神经科学与心理学2025nature.com
儿童算术技能在应用数学与学术数学之间并不迁移
Children's arithmetic skills do not transfer between applied and academic math
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这篇论文考察儿童在应用情境中获得的算术能力是否能迁移到学校里的学术数学，反之亦然。核心发现是两者之间并不自动迁移：儿童在一种情境中会算，不等于在另一种情境中也会算。
HN 关注点：触及数学教育、学习迁移以及学校数学是否真正培养理解而非死记硬背。
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这几条评论里：支持 1 补充 3
补充认为学校数学重记忆轻理解，可能是迁移失败的原因。
我担心这是因为学术数学的教学和考试方式往往奖励记忆而非理解。下面是 Richard Feynman 对这个问题的看法：https://v.cx/2010/04/feynman-brazil-education
delichon查看英文原文
I'm afraid that this is because academic math is often taught and tested in a way that rewards memorization rather than understanding. Here's Richard Feynman's take on the problem: https://v.cx/2010/04/feynman-brazil-education
补充数学教学过于抽象和游戏化，应从工程与科学应用视角来教。
我的个人理论是：数学大多由喜欢数学的人来教，他们把数学看成一个有规则可循的解谜游戏，就像沉迷数独或 Wordle 的人。因此数学从完全抽象的角度被教授，只吸引那些喜欢这种数学游戏的人。而我认为，如果从工程或科学的角度教数学——把数学当作探索世界的工具，而不是报纸背面那种游戏——数学的影响会大得多。
Workaccount2查看英文原文
My pet theory is that mathematics is largely taught by people who enjoy math, and who see math as a puzzle game with rules you follow to solve puzzles. Kind of like people who are addicted to sudoku or wordle. Therefore it is taught from this totally abstract perspective and just hooks others who like the game of math. Whereas I think math would have a much greater impact if it was taught from an engineering or science perspective, where math is a tool used to explore the world rather than as something that would be a game you find on the back page of the newspaper.
补充迁移虽不直接，但数学表现可能是能力与“信号”的指标。
关键在于：我敢打赌，如果把在复杂抽象数学题上表现好的孩子放到需要复杂应用数学技能的工作中，最终表现最好的还会是同一批人；反之亦然。所以数学能力也许不能立即迁移，但会是有用的能力指标。这关系到一种有争议的经济学理论：高等教育很多不是在训练或创造可迁移技能，而是在“信号传递”。我们让孩子处在模拟准工作环境中，据此判断谁拥有某些有经济价值的能力。抽象数学表现好，信号表明孩子具备处理类似复杂现实问题所需的心智能力，也表明能服从权威、勤勉工作、延迟满足等。
chilmers查看英文原文
Here's the thing: I bet if you were to take the children who performed well at complex abstract mathematical problems and placed them in a job that required complex applied mathematical skill, the ones who eventually performed best would be the same. And vice-versa for the children who excelled at complex applied mathematics. So mathematical skill might not be immediately transferable, but would be a useful indicator of innate ability. This relates to the (somewhat controversial) economic theory that much of higher education is not about training or creating transferable skills, and instead is about "signaling". Essentially, we place children in simulated quasi-work settings and use it to determine who has the most of certain economically valuable abilities. By performing well at abstract mathematics, a child signals that they have the requisite mental ability to tackle similarly complex "real world" problems. But also, they signal that they are capable of obeying authority, working with diligence, delaying gratification, etc.
支持迁移本身是一种需要练习的技能，不能默认自动发生。
我很好奇。我的直觉是：默认情况下什么都不会跨情境迁移。相反，学会把某样东西迁移到另一情境本身就是一种需要努力培养的技能。简单例子：数节拍显然只是数数，但数节拍并使转换或变化落在拍上或拍外，是需要练习的技能。同样的数数可以帮助跑步者均匀呼吸。简单冥想常让你吸气数一、呼气数一。你会数数不等于自动擅长这些。还有一个问题：数数意味着什么？你脑中真的听到一个声音在念数字吗？你看到计数器吗？还是有别的心理计数系统？
taeric查看英文原文
I'm curious on this. My gut would be that NOTHING transfers between contexts by default. Instead, learning to transfer something between contexts is itself a skill that needs effort. As an easy example, just counting beats is clearly just counting. Yet counting beats and aligning transitions/changes on or off a beat is a skill you have to work on. Indeed, the same counting can help people that are running to start to even breaths out. Simple meditations often have you count a breath in, and then count it out. Just because you can count doesn't mean you will automatically be good at any of these things. There is also the question of what it means to count? Do you literally hear a voice in your head speaking the numbers away? Do you see a ticker? Do you have some other mental tally system?
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