As Dropout Nation readers already know, your editor has some strong thoughts about the myth of the unmotivated student held by far too many inside and outside of education; the problem isn’t the kids, but the years of educational malpractice and neglect that transform bright young minds into adolescents looking to escape from poor instruction and curriculum.
In this latest piece in this collection on reforming instruction in American public education, Contributing Editor Steve Peha discusses some of the instructional practices that hinder curiosity and student achievement. Read, ponder and offer your own thoughts.
When kids are little, they seem to love school. They’re also very willing to please; there’s hardly anything they won’t at least try to accomplish. But as they get older and the difficulty of school work increases, some remain highly-motivated while others become less-motivated to finish school.
The difference between kids who are self-motivated and those who aren’t is dramatic. So much so that the motivation problem—even though it doesn’t show up explicitly on a test or a report card—may be one of the most important problems we need to solve in our schools.
As important as we all know motivation is, we don’t seem motivated to understanding how it works or improving it in our classrooms. For the most part, we just take what we get. In general, kids who do better in school are more motivated than those who don’t. But this observation gives us little leverage on the problem.
It’s a serious problem, too. One reason why kids drop of out of school is a lack of motivation to continue. For a variety of reasons, school simply becomes less important than something else. Along the way, less motivated kids are less engaged in class and less likely to do their homework, which makes them less likely to succeed.
We know motivation is a big part of student success, but we don’t seem to have a solid game plan for how to deal with it—unless you call nagging a game plan. We bug kids about paying attention in class and getting their work turned in on time; occasionally we offer small incentives or threaten to mete out minor penalties. But we know these things don’t work very well.
Some teachers can motivate kids simply by the force of their personalities. These teachers are rare but they do exist. Some teachers use elaborate reward and punishment systems. These work to a certain extent but require management on the teachers’ part and sometimes have unintended negative consequences. Finally, some teachers are fortunate to teach classes kids are more inclined to like. Kids seem much more motivated to take Media Production or Yearbook than they do to take Biology or World History.
Each of these approaches to motivation relies on an external circumstance: a charismatic teacher, meaningful rewards and appropriate punishments, inherently interesting subject matter. These are all examples of external motivators. What we’d really like, however, is for kids to be internally or self-motivated. If they were, we wouldn’t have to worry so much about how to keep them motivated day after day—especially in classes like Biology or World History.
Motivation From Inside Out
In Drive: The Surprising Truth About What Motivates Us, Daniel Pink points to the Self-Determination Theory formulated by Edward L. Deci and Richard M. Ryan. Although it is generally applies to the workplace, it also relates to what happens in schools. The aspects of this theory include:
- Competence. Imagine going to work every day and not being able to do your job. Imagine being perpetually incompetent. Would that raise or lower your motivation to work? Now think about it the other way around. Imagine going to work every day and having what it takes to do your job well. Competence is a big internal motivator. But for kids who start school behind, or who fall behind later on, school becomes a perpetual lesson in incompetence, with a resulting loss of motivation in situations where many need it most. Finding the right level of challenge for learners is vital to optimizing their growth. When just about everything you’re doing is over your head, a sense of hopelessness or helplessness creeps into your thinking, and self-motivation is pushed out. We have to have kids working at the right level of challenge so they can experience competence at the same time that they are experiencing new learning.
- Autonomy. Human beings seem to benefit from a certain amount of independence. In school, of necessity, we control much of what kids do. But often we control things so much, there’s little reason for kids to bring their own self-control to the challenges of their academic lives. Autonomy in this case doesn’t mean total freedom or complete freedom of choice. It means that kids have reasonable and responsible degrees of freedom over tools, time, technique, and task. When we give kids a reasonable and responsible range of choices over the work they do and how they do it, they exercise more self-control and develop more self-motivation. We often say that we want our kids to learn to make good choices. But this can’t happen if we make all their choices for them. Autonomy is a generator of self-motivation, and we tend to take it away from kids as they enter secondary school, exactly the time when they begin to need it most.
- Relatedness. While we all have needs to make some choices on our own, most of us don’t like feeling alone. Feeling disconnected from others, or excluded from a group, is de-motivating. If you’ve ever played a team sport, you know how easily you can motivate yourself to contribute to the goals of a team you feel proud to belong to. Unfortunately, school is almost always an individual sport. There aren’t many opportunities built in for people to work together toward a shared result. Of course, there are always social groupings outside the classroom that include some kids and exclude others. But if kids don’t feel a strong sense of relatedness to the academic culture of a school, they can lose their intrinsic motivation to achieve academically.
If you think about the way we treat low-performing kids, you can see why they might never develop the internal strength they need to make up ground and succeed in school. First, they’re usually working on work they can’t do; they rarely experience competence. Second, we control almost every aspect of what they do and how they do it; by virtue of their low academic performance we take away many of the freedoms afforded to other students. Third, low-performing kids often self-isolate from the mainstream; or, in many cases, we isolate them deliberately by pulling them out of regular classes.
Why Self-Motivation Matters
School is designed so that self-motivation doesn’t matter very much—or at least that’s the value judgment we communicate to our students. Kids are heavily controlled and only a favored few experience consistent competence or feelings of true relatedness. This is the natural state of affairs. Rather than creating environments designed to strengthen intrinsic motivation, school is designed to weaken it, and to strengthen kids’ dependence on external motivating factors so they can be more easily controlled. This aspect of school probably hurts almost all students, but it has an especially significant downside for low-performing kids.
Kids performing below grade level are behind. It may seem at times that they are not that far behind, and that if they just “applied themselves”, they could catch up. If they just tried a little harder, we think to ourselves, they might make it. But where do we think that extra bit of “try” will come from? By the language we use, we obviously recognize that effort is a function of self-motivation. Yet we do just about everything we can to reduce the capacity of students—especially at-risk students—to develop self-motivation.
Think about how much internal motivation a new middle school student might need if he entered sixth grade a couple of grade levels behind in math and reading. Here’s a kid who has probably been learning at a rate of 75 percent of standard each year. Now, to catch up for high school, this student may have to learn at a rate of 150 percent of standard for three years in a row—twice as fast as he has ever learned in his life. It’s not just a little bit of effort that’s required here. This student has to maintain a blistering pace over several years in a row, something he’s never done before in his life.
This is why motivation matters so much. It’s the key to keeping most kids on track. It’s also an essential component in giving those who fall behind even the slimmest chance of catching up. When school is consistently de-motivating, or when all attempts to motivate students are of the external variety, valuable internal motivation is often lost—and many of our kids are lost right along with it.
But How Do We Do It?
Helping kids build internal motivation is counter to the nature of traditional schooling. In the traditional model of education, we attempt to educate kids through an authority-driven approach characterized by a range of external controls. In most cases, we do this through a combination of limited choice and the use of reward and punishment systems. Many children do well in this type of environment. But many do not.
