Back in the fall when I was a baby blogger I wrote a discussion of Carol Dweck’s research about intelligence praise. I did this because I think this research is intensely important. However, I didn’t really let loose on the subject with the full force of what I have to say about it. The truth is I was shy, because a) I’d just had a kind of frustrating conversation on the subject with Unapologetic at Jesse Johnson’s blog, so I was wary of being misunderstood, and b) more embarrassingly, I was excited by the positive response to my previous post about Clever Hans and I didn’t want to alienate any of my new audience.
Now I am a toddler blogger. My godson, with whom I spent the day a few weeks ago, is an actual toddler.
He is profoundly unconcerned with anybody’s opinion of him, and just blazes forth expressing himself (climbing on things; coveting whatever his big sister is playing with; being turned upside down as much as possible) all day long. I am going to take this as inspiration, and commence a series of posts about the idea of “math smarts” and talent and intelligence more broadly. These posts have two central contentions:
1) People constantly interpret mathematical accomplishment through the lens of math talent or giftedness.
2) This is both factually misleading and horrible for everyone.
Tentatively, here is the table of contents for this series. I may edit these titles, add or remove some, and I’ll add links when I’ve got the posts up. But here’s the plan for now:
I. Why the talent lie is a lie; how to understand math accomplishment outside of it
II. How the talent lie is spread (in pop culture, and inside the discipline of mathematics)
III. How the talent lie hurts people who are “good at math”
IV. How the talent lie hurts people who are “bad at math”
V. How to train students to understand math accomplishment outside of the talent lie
VI. Why the talent lie is so entrenched, even though it is stupid and harmful
I should make more precise what I mean by “the talent lie.” It’s really several variants on a fundamental idea. People who are really good at math must have been born with a gift, for example. That they must be extra smart. That being good at math (or not) is something that doesn’t change over time. That being smart (or not) doesn’t change. In short, that your intellectual worth, and the worth of your engagement with the field of mathematics in particular, is an already-determined quantity that’s not up to you. That’s the talent lie.
Some examples of the talent lie at work:
* Any time anyone has ever said, “I’m bad at math.”
* The “gifted” in gifted education.
* Just about any time anybody makes a big deal about the age by which a young person does something intellectual. (Starts talking, starts reading, starts learning calculus…)
(In that last bullet, the “just about” is there only because of the theoretical possibility that a big deal might get made for a reason other than to prognosticate about the person’s ultimate intellectual worth.)
I give you these examples to show that I am not talking about a fringe, outmoded idea but something very mainstream. I will have much more to say about how the talent lie is manifested in the forthcoming posts.
I expect to spend a long time writing them. This project may take all fall year the next several years decade. I believe the message I’m communicating is vital for our field and important more broadly as well. It’s also a very personal message. Like all urban educators and all math teachers, I have a lot of first-hand experience with the damage that the labels “not smart” and “not good at math” can inflict. But I am also speaking as someone who spent my early years being seen by others, and regarding myself, as mathematically gifted. This was a heady and thrilling thing when I was in middle school, but I became vaguely aware of the complications by the end of high school, and with hindsight it’s clear that it left me with baggage that took a decade of teaching, learning and introspection to shake. So my own journey is a big part of the story I’m telling here.
I will save the detailed analysis for the forthcoming posts, which means that I am going to defer a lot of clarification and answering-questions-you-might-have for later. But I would like now to articulate in broad terms what I believe needs to change.
According to the Calvinist doctrine of unconditional election, God already decided whether you are going to be damned or saved, and did this way before you were born. Nothing you can do – not a life of good acts, not a wholehearted and humble commitment to acceptance or faith – can have any effect. The most you can do is scan your life for signs of God’s favor, and read the clues like tea-leaves to see if you are chosen or cast away. Modern American culture doesn’t buy this doctrine from a theological point of view, but is 100% bought in when it comes to math. When a person performs mathematically, we obsessively look at the performance, not on its own terms, but as a sign one way or the other on the person’s underlying mathematical worth, a quantity we imagine was fixed long ago.
We need, as a culture, to gut-renovate our understanding of what’s going on when we see people accomplish impressive mathematical feats. Likewise, when people fail at mathematical tasks. We need to stop seeing people’s mathematical performance as nothing more than the surface manifestation of a well-spring of mathematical gifts or talent they may or may not have. Relatedly but even more importantly, we need to stop reading the tea-leaves of this performance to determine these gifts’ presence or absence. This whole game is bunk.
Not only is it bunk but it’s a crippling distraction, for everyone – teachers, students, parents, and our culture as a whole – from the real job of studying, wandering through, becoming intimate with and standing in awe of the magnificent edifice known as the discipline of mathematics.
