Jeff Catania:

By the way, I don’t think you don’t have to *teach* conceptual curiosity as the human brain is naturally curious if we let it make connections between ideas to build concepts (constructivism) naturally. We only *think* we have to teach curiosity because student brains have been so dulled by procedures that they merely memorize without stimulating existing neural pathways.

Incidentally, I am in the middle of a post which may never see the light of blog, one which attempts to answer the question, “How should we capture and present digital media for classroom use?” and sets a personal record for most uses of the phrase “for lack of a better word.” The post has tangled around so many media, including but not limited to The Shield, The Wire, No Country For Old Men, Off-Road Algebra, Discovery Education streaming, Caché, David Mamet’s On Directing Film, What Can You Do With This?, Problem Pictures, Graphing Stories, and Dogme 95’s Vow of Chastity. This is fun and maddening, all at once.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Interested in how all those resources fit, especially the Mamet, an old college chum of mine lo these many years ago.

    As for inquisitiveness, my experience is that we drill it and school it out of kids by about third grade, if math lessons are any indicator. By that grade level, kids have learned not to put themselves at risk by venturing answers unless the questions are simply numerical and simple and they are 100% sure that they have the correct number. Otherwise, they stay silent and let the teacher answer his/her own question, which happens inevitably, generally in less than 5 seconds.

  2. Tufte’s books are good—-I assumed that Dan had already read at least one of them. I understand that Tufte’s workshops are also worth going to (according to some grad students who have been to them in the Bay Area), but I’ve not gone to one myself.

  3. Is Jeff’s comment actually true? Do children raised without schools or formal education normally display more curiousity? I don’t know one way or another, but I question it because Adam Smith, in his book the Wealth of Nations, did not present the uneducated as naturally curious. To quote from Book 5, chapter 1, part 3, article II:

    He naturally loses, therefore, the habit of such exertion, and generally becomes as stupid and ignorant as it is possible for a human creature to become. … The same thing may be said of the gross ignorance and stupidity which, in a civilised society, seem so frequently to benumb the understandings of all the inferior ranks of people. A man without the proper use of the intellectual faculties of a man, is, if possible, more contemptible than even a coward, and seems to be mutilated and deformed in a still more essential part of the character of human nature. …An instructed and intelligent people, besides, are always more decent and orderly than an ignorant and stupid one. They feel themselves, each individually, more respectable and more likely to obtain the respect of their lawful superiors, and they are therefore more disposed to respect those superiors. They are more disposed to examine, and more capable of seeing through, the interested complaints of faction and sedition…

    Also there are different sorts of curiousity – even if children are naturally curious, what sorts of answers are they contented with? The first Just-So story that comes to mind?

  4. I don’t know about children raised without schooling but I liked your Adam Smith quotation.

    What I (think I) said was that *children schooled without a constructivist approach* will have their natural curiosity squelched. You can see the truth of this if you look into their mis-, pre- and partial-concepts.

    “Tom used a calculator to figure out the price of a purchase and it showed 6.125, how much is that in dollars and cents?”

    Many high school students will say this is $7.25 because of a misconcept about decimals constructed from their classrooms–can you figure it out?

    Misconceptions are proof-positive that the mind does enjoy making it’s own curious connections (even if wrong) and they’re good news too because it shows students *think* and learn all the time.

    Curiosity is the theme of the my favorite short book ever written on teaching math entitled “The Top 10 Reasons to Skip Math Class” (George Gadanidis) at

    Thanks Dan for bringing all these ideas to light.

  5. I don’t know about kids with no schooling, either, as they are hard to find in the US if they grew up here (though I imagine they do exist). Whether Smith was right that such kids would lose their natural curiosity would depend a great deal, I suspect, on what they’d be doing INSTEAD of going to school (including home-schooling, of course). If they were doing some six-day-a-week 12 to 14 hour per day factory job, as was common in Smith’s day, they’d likely be unable to stay awake past dinner, so curiosity wouldn’t matter even if it still existed: there would be neither time nor energy for it in the vast majority of cases.

