Ask the grumpies: Class size research

Fiona McQuarrie asks:

Just curious whether you have any opinion on the Hoxby class size research (in Connecticut) that Gladwell discusses.

Here’s an interesting summary of class size research from Brookings.  It is worth reading if you’re interested in the topic.

There’s a lot of stuff going on with class size research (it is, in fact, the topic going through the Stock and Watson undergraduate econometrics textbook because it has been attacked through most standard econometrics methods).

A couple of important things to note about external validity for these studies:

1.  Natural experiments (and, indeed, standard experiments) are only as externally valid as the experiment itself.  That means that a study that finds an effect on kindergarteners is not going to necessarily say much about high school students.  We know a lot about class size and K-3, we don’t know so much about middle grades or higher.  This particular experiment is on 4th and 6th grade.  It argues that it gets cumulative effects of class size by cohort size, but when a cohort is expected to be a certain size, districts may plan differently by moving bad teachers to small cohorts and good teachers to larger cohorts etc.  They may do the same with aides when deciding where to make a class-size split, or they may make specific decisions about where to put the problem kids or whether to do tracking or clustering.  That kind of planning would completely wash out the effect in a way that you would not see if all classes were restricted to a certain size because of a policy change.  That kind of planning is more likely to be going on in the type of natural experiment that Hoxby examines in this study.

2.  Class size decisions are not made in isolation.  A policy asking for extra money from the federal government to reduce class size is going to provide different results than a policy that is forced to take that extra money out of another budget.  Generally, research suggests that, believe it or not, most schools are doing the best that they can with the budgets that they have.  When you give them an unfunded mandate, outcomes are hurt in ways that they wouldn’t be if you gave them a funded mandate.  Hiring more new teachers and buying portables while taking money away from other programs may end up having a negative effect even if smaller class-sizes are beneficial.  The type of natural experiment Hoxby is looking at is one of these situations– the budget isn’t changing based on class-sizes, they get the same $/kid whether they’re in a large cohort or a small cohort.  The only thing that changes is the expense from economies of scale (whether they need one teacher/classroom or two).  That’s a different situation than one in which expenses for everything else stays the same but the district gets extra money to hire more teachers and buy portables.

So, do Hoxby’s results mean that class size is unimportant?  No.  They just show that it seems to be unimportant in the type of situation that she’s studying, one in which variations in elementary school class-size are caused by variations in cohort size.  That’s why there’s a large literature on this topic– the answer is different in different situations.  We need a lot of experiments and natural experiments to get the full picture.

Side note:  Caroline Hoxby is one of my personal heroes.  If I ever decide to give up this academia thing, I’m totally going to beg her for an RA job.  She is an amazing economist.  Also, rumor has it (aka multiple of her coauthors has mentioned) that she is one of those people who sleeps 4 hours/night every night because of low sleep need.

So… a hypothetical behavior problem

Let’s say, hypothetically, that you have an amazing wonderful DC1 who has been incredibly well-behaved for all 7 years of hir short life.  (Except during brief times when ze has been under-challenged, and occasionally when hanging out with hir favorite extended family relatives.) Hypothetically this 7 year old is in 3rd grade at a private school.

And during the first half of third grade at this private school, the then-6 year old was a complete and total angel.

But something about age 7 changed things.  DC1 tries really hard to be good, but is easily distracted.  Ze doesn’t always listen to hir teachers.  Ze tries to be silly in ways that are disruptive to the class.  Ze doesn’t show hir teachers the quiet respect that ze used to just last semester.  Ze starts forgetting to hand in hir homework.  It isn’t an every day problem, but it is becoming an every week problem.  DC1 also doesn’t always listen to hir parents and even occasionally talks back(!).

Third grade is a little difficult in this school– they start having more electives and different teachers early.  It isn’t like K-2 where there was one teacher for all subjects except art, music, PE, French, and Spanish.  There’s different teachers for the different subjects, with the maximum of two overlaps.  DC1 is really only having problems with two of the teachers (or rather, two of the teachers are having problems with hir– the other teachers probably deal with the misbehavior better).  Our first thought was that maybe ze was bored and has been acting out, but the class that gets the most notes home is the one that ze always talks about and is learning the most in (the teacher seems to be teaching the advanced students at middle or high school level, which is thrilling to DC1, and also mentos and coke are involved).