When you step to the gate and present yourself before it, math doesn’t give a sh*t about the particular profile of cognitive tasks that are easy and hard for you at this moment in time, and you shouldn’t either. There are institutions that are very keen to divine from this profile your worthiness to enter, but this is the curtain they hide behind to make themselves look bigger than they are. It’s time to tear that curtain down.
More on its way. In the meantime here is some related reading:
* I Speak Math recently tackled this same subject. I plan on drawing on some of the research she links.
* Jesse Johnson and I had a conversation about this stuff close to a year ago, and she wrote about it here and here. I’ll go into much more detail on these themes in the coming posts.
* While not as credentialed, the Wizard of Oz nonetheless has a fair amount in common with wolverine wranglers. See if you see what I mean.
Research in Practice 
Love the connection to Calvinism. To extend the metaphor, I prefer the catholic (small ‘c’) view of mathematics in that the gift is universally extended to all. It’s simply up to the individual to become who they already are.
Looking forward to the rest of these posts.
Thank you for taking up this issue… I will be a constant reader & reactor through the Fall.
In the meantime, as I work through the same issues (who gets to be smart, smart as heightened status) in my research and work in Mathematics Education, I grapple with the power and privilege issues that arise when particular ways of thinking and/or ways of knowing get deemed smart/fast/insightful/brilliant.
It is not as easy as saying, “we are all smart in our own ways” (Howard Gardner’s Multiple Intelligences, for example), or even “each of us is mathematically smart in our own ways.” There is a sort of cultural assumption, and also personal prejudice, that are both very difficult to overcome.
What do I mean–not quite sure, still working at the language. Maybe I don’t quite see the bridge, but I can sort of see the endgame: I would claim every one of us is mathematical, it is one of the ways we as human express our ways of knowing the world–that which we attribute to quantifying, patterning, and maybe something like knowing space. We have other ways of knowing the world as well, something about communication, (a third?… maybe:) intuition, hmmm…
So, back to the point: recognizing that we are all mathematical, and that you assume each mind creates amazingly interesting (intentionally avoiding words that sound like smart) ways of knowing, then each person is mathematically smart (sort of by definition).
The power, to me, of what I am trying to say is that the assumptions and structures of this idea flatten any possibility for hierarchy among knowers. More importantly, it requires our respect of (and interest in?) other’s ways of knowing in that it must add to our own.
Then what of (M)athematics? [meaning a “school mathematics”, a “European Mathematics”, that mathematics that people must know to have full access to the US culture/power structures????]
I think it is a rather simple answer, it is one way of knowing, and ought to be studied very precisely as that. As an object worthy of knowing, interesting in and of itself, but only *one* way of knowing/thinking/doing/being. It should also be studied in its segregationist roles, as an oppressive force, as a tool for destruction/war/wealth/greed.
leaving these thoughts midstream for now. I will enjoy the conversation into the Fall…
I am in the middle of reading Dweck’s book – Mindset – and can totally relate! Looking forward to reading your blog throughout the fall.
Oh,I am sooooo glad I read this today while I am writing my syllabus! I teach community college math and I see evidence of the talent lie all the time. Not only am I eagerly anticipating your posts, I am going to use your posts as readings for my students. I am so glad you are at the “devil-may-care” toddler blogger stage and are taking this on!
@David – Word. I christen your words my new slightly-corny-but-I-totally-mean-it slogan: “Math is a gift extended to all.”
@blaw0013 – Thanks for the thoughtful engagement! Looking forward to this conversation developing through the fall.
@Kathy – Right on. I’m definitely going to be drawing on Mindset, especially in posts #3 and 4.
@Kelly – Awesome. If you do end up using some of what I write with your class, definitely let me know how what they make of it!
I just came across your blog and enjoy it immensely. I’m happy to read you, Jesse Johnson, DY/Dan and others who make the world safe for math!
Can you direct me to teachers you know who teach math in a project-based context?
