通过社区改善数学

由Adam Dionne.

Personally, I’ve found that there are two important ingredients to improvement: making goals and reflecting regularly. Goals are the more obvious component, since to improve you must be working towards something. But there is an important nuance in how you construct goals. Perhaps the ol’ reliable mnemonic serves best. Goals should be SMART: specific, measurable, attainable, relevant, and time based. None of these components can be understated, and all work towards preventing an all too common pitfall: setting yourself up for failure with nigh impossible goals. For math, understanding and avoiding this pitfall is essential. Some days you will solve all the problems you face and feel like a mathematical wizard. However, most days are spent being stuck, getting questions wrong, and seemingly making “no progress”. But as a detail oriented mathematician, you might retort and ask: how does one measure “progress”? It is natural, and even built into our education, to measure progress on problems solved and correct answers given. But in math, one can make a tremendous amount of progress while failing to solve a problem. Or, dare I say, getting a problem wrong. In fact, I would argue that is precisely when one makes the most progress. So, if you want to improve at math, I’d suggest constructing goals that embrace failure, getting questions wrong, and being stuck. But this is all a lot easier said than done. This mentality is difficult, to say the least, and is most difficult precisely when it is the most important. So, to remedy this, I suggest making use of a truly critical resource for anyone: community.

那么,我们如何将这些想法纳入我们的社区?好吧,我建议我们一起举行目标。我亦表明我们彼此持有符合现实健康目标的对象,如讨论所讨论的。重要的是,这些步骤有助于改变对基于社区的活动的改进,这提供了许多目的。对于一个人来说,很难认识到自己的改进,因为它是一个渐进的过程偷偷摸摸。这使得自己易于思考你没有改善。但是,承认同伴的改进是更容易的。因此,如果您与他人分享目标,您可以认识到彼此的增长,并通过代理您自己的增长。更重要的是,这些建议建立并加强了社区。

Let’s move onto the second ingredient for improvement: reflection. I believe reflection is absolutely crucial to improvement. For without reflection, important lessons and growth are being wasted. For example, let’s say you put a lot of time into working on a problem but made a mistake along the way. That mistake is a clear place for improvement. One should think about why they made that mistake, and more than just the surface level — truly investigate the process of what led to that mistake, and why you didn’t catch it sooner. People do this automatically — it is a natural process — but not with enough depth. As problems get harder and mistakes more intricate, it is important to actually devote time to this process. To spend time thinking about how you can improve and what to focus on. Reflection is making your improvement intentional and actionable, rather than an accidental byproduct of work.
并将其纳入我们的社区,我们只是需要一起反思。谈论什么是工作,什么不是,讨论您所做的改进,并谈论您学到的具体课程。这也允许其他人从错误中吸取教训,一个社区最令人难以置信的价值之一。它还再次加强社区并帮助持久联系。在一天结束时,数学是一个困难的主题,并使改进永远不会容易。但与朋友分享负担或导师,使其变得更加现实。所以,我想修改我的启动启发式:改善数学,你需要三个关键的成分:目标,反思和社区。

亚当迪翁

传:我是威廉姆斯学院的数学和物理双重专业。我对数学形式主义,极端图理论,软质物理和网络感兴趣。在我的空闲时间,我喜欢播放棋盘游戏和看电影。

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