Our second thought is that this particular teacher punishes kids a lot because last semester DC1 was always talking about the other kids getting into trouble in class.  At a Christmas function, the teacher had remarked to us how well behaved DC1 was compared to most of the other students.  (Not anymore, apparently.)  The next thing we heard about it, a quarter later, DC1 got a negative report card with a lengthy list of infractions.  Another teacher also commented on the report card that DC1 had been disrupting hir class more than once.  We asked DC1 about each of the items, but ze couldn’t remember any details, but did mention that ze had gotten into time out after school that day but couldn’t remember why, or even which class.

So, in theory, we sat down with DC1 and brainstormed ways to address every single one of hir infractions.  For example, DC1 was to pretend that the teacher controlled an electro-magnet keeping hir rear end in the chair.  No touching other students except at recess and in PE.  Devoting a special folder to the problem class that ze took home and to class every single day.  And so on.  All of these got rewritten into an apology letter to the teacher.  We also sent a parent note apologizing, explaining DC1’s list, and asking to be notified as soon as any future disruption occurred.  Also we sent a book on classroom management that we’d both found helpful.  A smaller apology about class disruptions went to the other teacher.  In the mornings we went over the list on the drive to school every day for a week.

And things were fine for a little while.  Then ze started forgetting homework assignments again.  Specifically ze had cryptic assignments written in hir assignment notebook (ex.  “mentos and baking soda”) and could not remember what ze was supposed to do (watch videos?  bring mentos and baking soda to class?).  So DH called the school to set up an appointment.  Instead he got a phonecall back from the teacher.  She explained that those cryptic assignments had been extra credit (since DC1 always finishes hir homework in the class), and that DC1 wasn’t so bad that a conference was necessary.

DH took DC1 in to the pedi to get hir hearing checked.  Just in case.  It was fine.

Then, a week later, a note requiring a parent signature came home.  DC1 had caused another class disruption.  After some memory prodding, ze recalled that there had been a fan on in the classroom and it was so cool talking into the fan that ze had ignored the teacher’s instructions, hadn’t gotten in hir seat, and hadn’t stopped when asked.  The teacher wanted a p/t conference and left an email address.   We signed the sheet and sent it back with DC1, but not in the special folder because ze has forgotten to bring it home.  Several days later, I noticed that the signed sheet was still in DC1’s backpack and the special folder had still not been brought home.

We also noted that, despite REPEATED reminders and warnings from us, and multiple picking out special sesame sticks treats at the grocery store for the express purpose of being brought to snack, DC1 had stopped bringing/eating afternoon snack.  The problem class in question turns out to be the last class of the day.  So more brainstorming about how to remember to pack and bring a snack (this week:  strawberries).  Because DC1 really is a pill when ze has low blood sugar.

The last note home was a week ago.  The teacher hasn’t emailed back with a time for a conference.  DC1 did hand in the paper.  Ze hasn’t gotten in trouble again, yet.

I ordered How to talk so kids will listen from the library, and it was not helpful, as apparently DH and I are already perfect parents.  (We already do what it says to do except the parts where their codicil warnings note that some kids may be super irritated by those specific suggestions.  Interestingly, I felt super irritated by their first chapter that was telling me that we did things that we do not do and felt things that I do not feel.   Ironic!)  In their illustrations of how to behave, we’re already the “Gallant” side.  (There must be parents who are more the “Goofus” side, but just reading those depictions made me cringe.)  So yay us, but completely and totally not useful for our current situation.

[Side-note:  My mother says she's a bit relieved that DC1 is getting in trouble, as ze has been preternaturally good.  She was a little worried there was something wrong.]

So, for the tl;dr set….

When your 7 year old starts acting like a 7 year old and is in a situation where the teacher can’t really handle 7 year olds acting like 7 year olds, and the 7 year old really wants to behave more like a 10 year old… How do you help that 7 year old listen more, respect hir teachers more, get distracted less, and remember to bring hir stuff places?

Any ideas?  Because we’re out of them.  Right now the best we’ve got is, “This too shall pass.”  But it would be nice to be able to do more than just wait it out.

Fractions and bases

So, we’ve been enjoying Hard Math for Elementary School (for somewhat complex definitions of “enjoying” that involve both frustration and eventual pride).

Today DC1 said, “Different bases is just like fractions.”  Explaining a little more, ze noted that when you’re doing fractions with a denominator of 8, the numerator works just like when you’re counting in base 8.

By golly, I thought, ze’s right!

In base 8 you count, 1, 2, 3, 4, 5, 6, 7, 10, 11..

When you’re counting eighths, it’s 1/8, 2/8…7/8, 1, 1 and 1/8.

Adding works the same way too… 2 + 7 in base 8 is 11.  2/8 + 7/8 is 1 and 1/8.