    On the other hand, of far greater concern in industrialized nations with mandatory education up to the mid-teens is why so many kids, including successful “smart” ones who get decent, good, or great grades in school, are intellectually diminished and so seemingly incurious so soon after they start their formal education. Granted, some kids have already had their natural curiosity stepped on by repressive experiences outside of school, very early in life. But for those who still come at age 5 or so brimming with ideas and full of energy to think, play, and speculate, why are so many of them unwilling and seemingly unable to do any risk-taking by about third grade?

    To me, this phenomenon, which I have observed in a lot of classrooms in a variety of districts, is the result of being “schooled” all too well in a kind of social attitude that is in fact, consciously or otherwise, a major point of public education in many countries, and clearly so in the US: don’t stand out. The nail that rises above the others gets hammered down first.

    Of course, kids do get schooled to compete, too. I went to a meeting for 8th grade parents at my son’s school last night, held by the principal, vice principal, and guidance counselors from the high school. The word “compete” came up a lot. As did “rigor” and a number of other buzz-words that frankly had me having to bite my tongue quite often. My son’s mom, who didn’t attend, would have been in hog heaven: those words speak directly to her ideas of what school is about (though she herself didn’t compete all that well and avoided “rigorous” mathematics, for example, a decision that resulted in her becoming a nurse rather than going to veterinary school as she had wanted).

    I, on the other hand, who did well when I actually made the effort, was sufficiently turned off by the whole school mentality by 9th grade that I more selectively shot myself in the foot, but was able later to actually learn much of what I slept through in high school, particularly in mathematics. And I am yet to buy into the sales pitch that I heard last night. I worry to this day that my son is still confused despite my efforts to dispel the illusion, that good grades mean actual learning, or that the grades themselves, not the process of learning and what you choose to do and how you do it, are the goal. He still shows signs of curiosity, however, so I believe there’s hope for him. But this is despite, not because of his school experiences for the most part.

    I think what we do to kids in school is a travesty for the most part, and as a mathematics educator, I see math class as one of the worst environments for kids when it in fact should and could readily be the best. Of course, like many American kids, I was given NO CLUE AT ALL about what math is when I was in school. I was a fine little calculator and got all As through 8th grade in math as a result. But I didn’t know that mathematics was a growing, living field; that there was new mathematics being created every day was never mentioned and I wonder if my teachers even knew that. Why we were being taught many of the things in the curriculum was a forbidden area of inquiry: I was shot down for asking about the point of “imaginary” numbers, for example. What a question for high school kid to ask!!! I wonder if the teacher knew himself even one application of complex numbers.

    I’d be interested in getting my hands on Gadanidis works, which sound potentially subversive in a good way. Thanks for that tip: hadn’t come across his name before.

  6. Well Adam Smith did argue that people in a hunter-gatherer soceity were naturally more curious and thoughtful – they had to be to survive. I don’t know how much anthropological evidence he had on this, I suspect not much, and regardless of how true his statement was, a hunter-gatherer economy is not a description of a developed nation’s economy. In a rich economy, it’s possible to get food without much in the way of thinking. So it strikes me as entirely possible that even if kids didn’t go to school, they would still lose their curiousity here. One of the things that seems clear about humans is that naturally we are deeply affected by the culture we grow up in, so to talk about what we naturally are like doesn’t tell us much unless we understand the cultural context of this naturalness (obviously everyone shares some things, like a need for food, and a sense of humour.).

    I’m still puzzling about the misconception behind Jeff’s $7.25 example. Thanks for it :)

    Michael, I share your pain. I don’t recall any bad experiences in maths classes, but I remember getting very fed up that every year for about 4 years we were taught “the one correct way” to write letters, and every year “the one correct way” of letter writing was different (as in did you put your name address or the addresse’s name and address at the top of the page, etc), and no teacher would ever acknowledge the constant changes in “the one correct way”.

  7. But I didn’t know that mathematics was a growing, living field; that there was new mathematics being created every day was never mentioned and I wonder if my teachers even knew that.

    I’ve written about this here.

    I will also be presenting other similar ideas at this conference.