
a behavior. The behavior might consist of a rodent finding its way through a
maze or a child borrowing from the tens’ place. For a behaviorist, these
actions are different only in degree, and the same theory applies equally
well to both. Thus, to justify sending students home with a worksheet full
of practice problems on the grounds that it reinforces skills is to say that
what matters is not understanding but behavior.
In the 1920s and ‘30s, when Watson was formulating his
theory that would come to dominate the way we teach students (not to mention the
way we raise children and manage employees), a much less famous researcher
named William Brownell was challenging the drill-and-practice approach to
mathematics that had already taken root. “If one is to be successful in
quantitative thinking, one needs a fund of meanings, not a myriad of
‘automatic responses,’” he wrote. “Drill does not develop meanings.
Repetition does not lead to understandings.” In fact, if “arithmetic becomes
meaningful, it becomes so in spite of drill.”
An emphasis on making meaning is directly opposed to the
view that learning consists of the acquisition of a collection of behaviors.
Brownell’s insights about math instruction have been expanded and enriched by
a long line of experts who have come to realize that the behaviorist model
is, if you’ll excuse the expression, deeply superficial. Learning isn’t just
a matter of absorbing new information or acquiring automatic responses to
stimuli. Rather, we human beings spend our entire lives constructing
theories about how the world works, and then reconstructing them in light of
new evidence. Not only educational theorists but “virtually all” cognitive
researchers today “[sub]scribe to this constructive view of learning and knowledge.”
The kind of teaching most consistent with it treats students as meaning
makers and offers carefully calibrated challenges that help them to develop
increasingly sophisticated theories. The point is for them to understand
ideas from the inside out.
This basic distinction between behavior and
understanding – with its implications regarding practice homework – applies
to just about every academic subject. Its relevance to math, however, is
particularly intriguing – and somewhat unsettling in light of the fact that most
of us still think in behaviorist terms. Mathematics is the subject in which
practice homework seems to be most commonly prescribed, so this is as good a
place as any to understand the limits of the whole idea.
An emphasis on practice to reinforce skills proceeds
naturally from the assumption that kids primarily need to learn “math
facts”: the ability to say “42” as soon as they hear the stimulus “6 x 7,”
and a familiarity with step-by-step procedures (sometimes called algorithms)
for all kinds of problems -- carrying numbers while subtracting, subtracting
while dividing, reducing fractions to the lowest common denominator, and so
forth. You do one problem after another until you’ve got it down cold. And,
as Brownell pointed out, if you have trouble producing the right answer,
that’s “taken as evidence only of the need of further drill.”
In reality, it’s the children who don’t understand the
underlying concepts who most need an approach to teaching that’s geared to
deep understanding. The more they’re given algorithms and told exactly what
to do, the farther behind they fall in terms of grasping these concepts. “Mindless
mimicry mathematics,” as the National Research Council calls it, is the norm
in our schools, from single-digit addition in first grade to trigonometry in
high school. Students may memorize the fact that 0.4 = 4/10, or successfully
follow a recipe to solve for x, but the traditional approach leaves them
clueless about the significance of what they’re doing. Without any feel for
the bigger picture, they tend to plug in numbers mechanically while applying the
technique they’ve been taught. As a result, they often can’t take these
methods and transfer them to problems even slightly different from those they’re
used to. Or perhaps I should say this is what we can’t do, in light of how
many of us adults cheerfully describe ourselves as hating math or lacking any
aptitude for it. (Rather curiously, some of us then become agitated if our
children aren’t taught the subject with the same traditional methods that
All of this has been noticed by people who make their
living thinking about math education. Several documents for reforming the
field, including, most notably, the standards disseminated by the National
Council of Teachers of Mathematics, have recommended that math classes
revolve around making meaning rather than memorizing rules. Students should
be encouraged to write and talk about their ideas, to understand the
underlying concepts and be able to put them into words.
There's a sharp contrast between math defined
principally in terms of skills and math defined principally in terms of
understanding. (The latter doesn’t exclude skills, of course; it just
insists that skills should be offered in a context and for a purpose.) But
even a classroom centered on understanding may not be enough. Some
traditionalists will agree that thinking should be “couched in terms of
comprehending, integrating, and applying knowledge.” But in their classrooms,
the student’s job is “comprehending how the teacher has integrated or applied
the ideas . . . and to reconstruct the teacher’s thinking on the next test.”
This returns us to the fundamental question of whether understanding is
passively absorbed or actively constructed. The best classrooms not only are
characterized by more thinking than remembering; they also have students
doing much of the thinking.
