“*I’m just not a math person*” is “the most self-destructive idea in America today,” write Miles Kimball and Noah Smith in *The Atlantic*. You’re not just limiting your own future. “You may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability.”

Mathematicians need high math ability, write Kimball and Smith, economics professors who’ve taught math. But few of us are aiming that high. “For *high-school* math, inborn talent is much less important than hard work, preparation, and self-confidence.”

Belief in inborn math ability may be responsible for much of the math gender gap, according to Oklahoma City researchers, they write.

Psychologist Carol Dweck and colleagues found students do much better if they believe “you can always greatly change how intelligent you are” than if they think “you have a certain amount of intelligence, and you really can’t do much to change it.”

In *Intelligence and How to Get It*, Richard Nisbett recounts what happened when Dweck and colleagues told poor minority junior high school students that intelligence is malleable and can be developed by hard work. Learning changes the brain by forming new connections and students are in charge of this change process, psychologists told the students.

Convincing students that they could make themselves smarter by hard work led them to work harder and get higher grades. The intervention had the biggest effect for students who started out believing intelligence was genetic. (A control group, who were taught how memory works, showed no such gains.

But improving grades was not the most dramatic effect, “Dweck reported that some of her tough junior high school boys were reduced to tears by the news that their intelligence was substantially under their control.”

Kimball and Smith conclude: “It is no picnic going through life believing that you were born dumb—and are doomed to stay that way.”

I would say most K-12 math is irrelevant to what mathematicians at universities spend their time doing. And the folk who end up solving new theorems and creating new fields of math don’t really need most elementary math education because they can figure it out on their own. I have a genius physicist brother-in-law who was confused as to why his sons were having to do math fact drills in school because “it’s just like adding rocks.” OK, my relative, not everyone is as brilliant as you. But with diligence and a good curriculum, I think nearly everyone else can get through basic calculus.

Here’s an example of what mathematicians do: http://www.math.illinois.edu/timetable/advanced-topics-courses.html

By “basic calculus”, I mean doing basic derivatives and integrals of fairly simple polynomial functions, such as they teach business majors in college. One really doesn’t need more than a good grasp of algebra and graphing to benefit from learning about derivatives of such functions. And it’s very valuable information for application in fields such as aerodynamics (differentiation of function describing position => velocity => acceleration, etc.). I don’t see why a high school student can’t be taught this fairly basic calculus even if they never make it through trigonometry, college algebra, and analytical geometry.

CT, do you have any evidence for the assertion that “with diligence and a good curriculum, I think nearly everyone else can get through basic calculus”? I mean aside from the fact that it just doesn’t seem that hard to you–and that people you know can do it.

This blog is read by lots of people (like you!) who are smart and care about academics. It is natural to think that something which you can do without excessive difficulty can be done by anyone. But that thought is wrong. And it is not a good foundation on which to build a curriculum.

No evidence other than my own observations from helping tutor business calculus students for three years while I was in college. There is a watered-down version of calculus that can be done without mastering all the material in the courses that I mentioned above. Kids who can do algebra (graphing, etc.) can learn about minimums, maximums, and differentiation and integration of fairly simple polynomials. That opens up a greater understanding of things like medication curves, supply functions, etc., which can be useful to a CNA, small business owner, investor, etc. For those not on a STEM track, I would recommend an “easy calculus” class be taught in high school soon after finishing algebra. However, until such a course comes into being, I agree that not all K-12 students can get through all the standard prerequisites to AP Calculus plus AP Calculus.

That’s an interesting idea, a “simple calculus you may actually use” right after algebra. I’d love to see some experiments done along those lines.

It is highly unlikely that you tutor many kids with IQ’s that are 85 or below. ThIs is only one standard deviation below the median, so it would include a significant percentage of our population. There is no nation on earth that has been able to make people in this IQ range capable of calculus.

Ray, you’re right. These were bright, but not really STEM-y kids. It was at BYU in the mid 1990s.

I don’t have experience with lower IQs. Do you? Am I so off in thinking that even kids with IQs of 85 or below can grasp derivatives of say, x^3 + 2x^2 + 4 and be shown how it applies to some real-world things? Maybe in science class as they look at possible climate models? How about in mechanic vocational ed class when they’re learning about velocity, acceleration, and maximizing fuel efficiency? Perhaps in consumer economics they could learn about supply and demand curves and maximizing/minimizing profits from price functions….I just don’t think all calculus needs to be taught only to those who can do limits and trigonometry. It’s a very useful subject to non-STEM folk, too.

CT, the answer is that nobody really knows for certain. I am skeptical that students with such low IQ’s could do this because no country in the world has been able to achieve this.

I actually read 3 years ago the book “Intelligence and How to Get it” by Nisbett in full.

Pretty weak book. No proofs, wishful thinking.

