The Homework Paradox

Robert Pondiscio's recent article in The Atlantic argues that while upper middle-class "gifted" kids may not need homework, for children in poor or less-well-educated households, homework can be an invaluable source of intellectual stimulation.  He's responding to people who--like me--wonder why our children's reading ability grows far more in two months of summer vacation than in nine months of education (the answer: she read something like a book a day when she didn't have homework to do).  These observations lead well-meaning liberals--like myself--to question the value of giving any homework at all.  As Pondiscio rightly points out, it's not fair or reasonable to impose on other people's children conditions (or, in this case, lack of conditions) simply because those conditions make sense for our own children.  He's right about that, and also when he carefully argues

The proper debate about homework – now and always – should not be “how much” but “what kind” and “what for?”  Using homework merely to cover material there was no time for in class is less helpful, for example, than “distributed practice”: reinforcing and reviewing essential skills and knowledge teachers want students to perfect or keep in long-term memory.  Independent reading is also important.  There are many more rare and unique words even in relatively simple texts than in the conversation of college graduates.  Reading widely and with stamina is an important way to build verbal proficiency and background knowledge, important keys to mature reading comprehension.

But I still worry about homework as an educational prescription for the poor, for a few reasons.

1. First, I think the same factors that disadvantage the children Pondiscio says need high-quality homework also make it less likely that they will get it.  These children are less likely to have access to the high-quality teachers who assign the thoughtful and thought-provoking tasks that Pondiscio praises.  (For a prime example, go back to the Summer Homework Remix Challenge, or simply look at the books full of repetitive worksheets textbook publishers use to sell their series.) And they're less likely to have the academic and intellectual support at home to complete those tasks: parents who understand what a genuine science experiment is, or how to think about a complex text.  This isn't racism, or classism, but simple logic:  if the problem that homework is supposed to fix is inadequate intellectual stimulation at home, why would we expect those homes to provide adequate intellectual support for challenging tasks?
2. Second, especially in high school, kids from poor backgrounds are likely to have circumstances that make it hard to get homework done.  Many of my economically disadvantaged students babysit for younger siblings so that their parent(s) can work, or for nieces and nephews whose own parents' income is essential for the functioning of the wider family.  Others work after school--not for money to blow on an iPad, but for essentials like winter coats or even the family rent.  Even those who don't have these responsibilities often lack the most basic requirement: a calm, reasonably quiet place to work.  So asking these students to do large quantities of homework isn't always reasonable.
3. Items #1 and #2 point to a perverse Matthew Effect of the exact sort that Pondiscio wants homework to overcome:  poor students are often in circumstances that make it harder to get homework done, less likely that they'll get what they're supposed to out of homework, and more likely that they'll find homework just another unreasonable demand of an already-harsh educational system.  At my school, inability to get homework done well is often one of the leading causes--and symptoms--of a student's failure to make a real go of it at all.  So relying on homework widens the gap between the educationally/economically advantaged and the disadvantaged.
4. Finally, I'll admit it: I'm a skeptic.  Not about homework, but about middle-class arguments that essentially boil down to saying "The poor need this, but not my children."  We've done a pretty crappy job educating other people's children differently from our own, and I guess my tendency is to err--pretty far--on the other side: if I wouldn't want a school, teacher, rule, or homework policy for my child, I'm hesitant to recommend it to anyone else.

Pondiscio raises good points, and I'm not--really, I'm not--saying that we should get rid of homework for everyone.  But I am wary of saying that homework is likely to solve the problem of socio-educational inequality, especially before we have a coherent way of ensuring that the students homework is supposed to help have equal access to the kinds of high-quality assignments, and homework support structures, that we'd want our own kids to have.

Department Chairperson

Frank May hired me in 1969 to teach at Evanston Township High School. Frank was my supervisor for the first part of my career, observed my classes, advised me, taught me, encouraged me and was a role model for what mathematics teachers could accomplish.

It would be hard to find two people more different than Frank and I. Frank never raised his voice; I never lowered my voice. I continually tried to find different ways to bring mathematics to students; Frank stood at the board and lectured. Frank was careful and meticulous. No one has ever described me in those terms. Frank May was a master teacher, and I was lucky to have him as my mentor and advisor.