Multiplying won’t be the same because we tend to cancel things out on the bottom, but in a world where we didn’t do that and we didn’t allow improper fractions, I think it would be the same.  So it could be the same.

Anyhow, that’s super cool.  Yay DC1!  And yay math!

A post for Ana on 529 plans

We were poking around on medical moms blogs when we came across this comment from reader Ana. She said she wanted to just be told what to do with 529 plans because she’d hit the paradox of choice and everything was all complicated.

The post was almost a month old so  we felt silly for replying to it there, so we figured we’d reply to it here and hope that Ana saw it.

Also:  a disclaimer.  We’re not financial advisers.  Take our “advice” such as it is at your own risk.

Step 1:  Check to see if you live in one of these states that offer tax breaks for 529 contributions.

1a.  If you do, then go with your state’s 529 plan.

1b.  If you don’t, then go with Utah.  There are some other 529 plans that are now just as good as Utah’s but Utah’s has always been ranked among the top and we hope will continue to be ranked so.

Step 2:  Pick a plan company within the plan.

2a.  If Vanguard is one of your options, go with that.

2b.  If not, then look at the fees.  Pick one with low fees.

Step 3:  Pick a fund from your choices.

3a.  You want to look for terms “age-based”, “life-cycle” or “target-date”.

3b.  If there are multiple choices among these options, then it doesn’t really matter which one you pick.  They’ll be different in terms of risk and possibly fees.  You’ll again want to focus on the lowest fee plan first.  If your kids are little, more risk is better, if they’re closer to college, less risk is fine.  Don’t worry about the risk if you can’t decide– flip a coin or something.  It’s better to pick something randomly than to pick nothing at all because you’re worried about getting the “best”.

So, if you’re in a state that doesn’t give a tax advantage, you want the Utah UESP Vanguard Age-Based Aggressive Global fund.  And you’re done.  If you’re in another state we’d be happy to poke at their options for you.

Put in what you can.  We like putting some away automatically each month.  Something is better than nothing.

Are you saving for your kids’ college?  How?

Ask the Grumpies: Why are college costs increasing faster than inflation?

FGA asks:

I’d like to hear your take on Student Loans. Specifically, do you think access to student loans is enabling these costs to spiral out of control? I mean I couldn’t have gone to university without them, but I also majored in something where I knew I could pay them off when I was done. I also think it’s a little odd that this is the only type of debt that can’t be wiped clean with bankruptcy, so it’s an incentive to banks to loan as much as possible. In fact, when I was in college, they were actually trying to lend me more money than I needed.

It is well known that college costs are increasing at a rate faster than inflation.  Though this increase isn’t as large as many people think because often people compare the sticker costs of private colleges rather than the actual realized costs of college once grant-based financial aid has been applied.

I’m not sure if we’ve really nailed down the answer here.  One explanation I’ve seen links the increasing costs of college to the increasing costs of health care.  As developed nations become richer, there’s only so much more stuff we can get, so we start paying more for services like better health and education.  We’re paying more, but that’s because we’re demanding more and we’re getting more in return.

A big factor at the public university level in terms of increasing costs is the loss of government support for public education.  States are sending less money to the state universities and the universities have to make that money up.

It is true that dorms have gotten fancier and more expensive, but apparently that’s only a small share of the increased costs, and can’t explain it, as much as we’d like that to be an explanation.  In addition, Dean Dad points out that colleges keep getting unfunded mandates: such as keeping track of mad details for financial aid; more services for disabilities, returning students, veterans, students with families, etc… enrollment verification for employment; tutoring centers for the mountains of remedial students… these are great things for schools to have but are often not funded in a budget line, so money has to come from students.

We do know that the loan situation is keeping for-profit institutions in business that should not be in business.  Some of them prey on potential students and return very little for high tuition.  We definitely need better regulation there.

I don’t think we know so much about publics and non-profits.  They have different functions.  If we cut student loans, would colleges get less expensive?  Well, many of them would go out of business.  Rich people would still get degrees.   Poor people would probably still get grants, though many people wouldn’t even apply because they wouldn’t realize they could get grants, or they couldn’t afford the tiny amount they still needed to be funded without loans.  The middle class would probably be the biggest losers.  The return to a college degree would also get larger as fewer people got degrees.   Economic inequality would increase.  Productivity would go down.  Companies would have to offer more on-the-job training.  It would be the reverse of the GI bill.

Economic theory suggests that loans for college are a good thing– we lose a ton of efficiency when people would benefit economically from getting education but are credit constrained so they can’t pay for it.  Borrowing from future earnings allows people to jump into higher income brackets and is good for the economy.