This is how school is designed by default, so we shouldn’t make light of the fact that changing an environment designed to function via external motivation into an environment where we help kids build internal motivation is a difficult task. But it’s also an essential task, one we must take on if we want kids—especially at-risk kids—to make good progress in school.
Here are a few things we can do:
- Praise the effort, not the result. If effort is so important to us, if we wish kids would put more of it into their work, why not praise them for it? Why not shift at least some of our assessment and interactions to the type and quality of the effort kids demonstrate? The advantage of this is that it can be applied successfully to students of all ability levels in tasks of all levels of difficulty. Everyone can muster a little more effort. And everyone can improve by doing so.
- Work with what’s there, not with what’s missing. All kids have positive qualities and essential strengths that help them learn—even the kids who don’t seem to learn very much. Taking a strengths-based approach can make a big difference. Here’s a useful guideline: if you can’t find a strength in a student, you’re giving that student the wrong work to do. Every kid has strengths. They just don’t show up in all situations.
- Meet kids where they are. With all the pressure these days to get kids ready for tests, there’s a sense in many classrooms that kids have to be where we want them to be. While this is an important aspiration, it requires a basic responsibility on our part. In order to get kids over the line, we have to start by meeting them where they are and moving them up in gradual, logical steps. We can’t just put a standard on the board and tell kids they need to meet it. We can’t just ask kids to meet us where we are; we have to begin by meeting them where they are.
- Provide a reasonable range of responsible choices. Somewhere, within all the inflexible scheduling and assigning we do for kids, we can surely carve out some elements where meaningful degrees of choice are possible. This need not be free choice—and probably shouldn’t be in most cases—rather, we should provide all students with some form of guided choice based on a small set of options we feel would be most valuable.
- Teach kids to assess the quality of their work and behavior: We’d all like to see kids taking more ownership of their work and behavior. One of the best ways to do this is to give them some responsibility for assessing these things. With small amounts of training, kids can become quite accurate at determining their performance. They can then take more personal responsibility for how they perform in school.
- Keep kids working at the right level of challenge: Keeping kids working at the right level of challenge means differentiating instruction. Many subjects—especially at the secondary level—are not set up for this, and few teachers who have the opportunity to differentiate have the talent and experience to do it well. As with so many of the issues listed here, this one affects students at all ability levels. It also connects with important ideas like teaching kids self-assessment, giving them responsible degrees of choice, meeting kids where they are, and so on. It is probably the single most important issue in teaching. Even though it is difficult, it is still worthy of our attention.
- Use goal setting. Helping kids set explicit goals for their performance and behavior gives them tangible targets to shoot for. While a goal may start out as an external motivator, it quickly becomes an internal motivation, especially when we teach kids how to assess their own progress and potential completion.
- Provide actionable feedback via constructive criticism. In order to improve, learners need feedback they can work with. They can’t work with feedback like “B-minus” or “This idea needs more support.” Feedback has to be actionable. That is, the student has to be able to take action on it. Knowing that an idea needs more support doesn’t help a student take action when the student obviously didn’t know how to add the required support in the first place. True constructive criticism carries with it the information the learner needs to construct a solution to the problem identified.
This is a long list of things that school is not designed to provide. Yet it is precisely because school is designed in this way that so many kids fail. This isn’t to say that the failure of kids can be connected solely to the culture and structure of their schooling. But we could make significant progress on many of the most serious problems kids have if we made changes to school that supported, rather than sapped, intrinsic motivation.
Again and again, we must come back to the most basic realization that we cannot force kids to learn. We can command but they need not follow our orders. Everything for kids in school is a choice. And each choice has to be motivated in some way. When we ignore internal motivation, or we rely primarily on coercive reward and punishment approaches as tools of external motivation, we get less out of kids as time passes because they tend to give us less as time goes by. As school gets harder, they become hardened, too.
Motivation is a challenge for almost all kids. But it’s especially challenging for at-risk kids. They’re behind, sometimes far behind. Being behind is, in and of itself, de-motivating. Without sufficient internal motivation, these kids often find themselves on the path to dropping out. We can pretend that our efforts to motivate them from the outside will be successful. But ultimately, especially as kids reach young adulthood, the pushing has to come from within. Rather than pushing kids, we would do better to create school cultures and structures that supported kids in developing the capacity to go the distance on their own.
When it comes to how kids memorize and remember content, teachers do little and kids get even less. We simply accept that large amounts of the information teachers transmitted to students would be lost and yet, we still don’t do much about it. We allow students to go through their academic careers flailing without helping them improve their content acquisition skills.
Unless they have naturally good memory or they are taught such skills elsewhere, they carry their underachievement throughout their time in school.This doesn’t have to be the case. And as teachers, we can do much better.
No Matter What the Future Brings
If you know something on one day but you forget it a month later, have you learned it? We can have “if a tree falls in the woods…” debates all we want, but answering practically from the standpoint of a teacher’s unit test or a state’s end or course exam, the answer is clearly “No.”
Whether kids consciously try or not, there’s simply no way around memorization. Think about how much information you had to memorize during just your high school years. Did anyone ever tell you how to go about it? Probably not.
We know kids have to memorize things in order to be successful academically, but we rarely teach them anything about how human beings keep things in memory.
Perhaps the simplest and most valuable thing to know about memory is this: we remember what we pay attention to; attention and memory go hand in hand. The word “attention” here is important, especially for students who might rather doodle in their notebooks in the back of the classroom.
We can sit in class staring at a textbook all period, and even reading the words, but we may not remember much, even right after class, if we don’t pay attention to our reading as we do it.
One of the most interesting things about memories is that we recreate them every time we remember them. Typically, we’re cued to do this by some stimulus. For example, hearing a bit of a popular song may remind an excited teenager about an upcoming dance. The cue and the memory are associated with each other in your mind. Better and more frequently-presented cues equals stronger and more easily retrieved. So one of the best things we can do for kids is help them develop useful cues.
A teenager who loves music and the social interaction of dances, doesn’t need our help in finding good cues. But how can we use cueing to help kids remember events in American history or math formulas or scientific facts? How do we remember things we probably wouldn’t be interested in otherwise?
One common answer is to “make it relevant” to students. That’s great. But is it always possible? And is it possible for every kid when what relevance is such a personal thing?
Books abound with memorization techniques, simple mental devices people have used for centuries. One of the most famous of these, and probably still the cheapest, is The Memory Book by Harry Lorrayne and former New York Knicks basketball star Jerry Lucas. These technique will work but for some ironic reason they haven’t ever become a common part of education.
Specific memorization techniques aside, there are two general categories of academic activities that can strengthen our memories whether we know any memorization techniques or not: recall activities and elaboration activities, both of which can help kids develop strong cues to the things we want them to remember.
