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So... I'm kind of ticked off at the whole education system, in terms of math education. It seems like in every single class I take now (algebra 2, precalculus, calculus 1, calculus 2) every textbook and teacher presents a problem with no reason, tells you the answer to it immediately (the "why" of it is only included half the time), then asks you to do thirty problems like it, using the solution you've just been given.

As I'm sure anyone who has asked a linear algebra on the dbpro forum knows (), I like math. I think that learning DBPro and being forced to solve linear algebra problems for practical purposes really got me started on the mathematics path. Since I see a problem (math education), and I see a possible solution (education with programming and a better layout), I want to try to do something about it. I don't mean that I want to go out and protest on the school board's doorstep, what I want to do is to try and teach programming (in DBPro!) and mathematics to eighth graders. The primary idea is to give them ideas about what to investigate and how to investigate it.

I want to focus on things that are really cool, but that can't usually be calculated by hand. I want to get into derivatives and integrals, because really they are easy to informally comprehend (I mean, you can't program a sidescroller if you don't have an intuitive idea of Euler integration. You don't call it that, but that's what it is.)

I'm starting to write up a course guideline, and I'm going to talk to one of my middle school teachers about teaching, and ask him to review what I've written. Eventually I want to start out finding three or four kids with laptops that can run DBPro, and setting up a 2x a week class using my course material.

So: What topics would you be interested in me attempting to teach? It takes a lot of time to get a good understanding of some math concepts, so the very first thing I want to do is make people ask themselves "Why is that happening?"

I plan to consider a lot of the stuff in my image gallery. things like circle inversions and base-motif fractals couldn't be covered methinks, because there's a lot of algebra, linear algebra, and programming involved.

English.


Integration by parts would be nice. I never got to learn about it at school, I did what's called "Extention 1" maths and it was taught in "Extention 2". It's probably not that hard but since you're offering. Oh and implicit differentiation would be nice as well.

Could you teach why you need integration for a side scroller? In fact, I've never really understood any need for integration, like you said, at college I'm just presented with a question with no hint to the problem or why I'm doing it.

Oh god... bad memories from school coming back.... thank god i switched out of that trig class just in time.

I always thought my brain hated algebra level (and above) math. I barley managed to BS my math classes in highschool to get me to pass. Infact i BSed 11th grade algebra 2 so well, that my teacher actually thought i could handle trigonometry next year. anything above basic math is beyond the ability of my brain comperehantion.

Neuro... you still have not asked me about that pic...

Can we interlink each others blogs? I would like to link to yours...

I saw you do a lot of line drawings in DB? [well i saw the one pic lol...

Please read my latest blog post about my Dev Community Project...

I think perhaps you can design an app that visualises maths... this I think would personally simplify maths for anybody...

teach... perhaps equations and math structures and explain why and how to handle bracketed numbers first and then non brackerted numbers... and teach the relationship between the two.. if you get me... 8x4 + (45-(6x4)+8) kind of thing... they always freaked me out of maths... I am good at % multiplication by 2 lol and umm averages and circa hehe...

hope my post made sense I was just about to eat now mmm spicy vege pizza might take apic of the half pizza for my blog lol

linky

PIZZA

non hidden link:
http://www.akaneaya.co.uk/vvdevblog/?p=656

and main blog direct link:
http://www.vaseemvalentine.co.uk/

EDIT

P... typo

I think this is pretty cool idea.

I always found the problem with maths is that there was very little explanation of where maths gets used and I mean down to the nitty gritty detail. I suspect that the maths teachers themselves didn't really know where maths is actually used or how it's used, just a vague notion that it's something that engineers and scientists use.

I work in engineering and find that maths has a habit of popping up. No one tells you it's a trigonometry problem or a differentiation problem. It doesn't happen like that. In the real world you will not be told what bit maths or science to use. All you'll be told is that you need to design a base for a machine that weighs 3 tonnes and needs to be moved using a fork lift truck. It's then about connecting theory with reality and this is something that you may not be taught very well at school, if at all.

