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.