Arc Functions
Through Auditory, Symbolic, Visual, and Kinesthetic Modalities

      The fact that you are reading this text is evidence that you are probalby very proficient in the traditional modalities: auditory and symbolic, perhaps even the visual. Now enrich/extend your options. Consider arc functions in all the modalities of the 21st century: auditory, symbolic, visual, and kinesthetic. All material is free and downloadable.


The Languages of the Math Classroom
© '98, '08, '09 Agnes Azzolino

Most Sophisticated and also the Most Basic

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   DIGITAL MANIPULATIVE
     symbol speak      calculator symbol   numeral
     calculatoreze/computereze   graph
     web speak   nonverbal body language


  • Choose a modality first.
    VERBAL / Auditory
    PICTORIAL / Visual
          WRITTEN / Symbolic
    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,

Arithmetic Stuff:
  • Inverse Math Spoken Here! dictionary definition
  • arc Math Spoken Here! dictionary definition
Precalc Stuff: Calc Stuff:
MATYCNJ23.pdf - of this page

Dowload inverse.gsp - Sketchpad of inverse functions
    0 - vertical, horizontal line tests
    1 - square root fx
    2 - any function
    3 - sqrt fx by parameters
    4 - restricted domain on inverse    
    5 - arcsine
    6 - arctangent
    7 - f and inverse
    8 - f, inverse, tangents

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

[MC,i. Home, site home page] [Good Stuff -- free & valuable resources] [tutorials & resource material arranged by topic [this semester's schedule w/links] [master list of all MSH! dictionary words] math ed stuff
spread sheet notes
    Languages of the Math Classroom
    Free Geometer's Sketchpad!
© 10/27/2023, A2