OT - Math brush up...

[Dekonick]

I haven't taken a math course since college and that was back in the early 90's...

Calc was as high as I ever aspired... but now I am on a mission. I have been reading a bunch of physics (I won't bore you with details - but it is neat chit!) and have found my math is just a bit rusty... :rolleyes:

So - I want to do it the right way... I am going to re-teach myself math from the fundamentals to algebra, geometry, trig, analyt, single variable calculus, multi-variable calculus and anything else suggested. What I do not want to do is go back to school. This is just to satisfy a curiosity I have and in no way will benefit me at work or even after I retire so I do not need another degree. What I am looking for are recommendations for text books, work books, online resources, etc. I don't mind shelling out some cash for texts, but as I am not seeking credit etc... older versions are fine with me. What I do prefer are texts and resources with lots of examples and pictures (self teaching... always a bonus!).

This forum always amazes me with the wealth of knowledge the members have... so it is almost always a good place to ask for unusual advice.

Thanks in advance!

(Yes - I know I am nuts.)

[Louis]

Soh Cah Toa

[Dekonick]

Soh Cah Toa

Oh boy... yeah... I remember that from trig... must have been 1987 or 88...

[rugbysecondrow]

You need a hobbie. ;)

My wife has a masters in engineering and was a double major in math for a while in college, I will ask her. She saved all of her text books and notebooks.

[thegunner]

heya, i have a few out of edition single variable calc -> multivariable calc -> ode books that i couldn't sell back if you want em. i also have pdfs of quite a few textbooks in engineering if fluid mechanics/materials design interest you :) :beer: here's to the age old adage that you're never too old to learn

but also... check out http://ocw.mit.edu/index.htm

it's an index of a bunch of MIT's courses made public. it saved my ass several times during undergrad (for classes that were awfully taught) and even grad school this past year.

[Ahneida Ride]

take a look at the Saxon math books. they are a series.

Many home schooled kids use them. I rate them as excellent.

They are great texts. !!!!!

After Calculus, the next step is ordinary differential equations and linear algebra. next step ... Vector Analysis/Advanced Calculus + Complex variables
and partial differential equations.

Next step are courses in Real analysis.

Math is always a struggle. Don't get frustrated.
Mathematics has taught me perseverance.

[learlove]

Complex variables


O the horror, need to find a happy place....

Math 401 - Linear Algebra and Complex Variables (required for MECH321 Aerodynamics) I should have taken Stats (then Gas Dynamics) like the rest of my fellow mechanical engineering pals but no I had to take Aero, so off to Math 401 I went.

That class gave me fits. something like i = the square of negative one???

Lesson = never take a class that has the word "Complex" in the title

[Ahneida Ride]

all of this could be put online once and for all.

with say 10 great instructors teaching each course.
you could tune to the Geek you like best.

Why go to class, sit there and just copy everything down in a rush
then go home and try to decipher it all? That is what I did and tons of
kids far smarter then yours truly.

Makes no sense.

all of undergrad math could be placed online as well as the first two
years of graduate math courses.

Math could be tons of FUN !!!!
One major Problem is that most math instruction sucks.

[Ahneida Ride]

Soh Cah Toa

Sock it to me ?

[thegunner]

Lesson = never take a class that has the word "Complex" in the title

ha i was deceived because my grad course was called 'math for materials science.' sounds innocent enough. turns out it's complex analysis and higher order partial differential equations squished into 1 semester. oh god that class destroyed my spirit.

[Lifelover]

I would randomly spam a few local, older college professors. They might be the best resource for "solved" problems. Pouring over solved problems, one line at a time, is where the understanding happens. ATMO

[swt]

Khan Academy (http://www.khanacademy.org/).

That should take you through multi-variable calculus and ODE's. That's good enough for mechanics. I would seriously try reading this Landau and Lif????z (http://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960/ref=sr_1_1?ie=UTF8&s=books&qid=1293597905&sr=8-1-spell). If that works for you, then you are really on to something. Sometimes I still read L&L Statistical mechanics for kicks.

Then you need a little bit of PDE's and Fourier analysis. There are a ton of good books on Mathematical physics that can do this for you. This is my all time favorite intro book on mathematical physics Mathematical Methods of Physics (http://www.amazon.com/Mathematical-Methods-Physics-2nd-Mathews/dp/0805370021/ref=sr_1_1?ie=UTF8&s=books&qid=1293598050&sr=1-1). It says Mathews and Walker, but it's actually Feynman. It's beautiful.

Then you're ready for quantum mechanics. I'd pick a good undergrad book off amazon. This one Griffiths (http://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927/ref=sr_1_1?s=books&ie=UTF8&qid=1293598152&sr=1-1) is OK.

Then you need to learn about electromagnetics. If you've made it this far, then I'd say you're ready to jump right into Jackson (http://www.amazon.com/Classical-Electrodynamics-Third-David-Jackson/dp/047130932X/ref=ntt_at_ep_dpt_1) , but get the red book it's cooler.

Along the way, these books Problems and solutions in X (http://www.amazon.com/Solutions-Electromagnetism-Universities-Qualifying-Questions/dp/9810206267/ref=sr_1_1?s=books&ie=UTF8&qid=1293598283&sr=1-1) are your friend.

At that point, you need to learn about statistical mechanics. I'd recommend a class or two in discrete mathematics and statistics (the kind CS undergrads have to take). Then you need a book. It think this one (http://www.amazon.com/Statistical-Physics-Third-Part-Theoretical/dp/0750633727/ref=sr_1_3?s=books&ie=UTF8&qid=1293598367&sr=1-3) is good.

OK, so at that point, you've got a state of the art physics education if you're living in 1930.

Enjoy.

[rounder]

I thought i was half way decent at math and started out in engineering. I was learning about points on a curve and whether they held water, when i realized that maybe i should change majors. I was talking to my nephew who is studying math and learned that he was helping his teacher write a book on finding patterns in randomness. That's when i realized that math is hard.

[qjetha]

+1 for Khan Academy. Good information, good teacher, and free.

[stephenmarklay]

Good for you. Math is strange for me. I seem to have forgotten more than I ever learned?

On books for some reason I always found the older books much more elegant. Not sure why but all the pretty color pictures and new ways of teaching never cut it for me. You can pick up old books at garage sales and second hand stores for next to nothing.

I did undergrad in physics with a math minor (well I think I took more math actually) and took everything offered. I really enjoyed it.

The bottom line, start at the beginning. Math is like a puzzle or better yet a thinking game. You just have to know the rules first and the rules start with remedial math...

[Ahneida Ride]

Ah Jackson .... E&M ... so many fond memories :crap:

the problems in there were horrific to solve.
and the math! made quantum mechanics look like cake.

solved problems is a great way to learn.
maybe the best out there.

[slowgoing]

my prediction is you'll find another diversion long before reaching laplace transforms. higher math is not fun, or easy.

[130R]

higher math IS fun BECAUSE it's not easy.

