Ask the grumpies: Time spent on housework by child status and gender

Laura Vanderkam asks:

Looking at the ATUS, how does having a kid affect how much time people devote to housework? Is this different for men and women? There are lots of different stories one could come up with: everyone does more housework because there’s more housework to be done. Everyone does less housework because there’s less available time to do it in. Mom does more and dad does less because they wind up conforming to traditional gender roles (and maybe mom winds up working less for pay, and so is the one around to do it). Maybe mom does a lot more and dad does a little more. So I’d love to know what the numbers actually show.

Lalalalala, Stata.  Ok, so I’m using the 2002-2012 ATUS here because I’m too lazy to download the 2013 one even though it’s now available.  In a bit I’ll show how things have changed if you limit to just 2011 and 2012.

How does having a kid affect how much time people devote to housework:

. ttest  bls_hhact_hwork, by(hh_child)

Two-sample t test with equal variances
——————————————————————————
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
———+——————————————————————–
No |   72370     39.6372    .3054511    82.17145    39.03851    40.23588
Yes |   64590    44.33705    .3295443    83.75224    43.69114    44.98296
———+——————————————————————–
combined |  136960    41.85364    .2241497    82.95358    41.41431    42.29297
———+——————————————————————–
diff |           -4.699851    .4488466               -5.579582    -3.82012
——————————————————————————
diff = mean(No) – mean(Yes)                                   t = -10.4710
Ho: diff = 0                                     degrees of freedom =   136958

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

Urgh, I can’t figure out how to make this pretty without making it a picture and I’m too lazy to do that (in word you make it courier new 9 or smaller and it’s all pretty).  Anyhow, this is saying that people with kids spend 44.33 minutes on housework and people without kids spend 39.63 minutes on housework during the reference day.  This is a difference of 4.7 minutes.  This difference (two-tailed is the one in the middle, since we didn’t have a prior about which direction it should go) is significant at the 5% level (also at the .0001% level).  So kids create housework.  (Which is no surprise, but the surprise is that people spend time doing housework– childcare is measured under a different variable.)

Note that theologyandgeometry reminded me that I’m supposed to be using sampling weights when I do this, and they do matter somewhat in the regression results.  Unfortunately, ttest doesn’t take weights.   The kludge is a pain in the rear in Stata 11 (which is what I have on my home computer), so I apologize, but you’re getting the unweighted results.

Next:  Is this different for men and women?

Let’s say I want to answer this question in one fell swoop.  I would do a regression with an interaction.  It would look something like this:

unweighted:
Housework_min = 18.96 + 37.47*Female – 1.04*hh_child + 8.21*(Femalehh_child)

I can’t get the standard errors to line up in wordpress, but the se for the intercept is 0.31, se for Female is 0.57, se for hh_child is 0.44, se for the interaction term is 0.82.   To see whether these coefficients are significant, you take the coeff and divide by the standard error to get the p-value.  If that number is bigger than 1.96, it is significant at the 5% level.  These coefficients are all significant.

weighted to take into account sampling weights:
Housework_min = 15.47 + 38.50*Female – 0.67*hh_child + 4.06*(Femalehh_child)

Here everything is significant at the 1% level except the main effect on hh_child is no longer significant even at the 10% level, with a se of 0.49.  So weights do matter.  Thanks for reminding me, theologyandgeometry!

Ok, so what does this regression *mean*?  Plug and chug, my dear Watson, plug and chug.

The way the dataset is coded, if you’re female, Female is coded as 1.  If you’re not female, then it is coded as 0 (it doesn’t allow for female and not female at the same time).  Similarly, hh_child is one if you have a child under age 18 in the household and 0 if you don’t.

So to answer: “how does having a kid affect how much time people devote to housework?” You would take [18.96 + 37.47*Female – 1.04*hh_child + 8.21*(Femalehh_child)] and plug in 1 for hh_child and then plug in 0 for hh_child.

