Um, you fail to grasp the analogy. Perhaps it is too abstract for you? We program brains from birth by how we parent, math is no different from reading in ths manner. By allowing kids free play, counting with them, playing with blocks and beads, doing real world algebra, we are setting kids up for success in math. If you neglect to precondition the brain of a young child then success is more illusive, but this is not flash cards or rote learning, you have to work with the system in place - that is child development and typical play as the system one has to work with.
The important bit is that they mention teaching âwithout formulasâ. This implies that they are teaching the concepts and underlying frameworks in child-friendly language that ties into real-world experiences. But then again I didnât RTFA because I usually find people who try and force their specific domain knowledge on young kids generally insufferable. (Ooooo look at me! I taught my kids Klingon!)
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Analogy? I donât think that word means what you think it means.
But yes, I was taking it too literary. After actually reading the article, I understand what he is getting at⌠with the caveat that we donât know building this kind of base actually does help in learning mathematics later in life. But hey, it canât hurt.
quv DaHutlh
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Cory asked me: âEven if 5-year-olds understand calculus, what would they use it for?â
I understand calculus and I havenât used it since my university days over 30 years ago.
A question for younger programmers/software engineers: What was the most advanced math(s) required for your computer science degree?
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Or you could also teach them LOGO and use calculus to draw pretty pictures.
Pret sure I damn well know what I mean and what the word means. That is offensive.
The analogy of prettier
That is offensive, and I damn well used it the right way and exactly as I intended.
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First two things to learn about calculus, before you get near derivatives and integrals: limits, and approximating complex calculations with simpler ones.
Before you even combine those ideas to get the calculus, you already have two massively useful tools added to your mental toolbox.
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Yes, thatâs the joke: not everyone accepts âfree playâ as a legitimate answer to, âWhat are the uses of math?â Erik Demaine, the youngest math professor at MIT, discussed this issue in âBetween the Foldsâ (a movie about mathematics of origami). But for people who do accept play as legit, we do need to provide more examples of how kids can play with calculus. One of my favorite types of play is making branching, substitution, and Droste fractals by hand or with art software. We will be collecting more examples. Here is this weekâs math circle report on objects of revolution.
Love the roleplay! For young kids, and more and more for adults, motivation comes from playing in âalternative extended universesâ (fandoms!) or even creating their own. This can be just open pretend-play, or real virtual worlds like EVE Online and Minecraft.
I think of integration in its most grounded form: âbuilding big things from small things.â Or building surfaces out of strips, and solids out of layers.
For todayâs math circle, celebrating the Pi Day, I packed up a collection of cylinders made of other cylinders (toilet paper) and of circles (a stack of CDs) - and weâll make a cylinder out of rectangles (LEGO) to integrate it the third most-popular way.
This can come handy for 3D modeling and 3D printing, especially with newer high-order programming or computing languages, such as GeoGebra 5 and Wolfram.
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