New way of teaching math?

[AndyC]

I've only been taught high school math so forgive me if I'm wrong. The method of teaching math and I guess doing math has always been done on paper because it's easy to reference in such a way. There are people who are developing ways to teach math without the symbols, but it still uses reference. Could we teach math without tools for reference? I think this could induce conceptual chunking, teaching math at a broader level. Obviously, this would at first be a slow approach, and wouldn't work if you're not someone good at math. Maybe it doesn't have to be learning, just practicing, but if we could move past reference, it would act as a catalyst for conceptual synesthesia (synesthesia has been proven to be inducible and produce greater scores in intelligence tests), or something of the sort. It would be like learning to read without subvocalization, not exactly but similar. This is just speculation, but if you've developed a loci method or some form of conceptual chunking or synesthesia, I'm sure you might agree with me. Personally, I use this for Ti, in which I often sense the various concepts and can use chunking to operate upon them via a loci method (sometimes intuitive, but intuition is still applicable). My idea of a loci method might be wrong, but I imagine it is used as a flexible tool of reference, but different to symbols, that is why I added 'flexible' to my description. You can predicate any synesthetic intuition using the loci method. For example when thinking about concept A, and it is made up of concepts a,...,z and have a concept B, with a,...,t and compare (or a function with an intuitive predicate so that it is similar) them (Imagine I am using basic set theory for a clear illustration), then I would imagine an appropriate (appropriate= intuitive function ^) shape and color, and visually, but not necessarily vividly because it's intuitive, perform the operation, completing my analysis quite quickly.

What I just described may be just how chunking works, but I doubt it defeats the credibility of my claim. Considering the broad scope of this idea, I'm sure research has been done into it, I have simply been relying on my own experiences, but will look into it properly given the opportunity. For now, I will start practicing this, that is learning and doing math in my head because I'm quite confident that this will have a positive impact.

 

[JR_IsP]

Hey, wich country are you from? Because here, in Venezuela (and in the American continent in general), math and science teaching has been quite dissapointing during the past years (I'm talking about high school, there are universities with a good level in math here)... I find interesting your idea, but I don't understand it 100%, would you please use an example?

Btw, I'm a strong Ti person as well, so I may like your method

 

[AndyC]

Is it the practice or how it works you don't get?
In terms of practice, just start with really basic mathematics. The idea is to avoid reference, and also to practice so much that you can 'sense' different concepts such as '7' as a form of synesthesia. I've done the practice part of this, so I don't use as much reference as someone else. I see numbers as personalities, and when I stop doing math for a while, the synesthesia weakens.
How: It's simply adaptation. It's forcing your mind to do math without reference so you can develop methods to continue doing math without reference.

Learn how to do this with basic principles, then move up higher to more complex ones, capturing new concepts within the same conceptual understanding.
If you've seen my thread on mastering thought, I posted something with sort of similar approaches but directed towards the general understanding of 'everything' using ontological categories.

Do have similar experiences with Ti? I mainly use the 'method' I described on topics that are too abstract to reference too, that is where my idea for a new learning of math originates.

 

[JR_IsP]

Oh, now I get it, sorry about that XD
Well, I think that it will work best for basic math and if you use it the time enough, you can create a whole non-math synesthesic asociations... I think that if you combine the asociations with aplications of math to real world things (specially for more abstract and complex ideas), that would make a brand new method of teaching math.

Good luck!

 

[redbaron]

I think people should be taught math by presenting a challenge without a formula. E.g: figure out the radius of this circle, based on the circumference.

See what people do, how they approach it. It's a lesson in problem solving. After some time, you explain the concept of pi and how to solve this particular problem.

Maths is so shitty currently because you're just rote learning a bunch of shit and not exercising your ability to think and solve problems logically and creatively, which is what maths essentially is. More fun, more applicable to real world, and also more freedom.

 

[JR_IsP]

That's the problem, I think that the method is not wrong, but the educative system in general, is made for making students graduate and that's it, it's not made for making students think.

If a system that priorizes thinking instead of graduating the most people at once rises today, I'd support it. But, the problem with that it's that our INTP way to see education is not shared by the others in general, the S-way to approach learning, for example, is radically different from this NT method.

That's why I'd bet for separated schools, like in Germany. There you go to a common kindergarden and primary, and depending of your capabilities and interests, you go to specialized High Schools, each with different approachs and goals. If you later show that you're above your level of High School, you can study one last year in the next one, and if you suceed very well in that one, you can go to the other. There are 3.

And of course, CHOOSABLE SUBJECTS! There're people that don't care about Physics, for example, and they're terriblity bad on it, so the fail, get bad grades... that makes them think taht they aren't good enough, depressing them and stop caring about education. THAT'S SO WRONG!

Maybe you're bad in physics, but you're good in sports, or english, or whatever. There should be a common subjects that you must take, like introduction to math, english, sports, and depending on your interest, you can choose later wich specialized subjects you're taking, in that system, everyone is happy and education becomes not a populist way to say "oh, look how many students graduated last year" and more like "wow, that guys really like what they're studying"