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Common Core Math


Incredulity

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10 minutes ago, Hawndoh said:

As a middle school math teacher I'll give you the short version. Then the thread will be overrun by the "back in my day!" crowd that can't think for two seconds. 

The goal of much of the stuff people think is overly complicating a simple algorithm is to instill number sense. Kids with good number sense can more quickly learn all sorts of more advanced things in later grades. 

The kids that only memorize lots of algorithms struggle later and have no natural number sense. 

I will likely not return to this thread as we've been down this road before and this topic brings the trolls out of the woodwork. 

Your post doesn't add up. 

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9 minutes ago, Hawndoh said:

As a middle school math teacher I'll give you the short version. Then the thread will be overrun by the "back in my day!" crowd that can't think for two seconds. 

The goal of much of the stuff people think is overly complicating a simple algorithm is to instill number sense. Kids with good number sense can more quickly learn all sorts of more advanced things in later grades. 

The kids that only memorize lots of algorithms struggle later and have no natural number sense. 

I will likely not return to this thread as we've been down this road before and this topic brings the trolls out of the woodwork. 

I came here to post almost exactly this but from the elementary perspective. It at least attempts to help the kids conceptualize what they are doing to numbers instead of following steps with no real understanding. It’s not perfect and makes some things more complicated than they need to be. Overall, I think it’s a benefit and my school scores well using it.

I know how these threads go and won’t be back.

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12 minutes ago, Hawndoh said:

As a middle school math teacher I'll give you the short version. Then the thread will be overrun by the "back in my day!" crowd that can't think for two seconds. 

The goal of much of the stuff people think is overly complicating a simple algorithm is to instill number sense. Kids with good number sense can more quickly learn all sorts of more advanced things in later grades. 

The kids that only memorize lots of algorithms struggle later and have no natural number sense. 

I will likely not return to this thread as we've been down this road before and this topic brings the trolls out of the woodwork. 

I hope you stick around for a few posts and I am not trying to bait a “back in the day” fest.

Can you give some examples of what you are describing?  I can “see” what it is trying to do, but it just seems so much more “work” than how I know it.

 Which is at face value frustrating,  because my career is based on not doing shit the “hard way”.

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I had stumbled across some examples common core math problems a while back. Looking at the solutions, I did get the impression that it was somewhat related to number sense, with regards to how you visualize the problem.

My opinion is that it's probably a worthwhile means of teaching younger generations; appears to involve a little more critical thought, and I'd be willing to bet it is a more efficient method for cementing concepts.

Now that said, the critical thought part is a two way street. Teachers (and administrators) who get their drawers in a wad because Johnny and Suzy didn't solve the problem using one particular method, they can bent

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Oddball thing.  My parents were somewhat horrified that my instruction in "new math" some 40 years ago did not include "times tables."  So they made me drill with flash cards, essentially memorizing 1- 9 x 1-12.  Perhaps in combination with the new math or something, that actually helped me with math (and helped avoid dumb mistakes when performing higher-level calculations).

I have some degree of mathematical aptitude, though.

All these newfangled math things seem to attempt to instill mathematical aptitude in those that lack it.

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7 minutes ago, TwiceHorn said:

Oddball thing.  My parents were somewhat horrified that my instruction in "new math" some 40 years ago did not include "times tables."  So they made me drill with flash cards, essentially memorizing 1- 9 x 1-12.  Perhaps in combination with the new math or something, that actually helped me with math (and helped avoid dumb mistakes when performing higher-level calculations).

I have some degree of mathematical aptitude, though.

All these newfangled math things seem to attempt to instill mathematical aptitude in those that lack it.

Your last sentence really describes my gut response, which I was unable to articulate. Thank you.

 

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9 minutes ago, TwiceHorn said:

Oddball thing.  My parents were somewhat horrified that my instruction in "new math" some 40 years ago did not include "times tables."  So they made me drill with flash cards, essentially memorizing 1- 9 x 1-12.  Perhaps in combination with the new math or something, that actually helped me with math (and helped avoid dumb mistakes when performing higher-level calculations).

I have some degree of mathematical aptitude, though.

All these newfangled math things seem to attempt to instill mathematical aptitude in those that lack it.

  I'd like to hear the actual concept explained by one of the guys who said they wouldn't come back. You know they're out there.... watching.....

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19 minutes ago, Incredulity said:

I hope you stick around for a few posts and I am not trying to bait a “back in the day” fest.