[18.96 + 37.47*Female – 1.04 + 8.21*(Female)] – [18.96 + 37.47*Female – 0 + 0)]

The 18.96 drops out, the 37.47 drops out, and you’re left with -1.04 + 8.21*Female.

For women:  [-1.04 + 8.21*1] => having kids correlates with 7.17 minutes more housework

For men:  [-1.04 + 0]  => having kids correlates with 1.04 minutes less of housework

The savvy econometrician will note here that we’ve seen these numbers before– that -1.04 is the coefficient for the hh_child variable, and the 7.17 is what you get if you add that coefficient to the interaction term.

Doing the weighted version, you get:

For women: [-0.67+4.06*1] = having kids correlates with 3.39 minutes more housework

For men:  [-0.67+0] => having kids correlates with 0.67 minutes less of housework

Now, one concern is that there are a lot more single parent households with women heads than with men.  Let’s see what happens when we limit to married households with both spouses present only.

ttest  bls_hhact_hwork if married==1, by(hh_child)

Two-sample t test with equal variances
——————————————————————————
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
———+——————————————————————–
0. No |   27875    40.94371    .5036533    84.08898    39.95653     41.9309
1. Yes |   40403    46.88803    .4207222    84.56725     46.0634    47.71265
———+——————————————————————–
combined |   68278    44.46122    .3230849    84.42228    43.82797    45.09446
———+——————————————————————–
diff |           -5.944315    .6569407               -7.231918   -4.656712
——————————————————————————
diff = mean(0. No) – mean(1. Yes)                             t =  -9.0485
Ho: diff = 0                                     degrees of freedom =    68276

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

Having a child makes time spent on housework go up even more for two parent households than it does for everybody (about 6 minutes).  The difference is about one minute for unmarried households.  Maybe dads make a lot of mess.  More likely single moms don’t have time to do additional household chores while single people do have more time.  (Doing the interaction, this difference in the effect of having children between married and single couples is significant.)

Limiting to married couples only:

Housework_min = 14.23 + 51.44*Female +4.14*hh_child + 2.31*(Femalehh_child)

The interaction term is only marginally significant, and note a sign change on the hh_child coefficient.  Having a child affects married people by 4.14 +2.31*female.  Married men’s housework goes up by 4.14 minutes after having a child, but married women’s goes up by 6.45 minutes.

When you do it weighted, everything is significant at the 5% level.

Housework_min = 13.16+ 50.95*Female +2.51*hh_child + 3.39*(Femalehh_child)

Having a child affects married people by 2.51 + 3.39*female.  Married men’s housework goes up by 2.51 minutes after having a child, but a married woman’s goes up by 5.9 minutes.

Limiting to unmarried people only:

Housework_min = 22.29 + 28.89*Female – 5.41*hh_child + 6.34*(Femalehh_child)

All coefficients are significant.  Having a child affects unmarried people by -5.41 + 6.34*female.  Unmarried men’s housework goes down by 5.41 minutes and Unmarried women’s goes up by 6.34 minutes.  (Note that there are ~8,000 single men with kids and 16,000 single women with kids here, though I’m including married people whose spouses are absent in the “not married” category because we’re talking about housework.  It is more standard to include them in the married category when you’re looking at outcomes we care about like child well-being.)

Weighting the unmarried people regression:

Housework_min = 17.68 + 26.93*Female – 4.36*hh_child + 1.60*(Femalehh_child)

Here the interaction term is no longer significant, which suggests there isn’t a difference by gender in terms how how having a child affects housework.  Makes me wonder who the sampling frame is over- or under- sampling!  Here having a child affects unmarried people by -4.36 + 1.60*female.  Unmarried men’s housework goes down by 4.36 minutes when having a child and unmarried women’s also goes down (!) by 2.76 minutes.

There are other cuts that can be made… by age, by race, by ethnicity, by education, by work status etc.