Never Out of Date
An easy type of recall activity is questioning. You can immediately understand how questioning might help. After all, much of what we do in school is answer questions. Asking questions, even very simple ones, while you take in new information, can help you remember it more thoroughly.
In one study, researchers found that having students simply ask themselves “Why?” after each sentence they read improved their memory of the text. This probably isn’t the most enjoyable way to read but you can see why it might work: forcing the question focuses your attention on the material, even if you don’t know the answer.
When we recall a memory, we strengthen it. Of course, we can make mistakes with recall activities, too. How many kids have “learned” that 6 × 7 = 44? The old adage, “Practice makes perfect.” is itself imperfect. The truth of learning and memory is that “practice makes permanent.” Practice only makes perfect if we practice perfectly. This is why flash cards and timed tests and other traditional classroom recall activities that emphasize mind-numbing speed over accuracy might not be as effective as activities that emphasize accuracy and focused attention—if we taught those type of activities to kids.
Attention helps us form a memory, recall helps us strengthen a memory, but how do we hold onto memories? How do we store things in so-called “long term memory”? What’s the best way to store information so we can remember it weeks, months, or even years later?
Memory expert Dr. Harold Pashler puts it this way: “Many studies have concluded that the key factor is elaboration: active processing that uncovers connections between a to-be-stored item and other information in long-term stor[age]. By contrast, mere intention or desire to remember seems relatively unimportant.”
So to put something into long term memory, we have to do something more with it. Writing is probably the easiest and most common thing we’d do in school. If you parse Dr. Pashler’s response, you can immediately tell why. Writing involves “active processing” and the “uncover[ing]” of connections between what we want to remember and what we already know. Elaboration would seem to give us all the benefits of attention plus the added benefits of recall.
To put all this in perspective, here’s an activity I use frequently when conveying information in a lecture format. First, kids know that I have already created the basic notes for the lecture so all their attention can be focused on what I’m talking about at the moment; having kids takes notes while we teach is often a disaster. After talking for maybe ten minutes at most, I ask kids to make lists of what they feel were the most important bits of information. We quickly share these bits around the classroom. Sometimes, I write them on the board. And often we reorganize them in some logical way.
Finally, I ask kids to write a quick paragraph or two elaborating on what we’ve just discussed. Now, when they leave class, they have lecture notes, what we all agreed was most important, and their own elaboration. This doesn’t work every time for every kid, but you can see that it follows the attention, recall, elaboration pattern that should give most kids the best chance of learning and remembering it.
On This You Can Rely
One thing is almost always true about school: not enough information about learning makes it through the classroom door. This is no one’s fault but it is everyone’s responsibility. Why, when we want our children to learn so much, do we tell them so little about how to learn it?
Because nobody told us.
Most of education is governed by tradition and most educators are creatures of habit. The way we do something now is the way we did something then. We don’t question many things. Often we don’t have the time or the energy; mostly we don’t have the interest. But when it comes to understanding a little bit about memory, and helping kids hold onto all that information they need, learning a bit about memory is an important step in solving the content acquisition problem.
Since repetition in a slightly different format enhances memory, here’s a bullet point summary of things we can do to help more kids learn more things that I hope will enhance your memory of the important ideas in this article:
- Provide a coherent curriculum that builds content knowledge. Of all learning strategies we know, nothing works better than actually knowing things. Kids need an information-packed curriculum that builds logically upon itself from year to year. Increasing non-fiction reading is one of the easiest ways to bring more knowledge into kids’ lives.
- Intervene earlier when kids are having problems that might cause them to miss crucial curriculum. We are practically panicked when kids can’t read, just as we should be. But we’re positively complacent when they fall behind in other subjects. While reading is, arguably, more important, the result of falling behind in just about any area is that kids never catch up. We must intervene early and often to plug gaps in students’ knowledge—regardless of the subject.
- Give kids different ways to work with the same information. Tell students about something, let them read about it, let them watch something, let them discuss, pose questions that shift their perspective, provide a variety of opportunities for kids to encounter the information we want them to learn. Again, a well-coordinated curriculum is an important piece of this part of the puzzle, too, as topics can be revisited with increasing complexity over time.
- Give kids opportunities to reason with the information they acquire. Ironically, if we want kids to take in a lot of information, we have to give them many opportunities to spit it out. Even if the information being studied is the same for every student, each will likely have different reactions, thoughts, questions, and connections they can make to other information. Each learner has to integrate new information with their own version of existing information. Reasoning with new information—trying to solve intellectual problems—is a great way to do it.
- Teach common memorization techniques. Explicit techniques exist for memorizing information. You can find them in books or in articles on the Internet. Sometimes they can very useful to students. At the very least, they are interesting to study for a lesson or two all by themselves because they give us some insight into the ways in which our memory works.
- Attend to attention while learning. As cognitive psychologist Dan Willingham so thoughtfully puts it, “Memory is the residue of thought.” We remember the things we think about and we think about the things we pay attention to. Giving thought to the meaning of information is more useful, in general, than merely attending to the information itself. (Reviewing information without attending to meaning is one of the biggest mistakes kids make when they study.) As students learn new material, encourage them to connect it to previous material. Invite them to question what they’re learning about and why it matters. “Why” may be the single best question of all.
- Use recall activities to strengthen memory. Memories fade. And it’s not very likely that kids are going to run home and watch a sitcom about osmosis or the Spanish-American War. So to keep new memories alive, they’re going to need recall activities, specifically those that give them useful cues to the information they are trying to retrieve. Just remember, practice doesn’t make perfect; practice makes permanent. So thoughtful, accurate practice is usually better than faster practice with more mistakes. Slow and steady makes good grades on tests and quizzes.
- Use elaboration activities to improve long term memory. To move ideas into long term memory, we want kids to extend what they’ve learned using their own abilities. Writing is one of the easiest ways to do this. Push kids to do just a little more, to find out one more thing, to puzzle out one more part of the mystery. Above all, encourage them to draw connections, support conclusions, and develop what we might think of as their own independent understanding of the material.
One of the hardest things about learning is that human beings have a tendency to over-estimate their ability to remember things. We think we know things better than we do. This encourages us at time to not work as hard as we might in school and to not study as much as we should when we get home. In a sense, then, to really know something, we often have to feel like we’ve over-learned it.
To solve the content acquisition problem in America, we’re going to have to do some over-learning, too. There’s no reason why every teacher can’t understand and apply a small amount of information about how memory works. There’s no reason why we can’t share this information with students in ways that help them optimize their learning. There’s no reason why we can’t recognize that much of what we ask kids to do at school is attend to, understand, manipulate, and remember information—and that there are some ways of doing these things that are much more effective than others.
This may sound like a silly question, but can you remember a single time in your 13 years of K-12 schooling when someone explicitly taught you how to learn new information in Social Studies, Science, Math or any other “content area” subject?