Can you give some examples of what you are describing?  I can “see” what it is trying to do, but it just seems so much more “work” than how I know it.

 Which is at face value frustrating,  because my career is based on not doing shit the “hard way”.

Did you learn no concepts that required a solid understanding of the fundamentals?  You used to have to three or four long form versions of solving derivatives/integration before you got to use the “easy” way.  At the time it seemed tedious, but it eventually helped you in the long run with higher level concepts.

Most of the Singapore Math concepts seem pretty intuitive when I compare it to how I do math in my head.  I really think it is like what was mentioned above - trying to instill number sense to those that don’t have it naturally.

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My wife is a teacher.  Lots of grown ups who are bad at math never understood the algorithms that most of us here find so easy and intuitive.  The new way of teaching math is just giving kids additional strategies and hopefully one will make sense.  Let each kid use the strategy that makes sense to him or her.  Hopefully fewer will be left behind with no number sense.

if it offends you, teach your own kid whatever the fuck you want on your own time.  Let the teachers teach.

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Is your career based on understanding rather than memorizing?

That's what it's trying to do.

I hope you stick around for a few posts and I am not trying to bait a “back in the day” fest.
Can you give some examples of what you are describing?  I can “see” what it is trying to do, but it just seems so much more “work” than how I know it.
 Which is at face value frustrating,  because my career is based on not doing shit the “hard way”.
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So in a society (the United States) that is increasingly dependent on "services" and "knowledge" you are against trying to install additional knowledge and aptitude in a seemingly critical skill?

Oddball thing.  My parents were somewhat horrified that my instruction in "new math" some 40 years ago did not include "times tables."  So they made me drill with flash cards, essentially memorizing 1- 9 x 1-12.  Perhaps in combination with the new math or something, that actually helped me with math (and helped avoid dumb mistakes when performing higher-level calculations).
I have some degree of mathematical aptitude, though.
All these newfangled math things seem to attempt to instill mathematical aptitude in those that lack it.


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9 minutes ago, HoustonHorn said:

Is your career based on understanding rather than memorizing?

That's what it's trying to do.

I think this strikes right at the heart of it.  I don't believe that you can make engineers, mathematicians, physicists, or statisticians out of people that just don't "get math" by giving them alternative means of maybe "getting it." 

They will only need to do the algorithms to get by in life. I'm a math apt surrounded, largely but not entirely, by math inapts that do just fine in their lives.  Now, perhaps their lives might be enriched by understanding L'Hopital's rule, but I'm not so sure.

So I'm not sure what is the point.

But you raise a valid point, I suppose, in that we are behind the world in STEM things.  But that may be more an issue of forcing lazy people to rigorous educations than of attempting to increase aptitude.

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That could be. Teachers aren't necessarily going to be good at teaching.

 I’ve definitely seen some newfangled techniques in my kids’ math work  but I don’t think it’s actually Common Core. I thought I  read somewhere a few years ago that Common Core is not taught in Texas public schools.  Am I wrong in that? 
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I don’t know if my kids’ school district uses common core, but I do notice that their math curriculum  (particularly in elementary school) emphasizes the intuition behind the correct answer and has the kids learn multiple ways to arrive at the correct answer. This is much more useful in my opinion than memorizing algorithms, which is all I was ever taught. 

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Here's the thing, and basically what this boils down to: some kids suck at math. They just do. They don't get it. You can help them to understand it, but when you are working with a student that has already had half a dozen math teachers, that is trying their best to entertain their current teacher, so they can get a better grade and set themselves up for future success, sometimes the best solution is showing them the easiest way possible for them - whether or not it leads to a better "understanding" of numbers. 

This is inconsequential to redesigning the entire system from the ground up - maybe we should do that - but every student is different. Teaching a C student the most difficult concepts of algebra, geometry, algebra 2, pre-calculus etc. may benefit them if they end up truly grasping it, but if they don't (and they likely won't), it's often a waste of time. 

In my experience it's more helpful to find out what they do understand, and help them to arrive at the right solution based on that. Because, ultimately, whether it be a test score or an SAT score or their performance at their job down the line, arriving at the correct solution is what is most important. There are many different ways to skin a cat. If "common core" helps a larger % of students skin that cat correctly then I'm all for it. But their understanding and demonstrated ability is basically constrained by: how much are you studying, how quality is your education, and how efficiently are you spending that time (inherent ability/intellect is part of efficiency here). 

