Math in grade school, hs and college.

kartelite wrote:

Because you are getting a constant change in ratio, by definition the value of the derivative must be proportional to the value of the function at all times, hence d/dx(e^x) = e^x.

You took a good stab at it, but I had trouble understanding what you were trying to write in your last paragraph. It's hard to explain mathematical concepts in English. But, the last sentence you wrote doesn't make sense unless you replace "proportional" to "equal", because d/dx(a^x)=ln(a)*a^x, which is proportional to a^x.

Anyhow, there are two definitions of e, the compound interest one, and the calculus one (e^x is the function f such that df/dx = f), and you can prove that they're the same number.

Some of my family friends were complaining how hard it was to memorize all of their combinations (for locks, passwords, credit cards, etc), so I told them I sometimes just use numbers I know (obviously for passwords you don't care about) like e, pi, the square root of two or three... at which point I was stopped and asked what e is.

Here is something to think about. There is no such thing as a combination lock. It should be called a permutation lock.

Well I wrote that about 10 months ago, but I was saying specifically d/dx(e^x)=e^x, which is true for "e." In general your formula is right, but ln(e)=1, so equal.

Great thread!

Sadly, I'm not a success story. I was an unbelievable math whiz all throughout grade school. Still can do arithmetic very easily in my head (useful for monitoring splits in races). Algebra I and II were a breeze, although I started struggling a bit in Trig and a lot in Calculus. Even then, my main problem was just that I assimilated the skills slowly compared to the other kids. My homework grades were a disaster but by the time the test rolled around, I knew it better than anyone. I always found this a little strange. Maybe someone else had a similar experience?

My first math course in college was Honors Calc I and II compressed into a single semester. That's when I started sinking. I absolutely loved the material, but we rarely spent enough time on any one concept for me to grasp it fully. And I had to keep a 3.5 to keep my scholarship, so struggling for a C wasn't an option. I do remember that the creative thinking needed to evaluate complicated integrals was a skill that seemed extraordinarily valuable. This was my favorite thing to do.

Now that I'm out in the working world, I'm beginning to see why I loved math as a kid. Simply, because it's beautiful. Hidden relationships between numbers and patterns that emerge seemingly from nowhere, until you dig deeply to try to understand it. I think one of my first great discoveries as a kid was the relationship between Pascal's Triangle and 11^n.

Just recently I realized that I could use special triangle rules and the pythagorean theorem to help read engineering plans and I started wondering if I missed out somehow.

I guess there's still time...

i did meth in grade school, hs, and college. now that i'm in the working world, i find i don't use it that much and i wonder if doing all that meth really helped me at all.

Sorry, I saw the 2 and thought it was a 12 :)

You CAN'T use math to determine a potential lotter number?

Ba dump BUMP

And you just plain S*ck for posting that.

Hmmm, I was archive searching and came upon this old thread and was very surprised to see it still alive.

JT:

A durable constitutional question? That reminds me of the days when I could feel the frustration in myself rising when we had math in grade school (4th grade I believe) and I-could-not-get-the-answer.

I remember being given ONE problem to work on in a class on basic math, it involved some multiplication question.

I got stuck on it, I could not loosen the grip I had in my head that MY answer was correct. The teacher PUT ME ALONE IN THE NEXT ROOM WITH THE QUESTION. She left me there for a period of time...ten minutes? 20 minutes?

She brought me back into the room and asked me the question, I totally choked and practically screamed out the wrong answer, the one I could not get out of my head.

Cripes this thread gives me flashbacks, LOL.

Just finished my very last math problem ever...in school...Final question in Calculus final exam, completing the math requirement for my major.

The problem was a U-substitution indefinite integral...too easy!

I want a math debate!

(say that 10X really fast)

I remember it would take me up to 20 minutes to struggle through some homework math exercises. There was no way I was ever going to get 100 problems done in a week.

Why do other nations do so well at math compared to the US?

hmmm, good questioni just noticed this thread for the first timei majored in math in undergrad and started a doctorate program (did 1 year) before moving to the phd program in economicsdespite loving math, i was never interested in teaching it or knowing why some countries were bad in it and some were goodone thing that is for certain... statistics can liewhat students does every country report on? do students concentrate in math very early on in other countries? are they teaching the same kinds of math?i grew up in pennsylvania and from what I can tell... who cares if my math education wasn't the greatest. i know it is not true for everyone, but was what i was learning in elementary school really going to matter for later onif other kids were ahead in math, i surely caught up at some point so i don't know that it mattered too much

100 math problems a week? wrote:

I remember it would take me up to 20 minutes to struggle through some homework math exercises. There was no way I was ever going to get 100 problems done in a week.

Why do other nations do so well at math compared to the US?

I believe that other countries do better in math because of curriculum, and who puts together the curriculum. It is no secret that mathematicians have had no input in this regard over the past 30 years. Imagine what our distance running program would be like if actual successful runners were not allowed to influence the sport, but rather, educators who had a smattering of phys ed knowledge from Ed. school were given full control.

math dude wrote:

I believe that other countries do better in math because of curriculum, and who puts together the curriculum. It is no secret that mathematicians have had no input in this regard over the past 30 years. Imagine what our distance running program would be like if actual successful runners were not allowed to influence the sport, but rather, educators who had a smattering of phys ed knowledge from Ed. school were given full control.

I'm not sure I agree. The "modern math" of the 1960s was a result of research mathematicians' suggestions for math curriculum. There was much criticism that students from this era were deficient in basic skills as a result.

"You CAN'T use math to determine a potential lotter number?" Sure we can it; just give the same odds for all valid numbers.

The traditional pedagogy of teaching subjects of algebra, trig, geometry, calculus, etc. was put in place largely by great, or at least fairly good mathematicians in the 17th-19th centuries, with proper pedagogy added by educators. The content was decided upon the professional mathematicans, whereas the delivery was decided on by educators. New math of the 60's was an attempt by mathematicians to get every Joe Shmoe to think like a mathematician, which probably didn't serve us very well. Math 1980-present has been exclusively the domain of math educators, much to the dismay of mathematicans, and the traditional content-driven approach has been subjugated in favor a random hodge podge of topics ushered with the sole purpose of keeping the below average student in the game as long as possible.

actually I'm not sure if this is true... math in education in the 60s was focused on practical applicationwe need to be good in math to win the space race, we need to be good at math to use in physics to win the arm race, we need to be good in math to make good economists, etc.there has been a lot of studies that have said that teaching math as something practical is exactly why math education fails... students are told, you need this, you need to know math it is practical... but you know what for most people, they don't need math beyond simple addition, mulplication, and maybe some geometry they figure this out and their desire to do math plummetsmath should be taught as a subject unto itself... if you really are a math dude i don't doubt that you do math simply for the sake of doing math... teach it as something beautiful, an art, which is how pure mathematicians view math... i know it is completely cheesy but i certainly considered my math my poetry... i loved doing math... topology, functional analysis, abstract algebra, number theory (not the algebra most of you will know)... just for the sake of doing math. same reason many writers writei don't know... i think we might have more success if we move to a more 'pure' form of math education

math dude wrote:

New math of the 60's was an attempt by mathematicians to get every Joe Shmoe to think like a mathematician, which probably didn't serve us very well.