Teachers always told us what to learn: answers to questions, information for a test, formulas for a math problem. Sometimes, most often in math, they modeled how a particular answer mght be conjured.
But then we were on our own.
I remember once looking through a chapter in a biology book and thinking, “If I really wanted to understand this information and remember it for a long time, what would I do?”
Fortunately, I never had to figure that out because working through the workbook exercises and stumbling through the occasional quiz was all I needed to do get a low “B”—an acceptable grade in my family—and I had no use for the information once the unit was over.
I was lucky, though. I had an extremely good memory; still do. But most of my friends didn’t, and I watched them struggle horribly, especially in high school, to retain basic information in class after class. They weren’t goof-offs; they came to class and paid attention; they could read. They just couldn’t remember.
And nobody ever taught them how.
The closing thing I had to “memorization” approach was what you might call “read-listen-watch-remember.” But that’s sort of like say the best way to remember something is to have a good memory; not very useful to a general audience. I was fortunate; even the most useless things seemed to stick in my head pretty well. My only “study skill” consisted of reading something over again—workable for a biology chapter, but not exactly a good idea for 800 pages of David Copperfield. (And, by the way, along with reading over notes, reading over a chapter right before a test is known to be a highly ineffective way to prepare. You end up thinking you know something because you went over it but you may not know it all because you failed to pay attention to what was most important.)
You Must Remember This
Kids today have the same challenges but there’s probably more information to learn and, with testing, more pressure for them to learn it. I notice that teachers are going heavy on the worksheets, quizzes, and reading assignments. “Read-listen-watch-remember” is probably still the best shot many kids have.
But it’s really no shot at all, and it’s far from the best shot we can give them.
Content acquisition is a big deal these days. Used to be we simply accepted, as a statistical reality, that large amounts of the information teachers transmitted to students would be lost. We were right about this. Now, however, this statistical assumption shows up in test scores so we worry about it more. But we still don’t do much about it.
It’s natural when we’re under pressure to do the same things we used to do, but to do them a little harder, a little faster, a little longer, or a little more often. Sometimes this works—for a while. But often it doesn’t. Often it just digs us deeper into the same hole. As challenging as it is, we usually have to do something different if we want to get a different result.
Never Out of Date
Before we rearrange the “tried and true” methods of American education, let’s get a sense for the scope of the problem to be solved. Prior to the era of testing, it was perfectly acceptable for schools to allow large percentages of kids to avoid learning. Almost a third of our kids drop out of high school now. A couple of generations ago, that number was probably a little higher. Think, too, about the “almost dropouts”, the kids who graduate with grade point averages below 2.0. How much do they retain from each of their classes?
Today our goals have, thankfully, shifted. We hold much higher expectations, both for what we will teach, and for what will be learned. Simply put, we expect literally millions more kids to acquire significantly more content than we used to. This is the content acquisition problem in American education—and we’re not solving it very effectively.
The Fundamental Things Apply
School may have changed a bit over the last 30 or 40 years, but kids’ brains and the information we try to cram into them probably hasn’t. There are fundamental ways most of us acquire new knowledge and those ways probably won’t change any time soon. If we want to solve the content acquisition problem, we can start getting serious about solving it by understanding how human memory works.
We could think of learning something new in school as a three-step process: understand, apply, memorize. Understanding comes first. It’s certainly possible to learn things we don’t understand, or things that have no meaning for us, but it’s harder, and we hope this isn’t the case for kids in school.
Intuitively, it seems like best ways to help kids understand things would come from the best lessons, given by the best teachers, using the best teaching techniques. That helps. But even the best teaching in the world isn’t as powerful as the knowledge kids bring with them.
Understanding something new is a lot easier if you understand something similar already. This is one reason why kids who get A’s tend to keep getting A’s and kids who get C’s tend to keep getting C’s. The A kids bring thorough knowledge from past learning opportunities to new ones. The C kids bring a partial understanding at best, and therefore have a tougher time filling in the gaps between what they know and what they need to know.
This simple idea, that prior learning is probably the greatest determiner of future learning, should guide us in much of what we do.
As Time Goes By
We tend to take our grades along with us as we go through school. Kids who get C’s and D’s are often tagged as being lazy or unintelligent. But in many cases, they just didn’t understand certain things in the past, and now they don’t understand certain things in the present. This makes learning new things so difficult that it is either exhausting (a common source of the “laziness” perception) or impossible (a common source of the “unintelligent” perception).
There are two things we’re not doing now in American education that we absolutely must do to solve the content acquisition problem: offer children a coherent curriculum and intervene with much more urgency when kids have trouble understanding important things we know they’ll need later.
Curriculum standards should help the curriculum problem, though they won’t solve it. And one very common teaching practice must change. Ironically, this is the practice of “teaching the standards”. We have tended to take the notion of standards and turned it on its head.
In classrooms all over the country, teachers proudly display the standard they are teaching at a given time. Unfortunately, we don’t teach standards, we teach students. The standard is a learning target, not a teaching target—a learning target that depends a lot more on what kids have already learned than on what want them to learn as expressed in the standard.
Often, teachers will launch into a series of standards-based lessons with little regard for where their kids are relative to the standard they are trying to master. Rather than “teaching the standards”, we must teach our students how to meet them. When gaps in prior knowledge are significant, this can be very hard for both teachers and students.
It’s Still the Same Old Story
Just as important as a coherent curriculum is the fact that kids actually learn what’s in it. We are still far too casual in most schools about kids whose performance will likely leave them unable to be successful when the information they haven’t learned is required of them again.
If a student gets a C in Algebra I, what is the likelihood that he or she will do better in Algebra II? This is not an idle musing, but a testable proposition. Every high school has grades for every class taken by every kid. Look at the distributions. Determine the probabilities. Then consider what it means to fall behind, even just a little bit, in math.
Go back even further into middle school and trace the grades within a subject from there. Even if the curricula between middle and high school are poorly coordinated, you’ll still find that results at previous grade levels (a measure of prior knowledge) are eerily predictive of results at future grade levels.
So consider this: when we “let” kids get C’s and D’s in one class, especially early in their school career, there is a significant probability that we are condemning them to years of future academic failure. Every school should know this probability for every group of students in every core course. But more importantly, they should do something about it.
We have to intervene with extra help for kids at the first signs of struggle. The intervention must be focused and it must be thorough. That is to say, we can’t intervene to help a struggling 5th grade math student and then just say, “Times up! Run along to middle school. Don’t forget your locker combination.” Interventions must be swift and successful. And everyone involved must understand the stakes.
A Case of Do or Die
Now that we understand the stakes of not knowing something, let’s think about improving kids’ understanding. Again, inspiring teachers with amazing lessons and activities go a long way to helping kids improve their understanding, but let’s consider this more generically.