I don't think a "one solution fits all" mentality is ever the right course of action. There will always be a student that doesn't grasp "common core" and needs to have it explained or taught differently. It's human nature. 

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When my wife taught 4th grade math, every year they would have multiple night time meetings with a roomful of angry parents because of this.  The angriest were usually engineer dads who never struggled a bit in math and couldn’t understand how anyone could find the old way difficult.  It really offended them that the teachers wouldn’t stick with the method that worked so well for them. 

I know they were engineers because this is the first thing they would tell her before they splained how she should do her job.  It drove her crazy since has 2 masters degrees (evolutionary fish biology and education) along with 2 BS’s (biology and chemistry) and her dad is one of the top physicists in the world.  She is pretty good at maths, especially at a forth grade level.

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When my wife taught 4th grade math, every year they would have multiple night time meetings with a roomful of angry parents because of this.  The angriest were usually engineer dads who never struggled a bit in math and couldn’t understand how anyone could find the old way difficult.  It really offended them that the teachers wouldn’t stick with the method that worked so well for them. 
I know they were engineers because this is the first thing they would tell her before they splained how she should do her job.  It drove her crazy since has 2 masters degrees (evolutionary fish biology and education) along with 2 BS’s (biology and chemistry) and her dad is one of the top physicists in the world.  She is pretty good at maths, especially at a forth grade level.
Funny. Her picture isn't showing up
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When my wife taught 4th grade math, every year they would have multiple night time meetings with a roomful of angry parents because of this.  The angriest were usually engineer dads who never struggled a bit in math and couldn’t understand how anyone could find the old way difficult.  It really offended them that the teachers wouldn’t stick with the method that worked so well for them. 
I know they were engineers because this is the first thing they would tell her before they splained how she should do her job.  It drove her crazy since has 2 masters degrees (evolutionary fish biology and education) along with 2 BS’s (biology and chemistry) and her dad is one of the top physicists in the world.  She is pretty good at maths, especially at a forth grade level.
Funny because I'm an engineer and can do crazy math in my head but usually it's because I see it in a different way than how I was"taught"which was memorization. I just can't see how it's a bad thing to teach kids different ways to understand concepts instead of memorization.

Maybe that's why I don't actually do "engineering" and pure design work is getting outsourced to India. My job requires actual thought, not running calculations. I think it's better to have kids understand concepts and figure out the most effective way for them to do it that makes sense for them. Or we can have them memorize a bunch of shit and never have them think.
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2 minutes ago, HoustonHorn said:

Funny because I'm an engineer and can do crazy math in my head but usually it's because I see it in a different way than how I was"taught"which was memorization. I just can't see how it's a bad thing to teach kids different ways to understand concepts instead of memorization.

Maybe that's why I don't actually do "engineering" and pure design work is getting outsourced to India. My job requires actual thought, not running calculations. I think it's better to have kids understand concepts and figure out the most effective way for them to do it that makes sense for them. Or we can have them memorize a bunch of shit and never have them think.

My dad’s an engineer and not like this.  I’m sure most aren’t.  I just found it weird that the most pissed off  always seemed to fit this profile.

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12 minutes ago, HoustonHorn said:

Funny because I'm an engineer and can do crazy math in my head but usually it's because I see it in a different way than how I was"taught"which was memorization. I just can't see how it's a bad thing to teach kids different ways to understand concepts instead of memorization.

Maybe that's why I don't actually do "engineering" and pure design work is getting outsourced to India. My job requires actual thought, not running calculations. I think it's better to have kids understand concepts and figure out the most effective way for them to do it that makes sense for them. Or we can have them memorize a bunch of shit and never have them think.

here is the thing.many of that engineer grunt work is getting outsourced, but the creative innovation is staying in-house. i deal with companies all the time in my line of work that have factories in china, taiwan, india, etc. they will have creative engineer types that are ethnic, but they make sure those folks are living in the states and well-paid.

i saw the same thing in japan. brilliant folks raised by rote memorization afraid AF to think outside the box.

full disclosure, i'm not an engineer who got lost in math circa middle school to high school, and finally dropped out of AP calculus because i just could not catch up. my ability to bullshit was eclipsed by the material. i got by thinking outside the box, but that doesn't work in classes like geometry (fuck proofs) and pre-calc and calc. 

i'm now a liberal arts english/history major with a classical civ minor who does math for a living. 

the funny thing: higher level math escaped me. chemistry balancing? fuck moles, whatever those are. but when i got into college physics, it was an a class for me. i excelled in astronomy, and outlining the math of how a star fails or how gravity actually works. who knows how things attach to the brain?

that's why i'm generally in support of common core. it's just a way to find the key to the brain, instead of just letting those apt students succeed and everyone else wash out.

