How to teach an 8th greater an intuitive understanding of mathematics?

My little sister will be going into 9th grade next year. The math curriculum of her school is utter nonsense: what’s apparently called integrated 1 (algebra and geometry). It’s just a bunch of formulas kids need to memorize to regurgitate and then forget on a test. This worries me, because as she approaches calculus she won’t really have mathematics ‘click’ in her head and really understand why methods for solving problems are the way they are, and so on.

 

Do you guys know of any resources that build on a first principle/foundational approach to mathematics that someone could stem off of when learning anything new? Something like brilliant.org, but maybe more foundational and less intimidating for a beginner. She keeps saying she hates math and I’m sure it’s the way she’s taught it. I want her to understand the joy and importance of mathematics, so she can train her brain to think, but I think if she continues doing math the way public schools are teaching she’ll only grow more and more illiterate, not truly understanding what or why she’s learning things.

Thanks in advance for all your help!

submitted by Nevin Manimala Nevin Manimala /u/KingShindo
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Getting lost in math is such a great feeling.

Sometimes when it’s cloudy outside, it’s just nice to settle down with a well-written math book. I especially like books that have a lot of history in them, so I know a bit about what mathematicians were thinking about back then. Or to be working on a math problem that just seems a bit out of reach but you know that with a bit more time or some hints, you can get it. That feeling of not worrying about chores or whatever and getting lost in something eternal and universal like math is so satisfying. Even though I don’t find all of math interesting, once I found a subject I enjoyed I just want to spend time understanding the structure. I’m sure many of you can relate. Just thought I’d get it off my chest.

submitted by Nevin Manimala Nevin Manimala /u/pomegranatemolasses
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I just came up with an interesting way to prove that x^2 + 1 = 0 has no real solutions.

Suppose otherwise. Then there exists some t ∈ ℝ such that x = tan(t). Then by a trig identity we have sec2 (t) = 0. Multiplying out by cos2 (t) we get 1 = 0. Contradiction.

So I was wondering, substitutions like this come up all the time in calculus. Can we use this idea to prove interesting algebraic facts as well?

submitted by Nevin Manimala Nevin Manimala /u/CheCheDaWaff
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Hosted my first conference today at age 18! AMA

Sorry for the terrible mobile formatting, but I generally do not Reddit on my computer.

Today I hosted a conference aimed at getting more girls in the middle school age group into pure mathematics. I invited a plenary speaker, three discussion/activity session leaders, one Rubik’s cube champion, and one puzzle demonstrator. The plenary and the activity leaders were renowned mathematicians from the Philadelphia area. The activities were marketed as ‘not your K-12 math curriculum’. They included Topology, Harmonic Analysis, and types of infinities. Overall, 29 girls registered and 28 showed up. It lasted from 9:00 to 3:00 (not including set up and tear down).

I have been planning this conference since May of last year. Feel free to ask about my process; I have documented it all very well over the time period.

submitted by Nevin Manimala Nevin Manimala /u/Emmanoether
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What is your “eye opening” explanation of a math topic?

The math topics I have in mind are along the lines of algebra, trigonometry etc.

Do you have a way of explaining some topic, for example dividing fractions, transformations of functions, etc. that makes students go “Whoa I finally get it!”

submitted by Nevin Manimala Nevin Manimala /u/Mathman1011
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Which master is better? MSc in Applied Mathematics or Machine Learning?

Hey, I have two offers from two French Universities. One is MSc Applied Mathematics (https://msiam.imag.fr) from a prestigious school in Grenoble, France. There is specialization in Data Science in second year of the two year master. Other one is MSc Machine Learning and Data Mining from a not so prestigious University in Saint Etienne, France (Jean Monnet University) (https://mldm.univ-st-etienne.fr/index.php). This is also two years programme. Saint Etienne programme has more machine learning and also introductory in artificial intelligence. Which one I should choose according to you? I am having a hard time in deciding because the content of programme is quite same. I don’t know if choosing a more marketable named degree is better, or one from a prestigious university. My goal is to make a career in Data Science/Machine Learning. my previous University education is in Mathematics and Statistics.

submitted by Nevin Manimala Nevin Manimala /u/robin-X
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Doubts which i had that got answered so i’m going to share the doubts i had and answer them for you.So some others might have the same doubts that i had.

Can we count infinity?

Can we divide or multiply infinite irrational numbers by a certain number to make them rational(finite)?

Is alef 0 the true amount of infinity?

Did aliens or intelligent extraterestrial life find out the exact pi number or sqrt of 2?

is math invented or was it already there and we discovered it?

are we biased to think that the only way maths works is in this sense of manner?