Frank taught me to pay attention to the details. In particular, he taught me to write complete mathematical sentences using equal signs, stating conclusions;. he took care to ensure students understood the underlying reasons for procedures and notation. He taught me the importance of using correct notation as well as language in the classroom. To this day, I can’t bring myself to describe congruent shapes as being equal.

It often strikes me, how much I learned from someone with a dramatically different personality and point of view. Part of it is that I always respected his knowledge, and part of it is that I am uncontrollably drawn to people who love mathematics.

His evaluation meetings after observing my class were more like math lessons than like criticisms of what I had done. It was clear that he had an abiding love for mathematics as well as a deep understanding of the subject and how students learned it. His quiet, soft-spoken manner allowed his beliefs and understandings to gradually sink into my brain without me actually realizing the impact he was having on my teaching.

He had a deep understanding of how topics related to each other and of why some things were difficult for students to understand. I often went to him when I had a difficult topic to teach, and he always started by agreeing with me that it was a difficult topic to teach and then uncovered two or three insights that helped me understand why students had trouble. He never told me what I should do, nor did he tell me what he always did. Instead, he made careful observations about why students found the particular topic difficult and sometimes made a suggestion or two as to what might be done to help them. He then let me figure out how to overcome student difficulties after he shed light on the nature of those difficulties. In short, he used exemplary teaching techniques to teach me how to become a better teacher. He would always check back to see if what I had done had worked better, and again he would offer an insight or two that would help me fine tune my approach, but he never insisted that I do it his way.

   At some point in my career I was asked to teach B.C. Calculus. It had been many years since I studied calculus, and I was not sure I ever really understood series. I touched base with Frank about one thing or another almost every day. He single handedly taught me how to teach Calculus.

School bureaucracy being what it is, Evanston eliminated the position of Department supervisor. Many of his fellow administrators retired or moved to other institutions. Only one went back to full time teaching, Frank.  He could have retired, but he wasn’t ready to stop teaching. He could have taken a supervisory position at a different school. Frank went back to the classroom and taught five classes a day for another ten or so years. I think he looked at the situation and determined what would be best for the students, for the school, and for him, and gracefully took a step down and finished his career doing what he did best: teaching students mathematics.  Of course he did more than that: he continued to mentor many of us even though it was no longer in his job description. He was still the person I went to when I needed math help, and he was still eager to talk math.

While he was a master teacher, he never boasted about his accomplishments, but he came close once. I complemented him on the incredibly high scores of his BC Calculus students one year. He told me that he had had the same group for pre-calc two years in a row and so was able to prepare them appropriately. I often wondered how successful students would have been if they had him for four years, or if they had someone as good as him for four years.

The reason I am writing this now is that Frank May passed away last week at the age of 89. There was no mention of his passing in the front page of The New York Times or The Chicago Tribune, because he was not a famous athlete, entertainer, or politician. All he did was  positively influence thousands of students and hundreds of teachers. Rarely a week passes when I don’t reflect on one of Frank’s insights about how people learn. He is the primary reason I have reverence for the Parallel Postulate, the Distributive Property of Multiplication over Addition, and the Differential. I learned from Frank that one can exhibit enthusiasm in a quiet, dignified manner, that it is not necessary to jump up on tables and throw things across the room to share with students how exciting mathematics is. Let this be one small instance of tribute to a great man. Thank you, Frank, for all you have done for our profession, and therefore for countless people. I am forever grateful for all that you did for me. 

My daughter's good, but don't call her smart!

This story on NPR reminded me -- again -- of how much it bothers me when we call kids smart.  In fact, calling successful kids smart is one of the worst things we can do: to (and for) them, and to (and for) other kids.

Many years ago I decided to stop using the word "smart" to describe my students, on the grounds that the word "smart" is so imprecise, using it is just an excuse for sloppy thinking.  There are a bunch of different ways a student can be "smart":

• Catches on to new ideas and techniques quickly.
• Doesn't forget things he or she has learned, even a long time ago.
• Anticipates consequences and implications of new ideas and issues.
• Sees generalizations; synthesizes readily.
• Sees new applications for already-learned facts and skills.
• Makes few, if any, mistakes in applying already-learned knowledge and skills.
• Generates new, unusual ideas.
• Is intellectually playful: likes wordplay, quasi-argumentative banter, hypotheticals.

After a year or two I backed off, but I still use lists like this when I'm writing college and scholarship recommendations: it doesn't help my students if my praise is essentially meaningless.

