Making a Computer Speak Math However You Want

AER International Conference 2012

Lois Frankel, Educational Testing Service ()

Susan Osterhaus, TexasSchool for the Blind and Visually Impaired ()

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R324A110355 to the Educational Testing Service. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.

Rules, Preferences and Exact Speech

Speech Rules for Exponents

In all cases it is desirable to have a short pause after the base is spoken

Exponents 2 and 3

If exponent is 2

[base] squared (pause)

If exponent is 3

[base] cubed (pause)

Integer Exponents from 4 through 9

[base] to the [exponent–ordinal] power (pause) (e.g. "x to the fourth power")

Exponents of the form
  • Number – integer or decimal except for integers from 2 through 9)
  • Indicator (e.g. x, y, z, etc.) or negative of indicator (e.g. –x, -y, -z) etc.
  • Number –integer or decimal- followed by indicator (e.g. 2x, -3y, 4.1z)
  • Fractions that would be spoken as common fractions by the rules

[base] raised to the power [exponent] (long pause)

All other exponents

[base] raised to the [exponent] power (long pause)

Speech Preferences for Exponents

Preferences override rules. For example, the use of "over" or "end fraction" can be forced.

Value / Speech
Auto / based on the rules
Terse: Take out "raised" where it occurs in the rules.
Squared or Cubed (long pause)
OrdinalPower / [base] to the [exponent-ordinal] power (long pause)
Ordinal / [base] to the [exponent-ordinal] (long pause)
AfterPower / [base] raised to the power [exponent] (long pause)
BeforePower / [base] raised to the [exponent] power (long pause)
Exponent / [base] (short pause) to the (short pause) exponent [exponent] end exponent

Exact Speech

Exact speech overrides rules and preferences. It can include explicit pauses, pitch, volume, and rate changes.

Selected Speech Examples used in Feedback Study

Speech Example 1

Clones:
Transcriptions of Original Example as spoken by the Three Styles:
Simple Speech

Open 2 close open 4 close open 5 plus 1 close open 3 close.

MathSpeak

Left parenthesis 2 right parenthesis left parenthesis 4 right parenthesis left parenthesis 5 plus right parenthesis left parenthesis 3 right parenthesis.

ClearSpeak

2 times 4 times open parenthesis 5 plus 1 close parenthesis times 3.

Math Questions:
  1. Compute the value of the math statement.
  2. Explain the steps you took in computing the value of the math statement.
Feedback Questions (similar questions for all expressions, all styles):
  1. What, if anything, did you do to help yourself understand the math statement and answer the math questions? (Mark all that apply.)
  1. Didn’t need to do anything
  2. Wrote it down using braille
  3. Wrote it down some other way
  4. Played it back again. If so, did you play it back

1)Just a few times

2)many times

  1. How much experience do you have with this type of math statement?
  1. none
  2. a little
  3. a moderate amount
  4. a lot
  1. Which of the following best describes the way the math statementwas spoken by the computer:
  1. Very easy to understand
  2. Somewhat easy to understand
  3. Somewhat hard to understand
  4. Very hard to understand
  1. How sure are you that you understood the math statement?
  1. Very sure
  2. Somewhat sure
  3. Not sure
  4. Definitely did not understand
  1. The way the computer spoke the math statement was
  1. Very familiar
  2. Somewhat familiar
  3. Not very familiar
  4. Very unfamiliar
  1. What did you particularly like about the way the computer read the math statement?
  1. What would you change about the way the computer read the math statement, in order to make it easier to understand?
    Speech Example 2

(Slightly varied from sample used in instrument, in order to illustrate preferences and exact speech variations)

Clones
Transcriptions of Example as Spoken by the Three Styles:
Simple Speech

Fraction y to the fifth z super negative 7 end super over y squared z super x minus 3 end super end fraction.

MathSpeak

Start fraction[nested one deep]. y superscript 5 baseline z superscript minus 7 over [nested one deep]y squared z superscript x minus 3. End fraction[nested one deep].

ClearSpeak* using Current Rules

The fraction with numerator y to the fifth power z raised to the power negative 7, and denominator y squared z raised to the x minus 3 power.

ClearSpeak with preference "Exponent":

The fraction with numerator y to the exponent 5 end exponent z to the exponent negative 7 end exponent, and denominator y to the exponent 2 end exponent z to the exponent x minus 3 end exponent.

ClearSpeak with preference "Before Power":

The fraction with numerator y raised to the 5 power z raised to the negative 7 power, and denominator y raised to the 2 power z raised to the x minus 3 power.

ClearSpeak with preference "After Power":

The fraction with numerator y raised to the power 5 z raised to the power negative 7, and denominator y raised to the power 2 z raised to the power x minus 3.

ClearSpeak with Exact Speech (Experimental—pitch rises when speaking the portion in bold-underline):

The fraction with numerator y raised to the power 5 times z raised to the power negative 7, and denominator y raised to the power 2 times z raised to the x minus 3power.

Handout_SpeakingMath_18Point.doc1 of 9

Copyright 2012 Educational Testing Service