I use this to help me get through my math tests. he does a great job explaining concepts and is clear with all the steps.

http://patrickjmt.com/

gl! :cool:

[Sandy]

Soh Cah Toa

I must be really old... and losing it. I saw the Soh Cah Toa and was clueless what they stood for.....until someone said trigonometry.......which I taught in high school many moons ago. So after my pea brain knew it was trigonometry, I thought and realized:

Soh- sine-opposite side divided by the hypotenuse

Cah- cosine-adjacent side divided by the hypotenuse

Tah- tangent- opposite side divided by adjacent



Senile Sandy

[130R]

Toa :)

[Sandy]

No wonder they fired me :)

Now I see why the $500,000,000 bridge collapsed that I helped design. I used Tah and not Toa. I always wondered why the 400 foot high bridge was 500 yards too short.....so did the 140,000 drivers who landed in the bay and never made it to dry land. :rolleyes:


Sine Simpleton Serotta Sandy

[William]

I must be really old... and losing it. I saw the Soh Cah Toa and was clueless what they stood for.....until someone said trigonometry.......which I taught in high school many moons ago. So after my pea brain knew it was trigonometry, I thought and realized:

Soh- sine-opposite side divided by the hypotenuse

Cah- cosine-adjacent side divided by the hypotenuse

Tah- tangent- opposite side divided by adjacent



Senile Sandy

Here's a practice exercise for you Sandy-Pal......


Oh, there's 1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18
wheels on a big rig;

(OK, everybody now!)

Oh, there's 1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18
wheels on a big rig;
And they're rollin' rollin' rollin', rollin', rollin', rollin'.

(Mighty fine, good buddy, let's back the big rig on up now!)

Oh, there's 18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1
wheels on a big rig;

(OK, now let's count just the even number wheels.)

Oh, there's 2-4-6-8-10-12-14-16-18
wheels on a big rig;
And they're rollin' rollin' rollin', rollin', rollin', rollin'.

(OK, let's go to the other side of the truck now and count just
the odd number wheels.)

Oh, there's 1-3-5-7-9-11...13.....15.......17 wheels on a big rig;
(Sounds like you might have a flat...I don't know.)

(OK, since you're so smart, why don't you try doing it in Roman numerals?)

(OK, I will.)
Oh, there's I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII
wheels on a big rig,
And they're rollin' rollin' rollin', rollin', rollin', rollin'.

(Top that, will you!)

(OK, I will now attempt to divide the wheels of a big rig by pi.)
Oh, there's 3.1431425679..11...million wheels on a big rig,
And they're rollin' rollin' rollin', rollin', rollin', rollin'.


C'mon Sandy, you know this.....Sing it again!!! :banana:





William ;)

[1centaur]

all of this could be put online once and for all.

with say 10 great instructors teaching each course.
you could tune to the Geek you like best.



If I were president, I think I might take up this idea. To the extent that the US is getting behind in science and engineering, some of the problem is the randomness of math education. I was horrified by the lack of teaching in my son's high school math books - they were obviously recently written by math people and approved by math people and by textbook panels that were not math people. Add to that a math teacher who failed to grade quizzes before tests, or show up at office hours, and a department head who seemed to think this was okay and there was no way my kid was going to advance in math. This at one of the better high schools in the supposed best state for education.

Math being a fixed body of knowledge up to a certain point, and being a priority for the nation, why not standardize that education around awesome video instruction and use high schools just as helpers for the online version. We'd have to find passionate teachers to agree on consensus methods, but boy, it sounds more efficient than what we have now. That would be a major accomplishment for a president...who did not care about teachers' unions.

[97CSI]

For the HS texts, get teacher's editions with their additional explanations and answers. Generally, try to find more 'traditional' texts. The newer methods of teaching math are generally BS and are geared to providing a method for lazy kids who attend schools with no standards and have parents with even fewer standards to pass (that's what is important today, isn't it?) while not really knowing anything. Anything to avoid actually having to do any work. Rant over.

[Dekonick]

If I were president, I think I might take up this idea. To the extent that the US is getting behind in science and engineering, some of the problem is the randomness of math education. I was horrified by the lack of teaching in my son's high school math books - they were obviously recently written by math people and approved by math people and by textbook panels that were not math people. Add to that a math teacher who failed to grade quizzes before tests, or show up at office hours, and a department head who seemed to think this was okay and there was no way my kid was going to advance in math. This at one of the better high schools in the supposed best state for education.

Math being a fixed body of knowledge up to a certain point, and being a priority for the nation, why not standardize that education around awesome video instruction and use high schools just as helpers for the online version. We'd have to find passionate teachers to agree on consensus methods, but boy, it sounds more efficient than what we have now. That would be a major accomplishment for a president...who did not care about teachers' unions.

I totally agree - why re-invent the wheel? Feynman did it for intro physics in the 60's (he is my hero - an amazing mind that could also teach) with his lecture series. The same could be done for math. There is still a need for teachers as not everyone learns the same way, but a good free source for this information could benefit the whole world, not just the US. The internet can be a great resource for anyone who wants to learn - if the information is made easy to access. Sounds like a good project! For me, I just want to learn more as a whole new world has opened before me. Physics is odd and beautiful (quantum mechanics) and so it math. Amazing we sent guys to the moon and back with slide rules!

[Dekonick]

If I were president, I think I might take up this idea. To the extent that the US is getting behind in science and engineering, some of the problem is the randomness of math education. I was horrified by the lack of teaching in my son's high school math books - they were obviously recently written by math people and approved by math people and by textbook panels that were not math people. Add to that a math teacher who failed to grade quizzes before tests, or show up at office hours, and a department head who seemed to think this was okay and there was no way my kid was going to advance in math. This at one of the better high schools in the supposed best state for education.

Math being a fixed body of knowledge up to a certain point, and being a priority for the nation, why not standardize that education around awesome video instruction and use high schools just as helpers for the online version. We'd have to find passionate teachers to agree on consensus methods, but boy, it sounds more efficient than what we have now. That would be a major accomplishment for a president...who did not care about teachers' unions.

Agree 100% - but why stop there? Undergrad math could have the same. It wouldn't even cost all that much to prepare and create a series like this. A budget in the several million dollar range could produce a phenominal production. Cheap for something that can be used everywhere by anyone!

[SamIAm]

take a look at the Saxon math books. they are a series.

Many home schooled kids use them. I rate them as excellent.

They are great texts. !!!!!

After Calculus, the next step is ordinary differential equations and linear algebra. next step ... Vector Analysis/Advanced Calculus + Complex variables
and partial differential equations.

Next step are courses in Real analysis.

Math is always a struggle. Don't get frustrated.
Mathematics has taught me perseverance.

Real analysis is real hard, I don't think I would ever go there again! The rest of it is pretty doable even without formal instruction.

[97CSI]

If I were president, I think I might take up this idea. To the extent that the US is getting behind in science and engineering, some of the problem is the randomness of math education. I was horrified by the lack of teaching in my son's high school math books - they were obviously recently written by math people and approved by math people and by textbook panels that were not math people. Add to that a math teacher who failed to grade quizzes before tests, or show up at office hours, and a department head who seemed to think this was okay and there was no way my kid was going to advance in math. This at one of the better high schools in the supposed best state for education.

