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Perfect method!
Thank you!
@wisdomlover: Glad it helped!
am a linguist, was never good at maths. Probably THIS i was really looking for … the real concept behind Maths. This is simply superb.
THAAAANKs
i thank you for the brief explanation and it has really given more ideals for teach my student. i think you are point about each topic is very good and i will always visit your site.
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reading dr robert h lewiss paper on math, had me searching for a deeper understanding this lead me to this page. after reading your article i picked up my copy of ‘trachtenberg speed system in math’ (which i bought a year ago without reading)
then i tried to find out why the system for finding 11 x n works. with this deeper understanding i was able to find my own (quick and simple) way of multipling any number by 12,6 and 7 in my head i assume i can find out (on my own with out the book) the rest of the formulas for multiplication…im hopeful and excited!
thanks for your article
Hey, cool article.
I found your site tonight and it is great.
One thing though, about the cows. The abstract version of negative cows you use makes no sense to me. I agree with the imaginary person arguing with you. You can’t gain three and jump six. Rather, I imagine it as this: Negative three cows means that YOU owe someone three cows, but have none. I have ten cows on my lot. I sell seven. I have three. 10-7=3. I then meet a man in the market. I promise to give him five cows, and he pays me for five cows. Uhoh. I only have three on my lot. I give him those. I have zero cows on my lot, but I owe the guy two more cows. I have negative two cows. When I recieve my next shipment of cows, the first two I get off the cow truck go to him. 3-5=-2. The shipment has only two cows. -2+2=0. I have zero cows.
Makes sense?
@Patrick: Thanks for the comment! I think I need to reword the example, as its purpose isn’t clear :-).
My key idea is that numbers don’t inherently exist, they’re ways to express relationships. Getting stuck on whether negatives exist or not means we’re missing the point: what type of relationship does it represent?
As you’ve mentioned, negatives can represent the idea of “debt” – and the cool thing is it exists “alongside” the positive numbers!
Here’s an example. Negatives were only invented (in Europe) in the 1700s. But clearly debts existed before then… so how did they track them? Credits and debits!
If you have 3 cows, then great, you have a credit of 3 cows. If you promise to pay someone 5, then you have a debit of 5 cows (and maybe you equalize it, so your Credit is 0, and your Debit is 2).
Negatives are a new type of relationship where the credits and debits exist on the same number line – pretty neat stuff! But it’s a bit of a mind-bender to see the numbers as one continuous line, instead of two buckets (what I have, what I owe).
The key idea for understanding new math (new types of numbers, etc.) is to focus on what type of new scenario it’s describing.
The deference between success and failure is success never stopped trying.
@Older man: Math is about not giving up :).
Very nice article. Having a separate site for school maths would be good for kids.
Please keep writing. God bless you!
Really fantastic article, a big help in my confidence to practicing math for college. Thank you so much!
@Hash: Thanks! Yep, some articles focused on kids topics would be a good idea.
@Jason: Awesome! One of the best part of really getting math is it increases your desire to learn more:).
its pleasure to read this article because i worried many times by seeing the mysterious formulas and equations without any physical meaning and visualization of what going inside it.
maths formulas acts like a calculator if we give the inputs it will show the output but we cant able to see what is going inside it
in order to see what is going inside it we want to figure it out how the formula is extracted, but it is not simple in order to know the starting point of one mysterious formula we want to extract 100s of formulas from their starting point that is incredible
but every thing is possible that is the faith
i request all the guys posted here to share their resources such as best maths videos and wonderful books for the overall development of the similar thinking people like you!!!
Thanks for the motivation. I realised it is always the relationship between mathematical concept and its application to the real world that make mathematics an eye opener to the common senses.
Wow, a fantastic article and an awesome website! Keep on the good work!