I’m going to look now at the most recent years, 2011 and 2012.  Men are supposed to be more equal partners these days so…

. ttest  bls_hhact_hwork if year>2010, by(hh_child)

Two-sample t test with equal variances
——————————————————————————
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
———+——————————————————————–
0. No |   13862    38.72681     .700486    82.47311    37.35376    40.09985
1. Yes |   11060    44.37197    .8187207    86.10202    42.76713    45.97681
———+——————————————————————–
combined |   24922    41.23204    .5330305    84.14795    40.18727    42.27682
———+——————————————————————–
diff |           -5.645164    1.072289               -7.746914   -3.543414
——————————————————————————
diff = mean(0. No) – mean(1. Yes)                             t =  -5.2646
Ho: diff = 0                                     degrees of freedom =    24920

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

Having a child still increases the amount of housework done by around 5.6 minutes (so more than for the 10-year period).

Housework_min = 20.34 + 33.75*Female – 0.42*hh_child + 8.68*(Femalehh_child)

Here the coefficient on hh_child is nowhere near significant.  The interaction term is still significant, but having a child has no significant effect on minutes worked by itself, only as it interacts with gender.  Men no longer work less when they have a child.  But women still work more!  Results are pretty similar with the weights.

Limiting to married only provides:

Housework_min = 16.35 + 46.28*Female + 4.04*hh_child + 2.50*(Femalehh_child)

Now hh_child is significant, but the interaction term is no longer significant!  Everyone in a married couple works 4 min more (you could argue that women work 6 min more, but that difference is not significant) once they have children.  Again the weights matter, because with them, you get:

Housework_min = 15.06 + 44.79*Female + 1.55*hh_child + 6.22*(Femalehh_child)

With the weights, hh_child is back to being no longer significant and the interaction term is significant at the 10% level.   Married women work marginally significantly more than married women do upon birth of a child.

Limiting to the unmarried (and those with absent spouses) provides:

Housework_min = 22.77 + 27.25*Female – 3.89*hh_child + 7.72*(Femalehh_child)

These are all significant.  Having a child decreases the amount of housework for unmarried men by 4 minutes, but increases it for unmarried women by around 4 minutes.  (These results hold if I drop people who are married with spouse absent, so it’s not like truckers are driving this result.)

Putting the weights in again changes things:

Housework_min =18.15 + 26.06*Female – 3.04*hh_child + 1.41*(Femalehh_child)

Female is significant (as is the constant) but the other terms are not.  This argues that there’s really no difference once you have a kid in how much housework you do if unmarried, either by gender or not.  It could be that there’s not enough unmarried fathers in the sample to say much of anything once the weights are added (perhaps they over-sample single dads, who knows!  Well, presumably ATUS knows.)  Also I should note that their sampling weights seem to be based on 2006 methodology, so if things have changed, they could be introducing measurement error which might tend to bias towards not finding anything.

All in all, there’s less significance with only the last two years of the data, but the story is still very similar.

So, to summarize:  Having kids increases the amount of housework that people do each day by 5-6 minutes on average, but about 1 minute for single-parent households.  On average, having kids means more housework for women and less housework for men.  However, in dual-parent married households with both spouses present, having a child increases rather than decreases the amount of time spent on housework for men.  In households with only one parent present, women do more housework and men do less (though with weighting it seems they both do less).  Potential reasons for this difference could be that men outsource the housework or that they’re more likely to substitute childcare for housework (or that they put their kids to work and women don’t!).

Now, the variable I used above assumes marriage.  It turns out there’s a variable in the ATUS that also gets at whether or not there’s an unmarried partner in the household.

tab spousepres

Spouse or unmarried partner in |
household |      Freq.     Percent        Cum.
—————————————-+———————————–
1. Spouse present |     69,359       50.64       50.64
2. Unmarried partner present |      4,224        3.08       53.73
3. No spouse or unmarried partner prese |     63,377       46.27      100.00
—————————————-+———————————–
Total |    136,960      100.00

You would think that this shouldn’t change the results much.  Except it does.
. ttest  bls_hhact_hwork if spousepres==1 | spousepres==2, by(hh_child)
Two-sample t test with equal variances
——————————————————————————
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
———+——————————————————————–

