3 "TOP" Tips to Study Math (Last Part) - Practice!

Just Somebody
Jul 3, 2021
8 min read

If you haven't reach the first two TOP tips, please go ahead and read first:

Finally, last but not least, the 3rd TOP tips would be Practice! I believe this idea is not new and often bundled together with when we’re talking about math. But the thing is most people are barely scratching the surface of this practice part only. So as usual, let’s dive in to this DSC Practices (P/S: Not Doctor of Science) which I’m going to introduce to you!

1) Dedication: Practice hard or die trying

This is the part which most people tend to assume is the full meaning of practices. All you going to do is to work hard and all in with your effort, you’ll eventually make it. Well, they’re right, only the first part and have missed out many tiny main points which I think is quite crucial as well. Like how to work hard? Or how to make your effort pays?

The work hard I’m referring here, is to just do it. Yeah~! like Nike~! Just Do It~! This would mean literally doing it without worrying for any consequences. It’s ok to try it out; it’s even ok to make mistakes; it’s definitely ok to go all the way to look stupid or even be stupid. Just practicing math, did you die trying?

Of course, ideally, we would always want to hit a home run or a hole in one. But for most cases, I think by making mistakes and learning it as your own experience is a fast way to grow and remember the lessons.

So, are you going to give up just because by knowing you’ll hit the wall or fall to the ground every time you learn something new? Of course not! Do you remember the time you put shoes on at the wrong feet? Made spelling mistakes? Learning how to tie shoelaces? Learning the proper way to hold a knife with a fork? Don't block your chance for self improvement!

Same goes to practicing math and don’t forget about first two TOP tips, Tools and Objectives. You’re your dedication by exploring every available tool, trying every angle or even consulting your teacher, family or friends.

2) Smart: Practice Smart, Flexible and Work Arounds变通

Not sure how many people have heard this before, “work smart, not hard!”. Err, yet again, not wrong but missed out some crucial points which I would like to point out later. Preferably, we will know the tools and objectives well enough and solve any questions or even work around for those tricky or more advanced questions.

However, I guess most of us, or at least myself is not born that smart or knowledgeable, which is good because there is always room for improvement and I’m happy when I get to learn something, like some kind of achievement unlocked. The big question is, even though I know my tools and objectives well enough, but I’m nowhere close to the solution, so how do people like me practice “smartly”?

A good example how to solve this would be how to learn a magic trick. Magic tricks are not magical anymore if you know the secrets or logics behind it. Actually, this would be the same when it refers to practicing math.

To walk you through the process I usually practice if I really have no idea what to do, but let us first borrow some of the dedication. Firstly, start with examples or easier questions with the steps to solution available. Then, we will perform something like a copy and paste of every step from the question to the solution. Next, by laying every step out, we can cross check with the tools and objectives we have and try to make every sense out of it. Kind of like a backward learning and sometimes it’s easier to understand by looking at this backward direction. After that, do it on your own and try to produce the same result by really understanding the rationale behind but not due to purely memorizing the steps. Lastly, do a few rounds of that last bit from front to back and back to front until you’re confident that you finally got it.

I guess this is “smart” enough for people like me, and eventually we will get better and farther away from where we were.

One last thing for practicing smart that I would want to point out is always remember to evaluate the appropriateness of your tools or the steps you’ve perform calculation or transformation to. There are two parts of the evaluation:

2.1) Have I efficiently and effectively met my objectives?

If not, then we will need to figure out how to make it more efficient, effective and meet the objectives at the same time.

2.2) Is there a better way?

If there is a better way which will significantly improve your overall performance, we should remember that and take that path when we face any similar questions again.

3) Consistency: Practice Consistently

Apart from practicing hard and smart, one more component that people tend to forget is to practice consistently. Practicing math is actually not much different than practicing singing, dancing or workout. It is like sports for your brain. There are 3 main reasons why you should be doing this and let us start with the most obvious one.

3.1) Faster

Do you still remember the Directional Thinking Process that we talked about at 2nd TOP tips? The only way to accelerate the thinking process would be think more by practicing consistently. In short, logical thinking is the process of gathering available information and try to deduce then make the optimal choice based on rationale. By practicing consistently, you will be faster in doing all the mini processes which eventually lead to faster thinking.

3.2) Prevent Regression

Second main reason would be to prevent regression. There’s one saying “If you’re not constantly learning, you’re actually falling behind”, so actually practicing if the bare minimum of prevention from regressing and you can only improve after combining the other two key DSC Practices, by putting more effort and thinking to your practices.

