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“You can’t think seriously about thinking without thinking about thinking about something”

I remember having “computer time” in elementary school. We’d go to the computer lab and play games like Oregon Trail and Carmen San Diego. There was another program that I vaguely remember using, something that involved a “turtle” (actually a triangle, but we called it a turtle). I remember that no one in the class had any idea what to do with this, but every once in a while someone would yell out something like “I got it to turn green!” “I made a line!”. That was my experience with LOGO.

When I chose Mindstorms: Children, Computers, And Powerful Ideas by Seymour Papert, I figured that it would be mostly a memoir about creating the LOGO programming environment. I was surprised to find the author wrote much more about the actual act of children learning and how programming can help shape the future of education.

“Difficulty with school math is often the first step of an invasive intellectual process that leads us all to define ourselves as bundles of aptitudes and ineptitudes, as being “mathematical” or “not mathematical, “artistic” or “not artistic,” “musical” or “not musical,” “profound” or “superficial,” “intelligent” or “dumb.” Thus deficiency becomes identity and learning is transformed from the early child’s free exploration of the world to a chore beset by insecurities and self-imposed restrictions.”

when I was a kid, mathematics came somewhat easily to me. That was not the case with my wife, however, and discussing this book I found she shared a lot of the frustrations Papert outlined. Math was an especially difficult subject for her since from a very early age she had decided she wasn’t good at it. And that raises an interesting question: why did she feel she wasn’t good at math? and how can parents or educators help a child not let that get in the way of learning?

I agree strongly with Papert that programming can be a sort of “gateway drug” that can get students hooked on problem solving, logical analysis as well as creative and artistic expression. Is this happening in schools? I’m aware of the Scratch programming environment as well as LEGO Mindstorms (both descendants from LOGO), but I haven’t been involved in education. Are these being taught in schools? Are they part of core curriculum or simply electives? I’m curious since I see them as valuable for all students, not just those interested in STEM subjects.

“PLATO WROTE over his door, “Let only geometers enter.” Times have changed. Most of those who now seek to enter Plato’s intellectual world neither know mathematics nor sense the least contradiction in their disregard for his injunction. Our culture’s schizophrenic split between “humanities” and “science” supports their sense of security. Plato was a philosopher, and philosophy belongs to the humanities as surely as mathematics belongs to the sciences. This great divide is thoroughly built into our language, our worldview, our social organization, our educational system, and, most recently, even our theories of neurophysiology. It is self-perpetuating: The more the culture is divided, the more each side builds separation into its new growth.”

I personally agree with this statement, but I’d be happy to know what others think. As one who has never been able to fully identify with either camp, I’ve seen this thinking in action. I’m so happy that ITP does a great job blending the arts with technology, but that wasn’t my experience in high school or my undergraduate degree. I had to choose whether I would pursue art or computer science – even the term computer science lets you know that there won’t be much art involved – for my major. Do you think there is a value to separate the humanities from sciences or are there ways to combine them effectively? Can I ever really sit between the two for a career or will I always have to choose one or the other?

The book was great and I highly recommend it (though it is rather dense). I thought a lot about the attitudes of learning I will work to instill in my own children over the years.

and here’s a house in LOGO:

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10 comments to “You can’t think seriously about thinking without thinking about thinking about something”

  • Ben Kauffman

    The book sounds awesome. Definitely going to check it out.

    I would say that most paths towards an academic career in philosophy (which bares little resemblance to what Plato did) do in fact require at least an understanding of advanced math, logic, etc. Analytic philosophy, the philosophy of science and medicine, philosophy as it relates to language, all require “harder” skills than just reading, writing and researching.

    I think you’re totally correct that the comforting division of disciplines is a huge problem. It causes young student like your wife and myself, to write off whole universes of knowledge. Only at ITP am I realizing my deep love of math and science. Not that I’m good at it, but still!

    Plato may have written “Let only geometers enter,” (he found music to be dangerous!) but men of a certain social/political status in ancient Greece learned all of the disciplines and didn’t focus the way we do. They also learned communications skills like rhetoric that we neglect in our modern education.