However, the reason that you tend to do a long list of the same sort problems in school is that when you are presented with a real life problem and you've correctly identified the maths / science theory that you need to use, you don't want to be struggling with the maths and, in the this regard, practice makes perfect. It's like learning a language, the more you use it the more fluent you'll be.

I'll admit that I've never had to do any calculus for work nor any for writing computer games. In mechanical engineering, which is what I do, calculus is normally used when you have values changing with respect to time...

velocity is rate of change with respect to time
acceleration is the rate of change of velocity with respect to time
or
acceleration is the rate of change of the rate of change of displacement with respect to time (before anyone asks, the repeated "rate of change" is supposed to be there)

... but because of the way programming works, time is dealt with naturally because of the looping nature of the code so I've never had to differentiate or integrate anything for a computer game. Maybe that's what you were talking about when you said "I want to get into derivatives and integrals, because really they are easy to informally comprehend... "

The question I would ask is: are you wanting to teach maths or are you wanting to teach the application of maths?

Personally, I would teach the application of maths, rather than the maths itself. This would then give the student's an idea of how to use the maths they are learning, it might even give them the motivation to learn.

If this was Britain, the sort of things that schools teach are:

GCSE: 11 to 16 years old (compulsory education)

calculating areas of geometric shapes
basic algebraic manipulation
quadratic equations
trigonometry
Pythagorus
graphing equation
basic vectors (I was taught it in terms of Cartesian co-ordinates)
...and I suspect a whole bunch of other things that I can't remember

A Level: 16 to 18 years old (further education, not compulsory)

simultaneous equations
Differentiation
Integration
Differential equations
statistics
Newton's laws of motion
free body diagrams for resolving forces acting on a body
resolving forces in beams and 2d frame works
calculating acceleration of weights and pulleys
ballistics
... and once again, a hole bunch of stuff I can't remember


So if I was showing an application of maths to a class of sixteen year olds, I would stear clear of calculus because you can make some pretty cool games with just knowing Pythagorus (the distance equations as people like to call it on this forum) and basic vectors. Then all you need to teach is some basic game logic and you're away. I might, toward the end of the course, introduce ballistics and then do a simple tank game. I wouldn't want to teach trigonometry or quadratic equations from the ground level. That's what teachers are for.

One thing you will have to be careful of is not to over stretch yourself. You need to be able to finish what you start and you might find that the pace of class is a lot slower than you think it is. I was involved with a project for a school and it was a disaster because of unrealistic expectations and poor planning. I felt really guilty because we had this group of bright, enthusiastic teenagers and, well, I suspect we put them off engineering for life. Or at the very least they thought we were idiots.

Anyway, I think what you're doing is really good idea and hope it works out.

Awesome, another math thread! I'm surprised these don't show up more often. Math is very important to gaming (if you didn't know already) so I expect there to be more discussion on it.

I have really been interested in math for a very long time. I've competed in many math competitions and taught many competitors. More recently I signed up for the honors calculus in college, which was awesome because the professor was, well just flat-out in every way the best professor I've ever had. He would go into extremely great detail on where concepts came from what they were used for.
So, I would love to teach a bit of math here as well.

Edit: One use of integration in side scrollers is in calculating how fast a character must jump to reach a certain height.

Surely calculating how fast a player must jump would only reall need the equations of motion (suvat?)

Well yes, you could use the kinematic equations, but I don't like memorizing equations. Instead, I prefer to derive them when I need them, some of them. BTW if it is not clear, the kinematic equations are derived from calculus.

Oh haha I never knew that I've used kinematics for nearly two years now and never even thought of where they come from

Position is a function of velocity, and since the velocity function is complicated (its changed at the program's whim), position can only be calculated numerically. This is what happens when you say position=position+velocity*timestep (euler integration). If you wanted it to be more accurate, you could so something like position=position+(last_velocity+new_velocity)*timestep/2 (trapezoidal rule).