The NPR story took a different tack.  It compared Western and Asian parents' comments to their children, both when their children are successful, and when their children are unsuccessful.  This ground has been trodden many times -- notably by Po Bronson and Ashley Merriman, in articles and in their awesome book Nurtureshock.  I'll summarize typical comments in the chart below:

	Western Parent	Asian Parent
Successful Child	“You’re so smart!”	“You worked so hard!”
Unsuccessful Child	“I wasn’t good at math either!”	“You must work harder!”

There are two major takeaways from an educational-policy perspective:

• Teaching kids that success is a result of being smart sets them up for failure.  When these kids encounter genuine struggle, they often conclude that they are simply not talented enough to be successful.
• Teaching kids that success is a result of working hard sets them up for further success, because attributing their success to the only factor that an individual can control (as opposed to talent, luck, and ease of task).

But I'd add a third issue--one that I've encountered with my students and my own child, and especially with talented girls who work hard.  These students are proud of their hard work, and when someone says "You're so smart" or "You're a genius," they don't experience those comments as praise.  Instead, they feel that their hard work has been devalued, because they've just been told, "Look, you're not successful because of anything you chose to do -- you're successful because you were born that way."  (The variation on this that drives my daughter bananas is "Of course you're good at math--your dad's a math teacher"--which is why she never lets me actually teach her math.)

So telling successful kids they're smart is bad for at least five reasons:

1. It tells successful kids that they shouldn't get credit for their success, because that success isn't due to anything they actually did. So it's insulting.
2. It sets successful kids up for failure, because it doesn't give them anything to fall back on when they encounter challenging tasks.
3. It tells unsuccessful kids that they can't do anything to become successful, because the successful kids are the ones who are already smart.  So it's implicitly insulting to unsuccessful kids:  you're not doing well because you're dumb.
4. It sets unsuccessful kids up for continued failure, because--in this worldview--there's nothing they can do to become smarter.
5. It's an inexcusably-sloppy way for a teacher to describe a student, because it doesn't say anything about what the student actually does.

So please do recognize your successful students' (and children's) achievements--just don't call them smart.

Thoughts on Collaboration

It's the first week of school, and I put in some time rewriting my course policies to articulate why, when, and how to collaborate on problem sets.  This issue is particularly crucial in my advanced Geometry class, where students solve college-level problems, not just exercises. Feel free to use some version of this in your own classes, and -- even more important -- to let me know what you think!
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Collaboration, Research, and Hard Problems

Contrary to stereotype, mathematics is best done as part of a community—not alone in a study.  I hope and expect that students will frequently discuss problems, ideas, and solutions in and out of class.  Some guidelines:

·         Make sure that when you are “working with” someone else, you are both really working and contributing.  Contributions can take many forms—clarifying, questioning, justifying, and restating, to name a few—not just coming up with “the idea”, but each of you should leave the collaboration feeling good about what you, and the other person, contributed to the session.

·         One test for how much you did in solving a problem is whether you can reconstruct the entire solution on your own afterwards.  If you need to look at your notes extensively, or get lost in the middle, you probably should have collaborated more actively.

·         One time when it is useful to be alone in your study is to check for your own understanding.  I recommend that students start problem sets by themselves, to see what they can accomplish and what ideas they can generate individually before working with other students.  I also recommend that students finish and write up problem sets by themselves, to make sure that they really understand the work they and their fellow students did together.

·         Give credit generously: it doesn’t subtract from the points you get (and in the real world of “karma points”, giving credit almost always adds to your own).  Write “Wolfgang suggested this auxiliary line” or “Credit to Seraphina for spotting the similar triangles.”  Taking ideas from other people without attribution is plagiarism; taking ideas with attribution is research.

·         Finally, unless specified in a particular project or assignment instruction, please DO NOT do research on the web (or in books, if you still remember those).  The essence of this course is learning to reason mathematically by solving problems and thinking through solutions, not regurgitating theorems and ideas you learned somewhere else.    

Summer Homework Remix Challenge

So I'm just getting back from three weeks teaching at HCSSiM (which in case you don't know about it, is an absolutely awesome summer math program for high school students), and one thing that really leapt out at me was the number of students trying to cram in several hours of summer homework on top of (literally) 45+ hours of mathematics each week.  (You read that right: four hours of class each morning, quasi-optional lecture at 5pm, three hours of problem session from 7:30-10:30pm.)

