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Operation Search Equations

Thing ? = Other Thing
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In the elementary schools, we are asked to solve equations with assumption that operators are already known. For example: 4 + X = 5, or 6 - X = 9, etc., mostly with the already defined operators, like PEMDAS. This is is damaging to our curiosity and creativity, as our minds are forced to live in someone's single computational universe.

However, what's more useful in real life, is the creativity and operation search. So, instead of providing "+", "-", "*", ... as given, teach kids to do operation search to satisfy conditions defined by the equality sign.

For example, 4 ? = 5, meaning, -- what can we do with 4 to get 5. Or 6 ? = 9 -- what can we do with 6 to get 9? Now, replace the numbers with real situations in kids' lives, and teaching operation search math can help them, fostering their creativity rather than life in one axiomatics of mathematics.

And, perhaps the question mark is not the best symbol here, as it is directional. Something like an infintie-dimensional circular question mark around one side of equation would be more appropriate...

Mindey, Apr 04 2020

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       It's going to generate confusion and ambiguity, and may actually inhibit learning.   

       The problem is that the notation and symbology isn't confined to mathematics. Those symbols are used in computation, as arguments to search engines and the like.   

       You either add new symbols (demanding more learning) or assign additional meanings to existing symbols (confusing and context-sensetive).
8th of 7, Apr 04 2020
  

       // confusion and ambiguity   

       I don't think so. The practical solutions to their everyday lives may actually make them get those solved, and then have time for other kind of equations. Solving what matters, not what's on textbook, is top priority, and most rewarding, thus, facilitating learning. Like, usefulness of learning to ride a bike, encourages further learning...   

       // Those symbols are used in computation, as arguments to search engines and the like.   

       // additional meanings to existing symbols (confusing and context- sensetive)   

       Can you elaborate on these, as, for your pre-trained mind, the symbols may already have some meaning, unlike for a kid without much knowledge, say, in GOFAI and grounding propositions.   

       And, making kids useful to how OUR specific minds are working (boxing them into our thinking), so they can work for us, is not a very noble cause. I'd go for diversity, and letting kids discover their new ways.   

       And, if you read the bottom line of the idea more closely, you see, that what I proposed is not a reuse of particular symbol, but "a symbol" for operation search requirement, where "?" is not the best option.
Mindey, Apr 04 2020
  

       //This is is damaging to our curiosity and creativity//   

       No it isn't. In fact, quite the opposite. I remember first coming across propositional logic (and then first-order predicate logic) as an undergraduate, and thinking "Where have you been all my life?" That's because, from quite early in childhood, I had had trains of thought which could be described in the language of formal logic - but, because I had not been taught this language, I had no way of sharing these thoughts with others, nor even of developing them in my own head.   

       Now, if I had been taught the language of formal logic at the same age at which I had been taught the language of arithmetic, I would have been able to take those thoughts and run with them, instead of just stewing in frustration.   

       If you don't give children tools of this kind, you're not liberating them; you're crippling them.   

       I get that you're trying to stimulate higher orders of reasoning (meta-reasoning, if you like) - but, to do that, you need first to establish lower orders of reasoning to build on. Have you read "Goedel, Escher, Bach"?
pertinax, Apr 04 2020
  

       // No it isn't. In fact, quite the opposite. [...] if I had been taught the language of formal logic at the same age at which I had been taught the language of arithmetic, I would have been able to take those thoughts and run with them. //   

       I could say the same about integral calculus or differential equations. But, I could not say that about my friend <Q>. She would have found the valence bond theory and molecular orbital theory empowering her creativity. Yet learning of something else, like integral calculus, premature and not as empowering, perhaps making her ask "why do I learn that?".   

       Knowledge being instrumental, it is an imperative to teach the most general-purpose tools that we have in our arsenal, and the standard set of operations are not them. Search for operations is. We do that every time we think of new idea here on Halfbakery -- an idea is essentially some operation X to be applied to a situation F to obtain an outcome Y, i.e., X, such that F X = Y, that is a solution to F ? = Y.   

       // I get that you're trying to stimulate higher orders of reasoning (meta- reasoning, if you like) - but, to do that, you need first to establish lower orders of reasoning to build on. //   

       It is my experience, that to learn modern mathematics, you need to follow the prerequisites very thoroughly, because results build one on top of another, and unless you're a genius that can reinvent entire fields of mathematics spot-on, or have read literature on the background topics, you'll be unable to follow. This idea is not to refute that pyramid of knowledge. It's to extract certain results, that, after all, do not require knowing the lower orders of reasoning, because operation search is so fundamental to intelligence and life, that it coincides with search for actions ("what to do to..?"), and would be natural for kids to comprehend.
Mindey, Apr 04 2020
  


 

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