Math question about teaching - Page 2 - PeachParts Mercedes-Benz Forum

Botnst · #16 12-06-2013, 09:09 AM

Quote:

Originally Posted by Honus

I am a product of Fairfax County Public Schools in Virginia, class of 1975. Based on my interactions with the people who went to college with me, I believe that I had exemplary math teachers in high school.

Every kid who is able should be required to learn at least some calculus, IMHO. Calculus provides insight into so many physical processes that we see in everyday life, it should be a part of every college kid's education, IMHO.

I think I agree with you on the calculus thing, but I am not certain. There is something about the way one approaches analytical problems that changes with success in calculus. I don't just mean how to attack a computation but how to think about complex problems.

The reason I am uncertain is that to me, the goal is to teach (and learn) how to attack complex problems, not so much how to teach computation.

There is something about the demanding rigor of mathematical thought that is different from other kinds of analytical thinking (I speculate here). For example, it takes an analytical mind to make sense of literature or music or law (etc) but it is a different quality of analysis, IMO.

This would be a good time to wish for a philosopher's opinion.....

kerry · #17 12-06-2013, 09:14 AM

Quote:

Originally Posted by Botnst

Suddenly it clicked in physics class. I had a natural epiphany and I could finally solve complex problems. Damned if I can explain it. After physics I took linear algebra and DE. Difficult courses, but I UNDERSTOOD. Amazing difference. Inexplicable to this day.

It is a bizarre phenomenon but not unusual I think. At my school we have literally dozens upon dozens of remedial math courses and the statistics concerning their success are about as dismal as can be imagined. I think it's less than 3% of the students who start at the lowest level ever earn a degree or certificate. In my view, one of the problems is that the measure of success and the focus of attention in almost all basic math courses is not that epiphany but the ability to perform routine operations.
My wife had that epiphany when she went back to school to get her educators license and had to take a Math education class which are often terrible classes. The teacher simply posed about 7 problems and told the class the students will spend the semester solving them. They had to develop the solutions themselves. They were not going to be taught the solutions.
Math really must be approached like Zen.

sloride · #18 12-06-2013, 10:01 AM

Quote:

Originally Posted by kerry

It is a bizarre phenomenon but not unusual I think. At my school we have literally dozens upon dozens of remedial math courses and the statistics concerning their success are about as dismal as can be imagined. I think it's less than 3% of the students who start at the lowest level ever earn a degree or certificate. In my view, one of the problems is that the measure of success and the focus of attention in almost all basic math courses is not that epiphany but the ability to perform routine operations.
My wife had that epiphany when she went back to school to get her educators license and had to take a Math education class which are often terrible classes. The teacher simply posed about 7 problems and told the class the students will spend the semester solving them. They had to develop the solutions themselves. They were not going to be taught the solutions.
Math really must be approached like Zen.

I don't remember at what age but my father taught me numbers around the dollar.
For reading a tape measure 1" = $1.00 / half inch= .50 - 1/4" =.25
For fractions 1 dollar = 1 same as above one quarter = .25 so .50 was two quarters so on. I had passed that lesson on to many adults that could not read a tape measure or understand fractions, but knew that .375 cents was more than .25 cents but less than .50 cents.

MTUpower · #19 12-06-2013, 10:01 AM

Quote:

Originally Posted by elchivito

The way most of us were taught is fine, but it isn't the only method. Some kids are able to conceptualize a problem better using the method described in the OP. I use both, plus some others depending on the kid's learning style. There is no "better" method. Good teachers keep abreast of these modalities and apply them as needed.

It's pointless to keep beating a kid over the head with one method that isn't working. The result is a kid who thinks he "sucks at math".

Quote:

Originally Posted by Botnst

...
The reason I am uncertain is that to me, the goal is to teach (and learn) how to attack complex problems, not so much how to teach computation. ...

Quote:

Originally Posted by kerry

...The teacher simply posed about 7 problems and told the class the students will spend the semester solving them. They had to develop the solutions themselves. They were not going to be taught the solutions.
Math really must be approached like Zen.

^^^^^^^^^^^
Here's the reasons why chess should be taught to all elementary students for at least one year. It's all of those rolled into one and if taught correctly is fun. Name another teaching method/subject which is fun and students learn a wide variety of things they will use later in life.

cmbdiesel · #20 12-06-2013, 10:53 AM

Quote:

Originally Posted by elchivito

The way most of us were taught is fine, but it isn't the only method. Some kids are able to conceptualize a problem better using the method described in the OP. I use both, plus some others depending on the kid's learning style. There is no "better" method. Good teachers keep abreast of these modalities and apply them as needed.

It's pointless to keep beating a kid over the head with one method that isn't working. The result is a kid who thinks he "sucks at math".

My approach exactly. My kids have also had to endure the new methods, which I have to figure out first before I can explain it to them. So, I have taught them the methods and shortcuts that I use, so they can be sure they have gotten the right answer, then they take the numbers and plug them into the equation methodology that the teacher wants. It is important for them to be able to solve the equation the way it is being taught, but equally important that they understand how and why they got the answer. When faced with a circumvent method, generating the answer first and then reverse engineering the equation to suit the method makes for a kid that can actually grasp the problem.

I also push rote memorization on them for all their times tables and division, squares and roots. Even though the schools say that isn't the best way, I still believe that just knowing the answer can't be beat.

MS Fowler · #21 12-06-2013, 01:24 PM

Quote:

Originally Posted by Honus

I am a product of Fairfax County Public Schools in Virginia, class of 1975. Based on my interactions with the people who went to college with me, I believe that I had exemplary math teachers in high school.

