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When homework is busywork (2009) (latimes.com)
19 points by EndXA 25 days ago | hide | past | web | favorite | 53 comments

>Vatterott questioned the quantity and the quality of assignments. If 10 math problems could demonstrate a child’s grasp of a concept, why assign 50, she asked? The solution, she said, was not to do away with homework but to clarify the reasons for assigning it.

Because repetition is important, especially in math. You don't learn something by doing it once, you must do it over and over again.

Is it really? I think repetition is dangerous, it might give you the impression that you understand something when in fact you only learned how to follow a specific formula.

What you need in math is lots of unique problems to solve, not repetition of the same equation with different constants.

Unless you are a math prodigy, drills are paramount to understanding the concepts, especially before about high school. Almost no one needs deep understanding why three and four make seven, or why long division works. But if they cannot call upon these elementary tools on demand, in an instant, they will be flummoxed in later math classes. Hence, drilling until they've nailed it.

But the problem is that we spend ~9 years on those drills which is more time than a typical engineering student spend on algebra and above. How come we can teach so much higher math in such a short amount of time? It is not possible from scratch, the reason we can do it is because some bored students played around with the drills instead of just doing them and thus learned a lot of related concepts which are cached in on in later years.

The losers are those who just spent years learning how to do the drills, getting good grades but didn't learn anything worthwhile at all. It would be good if we could catch those and correct their behavior before they had wasted 9 years on it, but as is we don't notice that most students fail to learn anything before we test them on more interesting problems in high-school.

Note: I am not saying that we shouldn't teach arithmetic, on the contrary I'd argue that arithmetic is one of the most important things to learn in math since everything else is built on top of that intuition. We just have to realize that we practice arithmetic to build intuition and not to become a human calculator.

Because it takes about 9 years for a kid with an underdeveloped brain to learn the skills and the self-discipline necessary to stick with a problem and call upon lower level math skills on demand.

And no, they don't need to understand the rationale behind things like carrying and borrowing. They just need to do it. Understanding can come later. It is much easier to drill known good practices to mastery than it is to explain why they work and teach them to mastery. These are kids whose parents are still in the "because I said so" stage of parenting.

Intuition comes from mastery. I can factor polynomials in my head; I'd be flummoxed at that task if I didn't know my times tables by heart. And I wouldn't know those if I didn't drill.

Drilling is paramount to early math education. Nothing else that's been tried works.

Let me put it this way: who is more likely to get a programming job, a bricoleur with an incorrigible need to understand HTTP, networking, etc. from first principles before he can use them, or a certified professional who has chosen a framework and practiced building apps using that framework and related best practices, while knowing nothing about how the framework actually works?

The world needs surprisingly few bricoleurs and surprisingly many people who can get shit done.

> How come we can teach so much higher math in such a short amount of time?

1. Because, higher ed students are a subset of school students who are on average better than and more interested in solving math problems.

2. Because, the mental micro-skills needed for higher math are many and diverse and learning one during school doesn't make you better at any other. You have to learn all of them, which is why initial training takes longer. Once you have most of the micro-skills trained, you can use them to cover new material faster. Micro-skills include fast mental arithmetic, application of logical tautologies (If A=>B, then NOT B=> NOT A), visualization skills, the hand-eye coordination to draw and recognize complex symbols. There are also macro-life-skills like being able to sit and listen to a teacher for an hour without getting bored.

An engineering student can learn more advanced math in a shorter time because a) they're older, b) they have mastered the elementary stuff already.

Also let's be honest, how many engineers actually learn the more advanced math. Most of them cram it into their brain for the test and then promptly forget it.

Surely the understanding is the main purpose though. The value of being able to do long division is pretty minimal; the value of understanding how division actually works and the fact that you can break down one hard problem into multiple easier sub problem is surely more important.

I've seen this helping my son with addition: he knew to carry the one, but no one had explained what that actually meant. It was just a magic series of steps that gave the right answer, with no connection to related issues of place value etc that they then teach separately.

