Funny picture thread

[Sky]

Yeah, this.  I have no idea how you could have a math problem where the work your doing to solve it would just 'confuse' the student.  Unless of course they just didn't know how to solve it.  The show work thing is important at the minimum because its an anti cheating filter.  When you have calculators that can solve just about everything, it helps the teacher avoid having to deal with shit like this:

My brain doesn't work that way, nor does a significant percentage of the population. Traditional education methods don't work for folks like me. I can zip through a math problem abstractly but I can't write out how I did it in any coherent manner, let alone the 'correct' manner.

But hey, I failed 9th grade math and that teacher had a false sense of security about cheaters, mission accomplished.

Luckily I had a 12th grade teacher who wasn't a mindless drone and allowed me to explain my methods after each test. Passed with high 90s, without ever showing the work on the test, thus no 'partial credit' nonsense (you get it right or wrong).

Be glad you're not in the minority who can't function in traditional schools.

[Ironwood]

Showing work on a math problem is important because it shows where you lost it.  A wrong answer with the right method, you just missed a decimal place or made a transcription error shouldn't be a 0 is should be almost full credit (And usually is, if you show your work).

Totally.  Bear in mind that teacher had to actually TEACH you.  Having a sheet of paper with numbers on it and a big fat score of Zero at the end doesn't really help anyone.

If the student is confused about steps to solve the problem the student is a fucking moron.  I can't even follow Skys argument.  'My Brain doesn't work that way because I don't understand the steps I took to solving the problem'.

What, were you using the fucking force ?

[Paelos]

What, were you using the fucking force ?

That's how I do tax returns, yes.

[Ironwood]

[Bzalthek]

No, there's a lot of people who just understand certain portions of math as intuitive.  The thing about numbers is there are many many ways to reach the correct answer, and the formulaic method taught in schools is just the currently accepted method.  But if you've even briefly covered the advances of teaching, and the changes of our understanding in how a person learns, you would know that the accepted method is not the best method for every student.  Hell, it very well may not be the best method for the majority of students.  But education is a system that has only recently been making major strides in changing how they look at things, and change is hard because "we've always done it that way" and "if it was good enough for me" is considered fucking gospel in this country.  It's practically as dogmatic as fucking religion.

[MahrinSkel]

Showing work on a math problem is important because it shows where you lost it.  A wrong answer with the right method, you just missed a decimal place or made a transcription error shouldn't be a 0 is should be almost full credit (And usually is, if you show your work).

Totally.  Bear in mind that teacher had to actually TEACH you.  Having a sheet of paper with numbers on it and a big fat score of Zero at the end doesn't really help anyone.

If the student is confused about steps to solve the problem the student is a fucking moron.  I can't even follow Skys argument.  'My Brain doesn't work that way because I don't understand the steps I took to solving the problem'.

What, were you using the fucking force ?

2 + 2 = x  Show your work.  

Imagine that the solution to a quadrinomial was as obvious to you as 2 + 2 = 4.  You didn't step through to the solution, you just saw it.  Now imagine some teacher wanted you to go through all the steps you didn't need to go through, over and over, the equivalent of writing "(1 and 1) and (1 and 1) are the same as 4" over and over again.

--Dave

[01101010]

 

[Chimpy]

Having scored the state math tests for three years I will give you another reason why showing work is important: many times, doing completely incorrect math will result in a proper numerical solution. If the student does not show their work there is no way for the teacher to know if the student did so and it does the student no service to be under the impression that they did the work correctly and use that same process in the future where it did not coincidentally result in a "correct" solution.

One of the things we had to watch for was ways students could arrive at the correct solution using improper method and document them so the state could evaluate the question and decide if it was worth using again or removing from circulation.

[MahrinSkel]

When a student turns in a worksheet of 50 problems and has correct answers for 49 of them, and can provide the answer to an arbitrary equation in seconds, and the answer for why that isn't good enough is "Our teaching methods suck", the answer is correct, but not for the reasons you think.

--Dave

[tgr]

If I were to be asked to write a sentence in english, or translate from english to norwegian or vice versa, I'd be able to do it without thinking much of it, and it would be a good translation. If, however, I were asked to explain the grammar rules used to transform the sentences, I'd just look at you like you were a fucking retard, because I literally can't be arsed to learn the grammatical rules at anything other than a subconcious level.

Doesn't change the fact that I seem to be doing just fine without knowing all the rules, though.

[Sky]

No, there's a lot of people who just understand certain portions of math as intuitive.  The thing about numbers is there are many many ways to reach the correct answer, and the formulaic method taught in schools is just the currently accepted method.  But if you've even briefly covered the advances of teaching, and the changes of our understanding in how a person learns, you would know that the accepted method is not the best method for every student.  Hell, it very well may not be the best method for the majority of students.  But education is a system that has only recently been making major strides in changing how they look at things, and change is hard because "we've always done it that way" and "if it was good enough for me" is considered fucking gospel in this country.  It's practically as dogmatic as fucking religion.

