Is it possible or i am kidding my self?

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Discussion Overview

The discussion revolves around a first-year college student’s experience with rapidly learning mathematics after a previous struggle with the subject. The participant expresses concerns about the adequacy of their study methods and whether their fast-paced learning will have long-term consequences. The scope includes personal experiences, study strategies, and the emotional aspects of learning mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) describes a significant turnaround in their mathematical abilities after self-studying various topics in a short time, expressing both pride and concern about the speed of their learning.
  • Some participants suggest that as long as the OP is aware of their gaps in knowledge and is willing to address them, they should be fine moving forward.
  • Others caution that studying too quickly might lead to weaker retention of concepts and recommend a more thorough approach to foundational material, such as working through Lang's basic mathematics book.
  • The OP expresses a desire to solve more exercises and a feeling of contradiction, as they believe they understand the material yet feel they lack depth due to their rapid study pace.
  • One participant notes that confidence in algebra skills can sometimes mask underlying weaknesses, particularly when applied in physics contexts.
  • Another participant emphasizes the importance of solving problems as a means of understanding and encourages the OP to continue moving forward with their studies.

Areas of Agreement / Disagreement

Participants express mixed views on the effectiveness of the OP's rapid study approach. While some believe it is acceptable as long as the OP is aware of their learning gaps, others warn that it may lead to issues in the future. The discussion remains unresolved regarding the long-term implications of the OP's study methods.

Contextual Notes

Participants highlight the potential for gaps in foundational knowledge due to the speed of study, but there is no consensus on the best approach to address these gaps or the impact of the OP's learning strategy on future studies.

brunopinto90
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Hello. I am in first year college studying electronics engineering and computer science and i am 20 years old.

I recently did the national mathematics exam to go to college and had 160 out of 200. Ironic, huh?

I failed math at 10 grade and stopped doing any math for 3 years. By the time of the exam i didnt know how to solve a first degree equation or add negative numbers. So i studied all the material tested in the exam, 4years worth on my own in 5 months from pre algebra - geometry - trigonometry to derivatives and complex numbers. I didnt study much deeply successions and statistics, didnt need.

I know i covered a lot of ground, mainly because i felt in love for math, proofs and rigor. I even read some stuff on langs basic mathematics book.

Now in college, taking integral calculus i have no problems in math, i love math. I put a lot of effort, prefering to understand, not just nemorize.

But am i kidding my self? Studying this fast will hurt me in the future? I want to know your sincere opinions.

Because sometimes i feel the strange notion that i should have done more exercises, read nore books,, again, have no problems though. Do you have the same feeling?
 
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I think you'll be fine if you keep working hard and feel your way along.

If you want to confirm a thorough knowledge of high school math, sign up for ALEKS pre-calculus. Students who are strong in all the areas blow through it in a couple of weeks or less. Students who need some brushing up take a couple of months. The system is thorough.
 
brunopinto90 said:
But am i kidding my self? Studying this fast will hurt me in the future? I want to know your sincere opinions.

Yes, it might, but as long as you realize this, you should have no problems. You should realize that there definitely are certain things you're less good at and that you don't know in math. As long as you are prepared to identify and fill in the gaps, you should have no problem.

I hope this was a one time thing though. Studying this fast later on will harm you even more, since it will not be possible to study this way. Also, studying this fast means you'll remember concepts less well.

If you can find the time, work through Lang's basic mathematics book on a profoud and slow level. This might identify and fill in many gaps.
 
But the thing is, i solve the problems well, i learn new concepts fast cause i have developed the previous concepts. I have no issues recalling and my algebra skills hasnt stop me yet in learning calculus. While studying i became passionate about math, try to prove some theorems, formulas. So overall i became good at learning math.

But i just want to solve every exercise out there, i feel the urge to solve every exercise i see. Its not i don't understand, i just miss the material, cause i studied so fast. Is this normal?
 
I don't understand. You seem to get everything well and you can solve any exercise. So what is the problem?
 
I want to do more exercises and i feel the notion i don't understand, despite i do. I know, i sound contradictory.
 
brunopinto90 said:
But the thing is, i solve the problems well, i learn new concepts fast cause i have developed the previous concepts. I have no issues recalling and my algebra skills hasnt stop me yet in learning calculus.

Perhaps. But I've known a lot of students who were confident in their algebra skills because of calculus, but consistently demonstrated weak and underdeveloped algebra skills on their physics problems. Too many calculus courses are designed for success by students that are poor at algebra.

brunopinto90 said:
But i just want to solve every exercise out there, i feel the urge to solve every exercise i see. Its not i don't understand, i just miss the material, cause i studied so fast. Is this normal?

I wouldn't worry about normal, I would just move forward. Solving problems is important in the process of understanding. If you are moving, you are learning. You will learn more when your pencil is moving.
 
I will just move forward and ocasionally do some past exercises. I will focus now and when i encounter something i don't do quite well i
study. Like learn on the way strayegy
 

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