No commentary topic starter #2: Mathematics Learning/teaching
- Thread starter Todd
- Start date
morninggirl5
Secret Dream Machine
- Joined
- May 6, 2001
- Posts
- 10,647
Educational theory........here's an opening, go for it
Teaching Mathematics well is all about teaching reasoning, thinking, and problem solving. All slightly different variations of the same process. It's HARD to teach Mathematics in this way, it's much simpler to teach a formula or algorythm and focus on "right" answers.
Teaching Mathematics well is all about teaching reasoning, thinking, and problem solving. All slightly different variations of the same process. It's HARD to teach Mathematics in this way, it's much simpler to teach a formula or algorythm and focus on "right" answers.
Weird Harold
Opinionated Old Fart
- Joined
- Mar 1, 2000
- Posts
- 23,768
2+2=4
It isn't really necessary to know why this is true, just that it is true.
12x12=144, and that's gross, but how and why it's true isn't all that important.
Once the basic arithmetic is memorized, getting the right answer to more complicated math problems and concepts is much easier.
Math is about "right answers" at it's very roots.
The answer might not be important in teaching the "process" but without a "correct" answer, how can you know the process was learned?
It isn't really necessary to know why this is true, just that it is true.
12x12=144, and that's gross, but how and why it's true isn't all that important.
Once the basic arithmetic is memorized, getting the right answer to more complicated math problems and concepts is much easier.
Math is about "right answers" at it's very roots.
The answer might not be important in teaching the "process" but without a "correct" answer, how can you know the process was learned?
sigh
chant mistress
- Joined
- Sep 19, 2001
- Posts
- 10,248
here's the fence-straddler for you...i think it's about both
it's much easier to get to the right answer if you understand the methods...you simply can't memorize all the right answers...it isn't possible...you have to learn how to get there
but in the end, the right answer is paramount...in my line of work, if i use the right method but come up with the wrong answer, a patient might die...there's no partial credit in real life
it's much easier to get to the right answer if you understand the methods...you simply can't memorize all the right answers...it isn't possible...you have to learn how to get there
but in the end, the right answer is paramount...in my line of work, if i use the right method but come up with the wrong answer, a patient might die...there's no partial credit in real life
Willing and Unsure
Stuffed Animal Princess
- Joined
- Apr 4, 2001
- Posts
- 8,654
Re: 2+2=4
just because you have a right answer doesnt mean you learned the process.. i'm taking multivariable calculus right now in college.. and i havent got the slightest idea what's going on, but somehow i managed to get an A on the first exam, only missing 2 questions.. i dont pay attention in class, the homework that actually gets done by me is done really half-assed.. but somehow i managed to get a right answer and i didnt even do it the right way. i dont know how to do it the right way.. you can know the process and still get a wrong answer
Weird Harold said:
just because you have a right answer doesnt mean you learned the process.. i'm taking multivariable calculus right now in college.. and i havent got the slightest idea what's going on, but somehow i managed to get an A on the first exam, only missing 2 questions.. i dont pay attention in class, the homework that actually gets done by me is done really half-assed.. but somehow i managed to get a right answer and i didnt even do it the right way. i dont know how to do it the right way.. you can know the process and still get a wrong answer
sigh
chant mistress
- Joined
- Sep 19, 2001
- Posts
- 10,248
yes, i did well in calculus in college too, without managing to learn a damn thing
fortunately, for most of us, calculus and the real world have nothing whatsoever in common...
what i DID like though, and did well in too, was physics...now there's discipline where knowing how to get to the answer is everything...the math at the end is usually trivial, it's the process that counts
but once again, the answer must be right
(been straddling this fence so long it's beginning to feel like some demented Dom's torture device...ouch)
fortunately, for most of us, calculus and the real world have nothing whatsoever in common...
what i DID like though, and did well in too, was physics...now there's discipline where knowing how to get to the answer is everything...the math at the end is usually trivial, it's the process that counts
but once again, the answer must be right
(been straddling this fence so long it's beginning to feel like some demented Dom's torture device...ouch)
morninggirl5
Secret Dream Machine
- Joined
- May 6, 2001
- Posts
- 10,647
Real world applications require more than just process and the right answer. Real world mathematics also require some decision making (reasoning) about what process to use.
Example Math Question: (approx. 3rd grade level) You have $5 to buy lunch at McDonalds. A Big Mac costs $2.95, french fries cost 95 cents, an apple pie costs $0.95, a drink costs $1.05, and a quarter pounder costs $1.95. How much change will the cashier give you if you order a quarter pounder, fries, and apple pie?
The addition, subtraction, and money skills needed to solve this problem are straight forward and can be taught fairly easily to most children. The hard part to teach and the most important part to learn is the problem solving ability necessary to determine the process to use.
Ask anyone what they hated about Math. 9 out of 10 people are going to mention word problems and probably 7 of those 9 will mention the two trains starting in different cities on the same track problem.
Example Math Question: (approx. 3rd grade level) You have $5 to buy lunch at McDonalds. A Big Mac costs $2.95, french fries cost 95 cents, an apple pie costs $0.95, a drink costs $1.05, and a quarter pounder costs $1.95. How much change will the cashier give you if you order a quarter pounder, fries, and apple pie?
The addition, subtraction, and money skills needed to solve this problem are straight forward and can be taught fairly easily to most children. The hard part to teach and the most important part to learn is the problem solving ability necessary to determine the process to use.
Ask anyone what they hated about Math. 9 out of 10 people are going to mention word problems and probably 7 of those 9 will mention the two trains starting in different cities on the same track problem.