  • Alexandra "Diracles"

    Thanks for your post Brett. I feel incredibly passionate about bringing programming and math into the life of my children (whenever I have them) for many of the reasons outlines above. For one, I think our country has started to be aware of this as being a nationwide epidemic in terms of our education system. I went to large, inner city, public schools my whole life and was hit very hard in terms of the lacking of inspiring or even meagerly talented teachers in the math and sciences. Also the class sizes were too large. Even if the teacher had any talent their lack of pay (30,000 a year), long days, and need to buy even the basic materials for their class out of pocket, completely disillusioned them. Many of my teachers were depressed and resentful of their lives and the school system. I remember in 4th grade completely missing out on fractions and decimals due to the lack of a capable teacher that year. For some reason the English teachers seemed to be happier…but that is besides the point.

    Learning to love a subject matter enough to master it takes influence, whether it be a parent, teacher, or friend. Every student deserves the opportunity to be surrounded by people who might inspire them but this is rarely the case in the public school system. Not to say that there are plenty of cases where people do blaze their own trail even when they lack positive influences in a certain subject matter, but this is the exception not the norm. I’m curious to know who influenced you in your life and if it had anything to do with your approach to math? We receive both nature and nurture from our parents followed by a great deal of influence from our friends and community throughout our life. I agree with what you say about ITP being a place where people are allowed to celebrate in the fact that we all want to learn about related things in our own unique way. I believe this could be a positive approach for many schools to take in the future. I’m passionate about continuing to adjust curriculums and advance innovation in learning to embrace many ways of approaching the same problem. We all learn differently to a certain extent, how can we use that as an advantage? I think ITP is figuring out ways to do that though there is still work to be done to perfect the process. I think one step in that direction may be dropping the idea of innate knowledge in replacement for time spent studying and being around certain subject matters.

    I recently read a book called “Minsset: the new psychology of success” by Carol Dweck and it breaks down into two categories: fixed mindset and growth mindset. She defines them as, “If you have a fixed mindset, you believe your talents and abilities are set in stone — either you have them or you don’t. You must prove yourself over and over, trying to look smart and talented at all costs. This is the path of stagnation. If you have a growth mindset, however, you know that talents can be developed and that great abilities are built over time. This is the path to opportunity and success.” It’s a good read though I believe we are all a bit of a mixture of the two. It reminds me of another article I read by David Brooks, the New York Times columnist. He wrote an incredible OpEd piece called “The New Humanism” ( which goes through many topics one of which being how we revere IQ but not character. He says it best and I have to quote him here as it is one of my favorite quotes of all time:

    “You get a different view of, say, human capital. Over the past few decades, we have tended to define human capital in the narrow way, emphasizing I.Q., degrees, and professional skills. Those are all important, obviously, but this research illuminates a range of deeper talents, which span reason and emotion and make a hash of both categories:

    Attunement: the ability to enter other minds and learn what they have to offer.

    Equipoise: the ability to serenely monitor the movements of one’s own mind and correct for biases and shortcomings.

    Metis: the ability to see patterns in the world and derive a gist from complex situations.

    Sympathy: the ability to fall into a rhythm with those around you and thrive in groups.

    Limerence: This isn’t a talent as much as a motivation. The conscious mind hungers for money and success, but the unconscious mind hungers for those moments of transcendence when the skull line falls away and we are lost in love for another, the challenge of a task or the love of God. Some people seem to experience this drive more powerfully than others.”

    I feel like there are many moments of limerance at ITP. We all have our individual motivations but fall into another (unreachable state as an individual) when we learn and share with one another.

  • Sergio "Majluf"

    Hello Brett,

    regarding your last question “Can I ever really sit between the two for a career or will I always have to choose one or the other?” I think it’s pretty clear right now that we are in the right place to sit in. I think that if ITP excels at something, is providing that blended – even diffuse – context where we can become comfortable with both sides at the same time. It pisses me so much that kids have to choose one area over the other.

