问题: 科学:数学教育

操作搜索方程

+4  

事物?=其他事物

YAML 想法

在小学校,要求我们在已经给出运算符的前提下解方程。 例如:"4 + X = 5""6 - X = 9",等等。大多使用已经定义的运算符,例如+, -, *,...等。然而在现实生活中更有用的是创造力和操作搜索。 因此,与其提供给定的+, -, *, ÷, , ,...等,不如教孩子进行操作搜索以满足等号定义的条件。

例如,"4 ? = 5",意思是用"4"做什么可以得到"5"。或是"6 ? = 9"——用"6"怎么得到"9"?现在,将数字替换为孩子们生活中的真实情境,操作搜索数学教学可以帮助他们,培养他们的创造力,而不是生活在数学公理中。

而且,问号可能不是这里的最佳符号,因为它是有方向性的。像在等式一侧的无限维圆形问号之类的东西会更合适。

最初由Mindey发布在 HalfBakery





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// 思考 ? = Other Thing”听起来像是通过创造力解决问题的框架。

是的,好吧,用“想要的东西”(Y)替换“其他东西”,用当前情况(F)替换第一个“东西”,用“X”替换问号,你基本上得到“F(X)=于”。

// Think ? = Other Thing" sounds like a framework for problem solving through creativity.

Yeah, well, replace "Other Thing" with 'Desired Thing' (Y), and the first "Thing" with current circumstances (F), and the question mark with "X", and you get essentially "F(X)=Y".


[Mindey] ,我想知道,作为课程/学习体验,这会是什么样子?你能举一些例子吗?

“Think ? = Other Thing”听起来像是通过创造力解决问题的框架。学习者会定义“其他事物”还是教师促进课程?

[Mindey] , I wonder, how would this look like as a Lesson / Learning Experience? Can you give some example?

"Think ? = Other Thing" sounds like a framework for problem solving through creativity. Would a learner define the "other thing" or a teacher facilitating a lesson?


我假设问题中总是有多个运算符,并且它们是按顺序应用的。

这正如你所说的编程。如果计算机可以进行操作搜索,我们就可以让计算机自己编程。

我不知道序列到序列神经网络是否可以提供帮助。它们用于翻译问题和句子树。

您在附加 GUI 页面上提到了 Github 的 OpenAI Codex,我认为这与这个想法有关。

我想要自己编程的系统,例如以下功能 -

F(数据库状态1,请求)=(输出HTML,数据库状态2,网络调用)

该程序可以搜索请求中使用的信息的引用,以创建 HTML 和数据库插入的串联字符串。如果您在请求中指定 order_number 对应于数据库状态 1 中的 Orders 表,那么计算机可能会计算出需要将哪些数据提取到输出 HTML 中。

I assumed there was always multiple operators in the problem and they are applied in order.

This as you say is programming. We can have computers programming themselves if they can do operation search.

I dont know if sequence to sequence neural networks can help. They are used for translation problems and sentence trees.

You mentioned Github's OpenAI Codex on additive GUI page, I think that is relevant on this idea.

I want systems that programs themselves such as the following function -

F(database state 1, request) = (output HTML, database state 2, network calls)

The program can search for references for information used in the request to create the concatenated strings of HTML and database inserts. If you specify that order_number in the request corresponds to Orders table in database state 1 then the computer can probably work out what data needs pulling out into the output HTML.


这里所描述的其实并不新鲜:求解操作搜索方程可以被证明等效于搜索 ground term 来求解由 truth函数,其中符号 = 是要求它的两边相等。

一个“操作”可以说是一个“基本项”或一个操作搜索方程的“解”。

我认为这里的新颖之处仅在于简化了描述,使其与教育系统相关,以赶上现代思维的抽象和实用水平:即,而不是让孩子们反刍现有的功能或操作符来插入解决给他们的问题,——让他们想象可能的操作符应用于资源来解决他们关心的问题:例如:

  • 编写计算机程序是一种运算符搜索,其中编写的程序是找到的运算符,
  • 制造像钻头一样的仪器,是一种操作员搜索,其中制造的仪器(钻头)是操作员找到的,

等等。

What is described here, is really not new: solving operation search equations can be shown to be equivalent to search for ground terms to solve truth equations made from truth functions, where symbol = is a requirement for both sides of it to be equal.

An "operation" then can be said to be a "ground term" or a "solution" to an operation search equation.

I think the novelty here is only in simplification of description to make it relevant to education systems to catch up in the levels of abstraction and pragmatics with the modern day thinking: i.e., instead of asking kids to regurgitate existing functions or operators to plug in to solve problems given to them, -- allowing them to imagine possible operators to apply to the resources to resolve a problem that they care about: for example:

  • writing a computer program is a kind of operator search, where the program written is the operator found,
  • making an instrument like a drill, is a kind of operator search, where the instrument (the drill) made is the operator found,

etc.



