Seriously, can we get this "-1 button" up and running immediately if not sooner.

+1 redhouse

blankflag, the hero of the common man. Give us the no-nonsense maths you stupid academics! We all know maths is nothing more than counting numbers, so stop with your bullshit "find x" and similar crap. I don't need some convoluted bullshit "proof" to see I have an iPad or I don't. You think your arbitrary notation makes things easier because it gives statements rigor, clarity and brevity? Retards.

@zultar ...

In 1946, Brown University started a new division to include a graduate program for applied mathematics. It's pretty new, but if you're looking for history, that program became an early leader in the push for mathematicians in the post-war era and set the stage for a lot of other developments. It's applicable in today's world too if you think that's beneficial. A link you might find useful if you want to look into it: http://www.brown.edu/Administration/News_Bureau/Databases/Encyclopedia/search.php?serial=A0420

There was also a thesis written by one of the recent graduates that looks back into the establishment of the division: http://www.dam.brown.edu/documents/ClareKim-HistoryThesis.pdf

Hope that's something you might find interest in.

@zul

I love math and teaching. I'll shoot you an email and we can chat.

"and the academic community has a whole other language to memorize."

Apologies that academics don't communicate in grunts and gestures. Once you get out of high school, you'll learn that the world doesn't limit conversation to a two syllable maximum. Learn to speak without using "Right Click > Synonyms".

Ok, so it looks like we have some initial interest. Here's what I'm thinking at the moment:

I've taught Algebra I, Geometry, Algebra II, Precalculus, and Calculus. So I am fairly certain that I can create the curricula for those subjects and everything would be taught year-round, not following the agrarian calendar. I would take 6-9 months to do Algebra (not splitting into two), 6 months to do Geometry (proof-based, start from points, lines, parallel postulate, and end before power chord theorems), 6-9 months to do Precalc (trig, polar, polynomials, end behaviors and basic limit work, with parametric and conics as optional), and 9-12 months to do Calculus (limits, derivatives, integrals, volumes, and basic multi-variables). I can fill out the rest of the topics later.

What I think I need is the curricula and pedagogy that would take you from basic computations to pre-algebra (which I refuse to believe needs to take 6 years as most educational systems do it) and the topics and curricula for post-calculus. I also need a number of good books about the history of mathematics, the puzzles that we have struggled with over the years and their solutions, and the current unanswered questions.

Websites, books, and such would be great, but as I think about this more, it would facilitate the process more if I can have volunteers to compile/organize/be responsible for a specific area. So for example, someone could volunteer to compile a series of the best damn interesting books about the history and development of math (this is where my expertise is most lacking), or someone could volunteer to spearhead the unanswered questions or current hot topics.

I hope that makes sense.

Zultar, I'm curious as to your purpose?

I will mention this: My kid's school district has started to develop and roll out their own internal texts, which the students can access on-line, in lieu of the school annually purchasing test books, etc.

Whether your purpose is self-satisaction, or for business/monetary purposes, i think it's a worthy task. frankly, I have found much of the modern curriculum lacking at times...in particular, my children are being taught "math", but they are not being taught fundamental principle...i.e. How and Why the math works. I'm not sure exactly how to explain what I mean...but I guess it's along the lines of they were taught to memorize multiplication tables, but never really taught to understand exatly what multiplication *is*. I mean, they knew...

I remember as a kid having multiplication drawn out for me in books with fruit...groups of fruit...etc...very picture oriented, visual education...which techniques work well for most.

I used to be involved in technical publications, and Ford Motor company was very focused on removing *as much* language from their dealaership service manuals and training material as possible, because pictures are so much easier to follow and understand.

OK...I'm rambling now....but I guess the point is, do not *just* study math and the history of math, but get down to the *very basics* of *education* and *how the mind works*, particularly in the area of learning. Best case is probably to engage multiple aspects of the mind...I alwasy taught me kids "read it, write it, say" in order to engage multiple parts fo the mind in learning a topic....which is why I *abhor* point and click computer education...that reduces it to read it/click it and leaves out the writing and the saying...

Anyway...that's my pi cents worth for now...

I know there are a lot of smart people who are working on improving math education. I doubt we can revolutionize the field, but I think we could make some real contribution. If nothing else, it should be a fun way to improve our own understanding of math.

I would recommend that the focus of this project should be on earlier math education, as that is the foundation on which everything else is based.

With that being said, I have agreed to spearhead post-calc courses. Because of my background, they will have an engineering focus to them. Furthermore, I think math for mathematicians at the collegiate level is already pretty good. What I'd really like to focus on is advanced math for people who need to use math as a tool to accomplish specific problems (such as engineers, scientists, economists, etc).

The most important courses I can think of are: Linear Algebra (unless zul is including this in Algebra), Discrete Math, Numerical Analysis, DiffEq, Probability, and Statistics.

So, are there people who would like to work on applied advanced math courses with me?

My purpose, if I may get a bit philosophical here instead of the practical pursuit of this project, is to eventually create and implement a math education that streamlines the learning of most students (unless there is a significant change in our neurological processing of information or inherited knowledge due to either natural evolution or artificial enhancement). It's not self-satisfaction nor monetary but long term self-interest of the survival of the species that drives me.

So, at this particular stage, I want to create a set of curricula that would work for mathematically inclined people, test it out (I'll try to see if I could teach my own daughter first), and refine it. Then to modify it so that it would become more inclusive so that an average student can do it.

Instead of trying to modify some school's current curriculum, I want to start with the end product (ideally what we would want to teach our kids) and then work backwards starting with our most gifted students and then to our average students and so forth.

