Screwing up math to add to the confusion

[This_person]

Real world problems don't necessary have to be filled with extraneous data to make it a "gotcha" or "trick" problem.

Your example of leaving out the units leads to mistakes. It may not be too bad when they are all similar units such as length in your concrete example, but in more complex problems the units should be left in for dimensional analysis. There are many times I didn't remember an equation off the top of my head but when thinking about the units of what I wanted out and what went in I could figure it out quickly that way forgoing the derivation. For those that don't know what dimensional analysis is here is a good example http://www2.ucdsb.on.ca/tiss/stretton/Basic_skills/Dimensional_Analysis_Contents.htm

So many of my non-degreed coworkers ask me about math, they say the only answer they ever got when they asked their math teacher what is this used for was "you will need this in the next math class you take", their reply to that was "well what if this is my last math class I ever take?"

They don't have to be filled with data like that, but often they are. It makes the teachers feel smarter, and tries to weed out students who are not paying attention. They claim that they are trying to show how the data is used and test for understanding of concepts, but the reality is they are just writing trick questions.

And, there are only so many ways you can say, "if you want to divide the apples among a group of X people, how do you find how many apples each gets?" The word questions become boring and predictable.

It's best to start out with simple equations (2+2=?) without the word parts. Then, you work that up to word problems, then you work it into "real world" problems. You want to know your students understand the basics.

It's not different than learning to write. You don't start with words or sentences or paragraphs, you start with letters - big, block capital letters. Then you add lower-case letters, then you add in small words, then build to simple sentences, etc., etc.

You don't start balancing a checkbook by figuring in compound interest rates, you start with 2+2=?.

 

[PeoplesElbow]

They don't have to be filled with data like that, but often they are. It makes the teachers feel smarter, and tries to weed out students who are not paying attention. They claim that they are trying to show how the data is used and test for understanding of concepts, but the reality is they are just writing trick questions.

And, there are only so many ways you can say, "if you want to divide the apples among a group of X people, how do you find how many apples each gets?" The word questions become boring and predictable.

It's best to start out with simple equations (2+2=?) without the word parts. Then, you work that up to word problems, then you work it into "real world" problems. You want to know your students understand the basics.

It's not different than learning to write. You don't start with words or sentences or paragraphs, you start with letters - big, block capital letters. Then you add lower-case letters, then you add in small words, then build to simple sentences, etc., etc.

You don't start balancing a checkbook by figuring in compound interest rates, you start with 2+2=?.

I think you are making the assumption that word problems are immediately harder, they are not. I think starting with something simple like my apple problem shows the student what exactly division is and that they probably already understand it, they just didn't know that they did.

Many people see some math and immediately tune out with the "i don't have to know that" attitude.

Real world problems don't necessarily have to be word problems that get tedious, but I think a page of numbers added together with a line under them is every bit as tedious.

People also operate with the assumption that you need a bunch of different problems to teach something, if the basics how you get there are taught then there doesn't have to be 100 problems in every lesson.

When I was a TA and tutor in college I noticed that most that had problems with the subject had already decided that they weren't going to understand it, they weren't going to be good at it etc. I managed to turn a few around, but I mostly just got students through it. I do have one shining example, one of the students in the Thermodynamics class I was the TA for was having a terrible time with it, he came to my office all the time for help completing the homework, hoping that doing all his homework would help him pull out a C. Finally I asked him if he understood the most basic part of Thermo, turns out he did not. When I explained to him that energy that goes into a system either stays in it or leaves it that was all it took.

People have already decided that math could probably be taught better, unfortunately they came up with that common core garbage.

 

[This_person]

I think you are making the assumption that word problems are immediately harder, they are not. I think starting with something simple like my apple problem shows the student what exactly division is and that they probably already understand it, they just didn't know that they did.

Many people see some math and immediately tune out with the "i don't have to know that" attitude.

Real world problems don't necessarily have to be word problems that get tedious, but I think a page of numbers added together with a line under them is every bit as tedious.

People also operate with the assumption that you need a bunch of different problems to teach something, if the basics how you get there are taught then there doesn't have to be 100 problems in every lesson.

When I was a TA and tutor in college I noticed that most that had problems with the subject had already decided that they weren't going to understand it, they weren't going to be good at it etc. I managed to turn a few around, but I mostly just got students through it. I do have one shining example, one of the students in the Thermodynamics class I was the TA for was having a terrible time with it, he came to my office all the time for help completing the homework, hoping that doing all his homework would help him pull out a C. Finally I asked him if he understood the most basic part of Thermo, turns out he did not. When I explained to him that energy that goes into a system either stays in it or leaves it that was all it took.