Math being a fixed body of knowledge up to a certain point, and being a priority for the nation, why not standardize that education around awesome video instruction and use high schools just as helpers for the online version. We'd have to find passionate teachers to agree on consensus methods, but boy, it sounds more efficient than what we have now. That would be a major accomplishment for a president...who did not care about teachers' unions.In public education it is all about 'passing the test'. Think NCLB and all its BS (started by dubya and continued by our present administration). As far as the teacher, did you demand better? Did you talk to the dept head's supervisor, complain to the school board? How about your student? Did he pay attention in class, ask questions, attempt to do his homework? Did you or your wife help? It is not just the teacher or the book. It is, first, the student. Then the parents (guardian) and teacher. Then the school admin and the then the admin's above them (local, county, state, nat'l). Public education is broken, but the answer is not the simple "it's the bad teachers and their union". Wish it were. Then we just replace them. But who wants to teach with lazy/rude students and parents who don't care and admins who don't support them and low pay and official abuse (think NJ's current governor). Plenty of blame to go around and it all focuses on money. As always, we want something for nothing. And talk is cheap (guess that's why we have so many blowhards about public education and it all focuses on the bottom-line of spending less money).

[avalonracing]

You guys are a bunch of geeks and I will be kicking your ass after gym class today.

[AngryScientist]

a good place to start, is the fundamentals of engineering exam (FE, or EIT) study material, they offer plenty of books to get you through the test, and they are a great way to brush up on basic math, and you'll get practice tests to see how much you learned.

[fiamme red]

higher math is not fun, or easy.It's not easy, but it is fun.

I've forgotten a lot of the math that I learned, but I did come away from college with a great appreciation for the elegance and simplicity of a well-constructed proof. My favorite math course was number theory.

[VTCaraco]

In public education it is all about 'passing the test'. Think NCLB and all its BS (started by dubya and continued by our present administration). ... Public education is broken, but the answer is not the simple "it's the bad teachers and their union".

It's not all about passing the test at all schools; and it sucks when that becomes the case (presuming the test is weak).
I'm a math teacher and department chair. And I'm going to skip jumping into the debate about how or why it's broken and how or why to fix it. As I see it (and I spent a ton of time thinking about and working on it), there's not a clear and simple solution that doesn't require equal change on the part of the other stakeholders (i.e. students, parents, governance).

As for the original request, I can probably get you some older textbooks. That would be easy. I'd also say that there's lots of good content on the internet. Prof Ed Burger (http://blog.mindbites.com/congratulations-again-to-professor-edward-burger/) from Williams College has been involved in a video textbook project through Thinkwell. I plug my most advanced students into his Calculus for the BC level AP prep and they've all been pretty pleased. Another option, presuming you don't need to work through the bones again, per se; would be to work through some of Exeter's materials (http://www.exeter.edu/academics/84_9408.aspx) . They do a remarkable job of polishing and refining problem sets with a very clear goal in mind. This would lack instruction or examples, but would be a pretty nifty way to get yourself back in math shape. Coupled with the myriad of free resources, I think you'd be able to satisfy a lot of your curiosities.
Other resources I'd recommend would include MIT's free online coursework (http://ocw.mit.edu/courses/mathematics/) , Wolfram's website (http://www.wolfram.com/) for specific content, and GeoGebra (http://www.geogebra.org/cms/) as a super-powerful (and free) tool for looking at and understanding content.
PM me if you want to talk some more.

[fiamme red]

Another thing: you can't learn math by just reading a textbook or website. You need to sit down with a pencil and paper and work out problems. That's the way to learn the material.

[Ahneida Ride]

If I were president, I think I might take up this idea. To the extent that the US is getting behind in science and engineering, some of the problem is the randomness of math education. I was horrified by the lack of teaching in my son's high school math books - they were obviously recently written by math people and approved by math people and by textbook panels that were not math people. Add to that a math teacher who failed to grade quizzes before tests, or show up at office hours, and a department head who seemed to think this was okay and there was no way my kid was going to advance in math. This at one of the better high schools in the supposed best state for education.

Math being a fixed body of knowledge up to a certain point, and being a priority for the nation, why not standardize that education around awesome video instruction and use high schools just as helpers for the online version. We'd have to find passionate teachers to agree on consensus methods, but boy, it sounds more efficient than what we have now. That would be a major accomplishment for a president...who did not care about teachers' unions.

Until 12 grade I had questionable math teachers. In 7th grade they told
my Mother I was "hopeless".

In 12 grade I encountered a true gentlemen with an MS in Math.
AN actual degree in Math !

He FORCED students to do the home work. If is was not satisfactory
you got an F and had to do the assignment all over again. You did
the assignment as many times as need until it was correct.
He saved my a**.

Imagine trying that today in our PC environment. He was also the most
popular teacher. He would help you. Kids loved him even though he was
strict.

Today's math text's are questionable.

PhD programs are being watered down constantly. (just like the frn)
In 1970, qualifying exams consisted of advanced undergrad and graduate
level material. Today ? Many top tired universities base these exams
on Freshman Calculus. Of course, this is not info that many would like
to be disseminated.

There was a line from the Simpsons ...

"Now whose Calculator can answer this question?"

[Ahneida Ride]

Another thing: you can't learn math by just reading a textbook or website. You need to sit down with a pencil and paper and work out problems. That's the way to learn the material.

Neither can one play the piano or shoot hoops by watching a video.

The video is to present the material in a format the student can absorb.
One can re-play till comprehension.

The video MUST be followed by copious exercises.

[Ahneida Ride]

You guys are a bunch of geeks and I will be kicking your ass after gym class today.

Ah ... I don't tink so ... :p

Remember the geek whose a** you kick now
will be your boss in 10 years. :banana:

[97CSI]

It's not all about passing the test at all schools; and it sucks when that becomes the case (presuming the test is weak).
I'm a math teacher and department chair. And I'm going to skip jumping into the debate about how or why it's broken and how or why to fix it. As I see it (and I spent a ton of time thinking about and working on it), there's not a clear and simple solution that doesn't require equal change on the part of the other stakeholders (i.e. students, parents, governance).Am sure it is not about 'passing the test' at all schools. Only the great majority. It is about money, unfortunately. And, in today's political climate where the great majority of folks don't want to pay for anything 'public', that is a problem. Definitely no a simple solution. Am also a math teacher (for three more days - I retire on the 31st :banana: ) and former admin, so know the battles you are fighting. Even in 'good' schools, 'expectations' can be/are unreasonable. The 'free-ride' dominates (whether that is good grades with no work or great teachers with low salaries). Good time to be retired.

[William]

Ah ... I don't tink so ... :p

Remember the geek whose a** you kick now
will be your boss in 10 years. :banana:


Plus, they have the means to have me on retainer. :D




William (a hired gun for HandleBra LLC.)