3.3) Brain Exercise

Lastly, the reason is to exercise and train your brain. I think this is one of most important elements of all learning or practicing. There aren’t many subjects out there that could give you the amount of brain exercise more than math can offer. By exercising your brain would train you to be better in cognitive thinking or mental processing which also directly impact how fast or efficient can your brain think. Although brain is not muscle, I believe by exercising it should give you a good brain “muscle” memory.

All things considered, I hope all my 3 TOP tips is not a bad read and manage to help someone out there who might need some guidance. Enough said, let’s practice and get the brains to exercise~! LOL~!

如果你还没阅读前面两个TOP贴士的话请先去读了再回来:

终于，最后一个TOP贴士但也相当重要的是，Practice 练习！我相信这个建议并不是什么新鲜事物，通常会在我们谈论数学时已经设定在一起了。但问题是，大多数人仅仅只是在摸索练习部分的表面。因此，像往常一样，让我们深入了解一下我将向你介绍的DSC练习模板（P / S：不是理学博士）！

1）Dedication 敬业：努力练习或尝试至死

这是大多数人倾向于认为这就是练习的全部含义。你要做的就是努力工作，全力以赴，最终你会成功的。好吧，他们是对的，只是第一部分而已，但是遗漏了许多微小的要点，我认为这些要点也都很重要。比如说如何努力练习？还是如何使你的努力有收获？

我在这里指的努力是去做吧了。是的〜！像Nike一样！去实践吧了〜！这也意味着不必过多担心任何后果地去实践。大可尝试一下；甚至可以犯错；就算看起来愚蠢甚至当个愚蛋也是绝对没有问题的。只是练习数学，你会死于尝试吗？

当然，理想情况下，我们总是希望打出全垒打或一杆进洞。但是对于大多数情况而言，我认为通过犯错误并让它成为自己的经验来学习是一个快速成长和可牢记此经验的方法。

那么，你是否会因为知道每次学习新东西都会碰壁或跌倒而放弃吗？当然不是！你还记得把鞋穿在错的脚上吗？拼写拼错？学习如何系鞋带？学习握住刀叉的正确方法吗？不要阻挡自己成长的机会！

练习数学也是如此，不要忘了前两个TOP贴士，即“工具”和“目标”。探索各种可用的工具，尝试各种角度，甚至咨询你的老师，家人或朋友，都是你可以尽力的地方。

2) Smart 精明：聪明的练习，灵活和变通

不确定有多少人听说过“不要死努力，要活用脑子！”。再一次，Err并没有错，但是也漏了一些关键点，我想在下面指出。理想的情况是，我们能充分的了解工具和又有确切的目标，然后成功解决任何问题，甚至解决那些棘手的或更高级的问题。

但是，我想我们大多数人，或者至少我自己不是天生聪明或知识渊博的人，这很好，因为总有改进的余地，当我学到一些东西时，我会很高兴，就好像有某种成就了。其实这里最大的问题是，就算我对工具和目标已经足够了解，但是我还是解不了题目，所以像我这样的人如何“聪明”地练习？

一个很好解决方案的例子是如何学习魔术。如果你知道魔术背后的原理或逻辑，魔术就不再是梦幻。实际上，说回练习数学题时，这也是相同的。

有时候在练习时我真的束手无策，但是我会逐步引导你我平时会做些什么，但是让我们先借鉴一些上面敬业的精神。首先，从例子或简单的问题入手，尤其是那些已经有解题步骤的。然后，我们将执行类似复制和粘贴的操作，从问题到答案每个步骤写出来。接下来，通过列出的每一步，我们可以与我们拥有的工具和目标进行交叉核对，并尽一切可能找出背后的原理。有点像逆向学习，有时通过在后往前看就会更容易理解。之后，你可以自己尝试通过真正理解到背后的原理解题，而不是仅仅因为记住了这些步骤而解题。最后再练习多几轮，从前往后，再从后往前的解题，直到你确信自己终于掌握了它。

我想这暂时对于像我这样的人来说已经足够“聪明”了，至少我们比以前更好，比以前进步。但是别忘了要继续进步。

最后一点我想指出关于聪明的练习是永远记住要评估你的工具或者已进行运算或转换的步骤的适当性。评估分为两个部分：

2.1）我是否有效地实现了我的目标？