Math...
 

I've been very quiet on CD recently and on my return, I thought it appropriate to share this picture I stumbled on this morning.






Pavan



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:) Spot on

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I didn't know that failing math or failing to doing homework for more than 15 minutes was gender-specific.

Jane

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This makes me laugh on the outside, and cry on the inside.

I wouldn't believe it if my girlfriend wasn't a teacher and already giving failing grades high school seniors in geometry...

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I wasn't allowed to bring in my slide rule during one of my calculus finals. Apparently It could lead to me cheating. Yet I was allowed to bring my programmable calculator. Odd.

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Many websites I've gone on state that the use of "he" as a gender-neutral pronoun is "archaic and sexist". I'm just a college freshman, and I learned to use "he" as a gender-neutral noun in elementary school, and that was less than ten years ago. :confused:

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This is why I had 3 calculators in highschool:

TI 83
HP 11C
Omron 12SR

I did nearly everything on the Omron (provided I was sitting near an electrical outlet so I could plug it into the wall). The thing was so slow that it meant I had to do the actual math myself and then check it with the calculator. I ended up being one of the fastest people in my calculus class, because I never bothered to learn how to make the TI-83 integrate for me.

It has paid off well.

PS: Yes, the calculator really was 8 years older than me.

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I believe HE'LL is capitalized because it implies that the person is going to Hell.

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I realize I may be toeing a sensitive line with this reply, but I can't resist:



If it's any consolation, the engineers of the 1960's complained that THEIR children had it easy and were lazy, too (I know my grandfather did). It's pretty much a universal truth that Generation N thinks that Generation N+1 is going to be the downfall of the human race.

Are kids today REALLY any different than they've ever been?

"It's amazing how long this country has been going to hell without ever having gotten there." - Andy Rooney

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I think the use of he was in reference to the astronaut-as in "He (the astronaut) landed on the moon. Your eigth grader does 15 minutes of homework. Where do you think he'll end up?"

If it's trying to say he'll go to hell, well that's just idiotic.

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To be fair to the poster, it loses its edge and becomes a lot more clumsy with "he or she", and "they're" isn't accepted by everyone as a proper term.

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I think there is/was a lot of potential in the message of the poster - it just is a little messy. Well, pretty messy. Or mixed. Mixed messy message.

That's nothing new either.

Jane

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The purpose of written communication is to gain an understanding between the writer and the reader.

Whether the writer is gender/politically correct or not, the information and meaning of the poster is well conveyed and its purpose served.

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So why is a slide rule needed to make a poster :confused:

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I like it.

Mostly because I'm terrible at understanding math, yet there's a bunch of technology around me, and a bunch of kids around me who don't even put in any effort to try to learn anything.

Yes I want to be a mechanical engineer and I have a hard time understanding math sometimes(when its not applied to real life examples, mind you).

Stuff like this goes from a student to student basis. I suck at math, just because I have a hard time understanding calculus, but that doesn't mean I (always) totally give up on it.

The technology doesn't have very much to do with it. The point of the poster is how much effort is put in by some kids. I do agree though, that this mindset is present in every generation.

Nice find, Pavan.

Know what's scary though? Stuff like this:

"Forty-four percent of American 4th grade students cannot read fluently, even when they read grade-level stories aloud under supportive testing conditions. " -National Assessment of Educational Progress (NAEP) Pinnell et al., 1995

"50 percent of American adults are unable to read an eighth grade level book."-Jonathan Kozol, Illiterate America

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What is really a shocker is how many high schools, or even middle schools, allow students to use calculators, but then when the students go to college, calculators are banned in the math department.

At least that's how it is where I go to school. You try to get a student raised upon using a calculator to get a B or higher in college Calculus. It's not easy. I'm not going to lie. I struggled and worked really hard to earn my measly B's.

It's not really the importance that they need to know how to do it just to know how to do it. It's more of understanding why certain concepts work the way they do.

Nice post Pavan.