This. And it's made more challenging because the majority of people learn well under the traditional methods, that's why they're in such widespread use. Given that most people who DON'T respond well to that learning environment tend to find their own way, you get a lot of formally educated people who are a unified front, because it worked for them and they can't understand that it doesn't work for everyone.

Not just math, I used to run chemical formulas in my head, too. After a while you just see how things naturally go together and it's easy. Then you butt up against formal education and either conform or quit. I got away with it through years of high school AP physics and chemistry getting high 90s, but hit college and had to drop the class because I got slaughtered. Not because I didn't understand the material, indeed I probably understood it better than anyone else in my class; but because I didn't follow the proper procedures for writing basic shit down (because I didn't think that way, anymore than I have to think of how to spell "intuitive" or how I don't think of all the notes in a Dm chord as I play it). The system utterly failed me: I learned the material better than anyone and had to drop out because I didn't do it the way some cut-rate professor was taught to teach it.

Sorry, it makes me angry when this topic comes up. Half the reason I ended up in a pro band was this; I had moved on from music briefly to hit college after high school. That didn't go well...and it still upsets me today because it wasn't because I wasn't learning, it's because I wasn't properly writing things on tests. Broken system.

[MuffinMan]

If I were to be asked to write a sentence in english, or translate from english to norwegian or vice versa, I'd be able to do it without thinking much of it, and it would be a good translation. If, however, I were asked to explain the grammar rules used to transform the sentences, I'd just look at you like you were a fucking retard, because I literally can't be arsed to learn the grammatical rules at anything other than a subconcious level.

Doesn't change the fact that I seem to be doing just fine without knowing all the rules, though.

I'm not sure if that is a good analogy. I would think the subset of people that subconsciously know grammar rules is much, much larger than those that can do anything beyond arithmetic subconsciously.

[Kail]

No, there's a lot of people who just understand certain portions of math as intuitive.

Maybe this is the problem, the word "Math" is pretty broad.  Some people here are discussing complex math that has a methodology which you need to understand if you're going to have a hope of solving problems beyond a high school level.  Some people are discussing "intuitive" math which works fine at grade school levels but falls apart at higher levels.  Most people don't really need to do much complex math beyond basic addition and multiplication, so intuitive math works fine for them, but they're still taught analytic math because that's the only way to solve a lot of the more difficult problems.

I suppose it's a question of grade school preparing people for life, versus preparing them for higher education.  Towards the end of my high school years, I know there were separate math courses along those lines, but for most of my education before that, everyone was taking the same thing.

[tgr]

If I were to be asked to write a sentence in english, or translate from english to norwegian or vice versa, I'd be able to do it without thinking much of it, and it would be a good translation. If, however, I were asked to explain the grammar rules used to transform the sentences, I'd just look at you like you were a fucking retard, because I literally can't be arsed to learn the grammatical rules at anything other than a subconcious level.

Doesn't change the fact that I seem to be doing just fine without knowing all the rules, though.

I'm not sure if that is a good analogy. I would think the subset of people that subconsciously know grammar rules is much, much larger than those that can do anything beyond arithmetic subconsciously.

The reason for this difference in ability to do math subconciously lie mostly in the amount of time spent doing it, there are of course those who just don't care or just can't. Those who aren't afflicted by "I don't care" or "I just can't", however, don't tend to sit and count up 2+2 or 2*2 or 2*3, or 110 + 20, they just do it, because they've gotten used to doing that kind of mathematics. Some people are much more interested in maths, and thus spend more time DOING maths, and as such get a much wider range of rules which they know subconciously.

As a contrast, I've got a coworker who, whenever he talks about APIs, what he actually says is "IPI" because he can't seem to vocalize A as an actual A, his english spelling is atrocious, the way he builds up sentences is an affront to my sensibilities, and the only reason I can't yell at him for it is because he's not my subordinate. The difference between me and him is probably the fact that I actually care about the english language, whereas I strongly doubt he does. It's not like he's dyslexic either, his written norwegian is fine.

[Kail]

The reason for this difference in ability to do math subconciously lie mostly in the amount of time spent doing it, there are of course those who just don't care or just can't. Those who aren't afflicted by "I don't care" or "I just can't", however, don't tend to sit and count up 2+2 or 2*2 or 2*3, or 110 + 20, they just do it, because they've gotten used to doing that kind of mathematics. Some people are much more interested in maths, and thus spend more time DOING maths, and as such get a much wider range of rules which they know subconciously.

That's not intuitive or subcounscious, though.  They still KNOW the process to solve the problems, they've done it a million times, they just don't feel the need to write it out because they're proficient at it.  That's fundamentally different from someone who arrives at an answer without going through a process at all.