However, given that we’re in a world without perfect information, and teenagers and 20-somethings can’t be trusted to have their long-term best interests in mind (ex.  spending high interest loan money on beer and fancy dorms because they don’t understand compound interest with their unsubsidized loans), caps for non-subsidized loans can still be argued for.  Some of these debts are so large that it would be incredibly difficult to pay them back given most post-college situations and the interest rates are high.  Subsidized loans don’t get you in too much trouble given their current constraints and the fact that they don’t compound while you’re not paying them off.

So in our opinion, subsidized loans probably aren’t enough.  We could probably give out a bit more than what we do.  But we wouldn’t increase that much more (and really, we’d expand the Pell grant first!)  We should look more at unsubsidized debt and reform that.  Maybe we should cap interest rates or allow bankruptcy defaults on it.  It’s generally thought that the lending agents are getting far too sweet a deal on the unsubsidized stuff, and predatory for-profit agencies are taking advantage as well.  Though, of course, we also have to think about how much we want to protect people from themselves (specifically from their past selves).  And that’s a big philosophical problem.

What are your thoughts on student loans, grumpy nation? 

Doing math multiple ways

On gifted forums, sometimes parents complain that the teacher says the kids have to do something X way, but DC gets the right answer doing it a different way.  So why should they have to do it X way when Y way is obviously working?

It’s kind of reminiscent of the argument that elementary schools no longer need to teach math because we have calculators now.

I disagree with that sentiment.  It’s important to do math multiple different ways.  There’s value in learning a different way to get the same answer.  You get a better understanding of how numbers (and later, symbols for numbers) are put together.  That leads to more accurate math, better estimates, faster calculations even without a calculator or pencil, and a greater knowledge of the possibilities of what can be done.

Even if we have computers that can do calculus, it’s still important to know how calculus works, because you know what is possible, you have ideas about what to try for things… and that’s even ignoring that math just makes you smarter.

DC1’s school just switched from Saxon math to Chicago math, but we’re doing Singapore math at home.  I’m glad ze’s learning the traditional computational methods at school (and we practice them in hir Brainquest workbook during summer and on the weekends), but I love love love that Singapore math looks at the same things in a different way.  For example, we just hit multiplication of 2 or 3 digits by a 1 digit number.  The traditional method ze’ll learn in school (and practice in brainquest) is to start with problems that don’t require any carrying.  Probably lots of x2 and x3 simple problems (23 x 2 = ?, 12 x 3 = ?), in order to cement the idea of multiplying the ones digit and then the 10s digit (and then the 100s digit another day).  Eventually they’ll introduce the concept of carrying (23 x 4 = ?).  (Then next year, the mechanics of double digit multiplication.)

The Singapore method, instead starts with some pictures.  It says, you remember when you learned multiplication how that was like having 3 rows of 4 balls?  And 3 * 4 = 12?  Well, what if, instead of each ball being worth one, that each ball is worth 10.  So you have 3 rows of 4 (10) balls.  (In pictures this is more obvious than in words.)  They’ve done the 10 ball representation previously with place value and with skip counting and x10s, so they’ve seen this idea before multiple times.  So 3 * 40 = 12 tens, and they know that 12 tens = 120.  Then they move on to 3 * 400 with the same pictorial representation.  Finally they finish up with 6 sample problems:  5*9, 5*90, 5*900, 9*5, 9*50, 9*500.  These last problems are set up in a way such that there’s pattern matching insights there for students who are good at getting insights from pattern matching, but it isn’t forced on kids who aren’t.  (At this point DC1 asked if 50*90 = 9*500 and 5*900.)  The next day moves on to 2 and 3 digit times 1 digit without carrying, but teaches it using these insights with the distributive property (13* 2 = 10*2 + 3*2), and this is not the first time they’ve seen the distributive property either– they’ve worked a lot with it with addition.  By the time Singapore math kids get to algebra a lot of tricky algebra concepts should seem pretty obvious.

I believe there’s value to being able to do math with both of these techniques.  They each provide different insights to how numbers are put together.  They each have different numerical problems for which they are the faster and easier method of solution.  In addition, the standard US method tends to be easiest when one has a pencil handy, whereas Singapore math is often best for mental math.  It isn’t that one technique is better than the other (though I confess that Singapore is more beautiful and I can see the sneaky ways it’s introducing higher level math while working with simple numeric problems, something beautiful in itself).

Being able to use multiple methods is even more valuable, however, than the sum of being able to use two individual methods.  Because of the insight given by seeing two different ways to solve the same problem, I would argue that the value of learning a second method isn’t even multiplicative, but instead exponential (or maybe factorial…)  Each new way provides a deeper insight into the magnificent world of numbers.