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I see a lot of truth in this poster. At my high school, my old one, I see that most kids undervalue or do not at all see the value of math or science, or any subject for that matter. During class I see kids who are just sitting in the back and spend the entire class on their iPhone texting or checking facebook. I see kids, kids in AP and honors, texting in class, disrespecting teachers (this part makes me really mad), cheating (you wouldn't believe how absurd this got), and just constantly complaining about how teacher so and so gives us "so much homework" (taking notes on a chapter due next week) or "Why do we have to learn history". I get frustrated with kids today (even though I am still one) because I see an overall devaluement of education and that most kids (at my old school) only care about facebook or other stuff like that. I see the importance of social interaction and having fun but I really do not think it is necessary to be on your computer, iPhone, or whatever for most of the day.
Also I understand what it is like to not be good at school, I have ADD (pretty bad too) and struggle everyday to focus on school and especially struggle to get homework done. I am not one of those kids who is just naturally smart and does not know why other kids aren't necessarily smart.

This poster does in my opinion embody what many of the modern day American students have become. I left my old high school because I disapproved of the cheating and apathetical attitude towards school. As a student who has had to deal with this I think the poster's message is quite spot on.

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It does in that it continues to underscore the male dominance and mentality in science, math, and technology. HE'LL helps move that attitude right along.

Good poster - good message - but could have been great by keeping to the comparison of the slide rule and the power of the cell phone. That's the true message: the use (and misuse) of power, knowledge, and meaningful application.

Jane

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I use a calculator with more computing power than used to go to the moon every time I do calculus. Why can we not get back to the moon people?

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I'm thinking that computers these days easily have more computing power than the lander and the command module combined, in a smaller package.

Why can't we go back to the moon? We don't want to. It's "been there, done that". My guess is that if we want to go back, we'll have to do it as a testing ground (supply depot, "halfway" point, etc.) for Mars. I'd rather have something go wrong on the Moon than on Mars--it's a LOT faster to get back, or get help out there.

On the original topic, apathy and distractedness are rampant these days. There is so much more fun stuff to do than homework... But guess what's more important?

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For the men and women responsible for Apollo, it was fun. (Or at least, enjoyable & worth their time). You don't work 24/7 without incentive, and as a government project, money wasn't the incentive.

These people are still around. A friend of a friend got hired by SpaceX, and if he's the average employee, they are both smart and incredibly hard working.

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These days, I think a lot of students think that homework (and chores, for that matter) is not fun. They don't want to do that. I would guess that the folks who did Apollo figured that it was a) fun, b) worth their time, and c) really cool. I'm also going to guess that most of them at least took the time to do their homework right...

There are companies out there where employees are passionate and have fun. SpaceX is just one example. That's the type of place you want to work, if you can, and you're passionate about the same sort of thing.

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"These days"? What's changed?

While I'm always against apathetic students who don't care, I'd rather we stop pretending that student apathy is a new, society-destroying problem. Apathetic students who didn't like school have been a part of every generation, and it's annoying and condescending to hear people older than me tell me how bad everyone who was born the same year as me is at everything.

I'd love to ask any of the engineers on the Apollo project if they LOVED slide rules, or if they seriously thought every eighth grade math assignment engaged them. I think the premise of this thread is a bit off. We're not doomed to societal decline because we don't care anymore, but rather school absolutely sucks at being engaging to the brightest children of today. Classes are too easy (and thus boring and a waste of time), too repetitive, and too intellectually empty for the best and brightest of today. That's one of the reasons the FIRST program is so important; it gives something to high schoolers that they can actually care enough about, and it shows them there's light at the end of the secondary school education tunnel.

We can't just pretend that telling students that they need to find mindless drivel "fun" will solve the world's problems.

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I agree with the opinion that many people seperate learning from fun. Somehow people got the notion that going to school and learning is not suppose to be enjoyable. It is suppose to be work.

I myself enjoyed doing calculations without a calculator and then afterwards checking if my calculations were right. I continue doing this until I reach a point where I need to use a calculator due to me being unable to do the calculation. If I recall correctly, in my area, the heavy use of calculators are when kids enter 6th grade. By the time they reach high school it is likely people forget how to even do 2 digit by 2 digit multiplication and long division with a pencil and paper. I don't know how it is in other parts of the United States.