0. No |   30366    40.27857    .4782439    83.33803    39.34119    41.21595
1. Yes |   43217     46.9683    .4089027    85.00556    46.16684    47.76976
———+——————————————————————–
combined |   73583     44.2076    .3110836    84.38513    43.59788    44.81733
———+——————————————————————–
diff |           -6.689731    .6314013               -7.927276   -5.452187
——————————————————————————
diff = mean(0. No) – mean(1. Yes)                             t = -10.5951
Ho: diff = 0                                     degrees of freedom =    73581

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

Having a child when you have a partner in the house increases housework by 6.7 min.

For cohabiters it’s an increase of 12 min!

. ttest  bls_hhact_hwork if spousepres==2, by(hh_child)

Two-sample t test with equal variances
——————————————————————————
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
———+——————————————————————–

0. No |    2112    33.51657    1.586618    72.91542    30.40507    36.62807
1. Yes |    2112    46.34943    1.895052    87.08996    42.63307     50.0658
———+——————————————————————–
combined |    4224      39.933    1.239569    80.56248    37.50279    42.36321
———+——————————————————————–
diff |           -12.83286    2.471554               -17.67841   -7.987314
——————————————————————————
diff = mean(0. No) – mean(1. Yes)                             t =  -5.1922
Ho: diff = 0                                     degrees of freedom =     4222

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

Married people spouse present:

Housework_min = 14.08 + 51.56*Female + 4.35*hh_child + 2.43*(Femalehh_child)

Everything significant at the 5% level.  (Results are similar with weighting)

Cohabiters:
Housework_min = 19.42 + 29.04*Female + 2.01*hh_child + 14.56*(Femalehh_child)
(results with weighting are pretty similar, with an even bigger interactive effect)

hh_child is not significant.  Note how much less housework cohabiting women do compared to married women!  (29.04 vs 51.56)  And look how much bigger that interaction of having a child is for cohabiting women– a child only adds 2.43 min (plus the 4.35 main effect that it adds to both parents) to married women, but it adds a full 14.56 minutes to cohabiting women (18.5 minutes in the weighted regression).  The story here is that cohabiters did less work and then were forced to be more traditional once a baby arrived.  With married women we’re probably seeing a lot of housewives increasing that female coeff.  There could also be differences in hiring out help between people who cohabit and people who are in more traditional marriages.  Or in how big the house/apartment is.  There are a lot of controls that could be put into these regressions (age, labor force status, etc.) if one wanted to try to get at causation instead of just the relationships.

Grumpy nation, how does this square with your experience, if applicable? And isn’t Stata awesome?

How would you do the division?

I was recently reading the comments section of an advice column (linked from that bad advice) and read this:

I figured this out after doing an activity in a personality styles class where I got people into groups of 10 and handed out a bag with 8 mini candy bars. I told them that the store didn’t have enough so that they’ll need to figure out how to divide them up.

It was fascinating to me as I watched class after class do the following: Group A (the group that was more people-focused in their preferences) would often try to solve this problem by first trying to figure out if anyone cannot eat candy (medical reasons or diet); then when a few dropped out that way, the others would often dither about and defer to others before they would take their own. I observed this type of personality continually considering individual circumstances in their quest for fairly dividing up the candy.

Group B, on the other hand (and these were the people that identified more as task-focused individuals), almost always used math or some really black and white tool to equally divide up the candy. There was no discussion about individual preferences, individual circumstances – they just figured everyone got the same side sliver as everyone else. End of story. It was amazing to watch.

I definitely fit into Group B here.  I think of the candy as an endowment, and they should be allowed to exchange their piece for goodwill or money or whatever it is they want, even if they don’t want to eat the candy themselves.  I’m not sure you get the same goodwill for saying in advance that you can’t have the candy because you’re diabetic as you do for giving someone else your piece.