With invariable respect of the noble work by Ms. Jacobs,

F.r.

Some people are born with more talent for math than others. This should be obvious, and a recent study “Number sense in infancy predicts mathematical abilities in childhood”, available online confirms this.

OK, but how smart to you have to be to do K-12 math? I would think a combination of hard work and optimism might actually help.

“OK, but how smart to you have to be to do K-12 math?”

It would help if you specified what you meant by K-12 math. A traditional American high school math sequence would have 12th graders ready for calculus as college freshmen … so K-12 (including 12th grade) would include things like Algebra, Algebra II, geometry (maybe with proofs), trigonometry, and pre-calculus.

This is actually hard. It is especially hard for folks with lower IQs.

And things change when you move from arithmetic (K-8, more or less) to algebra because algebra is where you start having to make lots of decisions on “what to do next.” Addition, subtraction, multiplication and division can all be learned by rote for integers, decimals and fractions. And the procedures to do these operations are pretty linear. *Solving* multiple equations with multiple unknowns often involves strategies: Do I isolate X or Y first? Or maybe I should scale both equations so that I can add/subtract them?

And algebra word problems also tend to be much nastier than those found in the earlier grades. Kids who don’t read well will also find that their math grades suffer because they won’t be able to understand the questions well enough to convert them to math.

About 1/6 of the population has an IQ of 85 or below. I do not expect these folks to be able to handle a “real” Algebra II course. I’d even be surprised if most of them could handle a “real” Algebra I course.

While this is true, the number of people who claim “I am just not a math person, I can’t do fractions/pre-algebra/algebra 1” is far higher than it ought to be and in most cases is due to a lack of effort and defeatist thinking before even beginning.

There’s also a genetic / thus ethnic/racial element to this (as a general rule; exceptions exist, of course) which is taboo to even discuss…

The number of people who haven’t mastered basic ES arithmetic (basic facts, algorithms, fractions, decimals, percentages and very basic stats – mean, SD etc) is MUCH higher than it should be. We have poorly prepared, math-disliking teachers, rotten curricula (like Everyday Math) and calculators (should never be allowed before REAL algebra 1) to thank. HS math should differ according to student path choices: through calc for STEM/competitive colleges/precalc for non-STEM and non-competitive colleges and math specifically relating to voc ed choice (less for cosmetology, shop-related math for carpentry, different math for medical/nursing fields etc) One-size-fits-all is a lousy idea, whether in school curricula, classroom assignment or bathrobes.

momof4,

I’d agree with you on the ES and MS math, but if the students don’t have a working knowledge of those, they’ll bomb out in high school (never mind college).

A student who cannot master fractions will never make it through algebra/geometry/algebra II/Trig, etc, but in a Seattle Times article which Joanne titled No Math, No Job, 9 of every 10 applicants who had a high school diploma couldn’t handle an 18 question, 30 minute test w/calculator when asked to figure out area, convert inches to feet, metric issues, and what most of us here would consider basic skills.

These were applicants for manufacturing jobs, which have changed considerably over the last 25 years, since most of it is computerized, and yes, you do have to know how to read blueprints and the math figures on the blueprints.

Sigh

“… that intelligence is malleable and can be developed by hard work.”

How about better teaching and curricula?

Intelligence is the biggest educational copout because nobody calibrates it or tries to separate the variables. It’s too conveeeeenient to let students believe that they are just not smart in math. Students will even believe it themselves. Then you have those (as in this article) who put the onus on students to change their thinking. They just have to work harder, be more engaged, and be more motivated. Then they confuse the issue by conflating better grades with higher intelligence.

Hard work may not get just anyone to differential equations, but kids in 7th grade are claiming they are just not good in math. Instead of looking at the most obvious variables, they blame the kids.

SteveH wrote, “Hard work may not get just anyone to differential equations, but kids in 7th grade are claiming they are just not good in math.”

Kids in 7th grade have been studying math in school for seven years, which is enough time for them to form an opinion of their math abilities.

Education Realist, a math teacher, has a blog post “Noahpinion on IQ–or maybe just no knowledge” where she expresses doubt that students with IQ below 100 can learn algebra, writing ” I have been asking nearly as long as I’ve had this blog if anyone can show evidence of successful mastery of algebra by IQs less than 100.”

I think there is defininte truth to this. Which is sad, since >60% of the general population has an IQ of 100 or less… This also means, that in a STEM-based economy of the 21st Century, what are all these people going to do for a living? Most of the jobs their parents and grandparents had don’t exist any more (or continue to exist, but in a 21st Century form that requires advanced skills). They can’t all work at hotels and in construction and at restaurants… There’s only so many of those jobs needed to go around. And any government that tries to invent jobs for them all will bankrupt itself into oblivion (as the U.S. may soon find out…)

While I don’t think the problem is as large as 60% of the population, there is an undeniable problem of an unemployable underclass. These people are unemployable for a variety of reasons, but lack of an education is almost universially one of the reasons.

