Basic Math Skills : Math Problem Solving

오늘은 한국의 수학 영재들이 미국 와서 가장 어려워하는 부분인 "word problem" 입니다. 오늘의 예제와 같이 수학 식은 아주 간단하지만 이걸 영어로 풀어 놓고 질문을 하면 평소 이런 영어에 적응되지 못한 학생들은 아주 힘겨워 합니다. 

Now, I’m gonna talk to you a little bit of math problem solving.  Math problem solving is little different from other types of problem solving because it is a definite mathematical answer to the problem you’re trying to solve.   

It can be useful in determining a numerical answer to word problem or for some other problem, for example, take two cars on a highway you wanna to find out the time it takes for a faster car behind to overtake a slower car ahead.  Now you know that there is original distance between them, x, which will affect the time to takes.  Also how fast the faster car’s going and how slow the slower car’s going will also affect the answer.  

So I’m gonna take a little bit of time to show you how you can transfer a word problem, a conceptual problem, into a mathematical problem that can be solved real to be easily.  

To find out how long it will take for the faster car to pass the slower car, we need to take into account the speeds and the distance.  Now, this distance (x) is in miles, and the speeds, we’re gonna say 100 miles per hour.  So the time it takes is gonna be the original distance in miles, divided by how fast the faster car is overtaking the slower one.  That’s gonna be a difference in speed.  If a car in front is going 50 miles an hour and the car behind is going 100 miles an hour, the rate are which the distance is closing is just a difference or 50.  Faster car v*2, (and) slower car v1, this bottom part (v2-v1) represents how fast this distance is closing.  X is the original distance, so now you have the time will takes for the faster car to overtake the slower car is given by this mathematical formula.  

                   Time (hour) = original distance, X (mile) 
                                          (v2 – v1) (mile /hour)

 And we found that using logic and basic math problem solving skill.      

v*: velocity (속도)의 약자로 쓰입니다.  들리기는 거의 'b'로 들리지만 원어민의 발음은 '브이 (v)'를 '뷔'로 발음합니다.  'b'는 '비'로 발음합니다.

이런 word problem (conceptual problem)은 미국의 중고등학교 그리고 이공계 대학 및 대학원에 이르기 까지 끊임없이 따라 다니는데, 이런 유형의 문제를 적극적으로 풀어 봄으로서 학생의 critical thinking capability를 배양하는 것입니다.

특히 SAT, GRE, LSAT, MCAT, PCAT 등의 시험을 준비하시는 분들에게는 이런 word problem이 바로 Quantitative and/or Analytical Reasoning (Section)에서 곧바로 접하게 될 것입니다.  

English Pronunciation - PENURY - #222