Can Homework Software Emulate a Conscientious Human Tutor

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Can Homework Software Emulatea Conscientious
Human Tutor?
Presented at AMATYC 2006, Cincinnati, Nov. 2,
2006. This presentation includes audio. Please
adjust your audio settings as appropriate.Press
F5 if necessary to start the presentation.
John C. MillerProfessor EmeritusDepartment of
MathematicsThe City College of
C.U.N.Y.xyalgebra_at_mindspring.com www.xyalgebra.or
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Preliminaries

• No names of commercial products.

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Preliminaries

• No names of commercial products.
• Full disclosure
• I write tutorial algebra software.
• All my work is available free.
• Last program to be shownwill be my xyAlgebra.

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Preliminaries

• No names of commercial products.
• Full disclosure
• I write tutorial algebra software.
• All my work is available free.
• Last program to be shownwill be my xyAlgebra.
• I will try to be fair.

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When Do Students Need Help?

• Mathematics educators refer regularly to
• Critical thinking/reasoning skills.
• Higher order problem-solving skills.
• Yet all we truly require is mechanical skillin
  solving predictable types of problems,

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When Do Students Need Help?

• Mathematics educators refer regularly to
• Critical thinking/reasoning skills.
• Higher order problem-solving skills.
• Yet all we truly require is mechanical skillin
  solving predictable types of problems,
• skills mainly acquired when students solve
  repetitive practice problems for themselves.
• So thats when help is most needed!

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What Characterizes aConscientious Tutor?

• Watches while student attempts to solve problems.
• Points out incorrect steps (not just final
  answers).

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What Characterizes aConscientious Tutor?

• Watches while student attempts to solve problems.
• Points out incorrect steps (not just final
  answers).
• Reviews prerequisites as dictated by errors.

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What Characterizes aConscientious Tutor?

• Watches while student attempts to solve problems.
• Points out incorrect steps (not just final
  answers).
• Reviews prerequisites as dictated by errors.
• Makes up examples to illustrate needed
  principles.
• Asks student to do similar examples.

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So How Can We Provide Conscientious Tutoring?

• Students need intelligent help, available when
  doing practice problems.
• Faculty time is wholly inadequate.

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So How Can We Provide Conscientious Tutoring?

• Students need intelligent help, available when
  doing practice problems.
• Faculty time is wholly inadequate.
• So software-based approaches offerthe best hope
  for conscientious tutoring!

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History of Math Tutoring Software

• Commercial mathematics softwarehas been sadly
  simplistic.
• Prevailing short answer formats provide
  insufficient basis for intelligent response.

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Program 1 (a top-selling early
multi-media program)
Let a Leos age now. a 3 Steves age now. a
3 2a 1. 2 a.
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Program 1 (a top-selling early
multi-media program)
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Let a Leos age now. a 3 Steves age now. a
3 2a 1. 2 a.
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Program 1 (a top-selling early
multi-media program)
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Let a Leos age now. a 3 Steves age now. a
3 2a 1. 2 a.
YOUR ANSWER IS INCORRECT.
Leo is now 4 years old. Let Leos age now
x. Then Steves age now 2x - 1. Three years
ago, Steves age was (2x - 1) - 3. At that time,
Steve was as old as Leo is now. Steves age three
years ago Leos age now.
(2x - 1) - 3 x
2x - 4 x
x - 4 0
x 4 So Leo is now 4 years old.
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History of Math Tutoring Software

• Commercial mathematics softwarehas been sadly
  simplistic.
• Prevailing short answer formats provide
  insufficient basis for intelligent response.

• Problem variety is severely inadequate.

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The Problem of Problem Variety
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The Problem of Problem Variety
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Program 2 (a currently available
commercial program)

• Accepts only short answers.
• Uses algorithmically-generated problems,
  resulting in limited problem variety.

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Program 2 Problem
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Program 2 Problem Solutions
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Program 2 Problem Solutions
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Better Programs

• Student enters step-by-step solutions.

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Better Programs

• Student enters step-by-step solutions.
• Responses and suggested solution steps are
  computed, not stored.

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Better Programs

• Student enters step-by-step solutions.
• Responses and suggested solution steps are
  computed, not stored .
• Published directly by their authors,not by big
  commercial publishers.

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Program 3
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Program 3
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Program 3
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Program 4
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Program 4
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Program 4
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Program 4
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xyAlgebra(free program written by the presenter)
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xyAlgebra(free program written by the presenter)
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xyAlgebra(free program written by the presenter)
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xyAlgebra(free program written by the presenter)
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More About xyAlgebra

• Instructors using xyAlgebra will find that much
  greater practice problem variety is available
  than in most commercial programs.

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More About xyAlgebra

• Instructors using xyAlgebra will find that much
  greater practice problem variety is available
  than in most commercial programs.
• To download a Windows-only demo of theverbal
  problems component of xyAlgebra,go to
  www.xyalgebra.org and selectthe Verbal Problem
  Demo link locatednear the bottom of that home
  page.

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What Can Be Done?

• Our students deserve the best available help.
• When previewing software, look carefully at
• The variety of problems available.
• The form of solution entry.
• The help available while solving problems.
• Experiment to see what works best.

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For More Information

• Prof. John C. Miller
• The City College of C.U.N.Y.
• E-mail xyalgebra_at_mindspring.com
• Upon request, the presenter will be glad to
  identifythe commercial programs illustrated in
  this presentation.
• For information on xyAlgebra, go
  towww.xyalgebra.org