Part of the reason why I want to include the history and development of math is because it gives the context as to why we created certain ideas and disregarded others and why math works the way it works and why it was developed the way it was. To give a specific example in respond to your comment about multiplication, when I teach exponents with my students, I go through why we have multiplication in the first place (repeated addition) and why then we would extend that to exponents (repeated multiplication). The "why" is fundamental to their understanding and it can provide the context that would make math more interesting.

Zultar - I agree with every syllable you wrote.

Particular the notion of streamlining learning -- the fact is we live in a world in which there is much more to be learned if we are to continue advancing our science and our civilization at the pace it is growing.

One of the problems I see now if that we, at times, tend to lose some of what we once knew as we skip ahead to learn new things. I see my kids being introduced to various computer applications, for example, but not the basics of programming.

I will use an example from Software development in the automotive engineering world as an example of this problem: The engineering communities are moving increasingly towards a model-based development environment in which the code is auto-generated. This is advantageous in that a non-programming Engineer can spec out functionality for his hardware in a graphical environment, let the system auto-gen code and test out the concept.

While this can produce functional code, there are problems: First the code is almost always going to be less than optimal, and Second, if no-one knows how to dig in to the code to correct errors...then what happens when a tool fails and no programmers are available?

It is actually surprising the number of engineers doing systems development that can not code -- but again, it speaks to the growing wealth of knowledge our society has, which lends itself to finding shortcuts to advancement...which means you skip some basics to jump the current level of advancement and push on.

Does that make sense? So yes...streamlining education so that principles are taught once and taught well...in the proper *order* as well. Again, to reference my children's math education: It has skipped around, back and forth from principle to principle...it has been baffling at times...instead of a logical progression always advancing. For example, in grade school they were even introduced to algebraic concepts before they had mastered multiplication...and then they abandoned that algebra for years before they returned. I was intrigued at the time....now I just see it as lost time, particularly because the grade school (general education) teacher teaching math as part of the 6 other subjects she had to teach was not good at math herself; she was ill-equiped to *teach* the concepts other than to read from a book.

Actually that idea there -- the utilization of teachers that do not have the proper skills for a subject - it probably the 8worst* problem in school - particularly grade school, where fundamentals should be taught. the one-teacher-all-day-long in grade school I think is a huge mistake! Not sure how a curriculum could overcome this problem, though.

You might want to check this out, and the books that come with it:

http://www.artofproblemsolving.com/

I do honestly hope that none of you are Americans! Have you never heard of New Math? http://en.wikipedia.org/wiki/New_Math.
This sort of thing has been done before and it is generally agreed that it didn't work;
making mathematics education more formal and more rapid does not help children learn.
As mathematically inclined adults, we may tend to seriously overestimate people's mathematical capacities - going more slowly over the simple concepts will mean that the average person has a much better understanding of concepts that are likely to be much more 'important' to them than the historical reasons behind mathematics.
Aside from that, I like the idea - I'm a mathematical physics research student who has always been frustrated by the lack of accessible materials in mathematics for those who find the standard math curriculum dull, and I'll certainly be very interested in how you get on.

MATH!

If you're interested in mathematics education, I thoroughly recommend Paul Lockhart's essay "A Mathematician's Lament": http://www.maa.org/devlin/lockhartslament.pdf.

+1 Spartaculous

SFZ - Do you have any experience with *current* math education? It is by no means the same as the math education I received 30+ years ago, just before "new math" was introduced.

I will still insist that half the problem is the lack of knowledge of the "foundational" math teachers -- i.e. grade school teachers that teach all subjects, and are experts in none, certainly not math, and who therefore can not adequately instruct on foundational concepts.

I would recommend including at least book I, or maybe the first two books, of Euclid's Elements. Despite being 2300 years old, it is still clear, basic, and accessible, as good an introduction to basic geometry as just about any you'll find. It has the bonus of being a good start to the *history* of mathematics, for obvious reasons.

A wonderful companion to that could be Robin Hartshorne's "Geometry: Euclid and Beyond." It discusses the history of geometry, takes the reader through Euclid, and then discusses how the subject has developed in the intervening time. It is rigorous, accessible, and well-motivated, and it integrates history throughout as an organizing principle for the discussion.

(Some of the developments that Hartshorne points out are actual *errors* that were discovered in Euclid, but I don't think it's bad for students to be exposed to the nature of mathematical mistakes, either, especially in such an elementary context).

SFZ, your math knowledge is about 30-40 years out of date. There has been a lot of pedagogical research in the past 30-40 years, especially with our knowledge of neurochemistry and brain development. We have a much better idea of how people learn and why many "new" math programs don't work. Moreover, I'm planning to apply this project to mathematically inclined students first. If I can arrange it, I would love to use it as a curriculum for math prodigies. Then slowly adapt it so that eventually an 'average' person would be able to go through a similar curriculum (albeit at a much slower pace).

I will read that document, Spartaculous, once I get to print it out later this week.

abge, MATH is awesome. Just like nerds.

krellin, I agree that elementary teachers probably lack the proper training and knowledge to teach mathematics and likely, science as well. These two subjects, more than any other, require more training and a thorough understanding. It might serve kids much better if there are specialized math and science teachers in elementary school. So one teacher for math and science (or one for each) and one teacher for everything else.

semck, I will look at the Hartshorne's book, but I don't know if it's at all necessary to look at Euclid's Elements. Most mathematical training and ideas don't really need that much of geometry. Most proof-based geometry books give enough geometric understanding to anybody except for maybe serious mathematicians who plan to study euclidean and non-euclidean geometries in depth (in which case, you would learn the geometry axiomatically and the Elements would be a good companion).
I do like the ideas of including the historical context of mathematical mistakes/misconceptions. That would make things more interesting and it provides a good understanding of how all of mathematics have to be developed from first principles and that we are sure about all our assumptions.