Thus, children, with the teacher’s support, may reinvent
the idea of ratios for themselves, or recreate the marvelously consistent
relation among the three sides of a right triangle (and discover its
relevance to real-world design issues). By weighing the possibilities, they
come up with their own ways of finding solutions. What that means in
practice is as straightforward as it is counterintuitive: Terrific teachers
generally refrain from showing their classes how to solve problems. Rather
than demonstrating the “correct” procedure for subtracting 37 from 82, for
example, second-grade teachers might let the students (individually or in
pairs) find ways to solve it, encouraging them to try various techniques,
giving them ample time before calling them back together for a discussion so
they can explain what they did, challenge each other’s answers (in a
friendly, supportive way), ask questions, reconsider their own approaches,
and figure out what works -- and why it works. Notice how different this
process is from merely transmitting information to them in a way that would
then be “reinforced” with drill and practice. Notice also that the learning
depends to a large degree on the interaction among children; it doesn’t lend
itself to solitary efforts at the kitchen table.
Until you’ve watched this kind of teaching, the idea of
trusting children to solve unfamiliar problems, or the idea that math is a creative
enterprise involving invention, can be very hard to accept. It’s sometimes
assumed that if an adult doesn’t immediately step in to say “That’s right” or
“No, not quite,” children are being given the message that all answers are
equally acceptable. In fact, exactly the opposite is true. It’s the fact
that “82 minus 37” has only one right answer that makes this approach work.
“Children will eventually get to the truth if they think and debate long
enough because, in [math], absolutely nothing is arbitrary,” says Constance Kamii,
who has devoted her career to explaining – and proving -- the value of this
sort of math education.
By contrast, when students are simply told the most
efficient way of getting the answer, they get in the habit of looking to the
adult, or the book, instead of thinking things through. They become less
autonomous, more dependent. Stuck in the middle of a problem, they’re less
likely to try to figure out what makes sense to do next and more likely to
try to remember what they’re supposed to do next – that is, what behavioral
response they’ve been taught to produce. Lots of practice can help some
students get better at remembering the correct response, but not to get
better at – or even accustomed to -- thinking. “In traditional math, says Kamii,
“kids are given rules that don’t make sense to them, and repetition seems to
be necessary to memorize rules kids don’t understand.” She generally
recommends steering clear of homework, “partly because what kids do at school
is enough, and repetition is neither necessary nor desirable,” and partly
because when parents try to help their children with math assignments they
tend to teach them what they’ve been told are the “correct” ways to solve
problems. Again, this shuts down children’s thinking.
Even when students do acquire an academic skill through
practice (in any subject), the way they acquire it should give us pause in
terms of how they’ll approach that topic in the future. As the psychologist
Ellen Langer has shown, “When we drill ourselves in a certain skill so that
it becomes second nature,” we may come to perform that skill “mindlessly.”
Practicing some things until you can practically do them in your sleep often
interferes with flexibility and innovation. What can be done without
thinking usually is done without thinking, and that may lock people into
patterns and procedures that are less than ideal. Practice often leads to
habit – which is, by definition, a mindless repetition of behavior -- but not
to understanding. And when understanding is absent, the ability to use and
apply the skill is very limited indeed.
Even under those circumstances and for those topics where
a reasonable case can be made that practicing does make sense, we’re not
entitled to conclude that homework of this type is appropriate for most
students in any given classroom. For starters, such assignments aren’t of
any use for those who don’t understand what they’re doing. “Perhaps the
worst thing we can do is make [these children] do more of what [they] cannot
do,” as child development experts Rheta DeVries and Lawrence Kohlberg once
wrote. Giving practice problems to students who lack understanding can
have any of several effects:
* It may make them feel stupid. (Over and over again,
they’re reminded of what they can’t do.)
* It may get them accustomed to doing things the wrong
way, because what’s really “reinforced” are mistaken assumptions.
* It may teach them to fake it, perhaps by asking
someone else for the correct answers, to conceal what they don’t know.
* Finally, the whole exercise subtly teaches that math
– or whatever subject they’re doing -- is something people aren’t expected
At the same time, other students in the same class
already have the skill down cold, so further practice for them is a waste of
time. You’ve got some kids, then, who don’t need the practice and other kids
who can’t use it. Even if we were willing to put aside more basic concerns about
this kind of assignment, it’s entirely possible that only a handful of
students in any classroom at any given time would be likely to benefit from
it. Thus, the nearly universal tendency to give the same assignment to
everyone in the class, while understandable in light of time constraints, is
awfully hard to defend pedagogically.
