Maths uses intentionally cryptic and vague language in its curicculum? (Poll)

a reply to: funkadeliaaaa

This^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^, While I never had trouble understanding math, I always wondered when they would get to the practical application of it, and there IS practical application of math. I use it all the time.

Give a tangible explanation of the use of any of the maths being taught and it will be orders of magnitude more enjoyable to learn.

Unfortunately, most teachers are immersed in academia and don't know any PRACTICAL application of what they teach, so this becomes difficult.

Jaden

a reply to: Masterjaden

Educational practitioners are required to have continuous CPD, which includes keeping up to date on Educational policy and practice. This includes the realisation of the practical rationale for teaching the curriculum.

The Excellence Gateway is the governments go to objectives list when preparing lessons and it alludes to the rationale for objectives.

As I said previously there are constraints to complete the curriculum that sometimes doesn't facilitate creativity or focus on the practical applications. Often the focus is on checking learning, which can be very intensive depending on the class and ability levels.

originally posted by: Masterjaden

Unfortunately, most teachers are immersed in academia and don't know any PRACTICAL application of what they teach, so this becomes difficult.

Jaden

The first day in undergrad Differential Equations II, the teacher opened the class by saying something like "I don't normally teach this class, but no one wanted to teach it this semester and I drew the short straw. The problem with DE2 is that, unlike DE1, where there actually ARE some real world applications, for DE2, I can say in my life I've never run into a problem that was actually solvable with DE2 techniques. For any real world problem that requires this level of analysis, you will find that there are no solutions that can be obtained, since the equations you end up with don't fit any known methods, and you have to use numeric methods instead. In my opinion, we ought to drop this class except for math majors and teach the engineers and physicists two undergrad courses of numeric methods instead"

That was sort of depressing.

a reply to: Bedlam

Sounds almost exactly how I felt when I got to the higher maths. I didn't get as far as you, but it becomes completely meaningless the further you go. It is depressing, for young math geeks.

Its not that its meaningless, It's quite beautidul. But its a language that quickly starts to defy translation.

a reply to: ISawItFirst

Sure, the higher you go the less you can translate into English. But non math language doesn't have any real ability to express math concepts. How are you going to explain the contours on a large manifold in english?

"Well it starts at the x axis at 0 for y and 15 for z. Then, on the line for 15z it begins rising along y to 5 at 3x and then drops to -5 at 5x..." that's part of one line on the manifold, and there's none to infinitely more depending on boundaries.

Or we can write a single ~7 character formula that completely describes the manifold and paints a vibrant picture in my head, allowimg me to visualize that little sentence as a physical structure. "3z = (5-x)^2 +2y" (that doesn't describe my hypotehtical surface, it's just a surface).

Math is just a higher language than what we use to communicate, you have to understand it on the abstract level to derive any meaning the higher you go. That doesn't mean the meaning isn't there, it just means it's a book in English and a sentence in math.

a reply to: framedragged

Thanks. That was much clearer than my post, and was exactly what I was trying to say.

a reply to: framedragged

well said, I think that is a great "English" description....mathematical symbols are just that, they can represent a curve in a leaf, or a curve of light passing by a massive planet in space.

originally posted by: Bedlam
Yeah, I need to get off my lazy butt and go do some of that right now.

It's interesting when you're trying to solve something that there isn't a clearcut pre-done way to solve, and may have no solution anyway.

I've been playing with a couple of ideas lately... I'm a bit aimless. One is an image format based on layering rather than mixing RGB values and Huffman trees to create a compact lossless format. I'm 95% sure someone has already done this (my professor said it's similar to what jpg's do actually but those are lossy) but I've found it to be a neat puzzle to work out on my own.

The other is a variation on quadtrees where the information is stored in a polar coordinate system rather than x/y, my hope with that being that I can speed up circle and sphere colliders in game engines and reduce a lot of processing overhead on devices with weaker cpu's. The math for this second one is easy enough to work out, but doing so without using any trig or even squares is a bit more tricky (both are too slow for game engines where you have millions of objects to calculate in real time) though I think I've solved it, it's just a matter of writing it out and trying it at this point.

originally posted by: framedragged
Math is just a higher language than what we use to communicate, you have to understand it on the abstract level to derive any meaning the higher you go. That doesn't mean the meaning isn't there, it just means it's a book in English and a sentence in math.