[fiamme red]

Have a squirrel at hand to help you out when you're stuck on a problem. :)

http://www.gettyimages.com/detail/3325014/Hulton-Archive

http://cache2.asset-cache.net/xc/3325014.jpg?v=1&c=NewsMaker&k=2&d=45B0EB3381F7834D6D38DA775508BF19A79D84CA19B7B5E2 E23FEF406871B787

[rugbysecondrow]

I am a liberal arts guy, so I have little to add to this discussion directly. I will say that when my wife was in school and the University of Illinois, the math classes she took were rarely (likely never) accomplished by herself. She had study groups and friends who worked together to learn and help one an other. They also had professors and grad student types to work with, ask questions of and to help them. This was true of her physics classes as well.

I am not a naysayer, but I will say that this is a huge undertaking and one that will take years and may not be possible if done by yourself. Sure, anything is possible, but there is a difference between learning about something and learning and understanding how to do something. Understanding Hawkings theories as they are explained is one thing, understanding what was involved with and how one arrived at that point is a different level of knowledge. Being able to recreate it on your own is a very different level all together. What level of understanding do you want to attain about not just physics but also Math?

[avalonracing]

Man... First detention, then a lawsuit.

Plus, they have the means to have me on retainer. :D

[MadRocketSci]

math and physics are about the journey, as it will be a long long time before we reach the end if it exists at all.

So you have my respect for embarking on this journey on your own, and I wish you good travels!

I never understood why i had to take 4 years of English classes to graduate high school, but only "had" to take 1 year of science (of which Earth Science would suffice) and maybe 0.5 years of math to graduate?

As a result, knowledge of basic physics and math seems to be the exception rather than the rule.

Anyway, back to the original question, there are so many online resources that I would start there, and then go to the books for details. The MIT open courseware site and Itunes University have an a lot of material...I've downloaded the entire Stanford Fourier Transforms class lectures, as I had always meant to take the class but never got around to it, despite having to use it on a day to day basis.

I remember a lot of profs recommending various Schaum's Outlines, which are a sort of cliff's notes for many technical subjects. They give overviews and then many many examples and problems with solutions. Bought a couple, never really used them (was never the type to go for extra credit), but they seemed to have good material.

Schaum's Outlines link (http://www.mhprofessional.com/templates/index.php?cat=145) <- advantage: cheap!

And I agree, Real Analysis is hard. Complex not so much.

If you ever want a "fun" textbook to read, try this (http://www.amazon.com/Introduction-Physical-Gas-Dynamics-Vincenti/dp/0882753096/ref=sr_1_1?ie=UTF8&qid=1293651926&sr=8-1) . All textbooks should be written like this. This one in particular gives a good intro into statistics and how it is applied to gas dynamics, and also delves a little into old school quantum stuff like the Heisenberg uncertainty principle and Schrodinger's wave equation, iirc.

[1centaur]

A lot of textbooks make the same mistake that assembly instructions make: assuming true comfort with prior knowledge. "Place the grommet over the flange extension" is Greek to people who don't play with those terms on a regular basis; one unknown idea and the process hits a brick wall. In math it just takes a few weeks of "Greek" to demotivate a previously successful student permanently.

It would be nice for text books to start with a list of terms and concepts that must be mastered before starting the book at hand. If there were online clearinghouses of instruction, the books could reference those, and last year's teachers could be charged with delivering their students adequately prepared (while parents could use summers to work on remedial cases). Textbook publishers being businesses, they have would have an incentive to mention their own texts (soon to be out of print) if anything at all, but they don't really have alternatives.

Looking at K-12, it seems like the system is designed to weed out all but the naturally talented rather than maximize the learning rate of all involved. Just moving between school systems could be enough to throw off future learning curves in complex sequential subjects even if all teachers were talented/motivated and all students/parents focused on education. If math and science were actually national priorities, rather than lip service around elections, we would see a much different system. Our current system seems to reflect an idealized 1950s vision of cohesive communities with shared goals and pliant subjects.

To the teachers on this board: who in the US plans out the sequence of education from K-12? Is it effectively regional textbook approval boards in conjunction with textbook publishers? If I recall the stories correctly, Texas and California have disproportionate influence on the entire country because a textbook win in a big state creates enough volume to support those same textbooks elsewhere. I don't know about states rights and local control issues, but it seems to me a national priority should get national sequence determination just to get the basic coordination right.

[xjoex]

Dekonick - Sounds like you have what it takes to go back to grad school!

-Joe

[Louis]

Dekonick - Sounds like you have what it takes to go back to grad school!

You must mean that he has either 1) The ability to survive on 4-5 hours of sleep per night, or 2) The ability to magically add 2 hours to each and every day of the week. :p

[Ahneida Ride]

Dekonick - Sounds like you have what it takes to go back to grad school!

-Joe

work like a slave, feel like chit, study relentlessly, have no frns,
study all weekend, grade papers, solve horrendous homework problems
the Prof can't even do, fumble in the dark with research, attend an "institute"
where the male to female ratio is a google to one ...

the list goes on and on and on and on and on .....

I still have nightmares.

[VTCaraco]

To the teachers on this board: who in the US plans out the sequence of education from K-12? Is it effectively regional textbook approval boards in conjunction with textbook publishers?

The Common Core Curriculum (http://www.corestandards.org/) is about to become the new sheriff in town. It will surely shake-up a lot of the content and sequencing in math instruction (other disciplines, too; but I know less about the present and future in those domains).
I know the guys who initiated the whole process with a white paper dubbed fewer, deeper, clearer . Their background was in providing standardized test data. For them, this project was rooted in their initial dismay with the lack of actionable steps that they encountered when sharing student achievement results with the teachers/schools.

The math sequence will include influence from some of the top-achieving countries as well as the current ideas from neuroscience. For us (Vermont), implementation will begin in 2013-2014 with the next few years to be used for careful transition. Ideally, the change will be pretty profound.

[Dekonick]

Dekonick - Sounds like you have what it takes to go back to grad school!

-Joe

To what avail? I just am curious and want to better understand my working environment. I have no desire to work in a lab unless I get to pick the projects and timetable - and have unlimited funding of course! My neighbor is a physics worker bee at NASA - I love talking about what they are doing... but I don't want to freeze my ass off flying over the antartic measuring ice...

I would love to go to grad school if I could do it on my time table and terms. I am after the pursuit of knowledge... I have no need of another lambskin on the wall.

I have another 15 years before I retire - and at that point I will be 56 years old... don't think I would make a good grad student at 56. I plan on mastering as much as I can on my own - for the pleasure of it. I am lucky in that I am a good learner and do just fine with self study. Aced organic chem in college by myself - went to class 4 times - day one, two exams and the final. Second highest grade in the class. Same with inorganic chem (except I went to class for that as the prof could actually speak english.)