The vast majority underclass no longer sees education as a ticket out. (The ones that do are usually immigrants) The concept of “Acting White” was not invented by some racist White man. The very fact that the definition of “Acting White” usually means behaving and doing well in school is damning.

The bigger problem that we as a society need to deal with is: What do we do with them?

The Progressives were thinking about this at least 100 years ago. Planned Parenthood was openly founded by Progressives to reduce the number of undesirables. They had other even less savory ideas about population control.

I reject the answers the progressives had, but who is willing to begin a conversation on this topic?

There are very few people who are truly unemployable. There are lots of jobs that don’t require much in the way of school knowledge, even the ability to read or do arithmetic. The nursing home where my mother-in-law spent the end of her life employed many immigrants (legal? illegal? I don’t know.). Their qualification for the job was that they showed up each day on time and did what they were instructed to do. For a not terribly high wage.

There will always be jobs like that.

“Kids in 7th grade have been studying math in school for seven years, which is enough time for them to form an opinion of their math abilities.”

The wrong one. You’re completely guessing here. I’ve seen it over and over with kids I have taught and tutored. They have plenty of IQ, but trash their abilities. Success breeds success and failure breeds failure. When K-6 teachers hate math and don’t value mastery of basic skills – on a systemic basis(!), one cannot look at results to calibrate IQ.

“she expresses doubt that students with IQ below 100

can learn algebra,..”

Her doubt is driven by her beliefs. She sees what she wants to see. How many kids above 100 fail algebra? IQ advocates use vague calibrations to find excuses on the low side, but not to enforce expectations on the high side. What other calibration criteria do you guess at?

ER continues to raise questions with little effort to separate variables. There are clearly no black and white cutoff points. Curricula, pedagogy, and hard work are huge variables. There are plenty of examples of this. Tell me how you will set public or school policy based on this supposedly hard IQ criteria? This is really what it all comes down to. And how do you try to fix curricula and pedagogy if you play the IQ card at the drop of a hat?

Everyone knows that some kids are smarter than others, but IQ crazies love to think they have the uncomfortable answer that would change the educational world. Sure, some educators like to think that all kids are equal, and some like to think that all kids could or should go to college. Perhaps pseudo-algebra II is an unreasonable high school passing criteria for all, but those questions can be dealt with directly without getting on a self-righteous soapbox, playing the IQ card, and ignoring all other variables.

SteveH, You’re absolutely right that lots of relatively high IQ kids are held back by poor math instruction. Then there is a vicious circle: “Success breeds success and failure breeds failure.”

We all can agree that there is some point at which a person is just not bright enough to learn algebra–and I mean really learn rather than memorize a few algorithms for the test and forget the next month. Whether that cut-off corresponds to some IQ number, and just how many kids fall below it is an empirical question about which we have damn little good data. Alas, we may never have such data because educational researchers and funders want to avoid such politically loaded questions. If such data existed, I’m sure Education Realist would love to see it–and would be willing to change her mind if it told her she was wrong.

So what can we do? My suggestion is to be honest. Have good math instruction in the elementary grades and don’t move kids along just because they get older and you want them to stay with their age-mates. Bring kids to the next step when, and only when, they have mastered–really mastered–what they will build on.

I think it’s safe to say that math ability is distributed normally. If I had to take a wild stab at it, I’d say that:

99+% of people can learn to count

98+% can add and subtract

….

80+% can learn hs algebra

….

40+% can handle abstract algebra

…

1% can break new ground

….

some teeny percentage can win the Fields prize

I don’t think it does much good to look at the problem and say that EVERYONE can learn everything through HS calculus….oh, and then there are those mathematician types.

Everyone knows that some kids are smarter than others. Everyone knows that some kids work harder than others. There doesn’t have to be a discussion about IQ. There needs to be a discussion about separating kids who are willing or able (for whatever reason) from those who are unwilling or unable (for whatever reason). This separation is done in all high schools without resorting to checking students’ IQs.

Our K-6 schools, however, are known for their full inclusion and mainstreaming policy. People move to our town because of it. The schools chose this approach NOT because they think that all kids are equal. They chose it because they placed social goals above academic goals. They think that they can help students at all levels using “differentiated instruction”. They chose Everyday Math because it claims that their spiral approach works by definition. They tell teachers to just keep moving through the material and to “trust the spiral”. It doesn’t matter that it’s not a class spiral based on previous mastery of skills. It’s an individual spiral that is what I call repeated partial learning. The curriculum transfers all responsibility for learning to individuals because that’s the only way they can possibly get differentiated instruction to work. (Our schools even had the temerity to call it “differentiated learning”.) One might claim that this is a pure IQ learning system with not much help from the teacher or curriculum. However, IQ does not guarantee that students will achieve their best level without help from a good teacher (or mentor) and a good curriculum. Learning is not natural, especially for those subjects that take some effort to get to any sort of interesting or fun level.