All learning happens in the brain, so it’s good to keep the brain in mind (pun intended). The brain likes to learn the same thing in different ways. At a rudimentary level, you can learn a shape faster by studying it from different angles. Of course, this was handy for our ancestors if they encountered a shape (like the proverbial Saber-Toothed Tiger) more readily regardless of where it appeared in their field of vision and took appropriate action more quickly.
So one thing we need to do is give kids different ways of learning the same thing. Unfortunately, we tend not to do this. Rather, we do the opposite. We see that kids are struggling with times tables on those famous “60 problems in 60 seconds” tests and so we have the kids take more of these mile-a-minute-math tests.
We do the same thing with flash cards, worksheets, textbook chapters, and most traditional study aids—if you look at most published educational materials, you’ll notice that repetition is the over-riding theme; this is not what they brain wants; it induces boredom, which reduces attention, which increases errors, which degrades memory. As a famous physicist said, “The definition of insanity is doing the same thing over and over and expecting a different result.” This is often what we do to our kids in school.
Giving kids different ways to encounter and apply new information is vital, but it’s not the only thing we have to do. People who really know things well can reason with them and about them. That is, they can use this information to form original thoughts and they can validate that their thoughts are correct (or at least know how they might not be).
So imagine studying the origins of our nation. You study The Mayflower and The Pilgrims and learn that some Europeans came to our shores for religious freedom. But you also study Jamestown and learn that some came to make money.
If you study other groups, can you find connections between the desire for religious and economic freedom? Can you use these “themes” of our history to pluck out other examples? Have their been times when these ideas have come together? Or when they’ve conflicted? As you continue to study, will you be able to explain how these two freedoms, and our desire to live them out as fully as possible, have shaped the development of our nation?
These are just examples of deductive and inductive reasoning based on themes. But when we work with kids this way, we increase their understanding of facts through application. The “themes” serve as different ways of organizing events. American history could be reduced to names, dates, places, events, etc. We could put it into a big long list and give it to kids. But those events would be easier to remember if we developed simple applications, like themes, to reorganize them and let kids look at them from more than one perspective. We can ask kids to apply many kinds of information in many different ways. To the extent that the application involves applying individual attention, purposeful thought, and conscious reasoning, most kids will tend to understand it better.
On Thursday, I will go into the solutions for getting kids to memorize their lessons better.
As we discussed yesterday, writing is also the glue that helps students become college-ready and skilled for career achievement. Yet is one of the most-ignored aspects of school instruction. As a result, our kids are taught to write poorly and they rarely master it within school.
The solutions start with making writing a key component of academic instruction and improve teacher instruction. The Common Core standards are a good step in the right direction. But writing instruction isn’t easy, mostly because it is also individualistic.
Each student in a writing classroom must have his or her own thoughts and must express them in his or her own words. As such, teaching writing requires a degree of differentiation most teachers are not prepared to offer.
At the primary grades, kids have to develop fluency by writing about things that are familiar to them, things that happen in their lives, and stories they invent. At the upper elementary grades, we must try to split student effort between writing about their lives (to foster expression) and writing about their knowledge (to prepare them for formal writing in the content areas.)
At the upper grades, and especially in content area subjects, kids have to organize their thinking into logical arguments, a basic skill in which most fail to receive adequate amounts of explicit instruction. Forming a coherent written argument is not a trivial task. Kids need many opportunities to develop the skills.
Writing lays out an instructional challenge that we have yet to take up in most of our classrooms. The resources exist in the professional literature of teaching and in a new tradition of writing instruction that has developed over the last 25 years. These ideas, however, have not been embraced at scale.
We see the results of this in the large numbers of kids who lack sufficient writing skill even at the end of their high school careers. We see it also in the struggles of those who can barely make it through any class that requires even slight amounts of writing. Frustrated teachers, for their part, contribute to the problem by assigning less writing and lowering their expectations for quality.
The Write Stuff
Despite the rise of texting and Twitter, people still need to learn to write in real sentences, thoughtful paragraphs, and entire pieces that are clear, correct, and well-structured. We also have to give up on the misguided hope that spelling and grammar checkers will make up for a less-than-optimal writing education.
Writing isn’t just words on a page; it’s the thought that goes into those words as well. It’s not just the thoughts either; it’s the having of them, and the vetting of them, and the organizing of them that makes writing such an important activity for kids.
Kids who are less advantaged, those who don’t have computers at home or parents who are freelance journalists, are especially vulnerable to poor writing instruction. These children lose not only the opportunity to learn to write but also the opportunity to learn to think like writers, an opportunity that is not easily made up for later on in their schooling or in their lives.
Improving writing instruction in our schools requires both structural and cultural changes. Structurally, we need more time for writing and more writing assigned throughout the curriculum. Culturally, writing must reach co-equal status with reading as a vital piece of the literacy puzzle. A fully literate student must be regarded as one who both reads and writes.
Steps to Improving Writing Instruction
To move writing instruction forward, we must consider the following changes to the traditional curriculum:
- Schedule more time for writing in Language Arts. Students should receive at least 45 minutes of writing instruction every day. Ideally, this would continue through eighth grade, a change that would require the scheduling of two Language Arts periods at middle school.
- Assign more shorter pieces of writing. Writing requires the mastery of many sub-skills, some of which appear at different points in the writing process. To learn to write, then, students must produce many complete pieces of writing. To increase the number of pieces kids complete, we can reduce their length. There’s very little a student can learn from writing a 1200-word piece that can’t be learned better by writing three 400-word pieces.
- Require more writing in content area subjects. Kids would develop greater fluency in writing if they wrote more during the day. While essay writing is the staple of the Language Arts department, content area teachers can ask students to produce many short and informal types of writing likes notes, tables, timelines, descriptions, short answer and essay question responses in addition to traditional research reports and other informational writing.
- Assure that pre-service teachers are better writers prior to becoming certified. Teachers at all levels list their own feelings of inadequacy as writers as one of their main reasons for not teaching it. Until we take seriously the competence of teachers in this area, we will make little progress in improving instruction. To teach writing well, teachers need both confidence and competence. They must be confident in their skill and competent in their ability to pass that skill on to others.
- Provide at last one semester-long writing methods class to pre-service teachers. Many new teachers enter the classroom with no formal training in writing instruction at all. While ample resources exist in the professional literature to improve one’s skills, the fact that many teacher training programs offer little or no support for writing sends the message that it isn’t very important.
- Provide more training in writing to in-service teachers. Of all the areas where in-service teachers need additional training, writing is the most critical. Bearing in mind that writing cannot be taught effectively by textbook and that few teachers feel like competent writers themselves, we can imagine that in some classrooms no writing is taught because a teacher may have no way to teach it.
- Integrate reading and writing as much as possible. Writing can be easily and effectively integrated into early reading instruction. Teachers can use published texts as models for student achievement. Perhaps best of all, students can learn the mechanics of writing by studying the books they read, learning the rules of writing from correct examples, and modeling commonly used sentence structures.