One of my hobbies is 3d modeling, very often (though less often than I should) I'll build a component by creating profile curves via formula and then lofting those curves into a surface at which point I can 3d print it. It's very cool to see a formula turn into a tangible object.

I do a lot of it in game programming too where what you see is a graphical representation of 100 to 100,000 different formulas interacting with each other to give the user a cool experience.

originally posted by: Aazadan
One of my hobbies is 3d modeling, very often (though less often than I should) I'll build a component by creating profile curves via formula and then lofting those curves into a surface at which point I can 3d print it. It's very cool to see a formula turn into a tangible object.

Ooo, that's something that math programs should start introducing. You can even do 3-d surfaces with verying transparencies. That would be a great learning tool! Especially if you could melt the product down/powderize/whatever and make a new one; quick and cheap production for class time and school budgets.

I do a lot of it in game programming too where what you see is a graphical representation of 100 to 100,000 different formulas interacting with each other to give the user a cool experience.

And this is why I try to not get angry when things go wonky in video games heh.

originally posted by: framedragged
Ooo, that's something that math programs should start introducing. You can even do 3-d surfaces with verying transparencies. That would be a great learning tool! Especially if you could melt the product down/powderize/whatever and make a new one; quick and cheap production for class time and school budgets.

The technology isn't quite where I think you think it is yet and there are a few other issues. Take it from someone who has sat in 3d modeling classes and who has taught a couple. It's virtually useless to demonstrate this stuff to an audience because the software is quite complex and it just looks like wizardry. It's the sort of thing that requires hands on practice which means that in order to teach math we now have to teach modeling which seems like an extraneous step. Then the teachers need to know the software and be great with it. Then the students and the teacher need access to computers that can run the software, as well as pricey software licenses.

Lastly, while 3d printing is very fast in terms of creating custom objects, it's still a rather slow process, a small piece can take hours to print and if several classes need to print, that means you need several printers.

Where it can help is in seeing an image of the formula. For example if you have a pipe that is following a bend that can be replicated with a quadratic formula, and then you have a formula for an oval/circuar shape of the pipe you can input the curves these two formulas create and see the output as an actual object. Another example would be in using CV curves to profile a wine glass. At each segment you will have a formula for that segment, to control the line. By placing several of these together you can create a profile of the object, and then revolve that curve to make it 3d (at which point you could print it, if it's structurally sound).

www.youtube.com...

There's a short video as to what I'm talking about. In it they just put points wherever but you can adhere them to formulas too when drawing your curve. And from that formula, you get an object.

If you use the above method on a wine glass you have a set of 2d curves for the glass, a set of 2d curves for the rotation and you can intersect those for a 3d object. Then you can apply a material and shader which determines the reflection of light, so you get the equation of the base material (what colors it absorbs, transparency, different colors if a liquid inside is also present), the equation of the light (color, intensity, reflections). And before you know it, you're at 5 equations to describe the contour and shape of a wine glass as well as it's appearance.

But as I said, it's probably not viable below the collegiate level, and even then only for certain students. That said, it's something I always find to be cool when I do it.

a reply to: Aazadan

No no, not 3d shapes, I think Plato's solids are covered already and I didn't mean to suggest complex modeling for students.

I meant printing off relatively planar surfaces to help students visualize surfaces that aren't very intuitive on a page, not complex objects. Basically printing the equation in 3d space inside a transparent block so you can hold it and rotate it around and really see what the line or surface is doing (that's what I meant by 3d surfaces). "Here we are looking at the electrostatic laplace equation. This is a model of a section of the surface represented by -formula-." I'm sort of thinking about how awesome the 3-d phase plot models we got to play with in thermo were. Could even print some more off in a thermo class lol.

You, er a teacher, just wouldnt have to spend any (more) money if you could reuse a lot of material and could have a few things printed out to match a lesson plan. Then it gets passed around and kids can put the numbers to touch.