    : Ruta
    :  -- 
    :  -- 
    

Mindey,

这也与正向链接和反向链接逻辑推理有关。

要计算最终值,您需要一个距离函数和一个方向。

而 distance(current_value) 大于 0 {

对于 next_functions(function) 中的函数 (

 候选人 = 函数(current_value)

 如果距离(候选)小于距离(当前值)(

 Directions.append(函数)

Current_value = 候选人

 休息

)

)

)

This is also related to forward chaining and backward chaining logical inferences.

To calculate towards an end value you need a distance function and a direction.

While distance(current_value) greater than 0 {

For function in next_functions(function) (

 Candidate = Function(current_value)

 If distance(candidate) Less than distance(current_value) (

 Directions.append(function)

Current_value = Candidate

 Break

)

)

)


这个想法也和自动化API遍历——程序合成有关。

This idea is also related to Automated API traversal - Program synthesis.



    :  -- 
    : Mindey
    :  -- 
    

chronological,

我认为这个想法与建议引擎有关。

生活有点像决策树。

你不能只在第一步就去哈佛、牛津或剑桥这样的专属大学。你需要先做其他事情。

我也有一个实现引导浏览的想法。这是半面包店。这个想法是您在结束搜索之前浏览一组页面。就像一个对你到目前为止所做的事情有反应的教程。

https://www.halfbakery.com/idea/Guided_20web_20browsing

I think this idea is related to advice engine.

Life is a bit of a decision tree.

You can't just go to Harvard or Oxford or Cambridge an exclusive university at step 1. You need to do other things first.

I also had an idea for achieving guided browsing. Which is on half bakery. The idea is you go through a set of pages before concluding your search. Like a tutorial that is reactive to what you have done so far.

https://www.halfbakery.com/idea/Guided_20web_20browsing



    :  -- 
    : Mindey
    :  -- 
    

chronological,

I had an idea for computers to work out how to perform an action based on representations.

So If you have an image it might not be in the right format for a crop code. so you need to convert it to pixels first.

First it would detect the image format is PNG and find a PNG decoder. Then it would find an operation that works on decoded PNG. Such as crop.

https://github.com/samsquire/ideas#11-representational-computing



    : Mindey
    :  -- 
    :  -- 
    

chronological,

//电脑可以这样做吗?象征推理?

取决于“ x?= y”中的x和y是什么。如果它们是数字或一些低复杂度的对象,则计算机可以执行此操作(有时称为[实体接地](https://web.archive.org/web/20141130194155/http://tedsider.org/teaching/ground /HO_entity_grounding_and_truthmaking.pdf))。例如,很容易想象计算机可以如何搜索路径,例如[技术方法](https://www.halfbakery.com/idea/Technology_20Maps_20_99),就像搜索道路的方式一样。

但是,如果x和y是非平凡的(对特征组合具有模糊的特征或模糊的值依赖性(只能由人对其进行评估并使用自己的价值体系来对其进行评估),或者在计算上是否复杂放入内存),那么计算机通常无法做到这一点,除非您将整个宇宙和人类视为计算机,这可能不是您所说的“计算机”的意思:)

// Can computers do this? Symbolic reasoning?

Depends on what is x and y in "x ? = y". If they are numbers or some low complexity objects, then computers can do this (it is sometimes called entity grounding). For example, it is easy to imagine how computers can do search for path, like technological method, in a similar way how it searches for driving directions.

However, if x and y are non-trivial (having vague features or vague value dependency on feature combinations (that can only be evaluated by a human looking at it and using one's value system to feel about it), or computationally complex, or not fitting into memory), then computers usually can't do it, unless you think of entire universe and humans as computers, which is probably not what you meant by "computers" :)


电脑可以这样做吗?

象征推理?

Can computers do this?

Symbolic reasoning?


这让我认为,这就是互联网搜索的工作方式-您指定当前的条件,目标条件(您要达到的目标)以及? -是搜索引擎应提供的行车路线或提示顺序,以帮助您到达目的地。为了做到这一点,它实际上确实需要掌握有关您当前情况的信息。大多数搜索引擎会自动执行此操作,因为我们使用了大量的服务(对于Google而言)。因此,他们知道每个人所处的情况。现在,任务是弄清楚每个人在生活中实际想要发生的事情^ __ ^,并在考虑到这种情况的情况下提供搜索结果,以使其成为现实。可能会出问题?

That makes me think, that this is how internet search should work -- you specify what is your current condition, and what is your target conditions (what you're trying to achieve), and the ? -- is the driving directions, or sequence of hints, that the search engine should provide to get you there. To be able to do that, it actually does require to have information about your current situation. Most search engines do that automatically, as we use a plethora of their services (in case of Google). So, they know what situation each person is in. Now, the task is to figure out what each person actually wants to happen in their lives ^__^ and provide search results with that context in mind, to make it happen... What could possibly go wrong?


所以我想知道:“运筹学”领域不是在潜意识里已经在试图将数学应用于发现这样的x-es吗?我想知道,该领域如何正式定义其问题领域...

So I wonder: isn't the field of "operations research" - subconsciously already trying to apply math to finding such x-es? I wonder, how does the field formally define its problem domain...


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