I can understand the dislike of tracking in the lower grades, but differentiated instruction is an abject failure, especially in math. If they continue not dealing with the issue, then all of the tracking (which is currently going on now) will be hidden away at home or with tutors. Is ignorance their solution to the fact that full inclusion and academic opportunity are incompatible?

The problem with tracking with bad teaching and curricula is that only those with help at home will get on the top tracks. Some urban parents want to track their kids to schools that set high standards, but public school educators fight that tooth and nail. Apparently it’s OK if affluent parents track their kids to private schools.

Educators are happy if little urban Johnnie or Suzie get to the local community college (even though they have the IQ or work ethic to get into Harvard), especially if they will be first in their families to go to college. I don’t know where this low expectation, multigenerational path comes from. They treat education as statistics, not individuals. All one has to do is look at El Sistema in Venezuela. Kids go from the barrios to playing at Carnegie Hall and the BBC Proms in one generation. They don’t have low expectation music for poor kids. They have “tocar y luchar”. Hard work. Good curricula. High expectations. Separation by results. Woe to those who think this is just about music. Somehow, many people think that if it’s academics and not sports, music, or dance, then separation in the early grades is psychologically damaging. They are wrong, and in doing so, they just keep ignoring the tracking that is done at home, with tutors, and with private schools by affluent families. They even stop urban parents from sending their kids to charter schools.

Math (and STEM altogether) is the basis of the 21st Century economy. The countries who have more citizens excel at it, will have more control of the world. Basically, STEM will be the difference between the U.S. remaining a superpower, or even keeping itself a global power. At current trends, in a few generations we’ll just be another 3rd world country… (just a big one)

IEEE has a recent article called: “The STEM Crisis is a Myth”. Philosophically, I don’t view education as a national economic tool. I see it as an individual educational and development tool. If we base education on what is best for individuals, everything else will take care of itself. Who wants schools that offer opportunities or sets expectations based on vague calibrations of IQ and not hard work and results?

The Common Core standards will not fix anything because they only define one path for all. Individual needs are ignored. Some curricula, by definition, do not prepare students for STEM careers in K-6. Life will go on about the same as before. Those with math help at home or with tutors will have open STEM career doors. Those without will be rationalized away with IQ and other excuses. In the article above, they place the onus on the student. Just work harder.

I feel fairly sure that at least half the American work force uses computers every day. I also feel fairly sure that very few of them know how their computer works, or how to program it, or how to fix it. But they don’t have to! Any more than drivers have to know how an internal combustion engine works or how to fix it when something goes wrong.

America needs a substantial number of good STEM people. However, there is no economic need for a majority of the population to have good STEM skills. I would guess the exact proportion is less than 10%.

Look at Apple. If it were composed completely of people who are good at STEM, it would have failed years ago. It has succeeded because it develops products that somehow fit with what people want and are willing to spend their money on.

I can guarantee very few of the passengers on an airplane understand the physics of flight.

The main issues with keeping a plane in the air:

Lift, Thrust, Drag, and Gravity.

Of course, a airplane is a collection of parts flying in close formation 🙂

“Look at Apple”

Steve Jobs wasn’t fundamentally a STEMs guy. He was a designer. He used STEMs people to develop what he wanted – to develop his vision. Of course, he had a deep understanding of the product but Wozniak was the tech guy.

Thanks, Stacy. I wish I’d said that.

The old Soviet Union was full of great STEM people. But because of their system, they couldn’t translate that knowledge into things that improved ordinary people’s standards of living.

To be economically successful, a country needs a certain number of STEM people but it also needs people who can connect STEM knowledge to people’s desires, and a system that provides incentives to do so.

Agreed 100%. But, without any STEM people at all… A nation would have to contract out to build its own military, communications infrastructure, etc. A dangerous game to play!

We definitely need STEM people, good ones and in fairly high numbers. Fortunately, we get them. I teach high school physics and many of my students have become engineers–as did my son, and he of course is a great one 🙂

The thread is called “Math isn’t just for ‘math people'”. This really is not just about STEM versus no-STEM. While the no-STEM people may never use algebra in their future jobs, they will have to pass a lot of math courses to get their non-STEM degree. Also, most K-6 schools teach only at a non-STEM level, which means that students will have STEM degree opportunities only if they get help at home. I got to calculus in high school with absolutely no help at home. My very mathy son could never have done it without my help. That is a big change since I was young. Full inclusion and lower expectations in the lower grades changed this. They use “understanding” and “problem solving” only as cover for lower expectations. They devalue mastery of skills as tools for understanding. They justify their pedagogy by redefining math.