Classification of Numerical Estimation Strategies by Eye Movement

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Classification of Numerical Estimation Strategies
by Eye Movement

• Robert T. Durette
• Mark H. Ashcraft
• University of Nevada, Las Vegas
• Math Cognition Lab

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Overview

• Estimation is a mathematical skill that has
  rarely been studied.
• An estimation task may have many different
  context
• This experiment focuses on non-contextual,
  numerical estimation
• Task is a simple number line used in grade
  schools throughout the country

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Overview

• Estimation performance on simple number lines in
  1st through 6th grade has a relationship to
  overall math performance
• Adults have performed almost exclusively in a
  linear fashion
• But, adults may have an underlying logarithmic
  mental representation

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Goal of this Experiment

• Eye movements may reveal strategies that
  individuals use when solving an estimation
  problem
• Detect an underlying logarithmic mental
  representation

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Method

• Subjects were asked to say out loud the number
  that corresponds to a vertical hatch mark on the
  number line
• Number lines were 0 to 100
• 26 different number lines with two practice
  trials at the beginning
• 3, 4, 6, 8, 12, 14, 17, 18, 21, 24, 25, 29, 33,
  39, 42, 48, 52, 57, 61, 64, 72, 79, 81, 84, 90
  and 96

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Example of 0 to 100 Stimulus
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Eyetracking Analysis

• Divide stimuli into Areas of Interest (AOIs)
• Start Area, End Area and the Mark
• Number of Fixations
• Look Duration (ms) spent in each Area

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Area of Interests
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Area of Interests
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Area of Interests
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Area of Interests
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Video of Eye Movements
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Number of Eye Fixations on the Start Area
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Video of Eye Movements
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Number of Eye Fixations on the End Area
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Eye Fixations on both the Start and End Areas
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Number of Eye Fixations on the Mark
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Fixations on the Start Area, End Area and the Mark
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Area of Interests
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Area of Interests
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Look Duration (ms) on the Start Area
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Look Duration (ms) on the End Area
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Look Duration on both the Start and End Areas
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Look Duration on the Mark
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Look Duration on the Start Area, End Area and the
Mark
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Conclusions

• Subjects do not appear to be using both end
  points of the number line
• As the mark decreases in value (towards the
  beginning of the line), subjects do not use the
  end area for estimation
• As the mark increases in value (towards the end
  of the line), subjects do not use the start area
  for estimation

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Next Step

• Complete the analysis of eye movement sequencing
• Complete the analysis of 0 to 1,000 and 0 to 723
  number lines

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Math Cognition Lab

• Caleb Orton
• Ricardo
• Tiffany
• Sandy Fung
• Timothy Lau
• Jaki
• Laura
• Elena

Mark Ashcraft Robert Durette Jeremy
Krause Michelle Guillaume Alex Moore Sintia
Segovia Ike Hurt Karina Partida Nathan Rudig
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Questions?