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?
*

November 30, 2012 at 3:00 am

English–words, language, grammar, linguistics–made sense to me. I cried in my algebra final, the last test I had to take before getting my BA. I screamed, ranted, and raved going down the hall to the restroom where I was definitely not sane. I passed the one algebra class and lived.

As soon as I earned the MA, I had the occasion to call the junior college and was asked if I wanted a job in ABE. I said yes, because I wanted a job. I did not know what ABE was. Well, the next day I was hired as a GED teacher. Then, I found out I had to teach algebra, geometry, and some other math. (I was a whi up to algebra.) I threw up the first day before class, had diarrhea until i was weak. Can you see the math anxiety I experienced?

When the first student asked me about an algebra problem, I was faint, barely able to walk to him. I looked at the directions in order to teach him. Then, someone asked me to help him with the same problem as soon as I finished. I walked six feet and could not remember how to work the problem. Finally, after about a month of this nonsense, I developed a mnemonics system to help me. I had the bright idea to teach mnemonics to the students. It worked brilliantly.

One thing I also had to do was explain to people why they were not good at math, frightened of math, and just did not get it. Yes, missing a step, preconceived notions, all you said. Then, I checked the student records. After an analysis of their reading scores, I realized most of the students had high reading scores and low math scores or vice versa. The lightbulb got brighter. THAT was why I am horrible at math, plus absences in grades 7, 8, and 9 when I had strep throat. No one explained anything and my life was not happy in math classes. I thought I was just stupid despite IQ tests that contradicted my low self-worth in math classrooms.

I became so proficient at math, teaching math, that I tutored algebra and geometry over the phone. My focus was always on how good the student really was, despite his or her opinions. I had to convince the students that, yes, they would use math everyday. When I taught GED in a men’s prison, one inmate was rebellious, saying he did not need to know how to estimate if he went in to buy shirts. Finally, he came over excitedly and told me that when he bought drugs to sell, he never knew how much he could make until all th drugs were sold. Now, when he got out and resumed sellig drugs, he could estimate how much he was going to profit. He did go on and learn algebra.

Students who had been in LD classes all through school learned algebra. One woman cried because she learned. One woman with an 80 IQ learned algebra and her case worker wondered what happened, how she did it.

The one thing a student does not need is someone getting frustrated because the student does not learn right away. I mastered the art of patience because impatient teachers whose egos were tied up in whether I learned or not hampered me.

My plans were to take a year off after my MA and to go back for a PhD and teach English and in a university.. But, getting a high school diploma or a GED is so important that I decided to get a PhD that would allow me to be better able to help other people to learn math.

Sorry, but I have taught and tutored hs and college math more than I have taught or tutored students in English. This topic interests me. I suppose I wrote a whole post here.

I taught a class at a university–math anxiety. The eight 50ish women in the class were wives of physicists, MDs, PhDs, engineers. None of the women could work fractions or anything beyond that. Their husbands were too impatient, snatching figures from them.

Tutoring math and seeing people “get it” really gives me a thrill. I promise not to comment for six months. It is 4 am, so I will stop. LOL

November 30, 2012 at 10:28 am

Love this comment/post. “No one explained anything” – YES. I did all right in math in high school but only because I ground away at it (family expectation of not getting less than a B). I remember a night of tears trying to do long division. … Bs in algebra, A in geometry, C in trig. Then got to college and took calculus and made an A thanks to a great teacher.

November 30, 2012 at 2:41 pm

Thank you so much for this wonderful, thoughtful, helpful reply!

November 30, 2012 at 3:52 am

I agree with most of the post, but I am a bit concerned about the emphasis on “family identity.” Most people in my family are pretty athletic — my brother played football, my sister and my mom played tennis, I ran track and played volleyball. But if anyone had pushed “we are all athletes” as some kind of family fact, it would have left out my other brother — the shy, bookish, mathematically-inclined one. Saying “we are all athletes” or forcing him into sports (which he has never shown the slightest interest in) wouldn’t have made him love or understand sports. It just would have made him feel inadequate and unhappy. It would be nice if the young man gets over his mathematical anxiety, and I think some great suggestions have been made here to help him. But if he doesn’t and keeps barely passing or even failing math, he shouldn’t be made to feel like he is also failing the family.

November 30, 2012 at 5:54 am

Athletics are not as important as academics. (Note that they are not required 8 hours a day in school and they rarely lead to employment options later.) Being healthy, however, is. The family identity can be being healthy so he’s not allowed to have his muscles atrophy. That’s important. Just as, “this family knows how to swim” is. Not, “this family is Olympic swimmers” but “this family is not likely to drown in a standard pool.”

Nobody is saying he has to major in math. However, he does have to get a competence, and unless he has a learning disability, something that has already been screened for, with enough effort he will get a competence. And he’ll feel better for it. Just like all my students who blossom under my tutelage. They are also not allowed to fail because my students who put in effort (the ones who come to class, do homework, and go to office hours) don’t. The ones in my required course don’t always get As but they often do, and they almost always get at least a B, and generally a solid one. (And many of them go on to take my next not-required math class!)