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My gut response to the technique (actually don’t know if it is precisely common core or not) she is being taught is that seems almost too smart by half.  I am sure the truth is it works better for some and worse for others, I was really just curious if any surl teachers had any experience and anecdotes of the different philosophy working better.  I guess its been around long enough now(20 years?) that there are few who lived through the change still at it.

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4 minutes ago, Incredulity said:

My gut response to the technique (actually don’t know if it is precisely common core or not) she is being taught is that seems almost too smart by half.  I am sure the truth is it works better for some and worse for others, I was really just curious if any surl teachers had any experience and anecdotes of the different philosophy working better.  I guess its been around long enough now(20 years?) that there are few who lived through the change still at it.

here's the cold, god's honest truth: she is smarter than you were at her age in an academic manner. her ability to process and understand information is at a completely different level. this is probably similar, though more exponential, than your life experience with your own folks. i was miles ahead of my parents. my kids aren't where i want them to be, but they can do shit i can barely believe.

i think this math is a reflexive approach to teaching for the amount of information kids can digest. where we were stuck with rote, they can now think their ways around problems in ways we can hardly imagine.

matter of fact (humblebrag that's not actually a humblebrag incoming), i often solved problems outside the boxes my math teachers wanted. as a result of a "show your work and do it our way" ideal, i failed. i failed a lot. 

i would get to the right answer the wrong way. "how did you solve for 12*5?" my teacher might ask. "well, i did 10*5, which is fifty and added 10, which is 2*5. that got me to 60." wrong. i was supposed to do the whole 2*5 = 10, carry the one, and do the 5*1 + 1 thing. that seemed too many steps to me and was counter-intuitive.

anyways. just an example. i got more problems wrong for being right than i can remember.

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4 hours ago, Incredulity said:

I hope you stick around for a few posts and I am not trying to bait a “back in the day” fest.

Can you give some examples of what you are describing?  I can “see” what it is trying to do, but it just seems so much more “work” than how I know it.

 Which is at face value frustrating,  because my career is based on not doing shit the “hard way”.

also, and it's possible i've not been clear.

it's about understanding the hard way now so the easy way can be had later. it's about fully understanding the concept so that later, the kid (adult) isn't using the goddamn slide ruler, but understands why the math makes the math.

so that when they are in the career, they can do the way easiest to them, instead of struggling to understand the meaning behind the goal. i've seen coworkers just battle math, trying to do it traditionally, and eventually wash out instead of being allowed the flexibility to understand a forecast can be built multiple ways and none of them is actually correct. we have had interviews come in and show perfect work, but miss the point of the exercise because they were too focused on that math bit, and it fucked their work up because they did a poor job identifying the actual goal, more focused on doing the math. that sort of thing. 

if that makes sense.

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yep.  I was always really good at math.  when the common core stuff came out.  i was against it because i thought the same thing that it was pure bullshit.  then I actually sat down and worked it and I realized these were concepts I had taught to myself growing up when I was looking for patterns on how to solve problems in my head.   so all the time that I had spent saying common core was bullshit was just me being against it because it wasn't something that was explicitly taught to me.  It was that I had a much better understanding of math than my peers.  I think overall it's a good thing.  one of the best math books out there is "Number Sense"  because of stuff like that you can almost instantly tell if you have a wrong answer because it doesn't fit the pattern.

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2 hours ago, Druggist said:

When my wife taught 4th grade math, every year they would have multiple night time meetings with a roomful of angry parents because of this.  The angriest were usually engineer dads who never struggled a bit in math and couldn’t understand how anyone could find the old way difficult.  It really offended them that the teachers wouldn’t stick with the method that worked so well for them. 

I know they were engineers because this is the first thing they would tell her before they splained how she should do her job.  It drove her crazy since has 2 masters degrees (evolutionary fish biology and education) along with 2 BS’s (biology and chemistry) and her dad is one of the top physicists in the world.  She is pretty good at maths, especially at a forth grade level.

Well since no one else has said it yet...

 

That’s a shit ton of degrees and debt to teach 4th grade math. 

