The Languages of the Math Classroom

© '98, Agnes Azzolino

The Verbal Language Family

Mother Tongue

Other Tongue(s)

Formal Spoken Mathematics

Informal Spoken Mathematics

Spoken Symbol

Symbol Speak


Web Speak

[Top] 1. The Mother Tongue

Language, as embodied in a mother tongue, was spoken long before mathematics was created.

This makes the mother tongue the most basic of math class languages even though the verbal languages are in general the most sophisticated.

If the listener doesn't understand the mathematics, speak the mathematics in the mother tongue or in a more concrete language.

Example: Use the mother tongue to make signed number computation more concrete, less abstract.

Simplify: -5 + 3 - 2 + 6
Translate as: Lose 5, win 3, lose 2, win 6. Find the result.

Teaching Strategy: DTWYP, Discuss This With Your Partner

This strategy was used in the Warm Up Exercises. It is the most valuable strategy for the teaching and learning of mathematics that I have ever employed.
My primary goals are to enable students: to learn on their own and to think mathematics.
DTWYP facilitates the achievement of both goals.
  • It teaches students to confer with others in order to gain knowledge.
  • It permits student who are stronger to assist the weaker and feel better about their own expertise. I didn't learn calc in college. I learned calc when I first taught it. Teaching & really learning the topic for me happened as an adult. Teaching & really learning the topic happens daily in class when my students DTWYP.
  • It permits the weaker to be in command of their own education by seeking help.
  • It permits students to communicate mathematics in the mother tongue, in other tongue(s), in formal spoken mathematics and in informal spoken mathematics
My students were reluctant at first to communicate with other students about mathematics.
Some are still reluctant to communicate with others about their work. Some just prefer to work without consultation. This is not appropriate in my classroom. Each must consult with at least one other. Each knows that their work on a problem is completed only after it is discussed with another student.

Try the following time-maximizing strategy:
  • Assign a short set of exercises, some challenging, some easy, so that students must work independently.
  • Demand that student DTWYP as independent work is complete.

It is not necessary for the teacher to "go over" everything.
It may be very benificial for the teacher to address only a few important points.
DTWYP demands the use of informal spoken mathematics and encourages the use of formal spoken mathematics.
It makes a group less of a threatning body of people when each student makes the oral presentation as part of their project [see Precalc Questionbook Project].

[Top] 2.Other Tongue(s)

No specific mathematics examples are necessary for this language. It is listed because other tongues are spoken in math classes and a list would not be complete without acknowledgement of this fact.

Teaching Strategy: DTWYP

Permit time in class for math discussion, it reviews the content and stimulates formal mathematics communication in both the mother tongue and other tongues.


3. Formal Spoken Mathematics

Say "mathematics" not "math."

4. Informal Spoken Mathematics

Say "math" not "mathematics."

Formal spoken mathematics is the only language spoken by many - usually the teacher or professor. Informal spoken mathematics is spoken by many - usually the student or novice.

Communication may not occur - the student may not understand the teacher, or the teacher may not understand the student - if some bilinguality does not exist.


"Simplify the radical expression." VS "Clean out the radical."
"Remove factors of one." VS "'Cancel' to simplify a fraction."

Teaching Strategy: Speak Both Formal and Informal Mathematics

Formal spoken mathematics is appropriate in the presentation of an oral report.
Written notes, such as a handout, supports an organized oral presentation. See Projects in the Precalc Questionbook Project.

[Top] 5. Spoken Symbol VS 6. Symbol Speak

Spoken Symbol
- formal mathematics - the meaning behind the code or message.
Symbol Speak
- used to say a symbolically stated expression or equation. It is best used in conjunction with the written symbol, as when writing on the board.


"one more than twice an number" VS "two 'eks' plus one"

"The square of the sum of two numbers equals the sum of the square of the first, the square of the second, and twice the product of the two numbers." VS "a plus b the quantity squared equals a squared plus two a, b, plus b squared"

"three 'eks' minus five is twenty" VS "Five less than the product of three and a number equals twenty."

[Top 7. Calculatoreze/computereze

This language is used to say a correct or corrupted calculator key which is not algebraic vocabulary.

Teaching Strategy:

  • Alternate between spoken symbols and calculatoreze - say both: the "first function" and "why won" for "Y1"

[Top 8. Web Speak

The language of the internet.


  • "To save a copy of just the coordinate plane, place the mouse on the plane, right click, then download and save the picture under any name you wish" or
  • "Place the mouse on the picture and read the picture's URL, then type the URL on your browser's address line to see just the picture." or
  • "Place the mouse on the picture to see if the curser becomes a hand with pointing finger indicating that the graphic is a hot spot. If it is a hot spot, click to jump to the new location."


Fall '98 Precalc QB
© 2/24/97, Agnes Azzolino, TXu 813-453
© 1/13/87, Agnes Azzolino, TX 2 020 938 and © 8/29/95, TX 4-140-039, ISBN 0-9623593-5-1

[Table of Contents] [Top of the Page] [Last Page] [Next Page]
[Verbal] [Written] [Pictorial] [Concrete]

The Languages of the Math Classroom

    Verbal, Written, Pictorial, and Concrete (the Hundreds Board, for example) are the four broad mathematics language families discussed in this electronic monograph found at and additional pages (ISBN: 1-929-870-01-9 © 1998, Agnes Azzolino).

[MC,i. Home] [Table] [Words] Classes [this semester's schedule w/links] [Good Stuff -- free & valuable resources] [next] [last]
© 2005, Agnes Azzolino