November 30, 2012 at 11:46 am

I’ll agree with the identity push, but I’d like to point out an important nuance. I’m a mathematician with a bunch of kids, some of whom are quite gifted at math and some of whom are . . . not. I think that doesn’t matter. We’re all people who just keep *trying* at math. I never praise my kids for being smart, nor do I berate them for having learning disabilities. But I praise them to the skies for working hard and for keeping going, and I get on their butts for half-hearted attempts. There’s lots of research that says that’s the most effective way to motivate kids to take chances (even smart kids will be nervous about taking hard classes, because they don’t want to risk losing the “smart” label, for example). My two sons, who are both way below grade level because of learning issues, will tell you that math is their favorite subject.

November 30, 2012 at 1:50 pm

Exactly. We are people who don’t give up.

November 30, 2012 at 6:50 am

Very interesting diagnosis – my parents did almost exactly down to the words – “FrugalEcologists don’t give up and you are a FrugalEcologist!”

We don’t have kids yet, but I am filing this advice away.

I had horrible test anxiety & math phobia (fractions and decimals) and my parents enrolled me in kumon. It was beyond awful at first as I was stuck doing addition/subtraction (with reactions like Practical Parsimony to the timed tests everyday) but after just a few months I got the concepts down, and testing under time-pressure became a non issue.

November 30, 2012 at 4:42 pm

Maybe we’re related!

November 30, 2012 at 10:29 am

I think this is brilliant. I agree that when a kid is bright in one area, it is highly unlikely he is actually missing ABILITY in other areas.

November 30, 2012 at 12:28 pm

Actually, my fantastic ability with words did not mean just ability. I took my ability/proficiency and ran with it. I focused on words and solved any problems like origin or spelling or meaning until I was beyond proficient. (In the third grade, teachers would never call on me even though I always knew the answers. Yes, because I always knew the answers and could get my hand up really fast. They were like the puzzles i loved, just word puzzles.

My mother yelled at me when I did math homework, so i did not want to be yelled at by the most important person in my life. (Okay, maybe she did not yell, but I felt disapproval.) When I finally figured out everything from algebra and up, I reveled in doing algebra and trig. I wish girls in the 1950s were encouraged and taught math more than i was. I wanted to be a scientist. But, the hs wanted me to take typing and shorthand and office subjects. One year of typing classes on big, black, manual typewriters was enough for me.

November 30, 2012 at 10:42 am

That is an amazing post. My husband is a community college math teacher, and I plan to have him read it. I’m an English CC teacher, and I’m wondering how much these kinds of ideas might apply to students’ reading and writing challenges.

Sometimes I am so struck by your knowledge and confidence that it seems like you are the Cesar Millan of life!

November 30, 2012 at 2:13 pm

We are awesome, it is true. It probably also helps that we tend to write about things we know about or know about by the time we write a post. (So we won’t comment on reading and writing challenges!)

November 30, 2012 at 11:07 am

This is a brilliant post, one I wish my parents had read (also: love that it’s the same for males as females here). Interesting insights into identity and second children too- that fits with my models of siblings, albeit not from direct experience.

I also completely agree with Practical Parsimony’s comment about students not needing teachers with ego wrapped up in how fast they learn. That was the problem with my Dad and I and math (seriously, who makes a second grader feel bad because they don’t know their multiplication tables? EVEN IF you learned them in Kindergarten. ESPECIALLY THEN, FFS…/still bitter). Students often need instructors who can remove the *students* ego from the equation- instructor ego has no place during the process.

Still, I’m not sure I would have been persuaded by all your points when I most needed to hear them. I still think that a lot of energy could have been saved, if people had approached the “must convince wise-ass kid she will actually use math” by, you know, teaching me neat things that need math. It might not be true for all flavors of people, but it seems to help a decent chunk. For me, fractions didn’t even start to click until sewing, calc didn’t mean much until physics, ect. And I never felt mathematically competent until several years into lab science, watching many very bright people have an occasional brain fart at setting up C1V1=C2V2 (NB: it should be considered educational malpractice to ask students to USE Avogadro’s number until they can do C1V1=C2V2 in their sleep). Then I realized I was at least as mathematically competent as many people doing science perfectly well, and that helped a lot.

The other thing I might take a minor quibble with is that (at least for a subset of student) it is very possible to fill in some gaps in math later. One of the things my parents said that did help me with math is “some people have more of an affinity for algebra, some for geometry, some for trig” (subtext: so if you don’t like one, don’t give up on the next course!). An extreme focus on the sequential nature of math can be very dispiriting if you don’t know what all you’ve missed and a lot of it is quite rusty. Also, from what I’ve heard from K-12 teachers, quite often students have actually learned the math,they simply haven’t retained it- but they will not take as long to get up to speed as someone learning truly from scratch. So sometimes “you aren’t bad at math, you just didn’t have some key part taught to you” might be a white lie; the literal truth is more like “you have understood this, you just haven’t needed to recently practice it enough to move on to the next step smoothly”. The distinction is probably only important in how people frame imperfect schooling experiences, but I think sometimes K-12 math teachers catch some hell for not teaching fractions… when that isn’t exactly what’s happening (it seems some students learn and forget fractions several times in the course of an academic career).