I just like knowing how the world works. Must be something genetic as my dad was an engineer in the 60's and 70's working on projects from Titan to Viking and Skylab... before calculators. In fact, I remember as a kid he had a calculator that had a metal plate with numbers on it and you used a metal tip on an electrode to tap the squares to enter data. 4 function only...
I remember my dad in the ICU when he was recovering from sepsis and he asked my sister if she could see the quadratic equations on the ceiling... I will probably be telling my sons the same only they will be Fenyman diagrams...

Thanks for all of the imput! I have 15 more years to study this chit... then I will have to make a choice.

:)

[Dekonick]

work like a slave, feel like chit, study relentlessly, have no frns,
study all weekend, grade papers, solve horrendous homework problems
the Prof can't even do, fumble in the dark with research, attend an "institute"
where the male to female ratio is a google to one ...

the list goes on and on and on and on and on .....

I still have nightmares.

+1

:crap: :beer: :hello:

[roydyates]

Another thing: you can't learn math by just reading a textbook or website. You need to sit down with a pencil and paper and work out problems. That's the way to learn the material.

+1000 but even solving the problems isn't enough.

First, math is conceptually hard. Even if you have the benefit of brilliant instructors and the excellent textbooks, you will eventually reach a level of math where your brain hurts trying to grasp the concepts. Second, any math you don't use regularly you forget in about a year.

[Louis]

Second, any math you don't use regularly you forget in about a year.

That's why every other day I solve a few partial differential equations before breakfast :p

[roydyates]

+1


Dekonick notes the negatives of grad school, but lots of people keep going. As an engineering prof who spends most of his time (at least when I'm off the bike) supervising EE grad students, I think the reason is because grad students have fewer obligations and greater freedom to pursue your own interests than perhaps at any other time of their adult lives. I spend a lot of time telling grad students to savor the research experience.

[97CSI]

The Common Core Curriculum (http://www.corestandards.org/) is about to become the new sheriff in town.NJ was on board for this, but is all ready back-pedalling as fast as they can. Feedback from the districts is that it will "cost too much". I'm guessing most other states will cave too, once they figure out will require some effort (time & money) on the part of all interested parties to make it happen. Sorry to be so cynical, but that is one reason I retired (again). Nothing but negatives from those in charge.

[Dekonick]

NJ was on board for this, but is all ready back-pedalling as fast as they can. Feedback from the districts is that it will "cost too much". I'm guessing most other states will cave too, once they figure out will require some effort (time & money) on the part of all interested parties to make it happen. Sorry to be so cynical, but that is one reason I retired. Nothing but negatives from those in charge.

Maryland is on board.

[Dekonick]

Dekonick notes the negatives of grad school, but lots of people keep going. As an engineering prof who spends most of his time (at least when I'm off the bike) supervising EE grad students, I think the reason is because grad students have fewer obligations and greater freedom to pursue your own interests than perhaps at any other time of their adult lives. I spend a lot of time telling grad students to savor the research experience.

Were I young again I would go... Now I have young kids and a family. It would be a waste for a man in his 50's to go to grad school... taking a spot that should go to a young mind. I am content to learn on my own, with a little help from my friends. :beer:

Do grad students have time to ride bikes? I plan on wrenching part time when I retire for fun - the remainder will be with my wife or on the bike.

[PaMtbRider]

I enjoyed math and physics in college and got pretty good grades. My boss is currently working on his masters and asked me to look at some of his math homework for him. It is amazing what you forget. I looked at problems that looked vaguely familiar, but I had no idea where to begin.

[97CSI]

Maryland is on board.Hope you are correct. Poor leadership and no money......... we'll see how long it lasts. Don't see the current national ethos of no personal responsibility and unwillingness to work hard changing very quickly. I do hope to be proved wrong. Very wrong would be best.

[thegunner]

work like a slave, feel like chit, study relentlessly, have no frns,
study all weekend, grade papers, solve horrendous homework problems
the Prof can't even do, fumble in the dark with research, attend an "institute"
where the male to female ratio is a google to one ...

the list goes on and on and on and on and on .....

I still have nightmares.

weird... i don't feel this way at all for the most part. horrendous homework problems yes, but the others aren't necessarily true :)

[roydyates]

Were I young again I would go... Now I have young kids and a family. It would be a waste for a man in his 50's to go to grad school... taking a spot that should go to a young mind. I am content to learn on my own, with a little help from my friends. :beer:

Do grad students have time to ride bikes? I plan on wrenching part time when I retire for fun - the remainder will be with my wife or on the bike.

I agree completely with your assessment of the choices. Grad school is very hard if you have a family and a life.

As for time to ride bikes ... everyone (even grad students) make choices about riding the bike vs doing something else, whether the something else is more family time, more work, more school, or more TV. My guess is that the average Serotta forumite spends at least 1000 hours per year riding the bike or thinking about the bike. (4500+ miles= 300+ hours, plus time fiddling with bikes, plus time on the forum, plus time thinking about buying bike stuff.) These hours are always instead of doing something else.

[Ahneida Ride]

That's why every other day I solve a few partial differential equations before breakfast :p

ah ... the magic of Raisin Bran and what is does for the constitution.

[Louis]

ah ... the magic of Raisin Bran and what is does for the constitution.

:) :) :)

[xjoex]

To what avail? ... SNIP

I felt the same way before I started grad school, I already have a research position at a prestigious university in the field I enjoy so why?

But I have been proven wrong, I really like the challenge. When you self learn (which I am all about, I have a book under my laptop waiting for me to finish going through) you/I learn the way you already think. But having someone else make you solve a problem their way is a fun challenge. Plus so far in my program I have been able to tailor the projects to my areas of interest.

I still ride 6 days a week, I have a full time job, a wife, and a help her with her small business on the side (http:/www.soulrun.com). I used to ride after work most days. Now I get up crazy early and ride in the morning... in the dark before work. I ride less with friends because I have to work around my schedule.

Anyhow, its not the best thing ever, some classes are a pain in the ass and a bore. But I have really enjoyed my time so far and will be done in 16 months. So maybe I'll have more to add then. I only mentioned it to begin with because this questions coupled with your physics question from a few weeks back made me think you would enjoy it. :)

Either way have fun, I bought a book a few years ago Cherneirs Practical Math and used it as a math refresher: http://makezine.com/pub/tool/Practical_Math

-Joe

[Dekonick]

I felt the same way before I started grad school, I already have a research position at a prestigious university in the field I enjoy so why?

But I have been proven wrong, I really like the challenge. When you self learn (which I am all about, I have a book under my laptop waiting for me to finish going through) you/I learn the way you already think. But having someone else make you solve a problem their way is a fun challenge. Plus so far in my program I have been able to tailor the projects to my areas of interest.

I still ride 6 days a week, I have a full time job, a wife, and a help her with her small business on the side (http:/www.soulrun.com). I used to ride after work most days. Now I get up crazy early and ride in the morning... in the dark before work. I ride less with friends because I have to work around my schedule.