- Use more writing in early reading instruction. Writing can be used to help young readers reinforce sound-symbol relationships. Kids can copy words, write the alphabet, take dictation of simple sentences, and demonstrate their level of phonemic awareness by translating sounds into letter patterns.
- Integrate essential elements of writing in Language Arts with writing across the curriculum. It may be unintuitive, but kids don’t automatically transfer skills and strategies learned in Language Arts over to other subjects. But if teachers share practice, and the vocabulary that cues kids to use it, they will. There’s no reason not to leverage Language Arts learning in other subjects. However, it takes coordination across departments, something that many schools aren’t used to.
- Give kids time in Language Arts to work on content area writing. Periodically, especially when they have big writing projects to work on, kids could benefit from having the help of their Language Arts teacher. Content area teachers don’t typically work with their students on style and mechanics. This can lead kids to think that these essential elements of written communication are valued in one class but not in others.
- Introduce students to a wider range of real-world writing forms. Teachers who are unconfident about writing tend to take the most conservative approach possible. For Language Arts teachers teaching writing, this means sticking to traditional academic assignments like character sketches and literary analysis. There’s nothing wrong with that—until kids have to write other things. Kids need explicit instruction in a wide range of forms, both academic and popular.
- Use reading to ground kids in mechanics, then teach it in the context of actual writing. It seems that even our brightest kids have trouble with punctuation, usage, and grammar. But the place to study these things is in real books not rule books. With teacher guidance, kids can see how the rules of punctuation play out on the page. They can mimic the sentence structures of successful authors. They can also improve their grammar.
- Balance self-expression and choice with formal writing that is preparatory to college and career. Throughout a student’s K-12 career, we must strive to strike a balance between writing that is assigned by teachers and writing that is chosen by the writer. The best way to be a writer, and to feel like a writer, is to have some choice over topic, length, organization, style, etc. If we want kids to become independent writers, we have to give them a little independence.
American students—even our very best—have serious challenges with written expression. This isn’t just a writing problem; it’s a thinking problem, too. Writing isn’t just another school subject; it’s a complex process that requires kids to rely on things they’ve learned in many subjects.
Writing is a lot of work, both for kids and teachers. It is, however, well worth the investment. Writing empowers kids in ways that other subjects do not. It’s a way in to the academic world and, for some kids, a way out of lives framed by unfortunate circumstances.
Reading is the core academic skill. But writing encircles at every turn; the two are always intimately related. If kids can read, they can learn just about anything. If they can write, they can share what they’ve learned with just about anyone who needs to know.
Depending on whose numbers you believe, 40 percent-to-60 percent of students entering two- and four-year colleges need at least one remedial writing course. This represents a significant percentage of our most successful kids, the ones who get past high school to some sort of post-secondary education. This makes you wonder about the writing skills of the kids who don’t go to college at all and the far too many kids who drop out before finishing high school.
Writing requires us to coordinate many different intellectual competencies in precise ways. For this reason, it is a very demanding skill to master. But it appears that we are not even approaching mastery at this time; we are barely achieving competence.
Traditionally, writing has been viewed as a narrowly-defined subject. However, it’s actually a broadly used process, one that requires kids to take raw ideas, form them into sensible bits of language, and then work those bits into polished prose.
An All-Around Player
Writing is required in almost all subject areas. Poor writing skills can take their toll across an entire report card. As pediatric neurologist Dr. Mel Levine writes in his book, The Myth of Laziness: “Writing is the largest orchestra a kid’s mind has to conduct…the very fact that writing is so complex justifies its leading role in a curriculum.”
But writing doesn’t have a leading role in our curriculum; in most schools, it’s barely an understudy. Dr. Levine feels that this robs students of valuable learning experiences from which they might otherwise benefit: The ability to “mesh multiple brain functions” , build the “brain pathways that connect diverse functions such as language, memory and motor control”, and learn the kind of “systemic thinking” and “problem solving” needed for critical thinking and career success.
Writing and reading are so intimately connected that improvements in one often lead to improvements in the other. More writing might help more kids succeed in both reading and math. Writing requires all the skills of reading (because you can’t write anything without being able to read it back) plus some of the logical skills associated with math and science. It is one of the best ways to teach critical thinking skills.
For very young children, writing improves small motor coordination. Phonics skills are also strengthened when kids write as they learn new sound-symbol correspondences. For some children, the first sentences they read are the ones they write.
For older kids, writing is typically the most common way teachers assess student learning. Written work is heavily weighted in some classes, especially at the high school level. Through note-taking in content-heavy classes, writing is also an important way learners organize and retain knowledge. It’s a powerful tool for helping kids reorganize and retain what they have learned.
Clearly, writing is a key component of college and career readiness. It’s also a powerful tool for exercising the mind. Yet we simply don’t give it the emphasis it deserves. It isn’t a priority at the national level, at the state level, among district administrators, or even among many teachers or policymakers. And our kids, especially those who may not have strong support for writing at home, pay dearly.
Why Do Kids Write So Poorly?
There are two reasons why our kids write so poorly: They don’t write very often; and they aren’t taught very well.
A Ford Foundation study conducted in the 1980s by writing expert Donald Graves found that kids wrote in school less than one day out of ten. Kids write more often than that today but not nearly enough to become sufficiently skilled.
In another Ford Foundation study, Graves asked two groups of adults — professional writers and corporate professionals who use writing as part of their work — how many teachers who taught them anything about writing that they use in the work. The average number of teachers listed in the non-professional writing group was two. The average in the professional writing group was zero. Obviously, writing instruction in the previous generation didn’t match up well with the needs of working professionals at the time.
Again, this situation is probably a little better today. But we’re still a long way from providing kids with the kind of instruction they need to meet the challenges of college and career.
Ironically, there has been an explosion in resources and support for writing during the last twenty years. Hundreds of excellent books are now available regarding successful approaches to teaching writing in schools Organizations like the National Writing Project reach thousands of teachers each year and offer a wide variety of valuable programs. But these resources are not translating into practice that is pushing its way through the classroom door.
In reading, we work hard to make sure everyone gets it. In math, we’re happy if some of our kids get it. In writing, almost no one gets it. And it doesn’t seem to bother us very much. We tend to have a fixed mindset about writing: writers are born not made, some people can do it, others can’t; instruction is irrelevant.
Lack of Training, Lack of Confidence
The most common reason Language Arts teachers give for not teaching writing very effectively is that they don’t know how. Instruction in writing methods is not a common part of pre-service teacher preparation; few teachers seek to master it on their own.
The second reason is that many Language Arts teachers will say about teaching writing is that they don’t feel like competent writers themselves. Language Arts has traditionally been focused on the acquisition of decoding, fluency, and literal comprehension at the lower grades and the appreciation of literature at the upper grades. Writing has never played a prominent role.