November 30, 2012 at 1:01 pm

My son would not learn to read in the second grade. I pointed out that he could not get a driver’s license unless he could read. The shock on his face and in his voice was memorable. He still did not learn until I gave him Call of the Wild. Now, he is a hs and college English teacher. I think anyone needs to know why learning a skill is important.

Grown men in their 40s could not handle fractions until I used a drawing of a Hershey bar on the board, the same way my son learned what fractions mean and how to manipulate them. I even had to break brand new pencils in half to prove that such a fraction as 5/2 did exist. My bare prison classroom had no other things to manipulate.

I was a super silly teacher to adults and they laughed at me. I told them to laugh at me, about me, ridicule me to their friends, telling them what I used for examples…..because they learned/reinforced and had a better grasp of things when they explained them to others. They quit laughing behind their hands and smirking when I explained my attitude toward toward being ridiculed by them–they were reinforcing what they learned.

Missing the week that quadratic equations were taught and having a male teacher tell me to catch up was a reality.

My children were given practical problems as they arose all summer as a means of keeping skills alive and working. They were impressed with my ability to do mental math, so tried very hard and even wanted me to teach them mental math. HA! How is that for motivation? They thought I was just smart. I reassured them that I worked at mental math and had been doing it for years. You cannot allow a child to think you are a genius just because you have 20 years experience at math! So, I told them they had to always try to get better than I was at everything, even the areas where I was already an “expert.” LOL Yes, they want to show me up now, but that’s okay.

My two-year-old knew her multiplication facts. But, her success is called pseudo learning. She could not grasp the concept or apply the concept and the facts. By the way, I taught multiplication facts differently from the schools. My children excelled. Even hardened, male prisoners were surprised at my easy peasy way to learn multiplication facts.

Somebody make me shut up.

November 30, 2012 at 2:52 pm

PP: No. Preach on.

November 30, 2012 at 1:58 pm

There are elementary school teachers in District 426 of the state in which I grew up that have said out loud that fractions are not important because we have calculators. And there are a lot of math phobic elementary ed majors. Regardless, it helps my college students (and previous younger tutees) lose the fear if I suggest that their long-term problems with math were because of some external problem and not their underlying ability.

November 30, 2012 at 2:42 pm

Practical Parsimony- I think what you did with your children is awesome. It also probably relates to one of the differences in advantaged/disadvantaged students, i.e. it’s not how much they gain over the school year, but how much they loose over the summer; at least for some contexts.

nicoleandmaggie- Yeah, double-yuck to “no fractions because calculators”. Come to think of it, I’m sure I haven’t seen or been hearing stories from the worst of the worst school districts (though I have seen a little of the worst in IL, IL is not particularly the worst state). It’s important to remember exactly how incredibly heterogeneous education is in this country.

And yes, I can see how important faith in one’s underlying ability is. It takes a really great instructor to build that up for some people, I’m glad you figured out a way to convince students!

November 30, 2012 at 5:06 pm

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).This reminded me of how in college I helped all my engineer fraternity brothers pass their thermo class. I was good at thermo in my honors physical chemistry class, and the professor was all like, “Why you study soft science like physiology? You should be hard scientist!”

November 30, 2012 at 5:09 pm

the joke is that phd physicists from places like Chicago end up as research assistants for social scientists or retrain to go into finance

November 30, 2012 at 5:15 pm

One other thing I just remembered is that the book Men of Mathematics got me really inspired about math, as it had just enough actual math in it to make it really cool and intriguing, but without being hard to understand.

http://en.wikipedia.org/wiki/Men_of_Mathematics

And yeah, it’s grossly sexist.

November 30, 2012 at 5:25 pm

I have my eye on a book called Family Math. I probably should have linked to it. (Amazon recommended it when I was looking to see if Math for Smarty Pants was still in print.)

December 1, 2012 at 9:59 am

Where is the book, Women of Mathematics?

One thing I pulled out of my bag of tricks, my repertoire for teaching, when I had discouraged and rather negative students:

Have you ever seen a baby just learning to walk? Did the baby fall down and just never try to walk again? (responses were abundant) No? The baby kept trying until the baby was proficient. You would not be able to walk if you tried to walk and quit or tried once a week to walk and just stayed on the floor when you fell. Do babies cry when the fall on their behinds? No, they get right up. Do they cry when they really hurt themselves? Does that stop any baby from learning to walk? Some people become so proficient at walking and running that they are basketball players or track stars. Others learn to walk and just keep stumbling around like I do. (they had seen me trip over dust on the floor and run into chairs and tables.) Well, you only open your math on Friday night when I am here and wonder why you cannot do math/algebra/geometry. Maybe trying it every day would work? (This is my best motivational speech.)

Of course, even the criminals had things to say about this. They broke out of their negative shells. They all smiled and relaxed. They really really like to talk about babies learning to walk. They also can relate to the concept of perserverance, since babies do not EVER give up on the walking skills. And, they know they were babies who overcame lack of skills. High school students and older adults in GED could also relate.