Anyhow, its not the best thing ever, some classes are a pain in the ass and a bore. But I have really enjoyed my time so far and will be done in 16 months. So maybe I'll have more to add then. I only mentioned it to begin with because this questions coupled with your physics question from a few weeks back made me think you would enjoy it. :)

Either way have fun, I bought a book a few years ago Cherneirs Practical Math and used it as a math refresher: http://makezine.com/pub/tool/Practical_Math

-Joe

Oh, I agree. It just does not fit with 2 young children, a full time job and another 600 hours a year either teaching or working overtime. I have plenty of idle time, but none that I can schedule.

[Karin Kirk]

To take another crack at Centaur's question about K-12 education, it does come down to standards. There are national standards and also state standards. Each state has its own statewide board of education who determines the standard for each grade and each course within that grade. Teachers have to teach to the standards, as the tests are based on that. The state board of ed also determines which courses are offered when, i.e. geometry in 10th grade, or earth science in 9th grade.

Texas has the largest purchasing power for textbooks because the whole state buys the same textbook for each course and grade level. Other populous states, NY and CA, don't necessarily buy all the same books, so that leaves TX with the most influence. So textbooks tend to reflect the Texas state standards, which are controversial to say the least. If you like science and you want to be scared, learn about what's going on in Texas. If you don't care for science, then everything is just fine.

In my opinion, K-12 is not about weeding out (that's what 100-level college courses are for) but it's about teaching to the middle. There is not a lot to offer the students outside the bell curve. That goes for ability, learning style, motivation, etc.

It's easy to knock the education system. Something so huge and so important is bound to have a lot of critics. But overall, things are improving. We are learning more about how students learn. Schools are better equipped to deal with diversity. Textbooks, in terms of pedagogy, are much better. The recent focus on improving teacher effectiveness is a brave move. This is very much against the grain of the old school union approach.

I'd put my money in improving teacher preparation. If we want to improve our students' abilities in math/science, we need to improve the teachers' abilities first. Check out your average elementary teacher's comfort level with math or science - pretty shaky stuff. This sets a tone very early on that math and science are scary and unpleasant.

Anyway, that's just my 2 cents. Like I said, it's not too hard to find fault and have opinions on this topic!

[Louis]

Check out your average elementary teacher's comfort level with math or science - pretty shaky stuff.

I have essentially zero experience with grade schools in the US, but nevertheless find this hard to believe. It's not like we're asking them to derive and solve the 3-D Wave Equation. This is pretty basic stuff, and adults whose job is to teach these topics should have no problem handling it. If the teachers we have now are on average not comfortable with math or science and not able to teach it in an engaging fashion to a semi-motivated class, then there's a serious problem with the entire system, not just with the teachers.

[Johny]

http://terrytao.wordpress.com/about/

One of my favorite sites. Not just about math, but also education, philosophy and science.

In case you don't know Terence Tao (http://en.wikipedia.org/wiki/Terence_Tao), he won the Fields Medal, often described as the "Nobel Prize of Mathematics." He is a prodigy but knows hard working and enjoying your work are the key to success (see his Career advice (http://terrytao.wordpress.com/career-advice/)).

Does one have to be a genius to do maths? (http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/) A topic everyone can benefit imho.

[97CSI]

I have essentially zero experience with grade schools in the US, but nevertheless find this hard to believe. It's not like we're asking them to derive and solve the 3-D Wave Equation. This is pretty basic stuff, and adults whose job is to teach these topics should have no problem handling it. If the teachers we have now are on average not comfortable with math or science and not able to teach it in an engaging fashion to a semi-motivated class, then there's a serious problem with the entire system, not just with the teachers.My experience as a HS math teacher is that elementary/middle school teachers hand the students a calculator for math. That's great. :confused: When they get to HS they know how to run a calculator but cannot do long division or multiplication or fractions, etc. They don't know any math but know how to run a calculator. It has gotten even worse. The district I retired from just received a multi-million dollar grant and has given laptops to most of the 6-7 grade students. Now they will know the computer but still not know math, science, grammar, etc. But, they will be hell-on-wheels running that laptop. Call me a luddite, but no student should have a calculator or comptuer for school use until middle school, after they have mastered the basics. And limited use until algebra and the use of graphing calculators.

To drag this out, the school system I was in has sending districts. One in particular concentrated on excellence in teaching math/science K-8. It was always a pleasure to have their students in the classroom. They did not use calculators until late and their kids, regardless of their level of intelligence, knew the basics.

It's easy to knock the education system. Something so huge and so important is bound to have a lot of critics. But overall, things are improving. We are learning more about how students learn. Schools are better equipped to deal with diversity. Textbooks, in terms of pedagogy, are much better. The recent focus on improving teacher effectiveness is a brave move. This is very much against the grain of the old school union approach. Wish your statement about 'things improving' were accurate. Per the latest reported international testing we are still down around 'pre-industrial' on average for our students' math/science abilities. We made no gain. As far as teacher effectiveness, we get what we pay for.

[William]

Part of the frustration we find right now with our children’s elementary school is all the different methods for solving math problems that they keep throwing at them. Some of them confused the heck out of me. And it seemed to be confusing to our kids at times as well. I guess on the one hand, if the child finds a method that works for them then fine. But the traditional method seems straight forward and works just fine to me.

There have been times when our kids have told us that their teachers said it was ok to use calculators to do their homework, but we make them work it out on paper anyway. We started early with our kids doing fun math exercises, flash cards, and story problems. Now when they have some difficulty with their homework we will give them hints and try to get them to work them out on their own, but we don’t just give them the answer or hand them a calculator. Today William Jr. is in his first year of Jr HS and our daughter is in elementary school and they are both A students in math (and across the board) and we hope to help them continue their success into the future.

Math is cool.




William

[Ahneida Ride]

If math education is improving .... why are the PhD programs being
watered down?

4 years of course work down to 3 years.
preliminary exams now reduced to Calculus.

10 years ago, a senior prof told me that that the students can't
even pass them.

Hey ... I'll even admit that I survived cause standards were diluted
for me.

Inferior teaching or lethargic students? :confused:

[Ahneida Ride]

How many HS math instructors earned a solid BS in Math/Physics/Engineering?
That is taking all math/engineering courses in Junior & Senior years?

food for thought ....

[97CSI]

Inferior teaching or lethargic students? :confused:Laziness at all levels. Easy road out, etc. Look around at successful people. They are, generally speaking, the harder workers. Not necessarily the smartest. Same holds true for students, parents, teachers, admin, etc. It is a 4th-order (or higher) equation.

How many HS math instructors earned a solid BS in Math/Physics/Engineering? That is taking all math/engineering courses in Junior & Senior years?
food for thought ....I taught in a poor district. At the HS level every one of our teachers has at least a BS in math or engineering. A couple picked up a minor in education. However, the same cannot be said of the admin folks and department heads.

[rugbysecondrow]

]

Not to chuck a wrench into this math lovefest, but lets be real about the "system". High School is about getting into College, College is about graduating. Period. I will articulate why I think that.