Also, I think a lot of kids discourage themselves from learning math. Thinking it is too hard and give up on understanding. In the middle school here you may pass a test in 5th grade or be recommended by a math teacher to take the math course that is one year ahead of your grade level. I hear people refer to it as "smart math." This shows people think they have to have a natural gift with mathematics to be able to do well in math to me. This "smart math" after all is suppose to be learned by the kid the very next school year. After associating math with smart people will use their lack of natural ability as an excuse to why they're not doing well instead of studying hard to understand.

Maybe the problem is with this country is how we view education. We don't think of it as a blessing to be able to go to a place where we could learn with a person that could help us understand the material face to face. People think of it as a chore you have to do almost all the days of the week for less than half the day. Your test and quiz aren't rude benchmarks to see if you know the material, they are the obstacle that you must overcome to get to your goal whether that is passing the class, getting money for doing well, or achieving a goal of a good "grade." I recognize that quizzes and tests aren't the only way to tell if a person learned the material for that is why I refer to it as rude.

People view summer vacation as a liberation from having to learn instead of a break from following the forced schedule of school. If only more people were willing to learn some new things during summer break. This further implies to me the thinking of how learning is a chore I do not wish to do.

Just some mumblings of what I think.

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Because no matter how powerful the computer is that you strap to your backside, you can't ride it to the moon.

Blake

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I'm curious if public schooling has actually declined in overall quality over the past 50 years. We like to say it has, but I'm willing to bet that your average student has significantly more access to higher level classes than they did 50 years ago. My Dad was an honors student who went on to get a degree in Engineering Physics and he graduated high school without taking Calculus I. Had I stayed at my original high school, I could've taken through Calc II, and since Maine has a magnet school I was lucky enough to take Statistics, Differential Equations, and Linear Algebra before I graduated.

On the other hand, access to hands-on classes has definitely declined in my area. All of the schools in Midcoast Maine got rid of their wood/metal/auto shops in the '90s. There is still a vocational school, but its schedule is designed to fit with the lower level classes, not the college prep ones.

Interesting discussion!

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I had to look up "slide rule" because I didn't know what it was. I guess that says something. :/

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Haha, I want to bring a slide rule to Calculus, just for laughs.
Especially since I have no idea how to use it.

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I think focusing on the "slide rule" bit is really missing the point entirely. The slide rule is for all intents and purposes a mechanical calculator - knowing how to use a slide rule doesn't make you better at math than someone using a calculator.

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What was posted is spot on. I only graduated in 2008 however, in my high school you had to learn how to do calculus, chemistry, and physics with out a calculator. If you couldn't, there was no mercy. Calculators need to be taken away and students need to be forced to learn the long hand way first, then learn their calculator, but only if it's necessary.

On a side note to the subject, I was playing blackjack at school with other students and they at one point had to use their cell phones to calculate what they had on the table. To me, that's sad.

Cass

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Where is the point that we become dependent on the tools that we create and what are the reasons (read that - excuses) that we create for that dependency? And how do those reasons (read that - excuses) ripple out into society and the decisions made as a consequence or result?

Offering some food for thought...

Jane

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This is how I was taught until 8th grade...

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whip up a simple simulation, crunch a few billion numerical integration floating-point calculations in a matter of seconds, and instantly plot a time-graph of the results (in color!),

create a spreadsheet and play with the inputs to see how they affect the outputs,

instantly plot a complex non-linear equation to visualize its behavior and help find its roots,

do a monte-carlo simulation of a probability or statistics problem,

fit a model to a set of experimental data,

etc etc etc

Using calculators, and especially personal computers, opens up worlds of understanding for those who will use these tools to gain insight, and not as a substitute for thinking.

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And you let them????

Is this what is known as a teachable moment?

Next time we are in the same town overnight, introduce me to those students so that I can assist with their education.

I'll teach them the importance of several branches of mathematics, the importance of being good at unassisted arthimetic, and help them figure out whether or not the universe is going to wait for them to wake up and smell the coffee.

I suspect they will remember the lesson for the rest of their lives, and in later years will consider the experience a beneficial one.