Every kid who is able should be required to learn at least some calculus, IMHO. Calculus provides insight into so many physical processes that we see in everyday life, it should be a part of every college kid's education, IMHO.

Calculus was a stone wall for me. I easily understood all math--set theory, algebra, trig --up to calculus, but couldn't get it. I share the blame with my teacher. Having said that, there have been several times when I could have used calculus. At least now I can use a spread sheet and just use as many iteration as required---its a slow method, but it works well enough.

engatwork · #22 12-06-2013, 02:02 PM

I can add numbers like in the op almost instantaneously in my head.

I graduated hs the same year you Honus. I have seen it presented both ways.

I agree to teach em chess. Speaking of chess I was the chess champion in 1975 in my high school

. I used to enjoy a good chess game.

kerry · #23 12-06-2013, 04:34 PM

Quote:

Originally Posted by MS Fowler

Calculus was a stone wall for me. I easily understood all math--set theory, algebra, trig --up to calculus, but couldn't get it. I share the blame with my teacher. Having said that, there have been several times when I could have used calculus. At least now I can use a spread sheet and just use as many iteration as required---its a slow method, but it works well enough.

I've served on a number of search committees seeking Calculus instructors. I can assert with a high degree of certainty that there are a lot of mathematicians who cannot teach Calculus and very few who can. The difference between the two groups is startling.

Simpler=Better · #24 12-06-2013, 04:45 PM

The old way is the best way. They're pushing the backwards way on kids and then wonder why they can't add.

Stretch · #25 12-06-2013, 05:02 PM

Quote:

Originally Posted by pj67coll

...

I was wondering how folks on this forum were taught basic math in grade school. A few hundred years ago when I was of that age if you wanted to add say 89 and 16 you would write 89 and then 16 beneath the 89. Add 9 and 6 and get 7 (oops sorry, that'd be 15

) so have a 5 under the 6, carry the 1 to he first column and add 8, 1 and 1 and get 10. Thus the answer of 105. I'd try to write it out numerically but I'm to tired to stuff around with that now.

Now my stepdaughter whose a special needs kid and despite being 12 is way behind in math, as well as many other things is being taught a method of addition that to be blunt looks utterly dumbass to me.

Instead of each number under the other they are all simply written out like a regular sentence. Such as 89 + 16 = and then by some weird rigamarole of separating the tens and ones you add them separately in columns beneath the problem and then stick em all together. So you add 80 and 10 and get 90. And you add 9 and 6 and get 15 and then you add 90 to 16 and you get 106. Seems to be massively lengthening what should be a pretty simple two column addition to me.

Needless to say with a kid that's only hardly beginning to grasp what I think of as the "traditional" method of addition having this curve ball thrown at her seems damm stupid to say the least.

What do others think?

- Peter.

The difference in the methods you show above is a way of looking at how number bases work.

If you apply the second method you can use it more easily and practically to less common (non base ten) systems of counting.

pj67coll · #26 12-06-2013, 06:04 PM

Quote:

Originally Posted by Stretch

The difference in the methods you show above is a way of looking at how number bases work.

If you apply the second method you can use it more easily and practically to less common (non base ten) systems of counting.

That may be. But how often in life do you ever use a non base ten system of counting?

- Peter.

layback40 · #27 12-06-2013, 06:17 PM

Quote:

Originally Posted by pj67coll

That may be. But how often in life do you ever use a non base ten system of counting?

- Peter.

Hmm, Peter

You count eggs by the dozen.
Pints & gallons
stones, pounds & ounces
miles feet & inches

Do I need to continue?

Now that you realize it you will probably have problems with them.
I am surprised your government hasnt gone metric so its easier for all the numnuts. The main reason for base ten is because we can count on our fingers.

MS Fowler · #28 12-06-2013, 07:31 PM

Quote:

Originally Posted by kerry

I've served on a number of search committees seeking Calculus instructors. I can assert with a high degree of certainty that there are a lot of mathematicians who cannot teach Calculus and very few who can. The difference between the two groups is startling.

Thanks,
My experience only increases my admiration for the man who originally came up with the idea. Amazing intellect.

elchivito · #29 12-06-2013, 09:27 PM

Quote:

Originally Posted by cmbdiesel

I also push rote memorization on them for all their times tables and division, squares and roots. Even though the schools say that isn't the best way, I still believe that just knowing the answer can't be beat.

That's an exaggeration. The memorization of basic single digit addition, subtraction and multiplication facts by rote is routinely taught and is widespread. There are curriculums that, in my opinion, spend too much time illustrating WHY 6 nines or 9 sixes are 54, but good teachers follow this up with rote practice. Under the new Common Core standards, single digit addition and subtraction facts are started in kindergarten. Previous NCLB standards for kindergarten only required being able to count orally and recognize (but not write) numbers to 100 by ones and tens.
In the kindergarten class I have been working with this fall, 16 out of 20 kids are already proficient with addition and subtraction facts through 10, and while they spent some time taking two plastic duckies away from 5 to find out how many were left, they also do 15 minutes a day of oral facts recitation.

Stretch · #30 12-07-2013, 02:41 AM

Quote:

Originally Posted by pj67coll

That may be. But how often in life do you ever use a non base ten system of counting?

- Peter.

You're using one now (binary) that potentially is also intermingled with hexadecimal somewhere in the back ground.

In my experience you can either go down the "trust me - just do this - turn the handle and it will come good" route or the "this method shows how it works - if you understand this then you can apply it to a wide range of situations". The "trust me - turn the handle route" gets the quickest results but often does not help with understanding; so mathematics / automatic transmissions / power steering boxes / combustion remains a dark art and frustration and myth take over!