Teachers feel bad about both of these realities and bad feelings lead to avoidance. In a test-driven age that privileges reading and math above all else, it’s easy to rationalize not teaching writing, especially when you’re uncomfortable with it and you’ve got a great set of classic novels on the shelves that you enjoy and have taught half a dozen times.
Writing isn’t a mandated element of the No Child Left Behind Act. So most tests at the K-12 level don’t involve writing outside of expository essays. Even though writing components have been added to popular college aptitude tests like the SAT, this incentive has provided insufficient motivation for changing the way we approach writing K-12. Kids receive more writing instruction now than they used to, and they are slightly more likely to experience a competent writing teacher, but the amount and quality of instruction young writers receive is still woefully inadequate.
The Cost of Insufficient and Ineffective Instruction
Reading and writing go together. They are not two separate subjects but two complementary halves of the same process of literacy. They should be taught in a thoughtfully integrated fashion. Yet they have always been separated in our curriculum and, for the most part, they continue to be separated today
In a sense, we’re prisoners of the oldest concept in all of American education: The Three “R’s”. Readin’, writin’, and ‘rithmetic have always been considered three separate subjects. Historically, reading and writing have been separated because writing wasn’t composition; it was handwriting, spelling, and grammar.
Prior to World War II, there wasn’t much need for most children to learn to express themselves in print. Most would leave school with 8th grade educations or high school diplomas at best, and then head off to blue collar work where the ability to read might be important but where there was little need for writing.
Times have changed, of course, but our curriculum has not. While it’s possible for students to graduate high school with poor writing skills, it is impossible for those who can’t write to pursue a college preparatory high school education, to experience success at a post-secondary institution, and to rise up in the world of work beyond a certain level.
New standards from the Common Core State Standards Initiative provide us with writing examples from K-12 students in a variety of modes and forms. As the samples reach up into high school, the quality demanded of students for career and college readiness is pretty good.
We can only assume that this level of quality will be expected of students on the new tests coming in just the next few years. If writing is rigorously tested it will receive more attention in the classroom.
But writing cannot be taught successfully from a textbook or other “pre-fab” resources. Nor can it easily be taught in a defined scope and sequence. A person teaching writing has to know how to write and how to transfer that skill to students.
Writing is a highly individual subject. Even when we ask writers to start from the same place, we don’t want them all to produce the same result. This is the opposite of most school subjects. In typical content area subjects, we present students with the same information, hope they retain it, and then ask them to give it back to us in nearly identical answers on tests.
If we looked at writing this way, and asked each student to turn in the same essay, we’d call it plagiarism, not writing. Individual expression is a key component of writing success. Teaching kids how to express themselves is not something schools are well-designed to do.
In tomorrow’s continuation on writing, we will talk more about how to improve writing instruction without losing student individuality.
With math there are two kinds of people: those who think they can and those who think they can’t. The truth bares little resemblance to these extremes but if perception is reality then the notion of math competence is clearly delineated within the general population.
Which is probably why it exists in a similar state in our schools.
Nobody says this about reading, however. Some people read more rapidly than others. Some have larger vocabularies. Others read more and more challenging books. We recognize these differences, but we don’t say things like, “I just never understood reading.” Yet we say things like this all the time about math.
Reading, apparently, is an aptitude; math is an attitude. Our feelings about math may come from the fact that most of our work is either right or wrong; judgment, therefore, may play a role. By contrast, our work with reading is fuzzier.
Either way, our self-identification with academic skills probably begins as soon as we cam easily compare ourselves to others. Children’s attitudes about numbers probably form just as early on in school as their attitudes about text. The die may be cast in the early years for future math achievement just as it often is for literacy.
What’s odd here is that math is just as arbitrary, just as abstract, and just as confusing as phonics. Yet we seem to react differently to it. Reading is a universal; everyone must learn to read. Math is only for some kids, the ones who “get it”.
There’s a big difference in how we present reading and math to small children. In math, we give kids problems; in reading, we give kids answers. This may have something to do with how more kids self-identify as literate than as numerate.
Virtually all the words small children encounter in school are correctly spelled. Even the words they attempt to write on their own, if handled properly by teachers, will be corrected in short order. Much of the way kids learn to read and to spell comes from matching phonemes with correct letter patterns in correctly spelled words.
In math, however, this type of pattern matching seems to work out differently. Some kids appear unable to match meaningful patterns at all. They get off to a slow start in kindergarten and find it hard to keep up as time goes by.
As with reading, the end of third grade marks a crucial point in development. Kids who are doing well with math at this time will probably continue to do well throughout the rest of their school careers. Kids who aren’t doing will likely face years of struggle.
While math deficiency probably doesn’t lead to as many high school dropouts as reading deficiency, it makes school very hard and definitely robs kids of opportunities for post-secondary education because the standard “college track” in high school requires four years of challenging coursework typically beginning with algebra and ending with calculus.
Reading is Part of the World, Math is Part of School
As soon as kids begin to recognize words they start to see them everywhere. We live in a print rich environment; reading is part of the world and early readers make meaning from environmental print all the time.
Math, by contrast, seems hidden from view. A kid might see a sign for 49th Street but the number probably doesn’t register as a counter of some kind. Walking one block over to 48th Street and then up to 50th Street probably doesn’t help kids learn to count (though it might help them learn the word “street”).
Math is a foreign language spoken only at school. Just like the difficulties many of us have had studying foreign languages, many of us find that we either “get” them or that we don’t. Or we find, during an exchange year in France, that a few months of exposure to the real world is worth a few year’s exposure in the school world.
Another reason kids may struggle so much with math early on might be connected to how we introduce it—or how we don’t. A significant percentage of kids enter kindergarten with basic reading abilities. In math, however, many kids can count but they aren’t clear that numbers represent quantities, and they don’t know how to write them, much less add or subtract them reliably.
We enculturate kids to literacy far earlier and far more thoroughly than we enculturate them to numeracy. Reading is normal; math is not. Reading is for everyone: math is for a few, the few who are good at math. Reading is something everyone attempts and most come to understand; math is something some of us never quite feel comfortable with.
It may be that we unconsciously pass along to our children our own troubles with math, not overtly but perhaps in the lack of time we spend with our kids doing math activities relative to the amount of time we spend with them on language activities. This bias seems as prevalent in pre-schools as it is in homes.
In reading, we’re hyper-aware when kids start out behind; language deficits are often easy to spot. We don’t seem to feel the same urgency, however, about math. We should.
Of all areas in the curriculum, math is the most cumulative. Kids can make all kinds of skips and jumps through Language Arts or Social Studies, but what they need to learn in math one week depends a lot on whether they learned foundational concepts from the week before. Allowing children to fall behind and out of sequence presents not only an intellectual problem for students but also a structural problem for schools.