No one needs to know long division of numbers, not anymore. Source: am mathematician who didn't learn long division until I had to do it with polynomials at university (at which point it was easy due to accumulated knowledge) and that was 20 years ago. IMHO long division of numbers has been thoroughly obsolete for decades, and shouldn't be taught except as a history lesson, like slide rules or log tables.

I don't disagree with your general point, about drilling essential skills, but I'm pretty sure long division isn't one.

I teach computer science, and you need to know long division in order to understand the % operator.

This is actually an issue I run up against because my 15 and 16 year olds ask to use a calculator for things like 23 - 7 ... And then I want them to do crazy math like 23 % 7.

You need to understand the idea of division, but not the method of long division (I understood % years before long division). Kids learn about remainders from division at primary school, and that's enough to understand %. The idea of remainders, and multiplication tables, make 23 % 7 easy by stepping through the 7 times table.

I think multiplication tables are still pretty important, but a lot of my first and second year university students are patchy on them. It doesn't bother me too much when someone learning about modulo arithmetic needs a calculator to figure out that 7 goes into 23 3 and a bit times. Then they can do 7 * 3 and figure out there's 2 left over.

Needing a calculator for 23 - 7 is concerning at 16 though!

I have taught university engineering freshmen in physics courses who routinely used a calculator to simplify fractions as simple as 4/2 or a group of four students who put down 1/3+1/2 = 2/5 and could not identify the mistake when it was pointed out to them. This is what happens when you stop the math drills in school.

Requiring math students to know the concepts and not be proficient at the mechanics is like telling a basketball player they just need to know that if they spin the ball when shooting, it is more likely to go in. That doesn't help them become better players. Shooting a spun ball 10,000 times is what does.

I didn't say anything about stopping drilling in general, just that I think long division is at this point merely a historical curiosity.

I totally agree that the number sense from drilling fundamentals at school is essential for higher maths. Addition, subtraction, multiplication, fractions, powers, etc. are all very important, as are intuitions about them that only come from practice. Fractions are something many first year university students are incredibly weak at - I've seen the same things you have.

> No one needs to know long division of numbers, not anymore.

I agree completely.

It made me sick to my stomach to be told this is the formula and here is how you must calculate it, but we won't tell you why it works even if you ask.

It is army culture. Here is your shovel, now dig.

It's also the only thing that produces proficiency at math.

This exact theory made me utterly sick of math at a very early age. The response of the school was to assign increasingly more time to math bookwork, which I had completely stalled on. The more I was forced to do it, the more it made me sick, and the slower I progressed. For me at least, having a real application for knowledge is key.

it might give you the impression that you understand something when in fact you only learned how to follow a specific formula.

Learning to follow the specific formula by rote is a good thing.

For example you really should know your multiplication table up to 10 basically by heart. And the algorithms for doing basic arithmetic on large numbers needs to be practiced until you don't have to think about them. As should the algorithms for simple algebraic manipulation.

If you try to move on without having those and similar skills under control you will never get to the understanding part of mathematics since you'll spend all your time dealing with the mechanics of arithmetic.

What you need in math is lots of unique problems to solve, not repetition of the same equation with different constants.

Repetition of the same problem with different constants is how you learn to spot patterns and develop techniques you can build upon. Like if you find that f(x)=7, f(3x)=21, f(5x)=35, f(9x)=63 then you might spot a pattern that you can explore and that will make it really easy to solve the rest of the problems.

Rote learning of multiplication tables was the most useless waste of my entire education.

Whereas once I was older (as in like 20) I actually got the hang of them from real application, and then realised my struggles with memorisation were easily solved by finding simpler combinations to do so.

You need both. You cant solve more complex problem if you are deriving quadratic formula from first principles each time. You need to "see" it quickly in order to recognize it in more complex situation. Complex problems are composed of simple problems and if simple problems are something you are figuring out each time, you got problem.