This is exactly why a New York math teacher, who has at
various times taught students from second to eighth grade, told me that she
has "never found homework helpful. Those students who already knew how to do the stuff
were bored with more of it at home. Those students who didn’t understand it
made up their own ways to do things which were often wrong and repeated the
practice, making it that much harder to get them to see it another way in
eighth-grade English teacher in southern California arrived at the same conclusion:
I very rarely give my students any kind of
homework. I do not believe in homework, especially in a Language Arts
class. Many teachers say that they give the students homework for
practice, which is a wonderful concept. However, does every student in
the class need the exact same amount of practice? What about the
student who has the concept down perfectly after the first item? Why
does she have to do the other thirty-nine items? How about the student
who practices all forty problems wrong? What good did the homework
assignment do her? I want my students to do their learning in my
presence, so I can immediately correct them, or take them in a different
direction, or push them further, or learn from them.
Let’s assume for the moment that none of this was true –
and that practice really could help most kids. Even so, it still hasn’t been
shown that they need to do it at home. Proponents of homework simply assume
that if practice is worthwhile, it must take place after school is over – in
part because there’s not enough time for students to write or solve problems
during the day. But this raises the question of what students should be
doing. Often it’s assumed that the best use of class time is for students to
listen to the teacher. Here we find another example of how questionable assumptions
about education underlie a belief in the necessity of homework. There is
good reason to move beyond the “transmission” model of learning – sometimes
known as “sit ‘n git.” (The writer George Leonard once defined lecturing as
the “best way to get information from teacher’s notebook to student’s
notebook without touching the student’s mind.”) There’s a good case to be
made that if class time is limited, most of those hours are better spent
having students read and write, discuss and reflect.
Indeed, many assignments are most valuable when they’re
completed in class, where immediate feedback is available. Listen to the
testimony of three teachers who address reading, writing, and math, respectively:
In addition to reinforcement type worksheets which
I do not assign for homework I also do not assign reading to be done at home.
Instead, I begin each day with an article (1-2 pages tops) that relates to
the topics we're studying. Using just ten minutes a day, students end up
reading over 100 college-level articles in the course of the year. Using
class time enables us to go over the information collectively and
I have to give students time to write in class.
I’ve never walked into an art class where students aren’t actually engaged in
making art; imagine how silly art classes would become if the teacher
expected students to work on all of their projects at home alone, leaving
class time for lectures or slides. Of course we should expect students to
write at home regularly. But assessment depends on observation, and if we do
not allow students to write during class, we cannot observe their process or
find the time to give them the responses and ask the questions that matter.
I like to see students thinking through math. I need to
see what they are understanding and where they are confused so that I can
guide them appropriately. This, I find, only works in class.
The Learner’s Point of View
Even if practice homework really did help some students
to acquire a skill, any such benefit would have to be balanced against the
effect it has on their interest in learning. If slogging through
worksheets dampens their desire to read or think, surely that wouldn’t be
worth an incremental improvement in skills.
But let’s take this a step further. Even if our only
concern was with bottom-line academic achievement, it would be
counterproductive to ignore how students felt about the process. Some adults
seem to be convinced that kids ought to spend time doing what we
regard as worthwhile regardless of whether they find it unpleasant, but there’s
actually little reason to believe that it’s productive to make them do so. This
is because excellence tends to follow interest.
As I mentioned earlier, advocates of homework are fond
of pointing out that you don’t get to be proficient at activities like tennis
or basketball without spending an awful lot of time practicing. But even
here, what matters most is the fact that the would-be athlete wants to
be out on the court. Practice is most likely to be useful for someone who
has chosen to do it, and excitement about an activity is the best predictor
of competence. That’s why one of the main challenges for a teacher is to
help spark and sustain children’s intrinsic motivation to play with words and
numbers and ideas. Conversely, when an activity feels like drudgery, the
quality of learning tends to suffer. The fact that so many children regard homework
as something to finish as quickly as possible – or even as a significant
source of stress – helps to explain why there’s so little evidence that
it offers any academic advantage even for those who obediently sit down and
complete the tasks they’ve been assigned.
That fact makes perfect sense in light of a fundamental
insight that has emerged from the work of psychological theorists and
researchers who have transcended behaviorism: What matters most is not a
child’s action; it’s what underlies the action -- her needs, goals, and
attitudes. It’s not what she does that’s going to prove beneficial (or
not) in the long run; it’s why she does it, what she was hoping to get out of
it, whether it makes sense to her (and, if so, for what reason). Of course,
it’s much harder to measure these things than a variable like "time on task." By the
same token, it’s easier to make students spend hours practicing a skill than
it is to change their view of what they’re learning, how they see themselves
in relation to that task, how competent they think they are, and so on. But
that doesn’t alter the fact that the best predictor of results is how things
appear from the student’s point of view.