Could maths have evolved in a different way or is this the only way it could have evolved and the only way?

Take a kid for example and tell him 1+1 is 3 and 2+2 is 5 add one to each answer will the kid grow up and ever realise that what he learnt makes no sense?

If you add 1+0 is nothing actually something?so can 1+0 be 2?

How does infinity have different sizes?Isn’t infinity just one sized?

A triangle has an angle degree of 180 shouldn’t 360 be a diamond or a square and not a circle?

Ok , So first of all i want to thank my friend /u/paashpointo for answering all the doubts i had.

So can we count infinity? physically speaking that is impossible because the definition of infinity means that an amount that can never be reached or counted to.

We can’t divide or multiply an irrational number by a certain number to make it rational because dividing it or multiplying it will still make it an irrational number which is smaller as a whole for example instead of 3.325… it would just become 0.452… it will still be infinite does not change the fact that it is infinite.

Alef 0 is a certain size of infinity it does not explain different sizes of infinity so for example draw lines in a sequence starting by a line of length 10 cm smaller and smaller each line to a shape of a triangle it will reach to a point where the lines would disappear and the amount of lines from the starting point 10 cm smaller and smaller till it reaches 0 cm that corresponding amount from the start to an end is called alef 0 which explains infinity that infinity has an end, but now take another line with the length of 12cm that would also come to an end but does that now mean that there is two alef 0s(two infinities)? Then it can keep going on length of 13 14 15cm which will bring up more and more different sizes of infinity.

Well it is possible for someone who has an infinite amount of time to finally get the exact number of pi or sqrt of 2 but since there is not enough time to actually calculate the exact pi it is not possible, but you will ask what if i try my best to get as far as i can then pass it on to my next generation to continue well that is possible but if you made one mistake in one of the numbers you would have to start again from that number and it is just too long no one can ever reach it(knowing exact pi means knowing the exact circumference of a circle and other shapes which will help making alot more accurate measurements for buildings and we will evolve in building anything not just buildings).

Math is definitely invented in a manner that we humans can understand basically if something makes sense or works we use it, if it does not make sense and especially if it does not work we throw it out. Take a car for example can you say that it was invented or was it already there and we found out about it? No ofcourse it was invented and if it works we use it if it needs horses to pull it well then that is a cart and there would be no such thing called a car(which btw came from the word cart if that wasn’t obvious already).

Yes we are kinda biased to think this is the only way math works because it can mean a totally different thing to other extraterrestrial intelligent life, for example if we tell an alien that 1+1 is 2 how will he know what those signs mean for example he does understand those signs how will he know that 1 means one object what if aliens use numbers as a language and for them it means run or 2 means peace, what if they speak in numbers instead of letters, so to them it would look like run + run = peace huh?

Anyway if a kid grows up if he actually makes some research of what he learnt he would then later realise that all what he had learnt was actually wrong and that our way makes more sense to his(our) feeble mind.

Physically speaking 1+0 = 1 but theoretically or philosophically speaking 0 could mean something but since math wants a physical sense so 1+0= 1 and not 2, like if you add 1 person to nothing they don’t magically become 2 people(maybe if you know a crazy magic trick where you put 1 person in an empty box and they become 2).

So anyway next question, take this irrational number for example 2.153… it is infinite but it is a certain size of infinity for example add a 1 in its 3rd decimal place which makes it 2.154… so basically this infinity is larger than the previous one so basically you can say that there is an infinite size of infinity if that makes sense to you, for example take that number again and add 1 to its 2nd decimal place which makes it 2.164… which is also a larger infinite than previously, so you can keep adding 1s anywhere in that large infinite irrational number to keep and keep changing its size, so basically the size of infinity can keep and keep changing unlimited times.

And finally the last question, so a triangles angle degree is 180 and if you add to it another triangle becomes 360 which is a circle but if you use this equation S=180(n-2) it will show that the angle degree 360 has 4 sides but how does a circle have 4 sides? Ok so now for example take this inside out square like this + it is still 360 degree so if you draw around it a circle it will look like a cars driving wheel so the angle is still 360 but when it is a square it is drawn in a different way so to you it might look like a square but it can still be drawn as a circle and still be 360 degrees, that is why when you drive a car and to drive around in a 360 degrees you have to turn the wheel 4 times, 3 times to turn 180 degrees 5 times to turn 540 then you keep adding 180 each turn.

Thank you hopefully this answered your doubts like it did for me argue about anything that i’ve might said wrong or ask anything that you guys did not understand properly i will try to clear them up for you or i will leave my friend paashpointo to clear things up for you.

submitted by Nevin Manimala Nevin Manimala /u/Beerato123
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