Absement and 'nth Derivatives of Displacement' Presented Dynamically & Analytically

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Dowload absement.gsp     0 - toc     1 - time, t     2 - displacement, distance, s(t)     3 - definition of derivative     4 - s(t), s'(t)     5 - s(t), s'(t), s''(t)     6 - emojis, f, f', f'', tangent line     7 - trace derivatives     8 - PARTITION & SUMS 4 boxes     9 - Reimann & Sums     10 - SUMS absement, input [a,b]     11 - absement, n=32     12 - absement plus c     13 - play absement plus c     14 -arcsine actual fx graphed     15 - arcsine mesh - useF(x) plot to plot arcsine

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The Languages of the Math Classroom © '98, '08, '09 Agnes Azzolino   MOTHER TONGUE & OTHER TONGUE(S) Most Sophisticated and also the Most Basic   MOSTLY MATH TONGUES Most Sophisticated, Most Basic   VERBAL / Auditory     WRITTEN / Symbolic     PICTORIAL / Visual     CONCRETE / Kinesthetic       formal spoken mathematics   written word   DIGITAL MANIPULATIVE     object   informal spoken mathematics       written symbol   moving picture   model   spoken symbol   semisymbolic   static picture   manipulative/token   symbol speak   calculator symbol   numeral   calculatoreze/computereze   graph   web speak   nonverbal body language Communication Environments:       Private Conversation, Lab, Classroom, Lecture Hall, Remote Live, Video, Paper book, E-book, pdf File

Suggestions Choose a modality first.         VERBAL / Auditory         WRITTEN / Symbolic         PICTORIAL / Visual         CONCRETE / Kinesthetic   Usually, introduce in the most concrete.   Summarize in the most abstract.   The Mother Tongue is both the most concrete & the most abstract.   Sometimes use multiple modalities at the same time.   Strive for comfort in all modalities, not just your favorite.   Repeatition improves retention, especially in different modalities.   Need a review before new material? Don't review with a computation of symbols if you can review with a picture of the computation.   Before mentioning velocity or acceleration, dynamically/kinesthetically present a derivative with the definition, slope of the secant, slope of the tangent. Mention the word absement when you introduce displacement, velocity, and acceleration. At that time, just call it the total displacement.   The concept of "cumulative function" is much more important than "absement."

© 3/17/2023, A. Azzolino   www.mathnstuff.com/papers/KEAN2023.htm