    I remember so clearly when I was in elementary (I think 4th grade) and had LOGO classes. It wasn’t until I started reading this same book a few weeks ago that I realised how deep an impact it made in myself, as a person, and as a professional, in the way I analyse, relate to spatial dimensions, and in the fearless relationship I have with technology.

    Reading your post in the first place made me pick up this book; it was long ago in my to-read list. Thank you for choosing it!

  • Andrew Cerrito

    I taught after-school programs in Scratch and LEGO robotics before ITP. It seems like most schools, at least in the NYC area, relegate these topics to afterschool program contractors like the one I worked for. This means that children that have an outright interest in these subjects have opportunities to explore them further, but children who might not have explicit initial interest don’t really have a chance to be exposed to it, which is a shame.

    Find me in real life if you want to talk about this a bit more!

  • Brett

    I’m really happy to see the conversations happening here! I’ve been thinking more and more about education in general, and more specifically how I can influence education in my own (and my families lives). A few responses to some of what’s been said:

    Allie, you asked who influenced me in my life and whether it had an impact on my approach to math. When I was young (till about 12) the only extended family we lived near were my grandparents on my mother’s side. We spent a lot of time with them and it was really wonderful. My grandpa was a retired officer from the Air Force, working in a lab as a scientist. During his time there, he taught himself to use these machines called “computers”. He told me stories of sending punch cards off to a facility in Arizona when they wanted to run programs. Literally punching holes in cards, then sending a stack of them in an envelope. Anyway, he taught himself how to use computers and then taught computer science at a college in Sacramento. When we would come to visit I’d go on walks in a nature area with him and ask him about everything I saw. We’d identify trees, check out animal scat and tracks and look at the changing water level of the American river. We’d set up a telescope in the front yard and look at Venus and talk about the rotation of the planets. I’d have a crazy idea about something like building a raft out of bamboo and he’d encourage me to try it out. I really did learn so much about math, physics and the world around me and doing it while exploring and testing things out. That’s something I still feel strongly about; I’ve never done well at just memorizing things or “learning” just for the sake of passing a test. It has to mean something to me – it has to serve a purpose in what I’m trying to do or I don’t really learn.

    How do we give that experience to children? I remember trying to memorize my multiplication tables – and hating it. It didn’t make sense to me at first and I didn’t know why I needed it. Andrew, it seems like the after-school programs you taught would have been something I would have LOVED to participate in. Were there any opportunities to raise awareness of the programs? Were you ever allowed to go to the school during school hours and show the kids what they could be doing? Maybe there were programs at my schools that I just didn’t know about. I bet a lot of kids would go if they saw the Lego robots they could build, whether or not they knew beforehand that they had an interest in robotics.

    Thanks also Sergio for your comments. I agree that here at ITP I’ve felt more “at home” than any other time in school. I’ve gotten to tap into both sides of my brain and I’ve been loving it. I’m hoping that I’ll be able to continue to do that after our program, however. I thought I would be able to after my undergrad degree and that was not the case. That’s something I’ll definitely be looking for in a job after ITP.

  • Nancy

    Great discussion and hooray for ITP! WE need ITP in middle school!
    Brett.. that program with the triangle turtle was Logo. The precursor to MicroWorlds. Just a few words on Seymour Papert, an old friend,a nd one of the great mind of the 20th century. His influence is vast/boundless. Alan Kay says he is one of the ost influential people he’s ever met. He changed my life around completely. You also might want to check out The Children’s Machine. Papert was an epistemologist, meaning he studied how we acquire knowledge. Worked as an Research Assistant to Jean Piaget ( assuming you’ve heard of him, if not LMK).
    Seems to me re the issue of apathetic learners: that’s the job of teachers– to make enthusiastic learners, unafraid learners. People with non-fixed mindsets as Allie points out.

    Happy to have a discussion on these issues any time. This is the field I came from.
    And by the way, you all should read the “Two Cultures” essay by CP SNow…A classic, and just what you all are talking about and inventing yourselves!