Blake
PS: Folks - Red dot me if you care to - Don't be shy - I'll pay attention, but I won't be upset

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Interesting. My high school devoted almost 50% of its space to Career and Technical Education. We had an auto shop, a machine shop, a video production studio, a CISCO networking class, classes for all types of computer software...etc. These classes were often the saving grace of those students who hated math and science; they still found a passion and training in a useful technical skill in the CTE department.

Not everyone has a passion for math and science. But everyone has a passion for something, and everyone can become good at anything with enough motivation. The poster in the OP is comparing the brightest engineers in the world of forty years ago to the average schoolchild of today. That's an unfairly biased comparison. We still have NASA today, and the people who work there are still just as bright and passionate.

Also, the students of today have FIRST...:)

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Personally, I'm not that great at math and going into FIRST I didn't really care for it. But after working on designing and building a robot and seeing what practical application knowing Algebra, Geometry, and Calculus was and experiencing it first hand and after that I felt that I understood it better.

I think that the issue today is that students are pretty much educated in a vacuum, students learn about the theroy and how to perform it, but not so much the actual practice. Put it this way if you went into FRC and had someone explain how to build a robot without you personally laying hands on any tools, would you have any interest in it?

Going hands-on with a subject sometimes rather than just relying on a textbook is what can get a student to see the value in a subject, the Apollo Program wasn't just a bunch of guys sitting around a table discussing how one would go to the moon it was about actually achieving that goal.

On the slide rule subject, one of those has got to be easier than using some of my TI-83's higher functions

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Niether is excelling. I have three daughters who have excelled in mathematics (all have passed through FRC (the youngest still active), but their passion for math predated robotics). Not all current students are math dummies. Not all 1960's students were math geniuses either.

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The journey is the reward. :)


-dave




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In dealing with math this is so true.

I do have to bring up the point though, is it really the student's fault they don't want to do their homework? I am going to quote from a paper I was reading when I clicked into this thread (isn't random coincidence funny?).

By sheer chance I was reading that paper yesterday (I am really taking my time to digest it) when a friend mentioned they were struggling with their math course. Their main sticking point was they did not understand what they were finding, when asked what a derivative was they rattled off some equation they had been told to memorize. Figuring I had just asked the question in a bad manner I tried again by asking what it represented. They merely shrugged and said they didn't know.

I guess, in my mind, students not wanting to do homework is a symptom of something far more disturbing. Math education seems to be so focused on wrote memorization instead of passionate exploration.

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This reminds me of some information our team coach likes to tell us, I don't have his sources.

80% of high school drop outs had passing grades. When the reason to their removal was investigated, they said they saw no application to what they were learning.

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In my experience, this is a systemic and massive problem that goes back to primary education. People are told "when you see this, do this" because it's easier and faster to teach that way, rather than defining what the symbols actually mean. Once you get past calculus, math gets taught the way it should be, with strict definitions based on other mathematical terms, and it throws so many math whizzes for a loop simply because they got through high school memorizing everything and taking an "if this do that" approach to math. So many students struggle with math classes because they can't make themselves do the what without knowing the why, rather than because they're inherently bad at math.

A bit depressing if you think about it too much...

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Differential equations are covered in two classes at Cal Poly; one professor taught how most teachers would, the other strictly taught using practical examples (even on the first day! So we're making this circuit, which you guys know nothing about, but pretend you do.... Or, An engineer is analyzing the vibration of this beam...). It made quite a difference, and was a heck of a lot more interesting.

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The future is ours to set, change, determine - FIRST has a great way of influencing careers and there are a great many teachers and future teachers that are being influenced, empowered, and entrusted with helping to shape and define this awesome adventure that is the future.

That is no small thing.

Jane

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Coming from an above-average math student in HS (whatever that's worth in todays standards...), I think the root of the problem is in the student's willingness to work for their grades.

A few days ago we were working on a worksheet about numerical patterns (Algebra 2). I finished the whole page in 3 minutes while the rest of the class was still on question #2 (Guess why it's so easy - programming for FRC), so the teacher told me to help the 2 students behind me. As soon as I turned around, they asked me "Can I just copy down your answers?". After saying no many times, they finally started actually working on the problems. Still, they would continually try to just copy my answers, even trying to trick me into giving them ("Hey can I have your paper to check my answers to #1-4"), to the point where they were working harder on cheating than on actually thinking about the questions. Think about it: Students in an honors class trying harder to cheat than to figure out the answers themselves. I don't even know why it deserves to be called an honors class.

