How can you determine if you have mastered a topic in math?

[GreenPrint]

Hi,

I'm studying Calculus II and was wondering how do you know when you have mastered a certain topic and should go on to the next one? I don't think I ever really got the hang of knowing when. Should you just solve every single problem in the book or what? How do you know when you have completely mastered the material of each section in your book? Like normally if you were taking a class at a college you attend lectures, take notes and solve the home work problems, but this is something every student does who's taking the class, at least is suppose to. What needs to be done to do well prior to examinations to completely master the material? Do you solve more similar problems again and again and again and again until it becomes second nature and solve every single one in the book or what? Like I'm lost as to how to go about ensuring I have mastered the material when studying math.

Thanks for any advice.

 

[DrummingAtom]

Hi,

I'm studying Calculus II and was wondering how do you know when you have mastered a certain topic and should go on to the next one? I don't think I ever really got the hang of knowing when. Should you just solve every single problem in the book or what?

I wouldn't; there's not enough time in a day for that. If I can look at a variety of problems and know how to start them then I feel that I understand that topic enough to move on.

How do you know when you have completely mastered the material of each section in your book?

Mastered? When I can rip through the challenge problems at the end of the sections.

Do you solve more similar problems again and again and again and again until it becomes second nature and solve every single one in the book or what?

In some cases, I have had to just "brute force" certain problems. I would figure out how solve the problem and then repeat until it felt comfortable. This is usually due to time restraints.

This site has a lot of great ideas for studying:

http://calnewport.com/blog/

Good luck.

 

[deRham]

If you mean "mastered" for the sake of the class, you should be able to give the main theorems of the section you're talking about and have a good idea how they fit together. You should probably even understand what the problems you solve are illustrating about the utility of those theorems.

This level of understanding means if you see something "new," it really won't be that new, and you'll be able to guess what to do pretty fast.

You should look at all the problems and find them all things you can reasonably approach (this is what the above poster said too).

Another thing is that you will not likely MASTER the material to the level where it's really intuitive to you until after you're done with the class, especially at the lower division level math, because they tend to present a lot of techniques, and you should get used to thinking in terms of ideas, not techniques.

 

[Aimless]

How do you know when you have completely mastered the material of each section in your book?

When you can teach that material to someone else (absent the book).

That said, that's not a practical level to reach when still taking the class. For that purpose, you're probably at a sufficient level of understanding when you can look at each problem at the end of the section and know the general procedure involved in solving each of them.

 

[Matrix0]

I understand the importance of mastering a topic in order to move on to the next one. In math, it is important to have a solid understanding of the fundamentals before moving on to more complex topics. Here are some tips to help you determine if you have mastered a certain topic in math:

1. Test yourself: One way to determine if you have mastered a topic is to test yourself. This can be done by solving practice problems or taking quizzes and tests. If you are consistently getting the correct answers and understanding the concepts, then you have likely mastered the topic.

2. Teach someone else: Teaching is a great way to solidify your understanding of a topic. If you can explain the concepts to someone else in a clear and concise manner, then you have likely mastered the material.

3. Apply the concepts: It's important to not just memorize formulas and procedures, but to also understand how and why they work. Try applying the concepts to real-world problems or creating your own practice problems to solve.

4. Seek help when needed: If you are struggling with a certain topic, don't be afraid to seek help from a teacher, tutor, or classmate. They can provide additional explanations and practice problems to help you master the material.

Overall, mastering a topic in math takes time and practice. It's important to not just solve problems, but to also understand the underlying concepts. Keep practicing and seeking help when needed, and you will eventually feel confident in your mastery of the material. Best of luck in your studies!