And, with that pattern matching turned on… if there are multiple ways to get to the right answer in math, maybe there’s multiple ways to get to a solution in other kinds of problems too.  If everyone had that particular insight, then maybe government policy wouldn’t be quite so messed up (a long shot, perhaps).

Do you think there’s a benefit to learning different ways to get the same answer?

On Flash Cards

One of the things parents of gifted kids get accused of a lot is forcing flashcards on their children.  In reality, that doesn’t happen a whole lot.  Gifted kids tend to learn to read and count without flashcards.  Many of them learn basic arithmetic and other facts just through repetition in day to day school stuff.

However, flashcards do have their place.

DC1 is ready to move on from 2nd grade math to 3rd grade.  There’s all sorts of neat new things to learn.  Unfortunately we started hitting perfectionist melt-down road-blocks.  DH finally figured out that these melt-downs were happening when multiplication was involved.  Coincidentally, DC1’s end of the year report-card came with a note to practice DC1’s multiplication facts over the summer.  (She also sent a reading fluency workbook that ze loved so much ze’s finished it, links to suggested booklists, and some handwriting practice.)

So I sat down and had a chat with DC1 about maybe learning hir times tables this summer.  At first ze was resistant, but I explained that when I was in 2nd or maybe 3rd grade, I had trouble with my times tables too and my mom had to eventually sit me down and drill me with them until I got them.  (And then I became the fastest in the class, sometimes tying with but usually beating another kid named Ahmed at Around the World, but I didn’t tell DC1 that.  Competition is out these days.)  I’ve also helped tons of people learn their times tables with flash cards, including DC1’s aunt.  So grudgingly ze agreed to try, and I promised ze’d know the times tables by the end of the summer, which was 2 months off.  Ze figured that was a good goal and was a little excited by it.

Day 1 went smoothly with DC1 giggling at already knowing all the times 0s.  Day 2 with the times 1s went similarly.  We had a few hiccups with times 2s on day 3, especially with 12.  Anytime ze didn’t know one, we’d stop and figure out how to get the answer.  Then I would put it back in the pack randomly.  If ze didn’t get it a second time, I’d put it back in the pack one card away so ze would see it again almost immediately.  We’d go through the entire deck once, removing cards ze got immediately and repeating cards ze got wrong or took time to get until the entire deck was gone through correctly and immediately.  The cards that ze didn’t know right away would show up the next day too as review.

On the times 3s, we had to take a break, but got through.  Ze started being able to figure out how to get 3*6 if ze already knew 3*5 using the techniques we’d used for times twos.

On the times 4s, we had a full blown melt-down.  Tears, daddy-intervention cuddles time, not knowing, snack breaks, the whole thing.  Horrible.  But when cajoled back, I showed hir 7*4 (a sticking point), and ze said immediately “28, but I’m just guessing”, and then 4*4 was “16 but I’m just guessing” and we explained that that’s how memorization works.  It was truly a lightbulb moment for DC1 and ze flipped through the times 4s as if ze had always known them.  Suddenly they were easy.  Ze ran off to get quizzed by DH, who was appropriately impressed.  “I’m just guessing and I get the answer,” DC1 explained.

Next day times 5s, which ze mostly knew and could easily figure out on hir own via skip counting.  A couple of the times 4s still giving trouble, but nothing major– more like 4*3 = 16 no? 12.

Times 6s were mostly unfamiliar (starting with 6*6, but reviewing 0-5*6), but we got through them without any fussing.  DC1 had gone through a mindset change, the likes of which ze probably hasn’t done since learning to ride a bike or finally being able to swim.  (Both of which happened long enough ago ze may not really remember.)  Ze realized that ze could do the seemingly impossible if ze just worked at it and practiced enough.

Next day we took a break from new numbers in order to clear out all the legacy times that could use more review.  To my surprise, after the first go-round only 6*6 remained.  DC1 was very proud of hirself and eager to do the times 7s the next day.  We also spent two days on the times 7s, with only one remaining.

And so on until we got through the times 12s.  (Honesty compels me to admit another small meltdown on the times 8s, though not as bad as the 4s.)  Then general review through all the cards, keeping the ones ze didn’t know automatically.  Then the pages of multiplication tables the teacher sent home, 5 minutes a day.

And now we can go onto more interesting math stuff.

So… flashcards.  Much maligned, but useful.  Even rote memorization can sometimes teach a real lesson about persistence and growth.

Do you have strong feelings about flash cards one way or another?

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