People have already decided that math could probably be taught better, unfortunately they came up with that common core garbage.

Well, we're going to be in VIOLENT agreement on common core

But, I get your point - I sucked horrible at math when I was little because I just didn't care. I was going to be a truck driver like my dad. So, my dad asked me how much fuel he needed for his day, and I had no idea how to figure that out ("just fill the tank"). Then he wanted to know, "if I am going to do seven loads today, and each load has this toll and that toll, and another toll, how much money do I need and what coins do I need?" I had no idea how to figure it out, but I got the point - I needed to pay attention in math class and know how to do all this stuff. I became an honors math student and went on to become a nuke.

So, getting the "point" and real world of doing math is certainly a part of it. But, to me, you start with the concept of dividing the apples between a couple of friends, then do the repetitive work to reinforce the concepts. You don't make every problem a word problem.

So, maybe in the end, I'm agreeing with you in concept.

 

[PeoplesElbow]

Well, we're going to be in VIOLENT agreement on common core

But, I get your point - I sucked horrible at math when I was little because I just didn't care. I was going to be a truck driver like my dad. So, my dad asked me how much fuel he needed for his day, and I had no idea how to figure that out ("just fill the tank"). Then he wanted to know, "if I am going to do seven loads today, and each load has this toll and that toll, and another toll, how much money do I need and what coins do I need?" I had no idea how to figure it out, but I got the point - I needed to pay attention in math class and know how to do all this stuff. I became an honors math student and went on to become a nuke.

So, getting the "point" and real world of doing math is certainly a part of it. But, to me, you start with the concept of dividing the apples between a couple of friends, then do the repetitive work to reinforce the concepts. You don't make every problem a word problem.

So, maybe in the end, I'm agreeing with you in concept.

I've thought we were mostly in agreement the entire time. Most people when I tell them my ideas on learning math and science give me a "are you ****ing nuts" look.

I am a big proponent of it because I went from spending 25-30 hrs/week outside of a classroom trying to learn and struggling to keep a 3.0 average to spending maybe 5-6 hours outside of a classroom and my average was always above a 3.5 after that. I never did manage to hit a 4.0 though, stupid German class....

 

[vraiblonde]

So many of my non-degreed coworkers ask me about math, they say the only answer they ever got when they asked their math teacher what is this used for was "you will need this in the next math class you take", their reply to that was "well what if this is my last math class I ever take?"

My maffs teachers at college level were pretty good about giving real world usage when asked. I'm okay with education for education's sake, but it helps me to learn if I can envision a scenario. Otherwise it's rote memorization and that has never been my strong suit. If I know why we're doing this, I'll never forget it.

 

[This_person]

My maffs teachers at college level were pretty good about giving real world usage when asked. I'm okay with education for education's sake, but it helps me to learn if I can envision a scenario. Otherwise it's rote memorization and that has never been my strong suit. If I know why we're doing this, I'll never forget it.

So you wouldn't have sanded Mr. Miyagi's floor?

 

[gemma_rae]

I learned what axiomatic means.

I don't have an Aunt Sally

 

[gemma_rae]

2 + 2 x 4 = ?

16, right?

Wrong.

The correct answer, according to PEMDAS rules, is 10. Which is stupid. Simple math should be read left to right, unless there is an exponent or parentheses. Apparently this last generation was confused by that simplicity (which explains why they also don't know how to read), so they had to come up with a convoluted system in order to solve a very simple problem.

In one explanation, the explainer says that without PEMDAS you wouldn't know which numbers to solve first. So I'm guessing he also has a crazy rule so that he knows which words to read first in a sentence. When I was a kid, we didn't have order of operations for simple math - it was done left to right (again, unless there were exponents or parentheses, which are solved first). 2+2x4=16; 2+(2x4)=10.

And that is my beef for the day.

But seriously, if the answer is ten just tell me it's ten.
Ain't nobody got time fo dis!

 

[vraiblonde]

I learned what axiomatic means.

The forums are just like school, only you don't get in trouble for passing notes.

 

[Kyle]

The forums are just like school, only you don't get in trouble for passing notes.

... Or get the opportunity to stuff Sappy in his locker.

 

[gemma_rae]

View attachment 135085

Disclaimer: If this were an actual engineering tool kit there would be a brick next to the duct tape.

 

[GWguy]

Disclaimer: If this were an actual engineering tool kit there would be a brick next to the duct tape.

...and WD-40.