Math...

[Andrew Schreiber]

Originally Posted by dlavery

The journey is the reward.

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?).

Originally Posted by Paul Lockhart (A Mathematician's Lament)

The main problem with school mathematics is that there are no problems. Oh, I know what passes for problems in math classes, these insipid “exercises.” “Here is a type of problem. Here is how to solve it. Yes it will be on the test. Do exercises 1-35 odd for homework.” What a sad way to learn mathematics: to be a trained chimpanzee.
But a problem, a genuine honest-to-goodness natural human question— that’s another thing. How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them).

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.

[ATannahill]

Originally Posted by Andrew Schreiber

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.

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.

[Chris is me]

Originally Posted by Andrew Schreiber

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.

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...

[AdamHeard]

Originally Posted by Andrew Schreiber

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.

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.

[JaneYoung]

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

[Radical Pi]

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?

[theprgramerdude]

Originally Posted by Andrew Schreiber

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.

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.

[Mageofdancingdr]

Originally Posted by theprgramerdude

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.

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.

[Ether]

Originally Posted by Mageofdancingdr

find and understand proofs of why the math works out for things like L'hopital's rule

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

[Molten]

Originally Posted by theprgramerdude

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.

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

[Garret]

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.

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.

[Andrew Schreiber]

Originally Posted by Garret

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.

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.

[Garret]

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.

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.

[JaneYoung]

Originally Posted by Garret

I apologize if my post sounded too angry.

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

Jane

[Al Skierkiewicz]

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.