This situation is appalling.

First, the kinds of high-performing kids who go to HCSSiM are working harder than ever during the year; they need a break from regular work.  Second, the work that gets sent home is--in general--the worst sort of homework you can imagine.  A sampling:

• Outline n chapters of a bio/history/government textbook, where n ≥ 3. My experience is that few kids, if any, are taught how to outline, so these wind up being lists of section headings.  Teachers typically don't even read or give feedback on this work.  I wonder, too: if a kid can get "enough" out of this type of learning experience, what do teachers think the are adding in the actual classroom?
• Write out, by hand, 100 vocabulary words and definitions.  (My colleague and friend Erica, soon to be a teacher in a Massachusetts middle school, asked "If the work is so low-level that it's impossible to tell whether one kid has copied another's assignment, why would you even assign it?"
• Read a 400 page, mostly stream-of-consciousness novel chosen by the teacher, with little or no guidance.
• Fill out dozens of worksheets practicing math facts, or vocabulary from a foreign langauge, or ...

Assignments like these replicate the worst parts of the school experience--repetitive, low-level work with little attention to context or purpose besides "get it done"--without any of the other experiences that can make going to school worthwhile.  What's more, they put this school-sucked-dry experience into the summer, which kids typically enjoy.

Why do kids who enjoy learning prefer summer to school?  I can think of three reasons:

1. During the summer, kids can choose what they will do and when they can do it.
   
   Of course, choice is more satisfying than constraint.  But study after study has shown that giving kids choices about what learning activities they do increases student engagement and the activities' effectiveness.  So taking the choice out of summer learning activities is a double-whammy.
2. During the summer, kids do things that they find relevant.
   
   In actual summer academic programs--like the ones my kids and my friends' kids do--the learning activities are focused on things kids actually want to know about.  And kids don't choose to do things that they find irrelevant.
3. During the summer, kids do things that are challenging.
   
   Have you seen a kid spend hours practicing a skateboard move, or throwing a football, or playing a videogame?  Kids don't do things they find easy--they find things that are at a "can't-quite-do-it-yet" level, and when they've mastered something, they move on.  

By contrast, the summer homework assignments listed above involve no choice, make little attempt to be relevant to kids' own interests, current issues, or anything else of interest, and are very much one-size-fits-all (in fact, because no teacher is available, they're usually way too easy--which reinforces the idea that they're mostly "get-it-done" work, not an opportunity to actually learn anything).

So here's my remix challenge, in three parts.

I.  Find an actual summer homework assignment passed out to kids in grades 6-12.
II.  Rework it to fit the three criteria--choice, relevance, adaptable challenge.
III. Post it here, in the comments, or via email to me at pjkarafiol@gmail.com.

Three guidelines:

• Obviously, the made-over assignment must address many of the same objectives and issues as the original.
• Obviously, the assignment must be one that students can complete, with some reasonable degree of success, on their own.  The assignment doesn't have to be easy, but (e.g.) feedback might be built-in or easy to obtain.
• Third, the assignment shouldn't take more than 4-5 hours of work, 8 tops.  Really, guys, this is the summer.  If you want the kids to attend summer school, teach an actual class.

As extra credit, ask a student to suggest a summer homework "makeover" of their own.

Here are two to get you going:

1.  For the AP Biology Chapter 1 assignment on basic physics and chemistry: read two articles from one of the following periodicals (Scientific American, New York Times Science Tuesday, Discover Magazine) written within the last year about a discovery or problem in biology.  For each, identify what chemical or physical processes are described in the article, and be ready to give a short (3-5) minute presentation on the underlying chemistry or physics described.

2.  For the vocabulary list -- given the same list of words, find instances of 20 of these words in recent writing (last five years) on the web, in periodicals, or published books.  For each, give the surrounding paragraph, explain what the word means in context, and write a sentence or two evaluating whether the author should have chosen a less-esoteric word (with a suggestion).

Happy end of summer!

PS: Full Disclosure -- I havea a summer assignment of my own, but it involves choice, is not onerous, and shouldn't take more than 3-4 hours to complete.  Here it is:  http://www.wpcp.org/StudentLife/SummerAssignments.aspx

Quiet

I suggest adding the book Quiet by Susan Cain to your summer reading list.

I read it at the suggestion of a former student. It is well written, researched, and short.

