The Languages of the Math Classroom
© '98, Agnes
The Verbal Language Family
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
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
- 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
- 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
- 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].
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
the Precalc Questionbook Project.
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"
||"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."
||"a plus b the quantity squared equals a squared
plus two a, b, plus b squared"
|"three 'eks' minus five is twenty"
||"Five less than the product of three and a number
- Speak each language. State in one language, then restate in the other.
- Don't symbol speak sound bytes, use formal spoken math.
- When teaching the "Laws of Exponents"
instead of writing a formula on the board and symbol-speaking
"eks to-the a times eks to-the b is eks to-the a plus b" speak
symbols with formal mathematics saying, "When multiplying two numbers
with same base, copy the base and add the exponents."
The statement of mathematics facilitates the transition
from simple exponents to exponents written as logs. "When multiplying two
numbers, add their logs."
- When writing the equivalent written symbols on the board, symbol speak.
Otherwise, speak the meaning.
This language is used to say a correct or corrupted calculator
key which is not algebraic vocabulary.
- "why won" for "Y1" the "first function"
- Words with a new math class meaning include: entry, home, key in,
pull down, screen, soft key, soft key pad, window, and zoom.
- New words with special calculator meanings are: ApLet®, built-in
function, CBL®, command line, tstep, y=.
- Alternate between spoken symbols and calculatoreze - say both:
the "first function" and "why won" for "Y1"
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
MATH SPOKEN HERE!
- © 1/13/87, Agnes Azzolino, TX 2 020 938 and © 8/29/95, TX 4-140-039,
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Verbal, Written, Pictorial, and Concrete (the
Hundreds Board, for example) are the four broad mathematics language
families discussed in this electronic monograph found at
www.mathnstuff.com/papers/langu/page0.htm and additional pages (ISBN: 1-929-870-01-9 © 1998,
© 2005, Agnes Azzolino