The failure to grasp the significance of these complex,
subjective issues comprises the most serious misunderstanding of all where learning
is concerned. Essays in favor of homework generally reflect a tendency to
regard children as inert objects to be acted on: Make them practice and
they’ll get better. My argument isn’t just that this viewpoint is
disrespectful, or that it’s a residue of an outdated stimulus-response psychology.
I’m also suggesting it just doesn’t work. Children cannot be made to acquire
skills. They aren’t vending machines such that we put in more homework and
get out more learning.
Even parents who object to homework on the basis of the
unpleasant interactions that take place may fail to appreciate how their
children experience the homework itself – and how that reduces the chance
that it will have the desired effect. Similarly, even researchers who
consider students’ perspectives tend to do so in the context of reporting
that homework elicits considerable resistance, but only because those darn
kids don’t understand that homework is good for them. Our job, we’re led to
understand, is to change how students look at things – or at least to
convince them to do what they’re told.
But what if our goal was to understand rather than to
convince? What if we made a serious effort to imagine – from the child’s
point of view -- what homework feels like and what it actually teaches? Do
all those assignments really impress upon kids the importance of
responsibility, achievement, and hard work? Or are their real messages that
learning has to be unpleasant, that my parents and teachers have formed an
alliance against me, that I’m not trusted to decide what to do with my spare
time? Perhaps we so rarely try to experience homework from the vantage point
of those who have to do it because this exercise would end up revealing its
I argued in chapter 2 that a careful review of the data
really doesn’t provide much support for the idea that homework is necessary
to help students learn better. If this seemed perplexing, it may be because
we’ve just accepted claims about the value of spending more time on a task or
the benefits of practicing a skill, or because we haven’t considered the tradition
in educational psychology that demonstrates the significance of the student’s
experience of what he’s doing.
Misconceptions about learning are pervasive in all sorts
of neighborhoods, and they’re held by parents and teachers alike. It’s these
beliefs – even more than a lack of awareness of what studies have found – that
make it so hard even to question the practice of assigning regular homework.
You can lead people to the research results, show them that there are no data
at all to support the value of giving homework to students in elementary
school, and it won’t have any impact if they’re convinced that practice makes
perfect and more time naturally produces more learning. If, in other words,
we assume homework is a necessary part of education, that may be because of
how little we know about how children actually become educated. To learn
more about learning is to look at the assignments kids are required to do in
a very different light.
[Full citations appear
in the book’s bibliography. Some endnotes in the book have been
1. Brownell 1935, pp. 10, 12. Emphasis added.
Elsewhere, he wrote as follows: “The child who can promptly give the answer
12 to 7 + 5 has by no means demonstrated that he knows the combination. He
does not ‘know’ the combination until he understands something of the reason
why 7 and 5 is 12, until he can demonstrate to himself and to others that 7
and 5 is 12 … and until he can use the combination in an intelligent manner –
in a word, until the combination possesses meaning for him” (Brownell 1928,
2. Putnam et al., p. 89. Lauren Resnick and other
experts have made the same point.
3. In so doing, it also invites them to think
critically about those ideas. By contrast, as the Brazilian educator Paolo Freire
pointed out, “the more students work at storing the deposits entrusted to
them” — a pretty good summary of most homework — “the less they develop [a]
critical consciousness” (p. 54). This raises the interesting possibility
that while a reluctance to ask provocative questions may help to perpetuate
the institution of homework, the institution of homework may also discourage
students from asking provocative questions.
4. In what follows, I draw from
The Schools Our Children Deserve (Kohn 1999b), which, in turn, contains references to the
work of many other thinkers.
5. Windschitl, p. 352.
6. Kamii, 1994, p. 67.
7. Langer, p. 13.
8. DeVries and Kohlberg, p. 374.
9. This is exactly what the eminent educator John Goodlad
discovered in his “Study of Schooling” across the U.S.: “A very large
percentage of children [in elementary schools] reported to us that they frequently
did not understand the directions for the work they were to do. The
consequence of this is that they did not get much done at school and so had a
good deal to do at home—but did not understand the work in the first place.
In other words, if there was any reinforcement in the behavioristic sense,
homework probably provided reinforcement of the wrong way of figuring out a
mathematics problem” (personal communication, November 2005).
10. All of this also applies to more sophisticated
homework, by the way. Even if the rationale is to promote “integration of
skills” – a current buzzphrase -- rather than the mere rehearsal of those
skills, the reality is often that “the only skills being integrated are those
of procrastination and panic” (Waldman).
11. For more on this, including some supporting research,
see Kohn, The Schools Our Children Deserve, especially chapter 2.