Obviously, there is also such a thing as too much repetition. But understanding of how it works alone and being able to prove the formula is not enough for ability to solve problems.

Nobody even learns how to derive any formula in high school. The teacher might show it once (if even that), but then everyone just forgets it and applies the formula like a robot. Same with chain rule, integration by substitution, or anything really. People only learn how to apply it, and essentially never the idea behind it. In my class (which was focused on math) I had to explain to someone how the derivatives relate to the speed and acceleration of a car, something that should have been understood for 2 years now. And yet, she did completely fine in classes. Fairly good grades - not the best, because she had trouble with the later tasks that required more thinking, but the first 80% of every test she aced because she just practiced doing the same thing over and over again, without actually understanding any of it.

Do I agree that this is a completely fine strategy for getting good grades? Sure. But you're gonna have a lot of catching up to do if you want to apply this knowledge to anything that isn't a text book task that was made up specifically for you without any context.

Yeah but applying stuff to anything that is not a text book is not school responsibility but everyones on his own.

It is like people blaming school for not teaching everything. There has to be some line because there is not enough time and money to teach people everything.

Bad side is that a lot of people think that everything they learn at school is enough. No one is going to teach you how to live your life. No one is going to hold your hand while applying complex math stuff because people who can do that have better things to do and they have limited time.

We did formula derivation and proves - and we exactly sucked in solving exercises. The understanding of how it works did not translated to being able to solve problems.

When I went to college and was ambitious in math class that required calculations, it sucked and I was loosing. Until someone recommended me book full of exercises and I started doing them including boring ones.

That is why I say you need both. Knowing that derivation is related to speed or that integral is area under the curve does not help to solve the integral at hand.

You mention exercises first and problems second. I completely agree on exercises. It's not that you can't solve them, but obviously you're way faster when you've solved what is essentially the same exercise 50 times before. And school (and college) tests tend to be designed in a way where 80% of the time you do the same exercise you did before and you just gotta be fast.

But for solving an actual problem, I would say that understanding is way more important. Because in actual problems you tend to spend most of your time transferring whatever information you have into solvable equations, and much less time (comparatively) solving those equations.

So maybe my problem is more that tests aren't a great representation of real life problems, and less that homework doesn't prepare you well for tests.

It is not just speed. Speed difference shows up in simple exercises. When you have to solve complex calculations and need to think hard about small ones, you wont figure big one out.

In homework we had equations and series that took hours till you figured it. On test, we had equations and series that took over 20 minutes to solve when you was smart and good. No because there were many of them, but because it was hard to figure out what to do and because it took multiple experiments to find it.

What I've seen generally is that teachers and homework teach how to do something, then reinforce that through endless dull repetition, instead of teaching the 'why', which would massively reduce the amount of reinforcement needed.

I gues the issue is that a lot of the time the teacher doesn't properly understand the subject.

Spaced repetition is important. Doing fifty problems in a row is a waste of time and almost certainly isn't any better than doing a handful in a row.

I think it depends on whether you are aiming for knowledge or speed/automatic-ness as well. Lots of problems in a row will get you speed, and then spaced repetition will help it stick long term. For really fundamental maths skills you don't want to need to actively remember it, just do it without thinking (so your thoughts can be devoted to the higher level problem you're working on).

>repetition is important

But so are the spaces between the repetitions. Would probably be more sensible to do 5 or 10 a day, for an extended number of days, than 50 all at once.

This is the perfect opportunity to test some anecdata of mine: I’m hard pressed to think of a more anti-homework audience than programmers.

An absurd percentage of programmers I met hated homework and did their best to do as little of it as possible.

Is my grouping just weird or are most programmers deeply homework averse?

We're waste-of-intellectual-time averse. Autodidacts like to learn things for the pleasure of learning, and there were very few homework assignments over the years (at least in the public US schools I attended) that were even worth the ditto paper they were printed on.

