From Chapter 6 of The Homework Myth
(Da Capo Press, 2006)
Copyright © 2006 by Alfie Kohn

Do Students Really Need Practice Homework?

By Alfie Kohn

Closely related to the [mostly false] notion that more 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.”[1]

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.”[2] 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.[3]

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.[4]

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 failed us!)

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.”[5]  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.[6]

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.”[7]  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.[8] 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.[9]

*  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 to understand.

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 class.”

An 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 immediately.

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[10] – 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.[11] 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 futility.

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.

 

NOTES

[Full citations appear in the book’s bibliography. Some endnotes in the book have been omitted here.]

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, p. 198).

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.

 

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