[MahrinSkel]

Math problems too complex to solve in my head are what computers are for.  And unless you're strictly using Mathematica, the way you do that is *completely* different from how you work them out on paper.

--Dave

[TheWalrus]

Wheres all the funny pictures yo?

[tgr]

That's not intuitive or subcounscious, though.  They still KNOW the process to solve the problems, they've done it a million times, they just don't feel the need to write it out because they're proficient at it.  That's fundamentally different from someone who arrives at an answer without going through a process at all.

If you've done something a million times, you'll have shortcircuited the answer. 2*2 is 4, 2+2 is 4, 2*3 is 6, 5*5 is 25, 25*10 is 250 etc, just like I know the derivative of X squared is 2X. It's not just that I can't be arsed to do the interim steps, I literally don't even remember how X^2 becomes 2X or 2X^2 becomes 4X, I just remember, because I've done it so much in class it's subconcious. And this is shit I haven't touched for more than 15 years, in fact it's closer to 20.

Ask me to do something about a sine or cosine of something, however, and I'm lost, because I didn't work with it sufficiently to make it subconcious.

[Amarr HM]

I've been doing Physics for last three years in college and I find Maths is all about practice, it's kind of a dark art.

[SurfD]

Next time they ask you to show your work, do it like this:

[tgr]

Ok, that one got me good.

[Amarr HM]

Bravo!

[Merusk]

A teacher that writes wtf on a page? That's happening now? 

[lamaros]

Showing the working is boring and tedious. Once you've done it you know how to do it. Why waste time shitting around? Also you can develop cramp from writing too much.

Showing working is a teaching and proving tool. Many people find repetition of things they have already learned to other people who have already learned them absurd. Working through 15 examples of the same question is lazy teaching, or pointless labour.

[Murgos]

Showing the working is boring and tedious. Once you've done it you know how to do it. Why waste time shitting around? Also you can develop cramp from writing too much.

Showing working is a teaching and proving tool. Many people find repetition of things they have already learned to other people who have already learned them absurd. Working through 15 examples of the same question is lazy teaching, or pointless labour.

Fine.  When someone is about to drop 35 million on an ASIC with a specific biquadratic filter implementation you just go ahead and and tell the customer (some mutli-billion dollar company or government agency, usually) that you didn't want to waste time shitting around and they should just accept your answer.

How about "No, Ma'am I can't explain how I know that 35.2 mg of deadly poison will cure you, I did that calculation in my head so I'm pretty sure I am right."?

Maybe, "Sir you need to by 3500 sq ft of Barzillian Hardwood at $15 a sq ft.  No, can't show you if that number is right I did it in my head."

Math is a description of the world around you, learning to be able to show other people that you got the right answer is as important as getting the right answer in many cases.

You actually don't have to go by rote method out of a text book in the real world, but everyone does need to be able to understand how you went from point A to point B with clarity.

[tgr]

The next time I go to the dentist and he wants to give me anaesthetics, I'll demand that he show me the calculations for how much anaesthetics he's going to give me. In excruciating detail.

[apocrypha]

The next time I go to the dentist and he wants to give me anaesthetics, I'll demand that he show me the calculations for how much anaesthetics he's going to give me. In excruciating detail.

What exactly is your point there?

Because a dentist will be able to give you exactly that information if you want. Local anaesthetic dosages are calculated based on the concentration of the anaesthetic they're using, what the recommended dosage is (which has been already empirically calculated usually) and things like whether or not they're using vasoconstrictors, e.g. adrenaline, to limit the spread of the drug through the local soft tissue.

Showing your working for a maths problem is about showing that you understand how the calculation is arrived at. In science papers it's crucial because it shows you understand the mechanisms behind your answer. If you understand something correctly it means you can adjust/adapt/interpret the situation when things are different or unexpected things happen.

The greater the complexity of the system that the calculations apply to then the greater the need for showing working, i.e. understanding mechanisms.

Edit: If anyone's genuinely interested then here's a discussion on a situation where being able to calculate correctly by understanding the precise mechanisms of the maths (i.e. showing the working) is very, very important.

The lack of basic maths skills can be a major problem when it comes to nurses administering drugs to patients. Calculations are still a significant source of drug error.

The opinion of the United Kingdom Central Council for Nursing, Midwifery and Health Visiting (UKCC) (now the Nursing and Midwifery Council) is that nurses should not rely too heavily on calculators.

The latest guidelines for the administration of medicines (UKCC, 2000) state that the use of calculators ‘should not act as a substitute for arithmetical knowledge and skill’.

Getting basic mechanisms wrong gets people killed. Getting the division the wrong way round can result in massive overdoses of anaesthetic - something that if you're working intuitively is much more likely to happen.