With limited time, higher pressure for extracurriculars as well as GPA and class rank pressure on students to get into college, I am not sure laziness is the succinct answer (from a laypersons perspective of course). High schools have way more classes than they did decades ago so there are many more options for kid to choose from. In addition, pressures to increase GPA prompt kids not to take on challenges and risk a lower grade (likey at their parents recommendation). My wife, when in High School, out performed all the math classes available at her school and had the option to go to the local college to take math classes as a high school student. She did that, but it was risky as in might have lowered her GPA. She is very good at Math and did well and was able to have a strong enough GPA to get into a very good engineering school. Had she gotten a lower grade, that might not have been the case. A "B" grade could make the difference between going to the Tier 1 or Tier 2 school.

In addition, college is about attaining a goal, the goal being a degree. I am not arguing whether it should or should not be that way, just saying that is the way it is. Colleges like to graduate students, that is one of their metrics, their goal. It is imposed on a student regardless of the students intent. For a student to finish in four years (a necessity for most due to finances) they need to find a tract to start freshman year and follow all the sequences through to senior year. It is all planned out and any deviation will likely cause extra semester meaning extra money they might not have. It is the fortunate student who is able to pursue knowledge and learning, but college is so expensive now and so orderly that the system does not lend itself to those pursuits. My wife picked engineering, had to take 132 credit hours (120 is the norm for a BS or BA) and from day one through the last day it was planned out. This is good for a student who is lucky enough to know at the age of 17 what they want to do with there life. Not so good for the others though, and I was an "other".

So, I guess what I am saying is that in the system of goal attainment, there is little time or room to become anything more than a generalist with a slight specialization. I took math classes, I had to check the box in my program, but I also had other boxes to check and, frankly, all the boxes are equal. I suspect graduate and PHD programs suffer due to what has occurred earlier in the pipeline.

[rugbysecondrow]

How many HS math instructors earned a solid BS in Math/Physics/Engineering?
That is taking all math/engineering courses in Junior & Senior years?

food for thought ....

My wife, as an Engineer, with both a BS and a MS in engineering has looked into teaching. The hoops she has to jump through are tedious and are a real deterant for professionals looking to cross train into the teaching profession.

[97CSI]

My wife, as an Engineer, with both a BS and a MS in engineering has looked into teaching. The hoops she has to jump through are tedious and are a real deterant for professionals looking to cross train into the teaching profession.Amen....... we actually lost a couple of the best young math/science teachers in the past couple of years as it was just not worth it to them to jump through these hoops. Not sure about MD and other states, but in NJ one must attend what amounts to 3-semesters of night classes, which they are forced to pay for out of their own funds while being paid at the lowest rung on the pay-scale, as they are not certified. Well over $1K last I checked. Then, they must pay another $1K+ to a 'mentor'. States go on and on about wanting the best teachers and then put any number of road-blocks in the way of getting them.

[Karin Kirk]

Louis - what I meant by elementary teacher prep was not so much that they aren't up to the task of teaching very basic math/science within their grade level, but that they don't have an overall comfort level with the topics. I have had in-service teachers in some of my courses and their overall science aptitude is a little scary. As you know, the most effective teachers are enthusiastic about the topics they teach and can illustrate how that topic connects to the real world in a cool way. I think this is a good target for improvement.

Kids, especially girls, learn that math/science is scary at a young age. Girls are particularly influenced by female teachers and role models, and by and large these role models are not enthusiastic about math and science.

As for the overall improvements in education, I don't think there is anything I could say to influence some of your entrenched opinions. I doubt there has ever been a time in modern history when the older generation didn't look scornfully upon the younger generation as lazy. (see Bjarne Riis thread for another example)

Are there problems? Sure. But the education system is changing, as it has to, to reflect modern educational research and the way students learn. Perhaps some folks see these changes as a watering down compared to the experiences they had. (Ray, on one hand you criticize your grad school experience up and down, yet a few posts later, today's programs are too watered down. Hmm.)

We now know that using visualizations, real-life experiences, interactive learning and group work all enhance student learning. (if you want the data, let me know) We know about learning styles, assessment strategies and metacognition, and all of this knowledge shapes textbooks and curricula. The old-school style of professors and teachers engaging in a strictly one-way flow of information is being replaced (over due time) by completely new methods. Now we have a new frontier of online and hybrid education unfolding. Very exciting stuff.

As with everything, the improvements are uneven. There will always be some bad teachers, disfunctional districts and lazy students. But that certainly does not mean that things are going backwards.

[Dekonick]

Amen....... we actually lost a couple of the best young math/science teachers in the past couple of years as it was just not worth it to them to jump through these hoops. Not sure about MD and other states, but in NJ one must attend what amounts to 3-semesters of night classes, which they are forced to pay for out of their own funds while being paid at the lowest rung on the pay-scale, as they are not certified. Well over $1K last I checked. Then, they must pay another $1K+ to a 'mentor'. States go on and on about wanting the best teachers and then put any number of road-blocks in the way of getting them.

Absolutely true. To become a teacher you have to major in education (at least that is how it works here...) and a major in education does not mean anything more than a concentration in a field with a bunch of learning and psych courses. It is important to understand how learners learn and teaching techniques (as we all know grad students often make the worst teachers yet teach many of the intro courses) but a mastery of your subject matter is key as well. We as a society also do not work well with the right side of the bell curve. There are mandates that you take care of and teach the left... but what about the next Newton, Aristotle, Pasteur, etc? I honestly believe some of the brightest minds get lost in the shuffle while we pander to the middle and coddle the left. A sad state of affairs.

[1centaur]

We now know that using visualizations, real-life experiences, interactive learning and group work all enhance student learning. (if you want the data, let me know) We know about learning styles, assessment strategies and metacognition, and all of this knowledge shapes textbooks and curricula. The old-school style of professors and teachers engaging in a strictly one-way flow of information is being replaced (over due time) by completely new methods. Now we have a new frontier of online and hybrid education unfolding. Very exciting stuff.

You can be sure I WON'T be reading the studies that back the wonders of all these new ways of teaching (since I am not going to devote 6 months to finding the counterarguments and weighing both sides for nobody's benefit but my own), and I am not saying that lectures are the best and only way, but stepping back to argue my impression and logic:

New ways of teaching necessarily involve kids/teachers/parents and their various personalities and experiences. It would be impossible for a study to correct for all these variables. A study that says group interaction enhances recall and understanding is swell, but does it fully account for shyness, or the greater communication skills of girls at a certain age, or the social dynamic of ruddy-faced Mr. Fotherspoon unenthusiastically running the group? Does it account for an inability of parents to reinforce the learning modality in practical ways at home? Personally I loathed interactive learning and group work - the social dynamic drowned out much of what I was doing. Give me a good lecture I can process in the silence of my head any day.

