How Can I Deepen My Understanding of High School Level Mathematics?

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SUMMARY

The discussion centers on the challenges faced by a student studying Mathematics, Applied Mathematics, and Physics at the Leaving Certificate level, particularly regarding the transition from memorizing methods to achieving a deeper understanding of mathematical concepts. The student expresses a desire to enhance their comprehension of mathematics without delving into college-level topics, specifically before starting Calculus. They highlight a specific example involving the quadratic formula (-b ± √(b² - 4ac)) as a method that feels memorized rather than understood. The conversation seeks general pointers for improving mathematical understanding at the A-level/High School level.

PREREQUISITES
  • Basic understanding of Algebra, including the quadratic formula.
  • Familiarity with mathematical terminology and concepts at the high school level.
  • Knowledge of the structure and expectations of the Leaving Certificate curriculum.
  • Awareness of the differences between memorization and conceptual understanding in mathematics.
NEXT STEPS
  • Explore resources on the foundational concepts of Algebra, focusing on the quadratic formula and its derivation.
  • Study mathematical proofs to enhance understanding of why methods work, rather than just how to apply them.
  • Investigate introductory materials on Calculus to prepare for upcoming topics and understand their relevance to previous mathematics.
  • Engage with online forums or study groups focused on high school mathematics to discuss concepts and clarify doubts.
USEFUL FOR

This discussion is beneficial for high school students studying Mathematics, particularly those preparing for the Leaving Certificate, as well as educators seeking to support students in developing a deeper understanding of mathematical concepts.

Not millenial
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Hello, I'm studying Mathematics, Applied Mathematics and Physics at something roughly slightly less detailed than a-levels (Leaving Certificate). The applied mathematics isn't a problem at all, and the "understanding" clicks properly for me. However, in mathematics I find that it sometimes comes down to memorizing methods than a true understanding. I don't want to go into college level detail, and we haven't started Calculus yet (we will be doing it soon). I'm just looking at general pointers for going into slightly more detailed mathematics, with more opportunity for understanding at roughly the A-level/High School level.

I've looked around and haven't seen anything specific to this, sorry if I'm wrong.
 
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Not millenial said:
Hello, I'm studying Mathematics, Applied Mathematics and Physics at something roughly slightly less detailed than a-levels (Leaving Certificate). The applied mathematics isn't a problem at all, and the "understanding" clicks properly for me. However, in mathematics I find that it sometimes comes down to memorizing methods than a true understanding. I don't want to go into college level detail, and we haven't started Calculus yet (we will be doing it soon). I'm just looking at general pointers for going into slightly more detailed mathematics, with more opportunity for understanding at roughly the A-level/High School level.

I've looked around and haven't seen anything specific to this, sorry if I'm wrong.

Can you give an example where you feel you are memorising the mathematics without understanding?
 
PeroK said:
Can you give an example where you feel you are memorising the mathematics without understanding?
It's not even like that, it's like I'm memorizing methods - I understand why they work but I just feel like I'm missing something. I don't know how to explain it. There was a piece in algebra to do with the minus b formula, where you use the -b2+4ac just to figure something out. I'll have a look for it.
 

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