Plus I’m not scared of doing things like figuring out how much 8/10 is (though cutting into fifths is a PITA).  All we need to make sure we have is a good clean knife and something to cut on.  I figure chocolate probably isn’t worth doing the extended fair division problem with.  (The one where one person cuts and the other person chooses the piece.  Actually, I think the process might be that 9 of the people make cuts, then the 1oth person chooses, then the 9th, and so on until the last person gets the dregs.  But that still sounds like too much hassle.)

Of course, it is possible that the person who drops the number from 9 to 8 gets everyone’s gratitude for not actually having to do the math or the cutting, even if the person who brings the number down from 10 to 9 isn’t worth much.

#2 notes:  I guess it would depend on context.  Are these people strangers? [So cultural expectations regarding first meetings are important!]  Are they going to have to work together again?  [So this is a repeated game!]

#1 agrees: I just assumed it was a class that was going to meet all semester.  And maybe you don’t want to be the person who pretends not to like chocolate when you really do because then you’re going to be a doormat the rest of the semester.  People take advantage of easy-going folks.  Better to show you’re giving a sacrifice, or a one-time sacrifice.

So, which type are you?

Sometimes you have to get the wrong answer first to get the right one

A good way to start a hard math problem is by playing around with it.  Poking at it.  Trying things to see what does and doesn’t work and to figure out why that is.

For a certain type of math problems, it’s helpful to just guess and then analyze why that guess isn’t right.

I don’t know if you’ve ever played the game Mastermind, but Mastermind is exactly this idea.  One player hides 4 pin colors, and the second player has to guess what the colors are and where they’re placed.  Each turn player two is given information on how much ze got wrong and how wrong it was.  The only way to start is with a completely blind guess.  If you guess right on the first try, the game isn’t very much fun.  That means you won by luck and not by being able to actually play the game.

DC1 had never heard of such a thing before we got the Hard Math book.  Ze was completely and totally frustrated by the first challenge problem (What is the largest possible answer to 782 + ABC =? [with carrying 1s above and above/left of the 7]?) because ze thought ze should just be able to do a math problem.  Even hard math problems were hard because ze was prone to make mistakes, and all one had to do was not make mistakes.  This idea that you have to learn about the problem first and maybe try a few things out was completely foreign to hir.

Life is like that too.  You can plan and plot and analyze situations, but sometimes that takes more time (and provides less information) than just doing and seeing what happens.  Sometimes you get what you want on the first try, but more often, you get clear information on what you need to do better and how and why.

Sometimes you have to fail before succeeding, and it’s the failure(s) itself that is instrumental to your eventual success.

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!

warm and fuzzy student things

One of the joys of my job is that I get to remove math phobia from students.  I teach a required math course for social science majors, many of whom come from backgrounds that are not math heavy.  Often this is the first math course they’ve taken since high school.  Many of them think they’re just not good at math.  I spend a lot of time filling in gaps of their knowledge, even doing silly things like going over every step of simplifying a fraction or solving for X, you know, just in case.  (I do this because my Calc 1 instructor SUCKED and I learned almost all of Calc 1 while taking Calc 2 from a different professor at the local university because he would go through every single step of what I’d missed whenever we needed to know it.)  I do extra tutoring in office hours.  I constantly push the growth mindset on students.

From about midterms to getting final grades, my students start to realize that hey, maybe they’re not so bad at math after all.  This week has been especially warm and fuzzy with students popping by during office hours to confide in me that they’re actually “getting” the class, something they thought impossible. (Last week they discovered and informed me that they’re several weeks ahead of the other section and have had much more difficult homework assignments– this has become a point of pride with them.)

Lots of students mentioned in office hours that it’s all coming together on this week’s homework.

One gentleman told me that his entire life he’s taken the easy way out, doing things that maximize how impressive they sound while minimizing actual need for thinking.  This semester he’s taken some (gen-ed fulfilling) classes from our department, including mine, and they’ve challenged him and he’s risen to the challenge and he’s realized he likes to be challenged.  He came by to tell me he’s changed his major to our department from communications.  He’s actually the second person to tell me this week that (s)he’s switched into our major because my class wasn’t anywhere near as frightening as (s)he had thought it would be, not because it’s easy, but because (s)he can do it.