Okay, I know that this is a math blog, this comment is not entirely about math, but hopefully it’s okay anyway. This analysis of the discourse and attitudes surrounding being “good” at math are totally spot on about both their ridiculousness and their crippling effect on students/learners. My question has to do with how this attitude is communicated in other areas of learning as well. In a way, it seems most pervasive, or most clearly articulated, or most accepted, in the area of maths. I wonder why that is? I wonder this because it seems to me that this attitude pervades many other areas of learning, particularly at high school and elementary school levels. You note this in your mention of the term and practice of “gifted education.” Children can be made to believe that they are either “good at” something or “not good at” something, whether the something is an individual subject like math or writing, or a larger concept like “school.” The way that many people talk about opportunities for “gifted” children seems to contribute to this discourse of ability being an attribute of birth, not accumulation. But it seems like it shows up unevenly in different subjects, and math seems like one of the clearer examples of its capacity for damage, as your blog talks about the number of people who are convinced that they are “bad at math.” I don’t think as many people come out of elementary and high school thinking that they are “bad at history.” I could be wrong here, but I think it might be interesting to think about the similarities and difference found in this issue as it is found in the subject of math, and as it is found in other the teaching of other subjects, disciplines, educational methodologies. Math is one area we see this issue very clearly. Is it clearer there than in other areas? If so, why?
@Jane – I just followed the link to your blog and based on what I saw there, I’m sure you’re much more up on fully project-based teachers than I am! Are you asking about math teachers specifically? Online, have you checked out Shawn Cornally (Think Thank Thunk) and Riley Lark (Point of Inflection)? Both are very interested in and thoughtful about building the motivation for math content around real-world contexts. (I don’t think they’d specifically identify their instruction as “project-based” but I’m sure they’ll have plenty of material you’d be interested in.) I’d also direct you to Jason Cushner and Sarah Bertucci, a pair of teachers in Vermont who have created beautiful curricula around real-world problems and really ought to be nationally famous, but I don’t think they have a web presence.
Personally I am very interested in figuring out how to make mathematics itself as gripping and as user-friendly a motivating context as the classic real-world problems.
@Laura – (1) Whatup sis! Awesome to see you here! (2) Obviously non-math questions are fine. (3) This is a really interesting question and I look forward to thinking about it more. I have one thought right now:
The issue comes up in a lot of areas but it is especially heightened in the area of math because math lies at the intersection of two largely separate domains:
a) areas where there is a well-developed competition infrastructure and relatedly a well-developed image of prodigy
b) core academic skills/knowledge
The ideas of prodigy, giftedness, etc. are most frequently associated with:
*math
*explicitly competitive intellectual pursuits like chess
*creative arts (especially music)
*sports
*and, in recent decades, business
These are all also areas in which people think (correctly or not) that you can judge performance objectively and there is a whole apparatus of competition in each of them aimed at getting kids interested by engaging their competitive drive.
There’s a chicken-egg-other question here, but the connection doesn’t strike me as coincidence.
But math is the only one of these areas that’s also regarded as a part of core academic knowledge and skill, which means it’s the only one that all students have to deal with, and the only one that gets directly connected to students’ overall sense of intellectual self-worth.
There isn’t really much of an idea of “history prodigy” or “reading prodigy.” People do make a big deal about a kid who reads really early, or knows all kinds of information about the Civil War at a tender age, but they don’t frame their excitement in a way specific to the domain in which the kid is showing precocity. They just think the child is “really smart” or something. (While I agree that probably far fewer students leave high school believing they are “bad at history” than “bad at math,” the number who think they are dumb in an overall way might be comparable.)
In other words, it seems to me math is the only area in which precocity in that one area is understood as a) a domain-specific gift, that also b) gives you by itself the imprimatur of general intellectual superiority. The situation is heightened because as a core academic subject, everyone must engage with math, so everyone is forced to evaluate themselves on these terms.
(Just because I think the issue is heightened with math doesn’t mean I don’t also think the same conversation I’m having here applies in any other field. Regardless of the field, I think that the idea of a domain-specific gift is horrible for everyone and the idea of innate overall intelligence is even worse. The arguments I’ll be laying forth here will sometimes invoke research conducted in fields other than math, and all of them will apply without significant change to other fields.)
I love this whole discussion, and particularly the question as to why this issue seems to be more severe in math than in other subjects.
It reminded me a bit of Dick DeVeaux’s paper “Math is music, Statistics is literature.” He writes: “Prodigies in math can develop at remarkably early ages because math creates its own self-consistent and isolated world” (as opposed to Statistics, which requires common sense and life experience).
Click to access Mathmusic.pdf
Presumably, in fields like classical music, chess, and math… when it’s possible to be (or at least be seen as) a prodigy — and where stories of legendary prodigies are commonly held up as something to aspire to be — people fall into the trap of believing they can tell they’re clearly not a prodigy.
Or maybe that’s more relevant to the problems in your own life you’ve alluded to… I’ve had similar experiences: “I used to be the best at math in my high school, but whoa, now in college I’m not the best any longer and some things are wicked hard, so I must not be a prodigy, so why bother trying to become a mathematician?”
