# 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 dilatorwax 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 = x² 6. x = y² 7. y = -2x² 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.