There also is a problem in the way we see teaching the students. Our district just passed a new rule that says teachers cannot fail students because they don't do homework (basically, if their homework grades put them below the fail threshold, then they still pass the class). We got that rule because too many students have been failing courses for not doing their homework...why don't they come up with some other way to get students to do homework? Or there are other problems like when a student who can't handle an honors class and refuses for come in on their free time for extra help is told by the teacher that the student needs to go to a regents level, the parent then calls and blames the teacher for not helping the student enough and forces the student to stay in honors class (I've seen it happen). What about sports? The rules in our district say that a student can have all their grades be C- (possibly even D+) and still be allowed to participate freely in sports. Why are the expectations so low?

My point is, why does the school and district do so little to provide incentives for the students to do well in their classes and even occasionally provide free passes to students who don't deserve to be in the class at all?

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The fact that we're not going back to the moon has nothing to do with education, computation skills or expertise.

We're landing vehicles on Mars. Consider the math involved.

Not going to the moon is a question of funding and political clout / deficits. There is no political will to go back to the moon.

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This is so, so true. At my school, there are numerous courses which students (including me) are required to take, yet they hate taking them, simply because they teach nothing of value. Or rather, we learn nothing of value. Teachers are trying to teach something we see no point in learning, like why, or rather, what types of dictatorships there are in the world. There's no point to all of this pseudo-learning going on. It does nothing to help us. When does the value of c cause the limit to exist for this equation.... all garbage.

Maybe I'm ranting too much due to the concussion and the pressure on my brain at the moment, but I've noticed there has definitely got to be something fundamentally wrong with the "teaching" in school today.

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I'm firmly in view all classes have an application (though maybe I'm just lucky enough to not have had boring classes). If you can't see the application of the class to the real world, your teacher has failed you, and you have failed yourself. Maybe you could cite some examples of classes you're referring to?

I don't have any experience with non advanced math classes, but in my AP math classes (Calc BC last year, Statistics this year) the major missing part was proofs. Over and over again we were taught subject material that I subsequently went home to wolfram, wikipedia, or even a used textbook to find and understand proofs of why the math works out for things like L'hopital's rule, or how r^2 works in statistics. Math classes have lost their depth (if they ever had it) of helping students to think in terms of the mathematics, as opposed to "simple" application. It's the third step of the what?, how? why? triad of questions that's gone missing. and something I desperately hope returns before I grow up and have my own children enter the school system.

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Calculus is a huge subject, and textbook authors have to choose what to include and omit.

If you want more rigorous coverage of "things like l'Hospital's Rule",
take a course in Real Analysis http://en.wikipedia.org/wiki/Real_analysis

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Just because you don't value it. Doesn't mean it has no value. I'm a tutor for pre-calculus. I know students think there isn't any use for algebra(unless your a farmer building a fence, creating a mixture, or any other stereotypical word problem) But the truth is, they can't comprehend the applications yet because you have to know algebra pretty good before you can actually follow their applications. Also, the reason there aren't many real world problems and proofs taught in school is because most students don't want them. They hate word problems and ignore the proof as long as they don't have to reproduce it. Perhaps the real problem is that the classes are catering to the students too much?

