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سرفصل: بخش ریاضی / سرفصل: استراتژی های کلی ریاضی / درس 8

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Learn from Your Mistakes

At first glance, this may look like a simple cliche, learn from your mistakes. Something that we’ve heard all the time, you probably have heard it for years as a student, learn from your mistakes. Exactly what does it mean? Suppose you get a math practice problem wrong. Exactly what should you do?

Well, first of all, if it is a Magoosh question, and if you’re serious about learning this math, then definitely watch the explanation video. It always blows my mind to see Magoosh students who have answered hundreds and hundreds of practice questions and yet they never watch explanation videos. A great deal of instruction happens in the, the lesson videos. But, also, a great deal of our instruction happens in the explanation videos.

And those are very important. In fact, if you had any uncertainty while doing the problem and happen to get it correct, you probably still should watch the video explanation to make sure you didn’t miss anything. Watching the video explanation, or reading the solution to a practice problem from a book or on the blog, is the bare minimum.

That’s the minimum, but there are many layers of what it can mean to learn from your mistakes. For example, many students think of math problems naively in terms of what to do. If they get the problem wrong, they read the solutions, then they think, oh, instead of doing this, I was supposed to do that. That analysis, in and of itself, does not constitute mathematical understanding of the situation.

In math, there’s a deeper logic that always governs each mathematical situation and the way to solve each problem. For starters, don’t run to the solution as soon as you’re frustrated or as soon as you get a question wrong. Instead, spend some time reflecting on what you do know, on what you thought was true when you solved the problem.

Think about what you know for sure, what you think is true, and what questions you have. All this primes your mind for getting the most from the solutions. You understand a mistake much more deeply when you understand why the specifics of the situation demanded doing one thing rather than another. Of course, as mentioned in an earlier video, many math problems on the test can be solved in more than one way.

And if you understand two or more correct ways to understand the same problem, you really understand it deeply. Often, mistakes on Quant problems result from superficial or imprecise understanding of mathematical concepts. If you thought you understood some mathematical concept. Then while reviewing the solution to a question you got wrong, you realize there is more to understand about that concept, that is pure gold.

Magoosh questions often have links to related lessons. Even if you have seen a related lesson already, you may find that after getting a question wrong, that you understand it at a deeper level. And I’ll say here also, this matter of understanding at a deeper level. Don’t think of understanding as a binary thing. Either I understand, or I don’t understand.

Always think in terms of lay, layers and levels. Okay, I’ve learned this vide, I’ve watched this video. I understand to some extent, what are deeper ways I can understand this thing, which I already understand at one level. Always be thinking in terms of getting a deeper understanding of the things you already understand.

One mark of a truly excellent student is, never making the same mistake twice. That’s a high standard, a difficult ideal to maintain in practice. Nevertheless, if you strive for this standard, you will see tremendous progress in your mathematical performance. In other words, for every question you got wrong, ask yourself not only how deeply you have to review the concept in play, but also how to avoid this same mistake in all future practice.

Either, on a question like this, it may even be a very different question which tests the same concept. How is it that you’re never gonna make a mistake on that particular concept again? It takes tremendous dedication and diligence to maintain such a standard, but when practiced consistently, it produces extraordinary progress. As you move through the, the math practice questions, you will make mistakes.

Set a high bar for what constitutes learning from your mistakes. The more you expect from yourself on each and every mistake, the faster you can advance in your understanding.

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