学习数学的AI

使用AI进行英语学习和数学学习可以带来许多好处，以下是一些方法和建议：[heading3]英语学习：[content]1.智能辅助工具：利用AI写作助手（如Grammarly）进行英语写作和语法纠错，帮助您改进英语表达和写作能力。2.语音识别和发音练习：使用语音识别应用（如Call Annie）进行口语练习和发音纠正，让AI提供实时反馈和建议。3.自适应学习平台：使用自适应学习平台（如Duolingo）利用AI技术为您量身定制学习计划，提供个性化的英语学习内容和练习。4.智能导师和对话机器人：利用智能对话机器人（如ChatGPT）进行英语会话练习和对话模拟，提高您的交流能力和语感。[heading3]数学学习：[content]1.自适应学习系统：使用自适应学习系统（如Khan Academy）结合AI技术为您提供个性化的数学学习路径和练习题，根据您的能力和需求进行精准推荐。2.智能题库和作业辅助：利用智能题库和作业辅助工具（如Photomath）通过图像识别和数学推理技术为您提供数学问题的解答和解题步骤。3.虚拟教学助手：使用虚拟教学助手（如Socratic）利用AI技术为您解答数学问题、提供教学视频和答疑服务，帮助您理解和掌握数学知识。4.交互式学习平台：参与交互式学习平台（如Wolfram Alpha）的数学学习课程和实践项目，利用AI技术进行数学建模和问题求解。通过结合AI技术和传统学习方法，您可以更高效、更个性化地进行英语学习和数学学习，并取得更好的学习效果。内容由AI大模型生成，请仔细甄别。

So can AI help with mathematics at this “fluid-dynamics-style” level?Potentially so,but mainly in what amounts to providing code assistance.We have something we want to express,say,in Wolfram Language.But we need help—“LLM style” —in going from our informal conception to explicit computational language.And insofar as what we’re doing follows the structural patterns of what’s been done before,we can expect something like an LLM to help.But insofar as what we’re expressing is “truly new”,and inasmuch as our computational language doesn’t involve much “boilerplate”,it’s hard to imagine that an AI trained on what’s been done before will help much.Instead,what we in effect have to do is some multicomputationally irreducible computation,that allows us to explore to some fresh part of the computational universe and the ruliad.那么人工智能可以在这种“流体动力学风格”的水平上帮助数学吗？可能是这样，但主要是提供代码帮助。我们有一些想要表达的东西，比如说，用Wolfram语言。但我们需要帮助——“LLM风格”——从我们的非正式概念转变为明确的计算语言。只要我们正在做的事情遵循之前所做的结构模式，我们就可以期待像LLM这样的东西来提供帮助。但就我们所表达的内容来说是“真正新的”，并且我们的计算语言不涉及太多“样板文件”，很难想象接受过以前做过的事情训练的人工智能会有多大帮助。相反，我们实际上要做的是一些多重计算的不可约计算，这使我们能够探索计算宇宙和ruliad的一些新鲜部分。

If we ask students to use AI for writing,they need to know what good writing looks like.That takes time.And effort.And a whole bunch of mistakes.If we want students to edit an AI generated text with their own voice,we need them to find their creative voice first.This is true of AI in writing but also AI in math.We don’t want students using AI to check their processes if they haven’t first learned the mathematical process.It’s true of computer coding,where we might start with a Scratch project,then hand-written code,then an AI and coding hybrid.Be Deliberate About What You Off-Load to AIA couple of months ago,I wrote about seven things we should consider when deciding to use AI.People often ask,“When is it okay to use AI?” The short answer is,“It depends on the learning task.” In using AI,we don’t want the machine to do the learning for us.This is why we should start with the learning tasks and then ask,“Does the AI help or hinder the learning in this situation?” The core idea here is that we need to use the learning targets to drive the AI and not the other way around.If you’re teaching a coding class,you might want to be tight with students on using generative AI to create any kind of code.You might want students to learn how to code by hand first and then,after mastering the language,use AI-generated code as a time-saving device.By contrast,if you’re teaching a health class where a student develops an app,you might not care if they use generative AI to help write the code.Instead,your focus is on helping students design a health campaign based on healthy habits.You might not have time to teach students to code by hand.You might not care about coding by hand.The app is merely a way for students to demonstrate their understanding of a health standard.