Thoughts on teaching calculus to five-year-olds

Maria Droujkova writes, "Last week, The Atlantic published my interview called 5-Year-Olds Can Learn Calculus. I have been following the discussions on blogs, forums, and news sites. The themes that emerge from discussions make me cautiously optimistic. Many grown-ups believe that young math will finally give them a second chance at making sense of algebra and calculus. Others look for the balance between conceptual understanding and the fluency at manipulating numbers. Even if 5-year-olds understand calculus, what would they use it for?

Can we even call activities 'algebra' or 'calculus' if there are no formulas? Are young kids capable of abstraction? Quite a few people come out saying they are already playing advanced math games with toddlers or young kids - or that their parents did so with them! My community Natural Math will be following up on these themes with an open event series, interviewing parents, teachers, researchers, and project leaders who work in related areas.

One theme that I wish was discussed more is the role of autonomy, decision-making, and openness. If kids can't have their free play, or can't say no to activities meaningless to them, math can hurt, whether you work on calculus or simple addition. That's where most of the 'math grief stories' I receive come from. If parents and teachers can't choose, adapt, localize, and remix activities, it severely limits how they can help children learn. And if materials don't have open licenses (I use Creative Commons), it is hard to share or even discuss these adaptations. How can we create diverse, robust, sustainable structures where children are free to learn mathematics, and grown-ups are free to help them?

5-Year-Olds Can Learn Calculus [Luba Vangelova/Atlantic]

(Thanks, Maria!)

Notable Replies

  1. They could recalibrate the warp field coil without adult supervision.

  2. What would they use it for? Is this a troll post? What would 5 year olds use toys for, or soccer, or paint sets?

    I think the loose point of the article was that 5 year olds can learn rather advanced math if it's given to them like a toy or a paint set. You aren't supposed to worry about the practical application, it's this kind of thinking that kills the subject.

    I probably deserve a thatsthejoke.jpg at this point.

  3. micah says:

    Last year my son's kindergarten was doing combinatorics problems nearly identical to the combinatorics problems my cousin was teaching to math and computer science majors at the University of Pennsylvania.

    The Ivy League college students were expected to use more sophisticated strategies to arrive at more precise and complete solutions than the kindergarteners (who were effectively brute-forcing the answers), but the questions were essentially the same.

    I talked a bit with the kindergarten teacher about it. She had never heard the term "combinatorics" and was a little surprised to hear that the same problems were being taught at such a high level. In her class the point wasn't to get the "right" answer, but for the kids to spend time thinking about the relationships of the numbers, and from my conversations with my son I think it succeeded.

    When folks read about kids doing algebra or calculus at age 5 they think back to their high school algebra and calculus courses and assume that kids are learning about slope intercepts, quadratic equations, derivatives and integrals. But just as my son's kindergarten class never heard the word "combinatorics" yet used combinatorics problems to learn more about how numbers work together, there are many ways for very young kids to learn concepts that are core to algebra and calculus without having to memorize formulas or visualize the X and Y axes. And spending time thinking about those concepts can help them tremendously later in life.

    Heck, I was doing geometry at age 5 when I had to learn about angles to make the Apple Logo turtle draw cool pictures on the computer screen. I don't think I realized it was "geometry" until I got to middle school, but that doesn't mean it wasn't helpful to my ultimate ability to understand math.

  4. "Even if 5-year-olds understand calculus, what would they use it for?"

    Calculating the integral for the area under the covers, I assume, to make sure there's no room for monsters.

  5. Maybe early learning of any math in a fun way allows for more acceptance later in life. I believe that fear of math is a big problem, so even if a 5 year old doesn't learn calculus as high school students learn it, at least they can learn it is not scary?

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