Jason

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I agree that there are some boring or irrelevant (at least to some people) courses in school. I have had some very negative experiences with teachers who seem to know nothing about the subject they are teaching. I have also had to endure some extremely boring classes that to me seemed to have nothing to with to do with my career path. However I also saw the immense value in these courses. So in this way I completely disagree that any courses have nothing of value. Every subject has something of value, however it is up to the student to determine how much they want to get out of the class. In other words, if you do not see the point of a class then it is because you do not want to see the point of the class; it is not because the class is not worth taking. I understand that there are some bad teachers out there, but just because a teacher is bad does not mean that the class/subject is worthless. In the post you seem to say that history/government classes and calculus are pointless; I could not disagree more. Classes such as history and government are incredibly important to everyone, not just history or political science majors. Without a solid understanding of history and the function of government then we will be unable to fully understand the present day. If you are in FIRST Robotics then I cannot fathom how you call calculus pointless. Without math you eliminate almost every technical career and even some non-technical careers. I used to have trouble understanding the point of English and writing, but I eventually learned that without a solid foundation in either someone cannot hope to succeed in college. Every class that the school forces you to take has a purpose; it is meant to make you into a more well-rounded person. If you see subjects that you don't like or find boring as being of such little value that you call it "all garbage" then you really do not understand the point of education. Education is meant to teach as many of the skills you will need to become a successful member of society not just those that are related only to a single subject. What would the world be like if each person only could do one thing: nothing would get done because no one would know how to interface with their team. If your teachers are failing to teach the subject adequately and you want to understand it better then you need to try to supplement it or ask the teacher for more clarification/background/help. I do believe that much of our education system is way too theoretical and does not have enough application taught in classes but if it is not given then you need to learn it on your own and not just complain about how it isn't taught.

My points are philosophical they are not meant to attack or chastise you in anyway. In many ways I agree with you but I really think that all education is important.

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What I believe theprgramerdude was trying to convey was that the class is useless. Understand, there is a firm distinction between a class and a subject. There are many useless classes but there are no useless subjects. There are also many ways of making a class useless. Some teachers make their classes useless; Sometimes it is the textbook. Sometimes it is even the student that makes the class not worthwhile. Often it is a combination of several factors that are all far too complex to classify or assign blame for.

So, instead of saying "it is the teacher's fault" or "the students don't want to learn" or blaming it on any single thing we should focus more on accepting that sometimes classes just are "meaningless" and then how we can minimize the number that is.

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I agree completely, there are a lot of reasons that a class can end up having no value. I responded the way I did because at my school(s) I often see/hear students criticizing a great teacher just because they do not think that curriculum is worthwhile.

I apologize if my post sounded too angry.

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Sorry this is so late, but yes I let them. I actually said put it away I will calculate for you. It was ridiculous. We we were not playing for money though. If we were then I would not have let that occur at all.

Cassie

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It wasn't, Garret. I enjoyed reading your contribution to the discussion.

Jane

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Interesting discussion about something that is largely just another tool. Calculators, slide rules, pencil and paper are all just tools. They don't make students better at math or calculus. They don't make them better engineers or scientists. They do make work easier. They can help get the job done faster, just like a power saw can cut a board or a power screwdriver can get something mounted in 1/4 the time. Calculus wasn't offered in my high school and likely I wouldn't have had the time to take it. Just trig took forever. Can you imagine having to look up the sin of 44 degrees in a table then try to calculate a four or five decimal place answer and get all the decimal points in the right place? A problem that takes a few seconds on a calculator took an half hour looking through the tables in a book and using a pencil and paper.
Another thing to ponder is cost. At the time I bought my first slide rule (1969), a Post Versalog, the student discount was nearly twenty times the minimum wage. I bought a Sharp pocket scientific calculator with more functions (including integration) than I can count (179 or 241 depending on what you believe) for $4.95 yesterday at Fry's. At that price there is almost no excuse not to have one in your back pocket and it is solar powered.
Tools give you the advantage to not use a limited amount of time performing simple tasks by hand. But the fundamental problem still remains. Students need to know why they are learning something. I didn't figure it out until I was in college and then it was tendered by a little "I don't want to work for minimum wage doing something I don't like". I couldn't see why we needed to study history for instance. Now I know that I don't want to reinvent the wheel for every project and learning history has given me the knowledge that someone has been here before. (did you know that slide rules were invented in the 1700's following Napier's work?) English has given me the tools to communicate and to appreciate the writings of others. Latin has given me insight to words in foreign languages, and Foreign Culture has given me the humility to understand others.
Now that I am approaching retirement, I still find myself thinking about school and learning. Take a look at my sig, learning something new everyday is important to me. A student gets that chance one hundred times over everyday. Why do homework? To get good at something. The first time you picked up a screwdriver, you likely hurt yourself, but you kept picking it up. Learn to use the tools, get good at studying, don't let something small get in your way, learn something new everyday.

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It's true. We fail at failing. Does that make us better or worse than those who succeed at failing?