I find that those who lie at that critical intersection of high intelligence and extreme laziness tend to get into programming. Perhaps it's the appeal of machines that can do your homework for you.

Anyway, that's why they end up making webshit for Facebook and not building rockets, curing cancer, or solving tricky economic problems for the President. Those jobs go to people with the sitzfleisch to do their homework.

Can confirm, hated homework. I understood things too quickly so I never had push myself to learn, thus homework felt like a chore or a petty punishment.

This burned me later in life because “remembering what the teacher said yesterday” and “using other test questions to answer the current question” only gets you so far.

I write my tests specifically so previous test questions do not answer future test questions on the same test. It's interesting how many "A students" get B's and C's on the first few tests I give...

It will be hard to find any group of people who enjoyed doing homework.

I certainly hated and skipped as much homework I could while maintaining my grades as a kid. My math homework? Unengaging, rote, and on the face of it pointless busywork. No meaningful reward or payoff.

And this is coming from someone who ate up the concepts. I have early memories of looking up cos/sin in an encyclopedia of my own violition to figure out how to draw circles in QBASIC before I had ready access to the internet. As an adult, I've rebuilt my knowledge of matrix math, and built new mental models enabling me to spot incorrect values and understand where it's gone wrong in 3d rendering for my gamedev carreer. I'll engage with math curios on youtube.

I don't hate homework quite as much as an Adult... then again, I'm not forced to do any ;). Homework is, at least in theory, a means of practicing and solidifying skills you're learning. For some skills, I'd like to motivate myself to do that a lot more! But unlike the satisfying click when a concept falls into place, homework can just grind without payoff other than a slight increase in speed for a skill I don't yet actually use for anything... either because I don't have an immediate use case for the skill, or because I'm completely unsatisfied with the end result at my current skill level.

This can be addressed somewhat with extrinisic rewards, gamification...

_Everyone_ hates homework. Would a lot of people/children do homework if not coerced into it by teachers, parents and the threat of "losing at life"? No.

Nobody likes homework. Programmers are not any more anti-homework than anyone else.

Personally, I don' think homework is a bad thing, although students shouldn't be having to spend 2 or 3 hours a night doing it. Repetition is an important part of learning, and having some of it done as homework isn't a bad thing if it means class time can be spent in different modes of learning.

And for a kid growing up, those nights are required for development of the brain by resting. Delaying the night rest with "learning" would be ineffective and might even hurt development.

I instead put my time at midnight programming and such, as most people on the IRC channel were online at that time for me...

I mean everyone hates homework, but I was a straight A student all throughout gradeschool. I did what I was told, but in college I learned that the professors aren't always doing what is in your best interest.

I think it really depends how early children and young adults encounter and take notice of this.

I largely hated the teacher's inability to plan it? In theory, my school limited them to assigning us 30 minutes of homework a night (which was still a 3 hour max with 6 classes).

That failed to account for a tendency to all assign things at the same time. Given the normal pacing of things, essays and tests tended to appear at the same time.

If we had been employed, there would have been a panic at the spikes of overtime.

The thing is: homework can be a rather powerful tool for learning. Students works on their own. In their own environment and at their own pace. They are usually done hours to days after the lesson was teached, so it gets better remembered. They provide an easy interface for parents to help their kids. They are not bound on the time limits of school lessons. And finally they take some churn (and boredom for faster students) out of the classroom.

All in all, it would be criminally stupid to outright ban homework.

If the problem is workload, which is just too understandable, then an agreed upon effort limit seems reasonable. But that would require teachers to coordinate.

The thing is, studies have failed to show a benefit for homework as we presently do it for elementary school students; and some even have shown harm.

If it was useful, it would show a benefit.

(Of course, there reaches a point where independent practice and work is clearly useful, but perhaps it isn't in young children. My theory is, the 1/10 times where the kid is set back, frustrated, or practicing something completely wrong, which is almost inevitable at one point or another, outweighs the 9/10 times where some slightly useful practice is obtained).