  • Brett

    Thanks Nancy, of course I know NOW that the program was called Logo but it wasn’t until I was maybe in high school that I found out more about it. At the time it was just that turtle game.

    I will definitely check out those books you mentioned. I’ve really started thinking a lot more about how we learn. I have a daughter who is just over a year old. I’m fascinated to see her learn so much every day and in such interesting ways. For example, with Christmas coming up, we received a couple books about the nativity. We pointed out baby Jesus to her and she started saying “Jesus” (well, something close) and pointing to him in the other books. That’s already interesting to me that she can identify a similar scene drawn in a completely different style and still associate it with the Jesus she saw in a different book. So then we’re in Church and she sees a painting of Jesus as an adult. A bearded, adult man. When we tell her that, too, is Jesus, she totally gets it, starts pointing at other paintings and calling out “Jesus!”. That, to me is incredible. I think about how I would have to program a computer and say something like “yeah, the little baby, ONLY if there’s animals around and probably a halo or glowing or something, that’s Jesus. And a much older bearded man, usually surrounded by people, that’s also Jesus” Absolutely fascinating.

  • ssb425

    While I was in school (around 4th grade) Logo was taught as a part of introduction to computers. I remember going to the lab for an hour every week where we created interesting geometric structures using logo. But never was it taught from the perspective of art or creation. We were supposed to analyze the movement of the turtle and why it was moving but were never asked to look at the creation. I believe such an approach to teaching leads to the split Brett is talking about. I was lucky that sketching was one of my hobbies during my childhood else I would not have been here at ITP (it’s scary when I think about it). And much of it has to do with the educational system.

    In my school (back in India), Art was not given nearly as much importance as the other fields of sciences or language. I remember most of my teachers (of Art) never really cared about teaching what the subject was about. As a result, the thought of Art as a feasible profession never really came up. It’s quite surprising that India now has a high adoption rate for technology and sciences but not in the case of Art and Humanities. A real shame looking back at it’s cultural heritage and significance.

  • Joseph Lim

    “Difficulty with school math is often the first step of an invasive intellectual process that leads us all to define ourselves as bundles of aptitudes and ineptitudes, as being “mathematical” or “not mathematical, “artistic” or “not artistic,” “musical” or “not musical,” “profound” or “superficial,” “intelligent” or “dumb.” Thus deficiency becomes identity and learning is transformed from the early child’s free exploration of the world to a chore beset by insecurities and self-imposed restrictions.”

    I totally agree with this. I struggled with math myself and a lot of the educational structure just works to undermine students’ confidence in their abilities after struggling briefly in a subject.

    One of the most difficult things I’ve had to do is to teach students to think logically about design problems to solve them in a programming language. Usually the excuses I hear are that the students think they are creative, not logical or that they think they are bad with math. It takes time to go from “following a recipe” to “writing the recipe,” but it is super rewarding as you watch them ‘get it’ and do something that they never thought possible. I’ve had students tell me they avoided math for years because they thought they were terrible at it and in the end it was simply a matter of finding a new way to frame it.

  • etb273

    The idea of mathematics in education that you point to is very apt. Even though I was a natural with music I was placed into the mathematical ineptitude group. Because of this I never learned how to work with mathematics and how to learn them. I struggle to this day with the stress I know associate with mathematics. I thoroughly understood Symbolic Logic yet was barely able to pass the class due to my early categorization and what I had learned from that. throughout my life I have lived with self imposed barriers that I learned in my early education. Through ITP I have been able to begin to learn how to remove those restrictions I learned. I do still get physical aversion responses to mathematical based work. It’s kind of insane because I am clearly naturally good at math. I never new understood this and was able to utilize that skill.

    It is extremely important that we work to rectify the categorization in our education. It has certainly slowed my process. I have definitely self imposed restrictions on my abilities due to how I was educated. To be honest I didn’t realize I was smart until I was in my late 20’s. I can’t imagine where I would be if I had realized this earlier