Math Foundations

MathFoundations (all videos): http://www.youtube.com/playlist?list=PL5A714C94D40392AB

This is the Felix Klein’s Vision of Elementary Math from an Advanced Standpoint“.

All the Math we learn are taught as such by teachers and professors, but why so? what are the foundations ? These 200 videos answer them !

Good for students to appreciate Math and, hopefully, they will love the Math subject after viewing most of these 200 great videos.

Video 1: Natural Number This should be taught in kindergartens to 3-year-old kids.

◇ What is number ? (strings of 1s),
◇ Equal, bigger, smaller concepts are “pairing up” (1-to-1 mapping) two strings of 1s.
◇ Don’t teach the kids how to write first 12345…, without prior building these mathematical foundational concepts.

Video 2: Arithemetic
Distributive Law:
k x (m+n) = (k x m) + (k x n) = k x m + k x n

Convention: ‘x’ (or its reverse ‘÷’) takes precedent over ‘+’ (or its reverse ‘-‘).
(先 x ÷ 后 + -)


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Video 31: Affine Geometry (仿射几何)
image

Video 32: Geometry Education in Primary Schools
◇ Use Grid paper to visualize concrete objects (line, square, triangle, circle…)
◇ Arithmetic is closely linked to Geometry which has been ignored in schools in the last 3 decades since the introduction of Modern Math (vector algebra).

Video 34: Signed Area of Polygon


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Video 106: What exactly is a Limit

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