I think one of the problems in K-12 education in the last 25 years has been the great willingness to thrust upon all players rotating experiments in learning styles (5 months of the recently introduced whole-language reading method had the teacher threatening to flunk my kid in first grade; 3 weeks of phonics at home and he was a star and a lifelong voracious reader; trendy math-teaching theories imported from California to Massachusetts led down the same path) that leave way too many people victims to good intentions. At some point the highest powers in education must decide on something that most people can work with most of the time and use new approaches only on the edges to save fringe players until the data is beyond overwhelming; evidence-based learning methods must be based on mass evidence. Mass experimentation following a good-sounding study on 300 kids by 2 enthusiastic teachers cannot be up to the whim of an education board enchanted by its own foresight. It's not fair to teachers to foist this stuff on them before it's beyond proven across circumstances, let alone on kids or parents. It's not practical either. Proving that new ways are better for 85% of the kids and that average teachers can easily accomplish the new ways is a very high hurdle to jump, and not one I've seen successfully jumped in my life. Boards who don't understand why their numbers are not better and textbook publishers love new methods, I am sure, but there is little aggregate evidence in recent years that all these changes are producing better students or better scores. Let the increasingly popular (necessary) after-school for-profit tutoring programs beta test new learning modalities for a few years at least before putting them in public schools.

The Core Curriculum site posted earlier looks like a good start, but in the inevitable effort not to offend the establishment they are emphatically hands-off on HOW the core curriculum goals will be met. I think the "how" will end up being defined as well, by necessity and following years of patchwork successes/failures. We're decades from that point (both in the future and in the past, if it comes to that). I understand the fear of stupid national standards pushing aside smart local standards, but I also doubt competing nations find this issue daunting. Aim high.

[Karin Kirk]

The data is absolutely "beyond overwhelming" that active learning is more effective than listening to a lecture. You are an anomaly (but we knew that already :) ) so this evidence may run contrary to your own experiences.

Educational research is generally done in relatively small batches (n=35, 50, or 150) but is repeated across various grade levels, classroom settings, teacher types and topics. Like all research, various statistical analyses are used to filter out some of the variables. But it's slow going. Many of the studies I read and I think, "well, duh, of course." They are measuring the effectiveness of something that seems intuitively true anyway. But that's how you build a body of knowledge - just one piece at a time. Overall the trends do emerge quite solidly.

Your example about group work is a potent one. Of all the teaching methods I mentioned, this is the one that can suffer most from a hamfisted application. You have to be careful in setting up groups and managing them. There are a range of different approaches though, so group work is not a blanket method where the same idea will work for everyone. Successful group work also takes a lot of management from the teacher, so not everyone is going to go there.

Even though working in groups can have drawbacks for both students and teachers, working functionally with other people is an unavoidable skill for real life. So preparing students for this has merit, even if it's hard to do.

[fiamme red]

Dekonick, I recommend that you get Calculus by Michael Spivak and work your way through it. It's an enjoyable and inspiring (though somewhat wordy) introduction to calculus and advanced real analysis, and in general to the methods of creating rigorous proofs.

[97CSI]

- what I meant by elementary teacher prep was not so much that they aren't up to the task of teaching very basic math/science within their grade level, but that they don't have an overall comfort level with the topics.And therefore take the easy way out. Hand the kid a calculator so they can get the answer with little or no undrstanding and at the end of the year pass them along. Whenever I hear a teacher talk about how much she loves her students and they love her it makes me cringe. How about loving your subject and the imparting of knowledge about same? Who gives a d*** if you love your students and they you. You aren't there to validate each other. You are there to teach and impart knowledge and they to learn. With a healthy respect for the position of each within the classroom.

We now know that using visualizations, real-life experiences, interactive learning and group work all enhance student learning. (if you want the data, let me know) We know about learning styles, assessment strategies and metacognition, and all of this knowledge shapes textbooks and curricula. The old-school style of professors and teachers engaging in a strictly one-way flow of information is being replaced (over due time) by completely new methods. Now we have a new frontier of online and hybrid education unfolding. Very exciting stuff.Just more academic hocus-pocus and mumble-jumble excuses for lack of a good work ethic on whomevers part. Quite frankly, we as a country don't have time for all these BS experiments. as we continue to fall further and further behind the rest of the industrialized world. We need the equivalent of "Gunnie" from the Geico commercial to take over our education system and get it done. Not everyone is college material and we need to stop treating them like they are.

[1centaur]

You are an anomaly (but we knew that already :)

Hey, Uncle Jam's Army likes white and red bikes too....

[Louis]

Just more academic hocus-pocus and mumble-jumble excuses for lack of a good work ethic on whomevers part. Quite frankly, we as a country don't have time for all these BS experiments. as we continue to fall further and further behind the rest of the industrialized world. We need the equivalent of "Gunnie" from the Geico commercial to take over our education system and get it done. Not everyone is college material and we need to stop treating them like they are.

Back in your days did you walk five miles to school, in the snow and rain, uphill both ways? ;)

[97CSI]

Back in your days did you walk five miles to school, in the snow and rain, uphill both ways? ;)Nope. We rode our horses. :)

We just went to school and did our work like most everyone else. Nothing special. Those who worked did well, those who did not work did not do well. Right up to this day, for the most part.

[Karin Kirk]

Just more academic hocus-pocus and mumble-jumble excuses for lack of a good work ethic on whomevers part. Well, at least my prediction was correct:

... I don't think there is anything I could say to influence some of your entrenched opinions....

Enjoy your retirement; sounds like the timing is right. :)

[97CSI]

Well, at least my prediction was correct:
Absolutely.....the excuse-makers are always correct.

Enjoy your retirement; sounds like the timing is right. :) Thanks. I plan to.

[Louis]

I just read part of Ed Rendell's radio rant against the NFL's decision to postpone the Sunday night game. Apparently he's been also posting on this forum under a psuedonym. (Aside: He's currently the outgoing governor of Pennsylvania. Seems to me that he might be getting ready to run for president.)

Here are a few choice bits:

“My biggest beef is that this is part of what’s happened in this country.”

“We’ve become a nation of wusses. The Chinese are kicking our butts in everything.”

“If this was China, do you think the Chinese would have called off the game? People would have been marching down to the stadium, they would have walked and they would have been doing calculus on the way down.”

[93legendti]

Nope. We rode our horses. :)

We just went to school and did our work like most everyone else. Nothing special. Those who worked did well, those who did not work did not do well. Right up to this day, for the most part.

I'm with you. My daughter's school has fantastic teachers and a lack of hocus pocus. I've volunteered there enough in the last 3 years to realize that they seem to be learning things sooner then when I went there.

According to the school's social worker, 1/2 of the 2nd grade kids have problems doing their homework. My daughter's best friend doesn't do homework, because her parents refuse to put up with her antics.

Our daughter gave us problems with hw, so now we go right to the library after school. When hw is done we go home. If the math is too easy, I make her do some extra, harder problems. My wife and others think they shouldn't have any hw-I think they should have more.
There has never been a fancy substitute for hard work. There never will be.

[Louis]

My wife and others think they shouldn't have any hw

What's the logic behind this thinking?

Figuring stuff out on your own is an important part of learning. School hours are for instruction, and homework is for you to apply that on your own.

It's not as if the children have to be out working in the fields or milking the cows. If they aren't doing homework they'll probably be watching TV, playing video games or the Sims or updating their Facebook pages.