Teachers, professors, instructors and students.

[uperkurk]

Having long passed the age of 16 and well into my early 20's I've finally decided to start learning algebra > geometry > trig and eventually calculus. I'm 2 weeks into teaching myself algebra and I have a question for the professors. When teaching students, what is the most common problems that students have when you're explaining something new?

Also to students, when learning something new, what is your biggest problem (if any)? For me it's remembering the rules and equivalences. Even though I have not learned any calculus yet and I can't even read calclus problems.

I've just started to learn about sin, tan and cos and remembering SOHCOHTOA is pretty simple but it gets pretty complicated by the looks of things once I get passed the first page of the book.

Do you lecturers literally never forget a formula? Never forget a rule or an equivalence? How do you remember it all !

 

[leroyjenkens]

I remember when I was learning algebra, I had a hard time grasping the implicit -1 in front of parentheses. Like -(a+b). Distributing the implicit -1 in front turns it into -a-b. I understood distributing numbers. Like if it was 2(a+b), I could turn that into 2a+2b no problem. But distributing the minus sign made no sense to me.

If you learn anything well, learn algebra well, that will help you in the rest of mathematics as far as I can tell. In my electricity and magnetism class, the stuff I don't understand is when the answer to a problem contains some kind of weird algebra moves that I either don't understand or need someone to point it out to me.
A lot of the time the answer will be an expression that did something weird algebraically that made me wonder how I was supposed to think of doing that, and why I would do that instead of leaving the expression the way it is.

 

[symbolipoint]

This was never a problem for me when I first studied "Algebra":

I remember when I was learning algebra, I had a hard time grasping the implicit -1 in front of parentheses. Like -(a+b). Distributing the implicit -1 in front turns it into -a-b. I understood distributing numbers. Like if it was 2(a+b), I could turn that into 2a+2b no problem. But distributing the minus sign made no sense to me.

The most difficult and confusing topics of Introductory and Intermediate Algebra were inequalities and inequalities with absolute values. Even during "College Algebra", that stuff was very difficult and I never mastered them..., until a few years after university graduation when I studied that stuff again on my own. When I was younger, even through a few years, I could not manage the logic and combine it with the concepts.

 

[homeomorphic]

Do you lecturers literally never forget a formula? Never forget a rule or an equivalence? How do you remember it all !

Don't be impressed by lecturers. They have all the time they want to prepare for class. They also have years of experience, sometimes, applying things over and over again until they are burned into their minds. And we do forget formulas sometimes.

But two tricks I have up my sleeve are doing a lot of review and understanding. Often, but not always, I can "see" or "feel" a meaning behind rules and equations. This might sound almost mystical to you, but the main point is just to try to understand things from yourself, rather than believing what you are told (believing what you are told is sometimes a valid strategy to save time, but it's good to try to avoid it whenever you can). If you understand why something is true, it's easier to remember, and even if you only half remember it, you can figure out the rest. If you just use rote memorization without understanding, it's easy to remember things wrong. This barely scratches the surface of all the things that can work together to help retain what you learn, but you can't learn how to learn over night, so I am just trying to convey some of what's involved.

 

[Matrix0]

I can say that the most common problem students have when learning something new is understanding the underlying concepts and how they relate to each other. Many students struggle with this because they may have memorized formulas and rules, but they don't truly understand the principles behind them. This can lead to difficulties in applying the concepts to new problems.

To address this issue, it is important for teachers to focus on explaining the fundamental concepts and providing real-world examples to help students understand how they are used. It is also helpful for students to actively engage with the material by practicing problems and asking questions to solidify their understanding.

As for remembering formulas and rules, it is not uncommon for even experienced scientists and educators to occasionally forget them. However, the key is to have a strong understanding of the underlying concepts, which can help in reconstructing the formula or rule when needed. Additionally, practicing and using the formulas regularly can help with retention.

Overall, it is important for both teachers and students to focus on understanding the concepts rather than just memorizing formulas and rules. With a strong foundation of understanding, students can better apply their knowledge to new and more complex problems.