I do think that things like Khan Academy may turn this around and be able to show efficacy. A kid can do work on something that gives him the basic instructions and immediate feedback, and the teacher can concentrate energy on coaching and individualized instruction. But still, until it's shown: one should be skeptical, IMO.

> The thing is: homework can be a rather powerful tool for learning.

Not for everyone. Once you've understood something, doing it 10 times won't help. Especially if you could do something more fun on the side.

I think it is just a symptom of the inability of teachers to adapt their teaching to their students. Some children will be able to learn something if it is presented some way. For the other? Just make them do homework, don't try to present things another way.

> They provide an easy interface for parents to help their kids.

Which is a good way to amplify the problems for people whom parents can't afford the time or never got the education to be able to help.

> Not for everyone.

Except for some rare counterexamples, it does.

> Once you've understood something, doing it 10 times won't help.

That is simply not true. Repitition helps to strengthen memory. Even if you understand something now, it does not necessarily mean you will still understand it tomorrow or next week. Repitition as a homework is actually a simple and efficient method to increase the likelihood that knowledge will be remembered.

> Which is a good way to amplify the problems for people whom parents can't afford the time or never got the education to be able to help.

This is also quite wrong. Do you really think it helps children that suffer from a lack of parental support if more children artificially suffer the same? Children need every little bit of support they can get.

Why not simply set aside some school time for students to work on their own? In highschool, I was lucky enough to have a study hall in the library. It was great because students had freedom to sit where they wanted, browse the books, use computers, do homework, spread materials out on a table when needed.

Some students have too many distractions at home and it may be difficult to travel to a conducive environment. Time to socialize and take part in extracurriculars is also important. The time-management and self-learning skills can be strengthened without the home part.

I think we need to separate which age groups we're talking about. What works best for a 16 year old might not be the best solution for an 8 year old.

As a parent of a younger child I think homework is a good thing because it makes it easy for me to track my daughters progress in the different subjects and gives a natural venue for me to sit with her and help her with whatever she might need help with.

I never did homework and did just fine. Only thing homework did for me was cause immense amounts of embarrassment and stress when the teacher asked us to hand it in and I hadn't done it. Even worse was writing worthless presentations, I can do them now at my job since I actually have something to say but presenting about stuff nobody cares about like you do in school is not for me.

If not homework, then what? Tests! Tests are great for learning, and the lack of external resources encourages you to be creative instead of just looking things up. So I'd say that you should have way more tests as a replacement for homework.

I find it hard to reconcile your suggestion with the fact that there's a testing overload crisis in US schools.

I think a lot of what we complain about in that vein (testing overloads) are standardized tests with significant consequences for schools, which in turn prompt intensive preparation and rigorous curriculum aimed at just excelling at the test. This is obviously not good.

(Aside: failing to measure schools probably isn't very good, either...)

I think continuous assessment and using technology to help individualize curriculum has huge potential, though. My eldest son often uses Khan Academy, and it is always measuring what he thinks he knows and what is probably next. When it raises a flag, it's time for individualized instruction.

Stress from tests depends more on what you test instead of how much. Of course if you just see it as an assessment tool instead of a teaching tool it can become a problem, but one of the best way to teach people is to test them before teaching.

In a classroom this could be done by asking the kids to write down their answers, then you discuss the answers in class, then you give your answer and then you discuss that. The important part is to teach kids that they can think on their own and often come to reasonable conclusions without any help at all. And even when they fail they now understand better the difference between their wrong answer and a correct answer.

More and more people every year turn into freelance mode of work. This is an inevitable trend, and I'm talking not only about Uber drivers. Programmers, writers, journalists, designers, many people who need a computer and a cup of coffee. Read this PDF from Zerocracy, they nailed it there: http://papers.zold.io/freelance-deck.pdf

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