Bringing the Urgency of Early Reading to Math
Compared to mastering literacy, mastering numeracy by 3rd grade involves far less content. Aside from small amounts of trivial geometry, like learning the names of properties of shapes, much of what kids need to know comes down to basic whole number calculations and simple problem-solving.
Like successful decoding and fluent reading, these calculations must be completed rapidly, accurately, and all in one’s head. Here’s where we tend to let kids down. When it comes to basic whole number calculation, we do not strive for accuracy and fluency to the same degree that we strive for these things in reading.
This lack of accuracy and fluency in basic calculation is extremely costly as kids move up the grade levels. Where a single whole number calculation might comprise an entire problem in first grade, a student might need four or five such calculations to add two fractions in fourth grade and eight or ten such calculations to solve an algebraic equation.
If these calculations are slow, inaccurate, or otherwise difficult, students have limited mental bandwidth for understanding new math concepts. They may also move so slowly through problem sets, and commit so many errors, that they can’t develop accuracy and fluency at subsequent levels of development.
If we thought of whole numbers more like we think of letters of the alphabet. And if we thought of mastering basic math facts the way we think of mastering decoding, we might not strand so many kids in the upper elementary grades with trouble understanding fractions or solving simple story problems.
Fractions, percentages, decimals, probabilities, exponents, area, perimeter, volume, all of these more advanced concepts are worked through using small amounts of conceptual understanding and large amounts of rapid, accurate whole number calculation.
Kids who lack this basic ability often cannot survive the crucible of algebra. At this point, where the conceptual load increases dramatically, kids who are still wondering if 6 × 8 = 48 simply won’t have the cognitive surplus to understand variables, functions, or plotting equations on a Cartesian plane.
In the primary grades, we must bring the same urgency to math that we bring to reading. “Decoding” whole numbers and learning to calculate them “fluently” allows small children to process math in the world just like they process text in the world. Memorizing frequently used problems, just like kids memorize frequently used spelling patterns, ensures kids’ early success and gives them both the confidence and the know-how to tackle more complex concepts down the road.
To accomplish this, we need to focus on the following areas of the math curriculum during the primary years.
- Rapid, Accurate Mastery of Basic Facts. Unfortunately, many kids get off on the wrong foot here because of traditional tools like timed tests and flash cards. These approaches prejudice speed over accuracy during learning which encourages errors. Better approaches involve writing out fact families based on trios of numbers like 3-9-27. With that simple combination, a kid can quickly write out two multiplication and two division problems within a fact family without ever making a mistake. These kinds of error-free “recall” activities strengthen memory and improve rapid recovery of accurate information.
- Daily Mental Math. We all know that most of the math we do in our daily lives is done in our heads. Why not make mental math a staple of daily classroom practice? Mental math practice is valuable for many reasons. It helps kids hold more information in working memory for longer periods of time. It strengthens recall of frequently-used computations. It increases speed and fluency. It also builds confidence. Kids who can work problems quickly and accurately in their heads know they have a solid understanding of the math they’ve studied.
- Banish Calculator Use. In the early grades, there is simply nothing a child needs a calculator for. Even in middle school, calculators can probably be avoided. Until graphing calculators are needed for advanced math in high school, there’s simply no good reason to use them and many good reasons not to.
- Real-World Problem-Solving. Kids need to learn that math is all around them. They also need to learn that people solve math problems every day even when they’re not in school. So rather than focusing on contrived textbook problems, kids should experience solving math problems from their own lives. How many minutes before lunch? How many days left in school? How many chores do I need to do to buy a Nintendo? How many home runs does Alex Rodriguez need to beat Barry Bonds? If your dad’s car gets 30 miles per gallon and it has a 16-gallon tank, how far can it go? In general, these problems are far more challenging than the ones kids will find in their math books. But because kids develop them from their own life experience, they tend to be more tenacious about solving them and more willing to stretch their skills.
- Disciplined Work with Paper and Pencil. Manipulatives can be useful. Having kids draw pictures to explain their process can be helpful. Worksheets are a staple of the school experience. But none of these things is nearly as useful as basic paper and pencil work. Why give a worksheet when kids can write out all the problems themselves? Why solve a problem with manipulatives and neglect to write it down? We have many resources for helping kids express mathematical knowledge, but few are as good for learning math as a pencil, a piece of paper, and a brain.
- Early Introduction of Key Concepts From Algebra. It’s possible to introduce key concepts from algebra at a very early age, provided kids have a solid grasp of basic whole number calculation. For example, the idea of a letter representing a number can be introduced by doing problems with money in which letters represent the values of coins (3p + 2n = 13). These letters represent constants but this practice can easily be turned into working with variables (How much is x if 3 + 2x = 13?). Without needing to know how to balance both sides of an equation, kids can figure out these simple problems with basic whole number calculations. They can learn to understand the concept of a function in the same way.
If we know how important it is for every child to be a reader, why don’t we seem to know this for math? Math is an under-privileged subject. We look at our own lives and see that most of us have gotten where we’ve gotten without a lot of math. We have spreadsheets, calculators, bookkeepers, accountants, and banks to keep track of the important numbers in our lives. It’s natural to conclude that math just isn’t that important.
What we don’t consider is what it’s like to go through school with a poor understanding of math. Kids will take math almost every year they’re in school. Facing something one doesn’t understand year after year, day in and day out, diminishes the spirit. Frustrations and fatigue over math can easily bleed over into other subjects—especially science.
We also don’t see the value inherent in the process of learning math apart from the content. It’s reasonably accurate to speculate that after kids have had 10th grade geometry, most will never face another geometry proof.
Even if they never repeat the task again, however, practicing the task in school, and learning how to do it well, strengthens their ability to think logically, a skill they’ll use every day, and builds confidence for other more commonly encountered logic problems.
We also have to be honest with ourselves about the post-secondary prospects available to kids who don’t succeed in math. By the time third grade is over, it is possible to determine, in some cases, who is on track to college and who is not—a judgment that may affect dozens of opportunities for a child over the course of an academic career.
Finally, I think our entire society needs to reconsider the acceptability of “math phobia.” Far too many of our citizens dread doing math. It is tiring. It is mind-boggling. The results are often unsatisfactory and frustrating. This is understandable. But do we really need to pass this on to the next generation?
Would we ever let kids develop “reading phobia”? A few kids might, but we wouldn’t think it was OK. Telling ourselves that it’s OK if some kids don’t “get” math shouldn’t be OK either. Letting children’s math difficulties to go untended and unresolved is an easy way to shirk our responsibility and to short-change our kids.
The content of traditional math may not be important to every child. But the discipline and logical development is. So is the feeling of mastering a challenging subject, a feeling that may be just what some kids need to keep themselves moving through their education all the way to graduation and beyond.