Word Problems: Seen Versus Not Seen

Allow me to explain a reality about word problems for me. There are two types of word problems as I see it: 1-Problems that I have seen before and 2-Problems I have not seen (questions usually found in standardized exams). I have no problems whatsoever answering word problems correctly if explained to me and then tested on.

Believe it or not, I did very well in my Pre-calculus class back in the Spring 1993 semester. The professor taught the material in class for several weeks and then we were tested in class on the topics learned during instructional delivery time. No problem at all.

My BIGGEST problem is answering questions that I have not seen before (questions usually found on standardized exams).

When I took the ASVAB in 1995, I prepared for the test months in advanced. I had a pretty good idea of the type of questions on the actual exam. My ASVAB score qualified me to enter Electrician's Mate "A" School after recruit training at NTC.

In my opinion, if you can answer random word problems on the GMAT, GRE or SAT, or any other standardized exam, you are a mathematician whether you know it or not. Answering never before seen word problems is my greatest challenge. This is what amazes me the most about the MHF. It does not matter if you have seen the question before or not. There is always someone (or a group of people here) who can answer each posted question without any difficulty. To those who can do this, I salute you. What do you say?

Re: Word Problems: Seen Versus Not Seen

Not to say anything about members who can take new problems and solve them from basic principles, but the first day of an Intro Physics class I teach I mention to the students that there are only so many different kinds of problems and I've seen a lot of them. So if they feel like I'm easily doing problems that they have trouble with they shouldn't feel bad. Sometimes it's just a matter of being in the field for a while.

-Dan

Re: Word Problems: Seen Versus Not Seen

There are many different **levels** of learning in any subject. One of the simplest is just regurgitating definitions or fact that you have been given. A slightly higher level is applying formulas that you have learned, first when you are given the exactly the information you need to plug into the formula, then where you are given information from which you can get the data for the formula. The highest and most important level of learning is learn to apply the **concepts** to totally new situations. Until that point you may have been memorizing formulas but you are not **thinking**! And what you **should** be learning in any class is how to think!

Re: Word Problems: Seen Versus Not Seen

Quote:

Originally Posted by

**topsquark** Not to say anything about members who can take new problems and solve them from basic principles, but the first day of an Intro Physics class I teach I mention to the students that there are only so many different kinds of problems and I've seen a lot of them. So if they feel like I'm easily doing problems that they have trouble with they shouldn't feel bad. Sometimes it's just a matter of being in the field for a while.

-Dan

During my sub teaching years, I was assigned as a homework helper for grades 3 to 5 in the after school program. Exposed to the same questions, same sample exams, etc made it a lot easier to answer questions. I am no expert. To be honest, the only difference was the numbers on the actual word problems. For example, on a given day, MARY HAD TWO BOXES. The next day, MARY HAD 4 BOXES but the same question.

Re: Word Problems: Seen Versus Not Seen

Quote:

Originally Posted by

**HallsofIvy** There are many different **levels** of learning in any subject. One of the simplest is just regurgitating definitions or fact that you have been given. A slightly higher level is applying formulas that you have learned, first when you are given the exactly the information you need to plug into the formula, then where you are given information from which you can get the data for the formula. The highest and most important level of learning is learn to apply the **concepts** to totally new situations. Until that point you may have been memorizing formulas but you are not **thinking**! And what you **should** be learning in any class is how to think!

Read my answers in brackets.

There are many differentlevelsof learning in any subject.

[I agree.]

One of the simplest is just regurgitating definitions or fact that you have been given. A slightly higher level is applying formulas that you have learned, first when you are given the exactly the information you need to plug into the formula, then where you are given information from which you can get the data for the formula.

[What if I forgot the formula learned years ago and/or forgot how to derive the formula from the given data?]

The highest and most important level of learning is learn to apply theconceptsto totally new situations.

[This has been my goal and only reason for solving math applications.]

Until that point you may have been memorizing formulas but you are notthinking!

[Unfortunately, students are not taught how to think in our public schools today. Everything is memorization and applying formulas without actually knowing what the formulas mean.]

And what youshould be learning in any class is how to think!

[As a former sub teacher, and the main reason why I lost interest in teaching full-time in NYC public schools is the fact that students are being trained to PASS THE TEST and nothing more. Test scores, unfortunately, determine how much money a particular school district gets from state funds. A huge chunk of money means more school books, more crayons, more tables, more chairs, etc. Also, a teacher's job is on the line depending on class standardized exam scores. It's really sad what is going on in the public schools. How many students can answer x + 5 = 10 without actually knowing that this is a linear equation and what makes it a linear equation?]