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12 minutes ago, hayden_horn said:

here's the cold, god's honest truth: she is smarter than you were at her age in an academic manner. her ability to process and understand information is at a completely different level. this is probably similar, though more exponential, than your life experience with your own folks. i was miles ahead of my parents. my kids aren't where i want them to be, but they can do shit i can barely believe.

i think this math is a reflexive approach to teaching for the amount of information kids can digest. where we were stuck with rote, they can now think their ways around problems in ways we can hardly imagine.

matter of fact (humblebrag that's not actually a humblebrag incoming), i often solved problems outside the boxes my math teachers wanted. as a result of a "show your work and do it our way" ideal, i failed. i failed a lot. 

i would get to the right answer the wrong way. "how did you solve for 12*5?" my teacher might ask. "well, i did 10*5, which is fifty and added 10, which is 2*5. that got me to 60." wrong. i was supposed to do the whole 2*5 = 10, carry the one, and do the 5*1 + 1 thing. that seemed too many steps to me and was counter-intuitive.

anyways. just an example. i got more problems wrong for being right than i can remember.

whynotboth.gif paired with allofit.gif

We taught ours, now 9 and 11, to hammer all of the + - * / facts.  Then, each new teacher was to be treated as a person with a new perspective, if not just slightly different, on the topics and strategies of + - * / as they cycle through the years.  Be sure to do as each teacher instructs, show your work always, and double check your work with your hammered facts.  Another thing is that in the elementary age years they are given plenty of time to do the work and almost another set of time.  So be diligent to double-check your work.

We used flash cards in K and 1st for + and - .  Then began early/mid second with multiplication that wasn't really asked for till 3rd by the public schools here in DFW.

Teach them the anything x 10 you add a zero.  Anything x 0 is 0.  Anything / by itself is 1.

Counting by 2's is just like multiplying by 2's to an extent.  Counting by 5's, by 10's. All makes it easy if you can just do it and shows them early on when you compare 5x5 to 5+5+5+5+5 how it is interrelated just like 25/5=5.  That * and / are the same 3 numbers just in a different order, so to speak.  

Math at elementary level is finite, always an answer that never changes which is beautiful.

Girls, Boys, makes no difference since it is cool and you are giving them the practice at home to kill it at school.

Then starting in 3rd grade when there are only 5 questions on the quiz how important it is to get every one correct since missing one is an 80.

TLDR: Rote math helps get the fundamentals and more time to think about what each individual math teacher is saying so they can focus on the potentially slightly different strategy of their new teacher while already understanding the basic concepts from their home practice.

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45 minutes ago, UT_OB1 said:

Well since no one else has said it yet...

 

That’s a shit ton of degrees and debt to teach 4th grade math. 

Yup and she’s added another masters since.  Now she’s a librarian.  I think this career might stick.  We’re running out of years until it’s retiring age.

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11 hours ago, ztejas said:

Here's the thing, and basically what this boils down to: some kids suck at math. They just do. They don't get it. You can help them to understand it, but when you are working with a student that has already had half a dozen math teachers, that is trying their best to entertain their current teacher, so they can get a better grade and set themselves up for future success, sometimes the best solution is showing them the easiest way possible for them - whether or not it leads to a better "understanding" of numbers. 

This is inconsequential to redesigning the entire system from the ground up - maybe we should do that - but every student is different. Teaching a C student the most difficult concepts of algebra, geometry, algebra 2, pre-calculus etc. may benefit them if they end up truly grasping it, but if they don't (and they likely won't), it's often a waste of time. 

In my experience it's more helpful to find out what they do understand, and help them to arrive at the right solution based on that. Because, ultimately, whether it be a test score or an SAT score or their performance at their job down the line, arriving at the correct solution is what is most important. There are many different ways to skin a cat. If "common core" helps a larger % of students skin that cat correctly then I'm all for it. But their understanding and demonstrated ability is basically constrained by: how much are you studying, how quality is your education, and how efficiently are you spending that time (inherent ability/intellect is part of efficiency here). 

I don't think a "one solution fits all" mentality is ever the right course of action. There will always be a student that doesn't grasp "common core" and needs to have it explained or taught differently. It's human nature. 

2

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I help my 6th grader with cc math homework almost every night. The materials she has don’t do a very good job of explaining the concepts, but the concepts are solid imo. I can totally see how in general kids will have a better understanding of math when they are done.

