Very High GPA but no understanding is this possible?

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SUMMARY

The discussion centers on the phenomenon of achieving high academic grades, specifically a GPA of 3.8, without a corresponding deep understanding of the material in mathematics and physics courses. Participants highlight that many students can excel by memorizing steps rather than grasping underlying concepts, particularly in calculus and special relativity. They emphasize the role of teaching methods that prioritize procedural knowledge over conceptual understanding, which can lead to superficial learning. Recommendations include engaging with rigorous texts like Spivak and Apostol to develop a more profound comprehension of mathematical theories.

PREREQUISITES
  • Understanding of basic calculus concepts, including the divergence theorem and integrals.
  • Familiarity with mathematical proofs and their significance in higher-level mathematics.
  • Knowledge of the differences between procedural and conceptual learning in mathematics.
  • Awareness of the educational challenges posed by teaching methodologies in STEM fields.
NEXT STEPS
  • Explore advanced calculus texts such as "Calculus on Manifolds" by Spivak or "Principles of Mathematical Analysis" by Apostol.
  • Research effective teaching strategies that promote conceptual understanding in mathematics.
  • Investigate the implications of "imposter syndrome" on academic performance and self-perception.
  • Study the relationship between problem-solving skills and conceptual understanding in physics and engineering contexts.
USEFUL FOR

Students in mathematics and physics, educators seeking to improve teaching methods, and anyone interested in the relationship between academic performance and true understanding of complex subjects.

  • #31
I think there's a strong correlation between getting good grades and understanding the material.

I think getting good grades involves just jumping through hoops. These include doing the homework on time, doing well on exams, showing up for labs.

Understanding the material, though, requires more than this. You need to really sit and think about things. You need to ask yourself the right questions, seek outside resources, etc.

I think it is fairly common to see people who don't jump through the hoops (and thus their grades suffer) and yet still think deeply about the material and understand it.

I think it is less common that people jump through the hoops and yet don't understand the material (especially in higher level courses where jumping through hoops requires solving tricky questions on exams that REQUIRE understanding).

Some people do get so caught up in getting good grades that they fail to think deeply enough and reflect on the material. Their understanding can suffer as a result.

Finally, there is something to be said about learning things outside of the scope of class. Trust me when I type that there is much more time and leeway for this in undergrad compared to grad. I wish I had taken advantage of this more. Sometimes, however, this outside learning can come at the price of a lower grade or two.

In my humble opinion, I think:

It is better to get an A- than an A if getting an A causes you to worry and fret about so many things that it takes away from the truly deep pondering and outside of the class learning.

It is better to get an A- than a B if you intend on graduate study, since admissions committees do weigh your grades, even if you feel like you are just jumping through hoops.

It is best to do the least work possible to get an A/A- for a class and use all of the time and effort you save to dig deep, make connections, study broadly, and ENJOY learning.
 
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  • #32
Thanks for the advice ZombieFeynman,

I guess I would fall into the second group that you described, but I am very fortunate because my school has still not switched to the +/- system.
 

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