(I’ve ended up becoming a statistician … and I still wonder how much that’s due to my desire to work with real-world data vs. a cop-out fear of not being “good enough” at pure math.)
I’m also trying to figure out what frustrated you about the conversation with Unapologetic. Of course some kids will be further along than others, especially in a topic like math where you can just tell who’s ahead (more so than in literature or history)… and there should be nothing wrong with giving them appropriately-challenging work to keep them from getting bored while other students need more time.
But by creating a separate “gifted” track, you can’t help letting everyone else know that you think they’re NOT “gifted”. No wonder that many folks tune out and do the minimum to pass (if that). Is that it?
Anyhow, I look forward to reading more of your thoughts about how to avoid these traps!
Fascinating comment, “prodigies in math can develop at remarkably early stages because math creates is own self-consistent and isolated world.”
Why have we elected to name this activity that of a prodigy rather than of a sociopath? Or maybe I should be asking who elected to call this way of being/knowing that of a mathematical prodigy?
More specifically in response to Jerzy, I think it is an assumption worth unpacking to be able to speak about “further along” in mathematics. “Further along” implies on a, at least somewhat, linear path; at minimum toward and endpoint in particular.
If we consider the mathematical course that seems to be defined by ____ Standards (fill in the blank), then the way of speaking may be reasonable.
But as a mathematician, and considering doing mathematics and/or being mathematical, there is by no means an end goal. It is the activity that is mathematics (mathematical).
In this case, I don’t believe an educator to name who is “ahead.”
The more practical question is amid the idea of providing “appropriately challenging work.” First, assume a “task” or “problem” lies somewhere on that linear path. Then this questino is very difficult, and in fact really can only be answered with the idea that each child must be provided their own task. OR, assemble kids in a room that are all at the same place on the progression (today) and give them all the same task.
Drop the idea of math pursuing a linear task. Any problem then is one that any and every mathematical mind can approach, experience, and be propelled further as a result of the experience (the problem). [I concur that the notion of access to the problem DOES rely on previous experiences. the example we could all come up with is something akin to asking a 5 year old to explore the distance between numbers on the complex plane.]
If the thoughts above seem half-formed, it is because they are. I do know that for me, considering the mathematics of the _____ Standards is a tiny portion of we as math educators should concern ourselves with in the math classroom.
@ blaw0013 & Jerzy – seriously, it’s awesome to see this generating such thoughtful conversation.
@ Jerzy re: your question about the conv. w/ Unapologetic. I think you basically got the idea. I didn’t think I or anyone else in the conversation was suggesting that different kids (“more advanced” or whatever) might not need different kinds of work; nonetheless Unapologetic seemed to consistently read me that way. I was arguing against the language and the way of thinking attendant to the idea of “good at math,” but I didn’t seem able to communicate this to Unapologetic, who continued to read me as advocating that we not give challenging work to accomplished students. This would be crazy. I want a student with developed skills to have appropriate work, are you kidding me? I just don’t want us all to walk around calling this kid “gifted” or acting like their skills are the result of some intrinsic thing that they can’t control. Why I don’t want this is certainly for the reason you say (it disses everyone not similarly labeled) and there are a lot of other reasons too, to be detailed in the forthcoming posts, which unfortunately are not coming forth for at least another month. One of the other reasons I wrote about here. But all this has nothing to do with the work they get.
Hello, thanks for opening this line of inquiry! I think you’re right about lumping math with performance arts in terms of perception. As for business, I’d love to know what you think of the Gallup organization’s “strengths-based psychology”. It’s a series of books that promote a psychometric test that purports to discover your strengths for you (which are thought to be either unchangeable or not worth the disproportionate time and energy it would take to change). It’s sweeping my campus, and I haven’t been able to find any independent research about it. I’m also wondering how this fits in with “positive psychology”. I can appreciate the benefits of focussing on what people are good at; at the same time, some of the approaches seem very rooted in a “fixed mindset.” Any insight would be welcome!
I don’t know about Gallup’s thing you’re mentioning, so I don’t know independent research about it; I’ll follow your link soon. In the meantime, your reference to “fixed mindset” makes me think you’re already familiar with Carol Dweck’s research – I was going to point you to it as research that shows that the idea of innate strengths can be very damaging to people who supposedly have them. I’ll be talking about this with reference to math in particular in a few posts. So I guess what I’m saying is, I’ll be very skeptical when I follow your link to Gallup’s thing, and if you don’t know Carol Dweck’s research you should, and it (and in particular her trade paperback Mindset) might help you advocate for caution about the Gallup thing among your colleagues.
thank you.(I was thinking about writing about this myself) I too WANT to belive that talent is a lie.:-)