 

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13 minutes ago, tbone_ said:

I help my 6th grader with cc math homework almost every night. The materials she has don’t do a very good job of explaining the concepts, but the concepts are solid imo. I can totally see how in general kids will have a better understanding of math when they are done.

 

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At the risk of being lumped in with the engineer dads who let teachers know they're engineer dads at the top of a conversation . . . I'm an engineer dad.  Furthermore, I never had any problem with abstract concepts.  I suspect times tables are "abstract" for a lot of people and it's extremely difficult for them to get the point.  Me?  I just memorized.  Same for trig identities, calc, DiffEQ and partial DiffEQ.  It was always nice to eventually tie some practical examples to the abstract theory ("local derivative = slope"), but it wasn't necessary for me.

It's obviously necessary for a lot of people.  As others have said, that appears to be the impetus behind Common Core.  I have no problem with that.

What I DO have a problem with is teachers marking a problem wrong because a kid was able to memorize the answer.  Yes, I've seen it happen.  Teach both ways so kids can find their learning wheelhouse.

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2 minutes ago, jimmyjazz said:

At the risk of being lumped in with the engineer dads who let teachers know they're engineer dads at the top of a conversation . . . I'm an engineer dad.  Furthermore, I never had any problem with abstract concepts.  I suspect times tables are "abstract" for a lot of people and it's extremely difficult for them to get the point.  Me?  I just memorized.  Same for trig identities, calc, DiffEQ and partial DiffEQ.  It was always nice to eventually tie some practical examples to the abstract theory ("local derivative = slope"), but it wasn't necessary for me.

It's obviously necessary for a lot of people.  As others have said, that appears to be the impetus behind Common Core.  I have no problem with that.

What I DO have a problem with is teachers marking a problem wrong because a kid was able to memorize the answer.  Yes, I've seen it happen.  Teach both ways so kids can find their learning wheelhouse.

The son is an engineer, and he had this strange way of solving math problems, and the teachers used to get pissed at him for doing it, but he was always right. Whatever works is what works best.

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30 minutes ago, jimmyjazz said:

At the risk of being lumped in with the engineer dads who let teachers know they're engineer dads at the top of a conversation . . . I'm an engineer dad.  Furthermore, I never had any problem with abstract concepts.  I suspect times tables are "abstract" for a lot of people and it's extremely difficult for them to get the point.  Me?  I just memorized.  Same for trig identities, calc, DiffEQ and partial DiffEQ.  It was always nice to eventually tie some practical examples to the abstract theory ("local derivative = slope"), but it wasn't necessary for me.

It's obviously necessary for a lot of people.  As others have said, that appears to be the impetus behind Common Core.  I have no problem with that.

What I DO have a problem with is teachers marking a problem wrong because a kid was able to memorize the answer.  Yes, I've seen it happen.  Teach both ways so kids can find their learning wheelhouse.

had a buddy in college who would get pissed because he always wrote down the right answers but got docked for not showing his work.  people who showed work but got the wrong answer would get more credit than him.  he would try to show the work, but he couldn't because the intermediate steps just confused the shit out of him.

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25 minutes ago, Onboard 2.0 said:

The son is an engineer, and he had this strange way of solving math problems, and the teachers used to get pissed at him for doing it, but he was always right. Whatever works is what works best.

As an engineer as well, I don’t really agree here, but obviously don’t know the specifics of the complaint.  Sometimes the teachers are trying to teach a specific method.  Sure you can solve a problem more than one way depending what information is available, but when the question is to solve it a specific way - there is only one path to take.  The final answer isn’t the goal of the question.  The thought process is the goal.  It is why showing your work is important.  

When you actually go out and work, you have to make all sorts of assumptions when the data isn’t available that you need different methods to solve the problem.

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Just now, Kringelbert Fishtybuns said:

As an engineer as well, I don’t really agree here, but obviously don’t know the specifics of the complaint.  Sometimes the teachers are trying to teach a specific method.  Sure you can solve a problem more than one way depending what information is available, but when the question is to solve it a specific way - there is only one path to take.  The final answer isn’t the goal of the question.  The thought process is the goal.  It is why showing your work is important.  

When you actually go out and work, you have to make all sorts of assumptions when the data isn’t available that you need different methods to solve the problem.

Yeah I get the teaching of concepts, and agree with it, to a point. Some people are just wired differently in how they process info. Math seems to point that out sometimes.  They actually accused him of cheating at first.

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