Another woman stopped by to tell me that she’s always been terrified of math and never thought she’d ever be able to do anything with computers, but she feels really powerful whenever she uses her statistical software on the homework.  She can’t wait to take my (more difficult, semi-elective) class next semester.

A senior stopped me in the hall and told me how surprised she’d been to see that A on her transcript last semester, an A she’d earned in my harder semi-elective.  The stuff she learned has been helping her this semester too.

It’s been a warm and fuzzy week.

Do you have any warm and fuzzy student stories to share?

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?

Ask the grumpies: Math-averse teen boy‏

Kingston asks:

Do you have any suggestions for motivating a math-averse 15-year-old boy? His interest in the subject and confidence in his skills are low. He avoids math and does only the barest minimum of work because it is a struggle; as a result, he is always just barely keeping up, or we’re in crisis as he’s failing. When he has been failing, I have taken him to a tutor, who kind of manages to drag him up to the necessary level, with great frustration on everyone’s part.

Any thoughts on how to help this adolescent see the beauty and utility of math? Do you think people who are not naturally gifted in math can be taught to be anything more than basically competent?

We are not a particularly math-y family (much more history-, literature- and arts-oriented) but our older son did pretty well and is not daunted by it. At times our older son loves it.

Maybe relevant: the math-averse guy does have an aptitude for athletics, foreign languages and for music, and is doing fine with fairly complex music theory. He does not like to read fiction or fantasy; in fact, he has little interest in reading anything at all, despite constant exposure since he was tiny. He does what he has to for school. No learning disabilities.

I would be grateful for any ideas.

It used to be that I would only get girls and women (of all ages) with this problem, but now I am getting more young men in my classes with this math aversion. I suspect this may have something to do with the changing dominance of academics from male-dominated to female-dominated, and that’s starting to bleed over even into mathematics. My advice will be the same for your son as it would be for your daughter.

Given that you have screened for learning disabilities in math, it is extremely unlikely that he (or anyone) is naturally not gifted in math.  The only cases in which I have not been able to bring someone up to speed in math is the occasional student we get who is a global learner and is trying to minor in our subject (generally with a major in fine arts– these folks want to run an arts-related business or manage a theater or museum when they get out).  These folks tend to think in clouds and cannot follow a list to save their souls.  When they get a math problem they just look at it and get the answer, but unless they are brilliant they get the answer wrong more often than not.  There probably is a way to teach them math, but I’m not set up to do that.  There are ways to teach people with dyscalculia all sorts of math (I know the tricks for arithmetic, but not later math).  A specialist can help there.

Instead, I suspect that there are two things going on.

The first is that your son is succumbing to second-child syndrome.  This happens a lot to the second children in bright families.   Given what you say about reading and other academics, it sounds like he has decided that your oldest is the “smart” one and he will be the “athletic/artistic” one.  Possibly he is also the “popular” one.  This isn’t about aptitude– this is about identity.  The way my family dealt with this with my (athletic and popular) little sister was to say that our family was academic.  So she could be a great catcher and a ballerina, but she also had to do well in school.  Our family works hard at academics and does well.  Period.

She had to be good at math because that is a gateway to a career (“keeping options open”).  Possibly a back-up career if dancing didn’t work out, but it is important to have such a back-up.  And yes, she did the minimum possible to get an A, but that’s a good skill too.  (She is now an engineer and makes tons of money.)  Another thing your oldest can do, but you should probably not do, is let your second know when he is struggling– I’m fairly sure my difficulties in physics helped spawn my sister’s love for the subject (don’t tell her I said that).

Regarding reading, my mom read a book about how to get your child to love reading, and as far as I can recall, the main change from that is that she stopped denigrating reading comics as not real reading and she signed my sister up for Seventeen magazine, something that would have been a heresy before.  The book helped her let go of the idea that there is acceptable and unacceptable reading, which allowed my little sister to read more.  Today she reads complicated literary books for her book-club.  (And I read lots of junk novels.  :)  )  Obviously Seventeen magazine will probably not be attractive to your son, but there must be magazines that fit his interest, or comic books or collections of Calvin and Hobbes.  Experiment.