It is not specifically about education but it is about assumptions our culture makes about quiet people. We all have quiet people in our classrooms. She challenged many of the assumptions that I had made about quiet people and forced me to rethink some of my long held beliefs about structuring my classes. She raises some interesting and profound ideas about things like group work, whole class instruction, brainstorming, problem solving, calling on students, and the role each student plays in the dynamic of the classroom.

I also found it insightful with regard to interactions with friends, neighbors and colleagues.

The Four Most Important Words in Teaching

My co-blogger, John, often mentions that a crucial part of his practice is standing at the door, greeting students as they come in.  Although this practice started as a way to keep order in the halls, for him it's persisted because it gives him an opportunity to check in with students individually.  I don't have anything like that kind of discipline, but I have to agree that the 3-5 second "touch" is incredibly important, wherever and however you make it happen.  So my candidate for the four most important words is "How are you doing?"

As a math teacher, I don't "get" the opportunity to talk with my students about their personal lives; I have to make that opportunity.  But I think that the kids who most need to talk are often the most fearful of actually opening up; the biggest secrets are just below the surface.  "How are you doing?" is a low-stakes way of saying "I'm interested, and if you want to talk, we can."  When a student has already opened up to me, "how are you doing?" is really a statement: "I know it's been rough, and I'm concerned."  It doesn't demand an extended exchange.  "Not so great thanks" -- "I'm sorry; find me at lunch if you want to talk" is almost always as long as it gets: five to ten seconds.

It's easy to misjudge the amount of effort needed to care for our students' social and emotional health on the basis of that very small number of students whose drama is like a riptide, dragging in friend after friend and teacher after teacher.  But most students aren't like that.  And I find that especially when a student is in crisis, or just coming out of one, regularly asking "How are you doing?" makes a huge impact--probably more than an hour-long "session" would, at least with this nonskilled practitioner.

This impact was demonstrated to me by an unusual coincidence during this last week of school.  I said goodbye to two boys who had been going through rough times this year (one just for the summer, one who is graduating); both were practically in tears.  One wrote in my yearbook that my checking in with him had made it possible for him to finish school and graduate, and he meant it.  Literally--I promise you--no conversation with this student had lasted more than five minutes.  Then our graduation speaker was an alum who, five years ago, had told his entire class and their parents (he was the graduation speaker at his own graduation, too) that my "How are you?"'s had been a lifeline during difficult times.  (And again, at the time, I was bowled over:  none of these conversations lasted more than 3 minutes, and only a few were even half that long.)

When I first started teaching, I envisioned long, soulful one-on-ones with students about all the bumps and pitfalls of adolescence, of which I'd had my own share.  But I've come to realize that most students don't want those conversations most of the time, and that they can't be forced.  Two of my mentors, at Andover, pointed me in the right direction.  Craig Thorn (beloved house counselor and English department chair) told me his secret the day I arrived: just be around, in their rooms or wherever, so that they see you and know you and talk around you.  Doug Kuhlmann, who was the math department chair, said something like this: when you ask a student a personal question, you need to be aware of your own stake in the answer.  What he meant, roughly, was that when you ask a student a personal question, you need to be aware of your own reasons:  are you asking because talking will help the student, or for the emotional buzz of reinforcing your relationship with the student, or to validate your own self-image as "the teacher who cares." It's easy, he warned, to think of yourself as asking for the student's benefit, when really it's about you, which is problematic:  as an authority figure, you're in a position to demand a response, even when you shouldn't. 

"How are you doing?" largely avoids this pitfall: asked in the hallway, or when you're checking in homework, or outside the lunchroom, it doesn't demand much, if anything, of the student.  Just saying "Okay" is enough--in fact, it's standard protocol.  The first couple of times, I might follow up with "Really?  Doing okay?" -- to indicate that I am really asking, not just following the script.  But then it's up to the student.  So "How are you doing?" is empowering, not disempowering: it says "Remember, I'm here if you need me, but I'm not going to push it if you don't."  And it's a "touch" I can make in front of other students, who may or may not know the backstory.

With 140 students per teacher, it's easy to fret about how little we can do.  But what I take away is that it only takes a little.  The key is -- to circle back to John -- to keep asking, to make it a regular routine.  The kids who thank me for it later remember this:  I asked them every time.  And that regularity--and the care behind it--mean more than you'd expect.