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Functions in 4 Modalities

Functions in 4 Modalities -- The Visual, Auditory, Symbolic, and Kinesthetic

    Functions are at the core of the high school core curriculum. Examine how they may be approached via different learning styles or modalities.

    Use the spoken word, written symbols and words, pictures, graphs, and manipulatives to introduce, address, expand upon function related standards.



Agenda
  • Examine NJ function related standards.
     
  • Language Families / Modalities
     
  • A Walk Down the Hall to Examine Modalities
    (Auditory, Symbolic, Visual, and Kinesthetic)
     
  • Discuss This With Your Partner (Auditory) To Decrease Sophistication.
    Debrief (Symbolic) To Increase Sophistication.
     
  • Materials
     
  • Calculator Composition of Functions (Symbolic, Visual)
     
  • Curve Shifting (Symbolic, Visual, Kinesthetic)
     
  • Solve Equations (Symbolic, Visual, Kinesthetic)
     
  • Math Exercises (Auditory, Symbolic, Kinesthetic)
     
  • Take an Inverse (Visual, Auditory, Symbolic, and Kinesthetic)
     
  • Debrief
     




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


A Walk Down the Hall to Examine Modalities


Use Discuss This With Your Partner (Auditory) To DECREASE SOPHISTICATION.
Debrief (Symbolic) To INCREASE SOPHISTICATION.

      The easiest way to increase the number of modalities is to introduce communication between students.   Have them DISCUSS THIS WITH THEIR PARTNER each time a problem or activity is completed.

      The second best way to increase the number of modalities is to DEBRIEF after an activity or problem is completed.

We use material from The Languages of the Math Classroom.



Calculator Composition of Functions (Symbolic, then Visual)

      (x - 3) + 4

Set up functions values as shown on the right, not left.
    Use [VARS] the [Y-VARS], then [FUNCTION] to access the y-variables as needed.
    Turn On/Off the equal signs (to display function) by sitting on it and pressing [ENTER].
 
In [TABLE] view table values for the 4th and 6th functions.
Scroll through table to compare symbolic values.
    This is really a PICTORIAL language or VISUAL modality.
 
Use [MODE] to edit screen to display Graph - Table, [G-T].
    This is using two PICTORIAL languages at once.


Materials
More planes found at: mathnstuff.com/papers/planes.htm.
 
Today we use
a 5x5 coordinate plane
the absolute value dilator
wax paper functions.
 
We use material from Exploring Functions Lecture Hand-Out.


Curve Shifting (Symbolic, Visual, Kinesthetic)

Please clear your notes and material and prepare for a lab.

Graph by placement on the coordinate plane. DTWYP.
a. (x). State the domain and range.
b. (x + 2). State the domain and range.
c. (x) + 1. State the domain and range.
d. - (x)
e. ( - x)
f. (x + 2) - 3
g. |x + 2| - 3
h. 2|x + 2| - 3. State the domain and range.
i. -(-x) State the domain and range.
j. the inverse of (x - 3) + 4
 
We use material from Exploring Functions, The Lecture Hand-Out.

Please take out your notes and debrief the lab by sketching the curves.



Solve (Symbolic, Visual, Kinesthetic)
Work with a partner to solve the statements by graphing 2 functions on the same plane. DTWYP.
a. (x) = x
b. (x - 2) = (-x)
c. (-x+4) = (x+1)-1
d. (-x+4) = (x+2)-1
 
Answers
 
We use material from Exploring Functions, The Lecture Hand-Out.


Who Has
  • Polynomial Functions (Auditory, Symbolic, Visual, (Kinesthetic))
  • Write Your Own "Who Has"

We use material from "Who Has" Games.



Math Exercises (Auditory, Symbolic, Kinesthetic)
a) Use your body, arms, and hands to represent the graph of:
1. y = 0
2. x = 0
3. y = x
4. y = -x
5. y = x
6. x = y
7. y = -2x
8. y = - |x|
9. y = 2|x|
10. y = |x| - 2
11. y = |x| + 2
12. y = 1/x
b) Please be seated.
 
We use material from Exploring Functions, The Lecture Hand-Out.


Take An Inverse in 4 Modalities (Auditory, Symbolic, Visual, and Kinesthetic)

(Verbally) Take the inverse of (x - 3) + 4

  • a number
  • subtract 3
  • square root
  • add 4
  • done
  • done
  • add 3
  • square
  • subtract 4
  • a number

We use material from Find an Inverse Function in Each of the 4 Language Families.



Debrief
  • Language Families / Modalities
Mother Tongue(s) is/are the most sophisticated and most basic.
The Language Families are Verbal, Written, Pictorial, Concrete
The Modalities are Auditory, Symbolic, Visual, and Kinesthetic.
Introduce in the most basic.
Summarize in the most sophisticated.
DTWYP, discuss this with your partner is the easiest way to introduce another modality.
Debrief after each activity.
Math stories are worth telling. Tell a story in as many languages or modalities as time permits.


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