[Lantyssa]

As long as my doctor/dentist factors in the 1.2 multiple for me being a red-head, I'm good with them not explaining themselves.

[Minvaren]

First, le funny picture:



Second, about "showing one's work":

This is a classical Sensor/Intuitive divide thing.  Most people naturally think and work in a step-by-step fashion.  A minority of people naturally perform leaps in thinking and/or working.  In a teaching environment, most teachers are Sensors and most students are Sensors, so teaching by rote and repetition is the preferred method, and you show your steps to prove mastery.  Unfortunately, this drives the Intuitives nuts, because it's diametrically opposed to their preferred way of doing things.  

As a strong Intuitive myself, having to document more than 2-3 steps per calculus problem was painful to me, because I had do things step by step instead of letting the natural leaps happen - and frequently made mistakes as a result.  It was the main reason I got out of hard sciences in college - I could do the work properly in my head, but it took 3 times longer to correctly document the process that the professors were looking for.  On the other hand, I kicked some serious ass at Number Sense back in high school - no work-showing required, or allowed.

[Samwise]

This is a classical Sensor/Intuitive divide thing.

Suddenly I realize why so many of my coworkers insist on giving me a lot of irrelevant background information as a lead-in to asking me a simple question, and why it irritates me so much.  Is there some kind of t-shirt I can get that says "I'm an Intuitive, just skip to the end part"?

[Nebu]

As a teacher for the last 22 years, I'll say this:

Intuitives benefit from writing things out.  Why?  It builds communication skills.  Intuitives need to learn how to communicate their thoughts and ideas to those that lack their intuition.

Non-intuitives need to learn to develop intuition.  They need to see the end without having to write every step in between.  I give exams that are a mixture of Multiple Choice and long answer for just this reason.  Intuitives will do the MC quickly and efficiently giving them time to do the long portion.  Non-intuitives are efficietn at writing things out and will use their time working through the multiple choice.

I am an intuitive.  Noone will EVER fund one of my grants or publish one of my papers unless I spell out every fucking detail.  Is it fair?  No.  Is life fair?  No. 

[Minvaren]

My experience is that Intuitives must learn to communicate effectively with Sensors to succeed.  The reverse, while helpful, is not required.

Oh yes, another funny picture:

[Selby]

I am an intuitive.  Noone will EVER fund one of my grants or publish one of my papers unless I spell out every fucking detail.  Is it fair?  No.  Is life fair?  No. 

Agreed.  I can't convince upper management to fund multi-million dollar upgrades to my machine if I just say "oh it's just gonna take this change and that change to keep the power levels the same without changing major components.  Trust me, I know what I'm doing."  I had to write out extremely detailed power calculations on every component in a presentation for them to see where the number came from, plus detailing every single assumption or standard even if it was obvious to me.  And it worked to convince them that the science and technology was sound.  Was it boring?  Yes.  Was it necessary?  Sure was.

[Lantyssa]

What's really fun is going over code with my intuitive boss who already knows the system really well, while I don't even know what the function we are looking at is for so I have to trace it out...

Oh... HI BOSS!

(To be fair to myself, I think I was figuring it out quite fast, just that wasn't any help to him.)

[lamaros]

Showing the working is boring and tedious. Once you've done it you know how to do it. Why waste time shitting around? Also you can develop cramp from writing too much.

Showing working is a teaching and proving tool. Many people find repetition of things they have already learned to other people who have already learned them absurd. Working through 15 examples of the same question is lazy teaching, or pointless labour.

Fine.  When someone is about to drop 35 million on an ASIC with a specific biquadratic filter implementation you just go ahead and and tell the customer (some mutli-billion dollar company or government agency, usually) that you didn't want to waste time shitting around and they should just accept your answer.

How about "No, Ma'am I can't explain how I know that 35.2 mg of deadly poison will cure you, I did that calculation in my head so I'm pretty sure I am right."?

Maybe, "Sir you need to by 3500 sq ft of Barzillian Hardwood at $15 a sq ft.  No, can't show you if that number is right I did it in my head."

Math is a description of the world around you, learning to be able to show other people that you got the right answer is as important as getting the right answer in many cases.

You actually don't have to go by rote method out of a text book in the real world, but everyone does need to be able to understand how you went from point A to point B with clarity.

Everyone? That's bullshit. Only the professional knows. Every time a house is built are the engendering elements explained in full to the guy who builds the thing? Who then checks the proof?

Needing to know how to demonstrate the working and having to show it every single time you do a calculation are different. I'm not saying people don't need to know. I'm not saying people shouldn't be able to do it. I'm just saying that often people tech by saying "do it 100 times until you get it down pat", which is counterproductive to people like myself who understood it after the rule was explained and I did one or two examples - the other 98 are just laborious and something that saps my energy and enthusiasm for learning.