The second thing going on is math phobia.  I generally see this when a student has missed out on some vital part of their math education.  Usually it is fractions (but not always).  Math builds on itself, and when you miss a basic building block, it is much more difficult to get through the entire structure.  (The “spiral” in most of the modern textbook series is supposed to take care of it, but it rarely does.)  It is possible your son lost out on one or more of these building blocks from inattention, but I generally blame it on a bad teacher, or maybe being sick and missing an important day of class.  And it only takes one bad teacher or extended absence to completely miss something important.  Not knowing that building block makes everything that comes after make less sense.

So what I generally do in these cases is explain that if you think you’re bad at math, you’re not.  You’re missing something important.  Math builds on itself.  If you had a bad teacher or missed school, you probably missed something important, like fractions.  (Generally the class makes noise at this point, “yeah.”)  If you can’t do fractions, you can’t do algebra, you can’t do algebra, the rest of math makes no sense.  Then later in office hours or in a review session, I identify where students have holes, starting at the very beginning with addition and subtraction, and I fill in those holes.  Teaching elementary arithmetic to college students doesn’t actually take very long, and once they can do something with numbers, it is an easy jump for them to do the same thing with variables.  But first you have to get at that fear.

So to sum up the steps:

1.  Change your son’s identity to one in which he belongs to a family of hard workers that don’t give up and *will* do well in math.  Use “We” a lot.  My mom would also use her last name, “Lastnames don’t give up, and you are half Lastname.”   Math is useful and important and you are not going out into the world without being able to do it.  (You may also want to read Mindset by Carol Dweck for tips on building a growth mindset.)

2.  Blame your son’s inability to do math on outside factors when he was younger.  (At some point did he stop being able to do math?  Third-Fifth grade?  Seventh or Eighth?)  Explain that there are holes in his understanding that have just made everything later difficult.  (Because in this family we can do math, and if we can’t we work on it until we can.)

3.  Diagnose and fill in those holes.  You can try to do this yourself, hire a tutor, use khanacademy or some combination.  Personally I’d give it a stab myself (or a co-parent if ze can be patient), at least for the elementary math part, to show your son that yes, the family does math (even if not for a career).  Singapore math (and other home-schooling math books) will often offer pretests that you can print out to test where someone is level-wise.  You can use these to also diagnose holes in understanding.  Tell him to be sure to show his work so you can see where he goes wrong.  Khan academy also offers pretests but they are all online.  If you do it, be sure to make it clear that this is for diagnostic purposes to see what he’s missing, and do not make him feel bad for getting something wrong– the point is to find that out.  If he gets everything right then you don’t know where to start.  Then he needs targeted lessons and practice in that part(s) he’s missing.  Again, you can do this yourself, hire a tutor, or use khanacademy.

Grumplings, do you have any suggestions for Kingston?

Percentage vs Percentage Point: A Primer

If your (ordinary least squares) regression coefficient is .047, that is an increase of .047 points, or an increase of 4.7 percentage points.  When X goes up by 1, Y goes up by 4.7 percentage points (or 4.7 ppt for short).

It is not an increase of 4.7%.

To determine what percent change it is, you need to start with a base or an average. If, for example, the mean of the Y variable is .47, then an increase of .047 would be: .047/.47*100 = an increase of 10% off the mean.

Note that 10% is not the same as 4.7%.

Percentage vs. percentage point is a way that people lie with statistics.  A small percentage point change can look large in percentage terms and a large percent change can look small in percentage point terms.  Most people don’t know the difference, and think both mean percent.

*disclaimer:  if both your X and Y variables are in natural logs then, because of the beauty of Taylor approximations, the regression coefficient can be read as a percent with certain assumptions about the size of the change etc.