RIGHT. Everytime I read that I was like "huh?" but got distracted before I made a post. The link thing would be great. I'm working on a new version of my site (and renaming it), so once I get that up I'll e-mail you. So... what pic?


Yeah... I've tutored a few people and it seems like I occasionally have unrealistic expectations. It's easy to ask someone to do something but forget about the massive amount of groundwork that came before it. I'm trying to get most of the naive new teacher optimism out of me before I start, and that's why I'm going to talk to some of my middle school and high school teachers before I start this.

I want to at least touch on calculus though. Numerically finding the area under a curve, and realizing that differentiation/integration are inverses of each other. I guess you're right, it could fail badly... Maybe I'll just try it at the end of the course.


Awesome! I did math club at my high school for a year and did pretty well in the competitions. Unfortunately there aren't nearly as many undergraduate competitions, but I still try to go through some competition questions from time to time.

Hmm... Speaking of math education, would anyone be interested if I put up some videos explaining some of the math programs I've done? I've done a crapton just in DBPro. I was thinking of hooking up a webcam and pointing it towards some graph paper, so that I could actually write stuff down.

And where do you think suvat comes from?

All suvat equations are derived from the idea of acceleration independent of time:
x'' = a

Integrate once, constant of integration is "u"- initial velocity, because at t = 0, x' = u.
x' = u + at

Integrate again, constant of integration is zero, because at t = 0, x = 0 since "x" is the displacement from the inital position.
x = ut + ½at²

All the other equations are obtained by substitution.

And now you know how to get equations of motion from a simple fact (ie. constant acceleration) it's possible to do the same thing for different situations.

For example, what if acceleration is not constant, but also depends on the velocity?

x'' = a + f(x')

Of course, getting x'' in terms of t from that requires solving a differential equation, but once you've done that, it's then just a case of integrating a couple of times to get x' and x in terms of t.

HERE IS THAT PIC I ALWAYS MENTIONED NEURO!!! >.<

EDIT

awesome I can link images from my gallery server ^^
I saw this while shopping a while ago and thought of you haha

EDIT

No points for guessing why haha

yeah if you need help for a new hosting platform look at my community project!!!

Nice to see another Australian here, and from the NSW HSC education system too. If you're heading to uni, don't worry, most top universities skim over IBP again in the first semester first year maths course (assuming you go into a mathematically centric degree). The same goes for implicit differentiation.

If you want to learn it right now though, I can post up some university notes which explain it very nicely and succinctly.

Right back at you!


I'm hoping to get into Computer Science at Sydney Uni so that's good to hear.


That'd be great, thanks Veron.

Good to see you're going into Computer Science, I tutor some first year CS subjects at UNSW so if you need any info I should be able to help.

IBP as taken from the textbook looks a little like this -> http://i41.tinypic.com/2pu0dqc.jpg - Sorry for the poor quality of the scan, you should be able to understand the general concept of it though. It's really just normal integration and differentiation, but seperating the integral into two components, and then integrating one component and differentiating the other, then applying the formula in the box (Fig. 8.2.2).

That's awesome, thanks Veron! Unfortunately UNSW is a bit of a journey from where I live and I don't quite reach the cut-offs.


Thanks for that. It looks like it's based off the product rule...well involves the product...somehow. Anyway, I'll make up a few equations, derive them and then use IBP to integrate them again.

got any teachings on perlin noise

fractals and stuff.

I keep coming across 'dot product' and 'cross product' everytime I look at maffs stuff for 3d programming but both of them still confuse me. It would be nice to see a very easy implementation of both of these and what exactly they are used for.

For a lot of people like me, struggling to learn something by themselves, digging it out on the tinterweb, it's hard to understand without examples and 'very' likely, patience. Even the very basics of calculus still has me flummoxed.

Woops! Accidentally deleted the thread, that was stupid of me.

@dartnub - Please don't double post, you can edit your posts with the edit button.