Math Learning: US vs Abroad - A Student's Perspective

[slam7211]

Im an undergrad physics student, who has lived and learned in the US all my life, for obvious reasons has taken a lot of math courses in college. A lot of these courses covered quite a few proofs, and a lot of conceptual proof-ish questions (aka not rigorous proofs but still requiring you to come up with logical reasoning etc). The funny thing I have noticed is how my fundamental understanding of math has basically left me stumped with most of these questions, I am not asking for answers here (I can read rules) I'm just noticing how the way I was taught math (aka learning formulas) has basically harmed my ability to answer such questions. its something I notice throughout my school.

I assume it has to do with the fact that because we have to learn math from such an early age, we learn by being fed assumptions about math, so we can do math (aka we are to young at some age to understand why something in math is so we are taught to just assume its true because our teacher says so). I am wondering if math teachers professors etc see this as well, and can think of ways that we could teach math better from an earlier age, given the cognitive limitations of children at young ages, to prevent this from happening, or if you happen to be from somewhere outside the US and learned math differently that seemed to work what was it?

Also if this needs to be moved elsewhere I am sorry

 

[HallsofIvy]

There appears to be evidence from Psychologists (such as Piaget) that children cannot grasp abstract proofs until about the age of 12 or 13. That's why you seldom see proof before that age (and why we tend to separate "elementary school" from "middle school" or "high school" at about that age). I'm no Psychologist so I don't know how accurate that is.

I am puzzled by your statement that "A lot of these courses covered quite a few proofs, and a lot of conceptual proof-ish questions" since you then say "I'm just noticing how the way I was taught math (aka learning formulas)". Which is it?

Yes, just learning formulas will hurt you when it comes time to try to make up formulas yourself for situations that don't quite fit the formula you have learned. But one reason for learning proofs is to see how those formulas are developed which will help you alter them to fit other situations.

Added: Sorry, I now see that you your first statement is in reference to college courses and your second to pre-college courses. Your secondary shchool courses should have expected you to read and understand, if not create yourself, proofs for statements and formulas you learned. I know mine did.

 

[Stephen Tashi]

I think some symbolic logic should be taught at the secondary school level. It shouldn't be strongly tied to mathematics at that point because parts of secondary school math don't use logic rigorously. It shouldn't be tied to English composition and "rhetoric" either. By the time they graduate from high school, most aspiring math and science majors should be able to deal with statements that have quantifiers. They should understand how to negate statements that have quantifiers and recognize the form of arguments such as "universal generalization".

There are certainly many people in the sciences that pick up the ability to do the various types of logical reasoning by reading proofs. However, I think that most students would benefit from formal instruction. As it is now, each time a novel logical topic is encountered in a math class ( e.g. quantifiers in "For each epsilon > 0 there exists...) the math instructor must attempt to teach both logic and math simultaneously.

slam7211,

See if you can take a course in symbolic logic from the Philosophy department. Perhaps it will count as credit for one of your liberal arts requirements.