Analyzing Student Equation Entries in a Computer Tutorial System - - PowerPoint PPT Presentation

Analyzing Student Equation Entries in a Computer Tutorial System

Joel A. Shapiro

• Dept. of Physics and Astronomy

Rutgers University shapiro@physics.rutgers.edu

AAPT meeting, Jan. 23, 2002, EH05

Intelligent Tutoring Systems

• Interactively helps students while they try to solve physics

problems:

• Not just a homework grader
• Not just right or wrong
• Models student understanding
• Which parts of solving the problem does the student

already know

• What approach are they taking
• Provides tutorial help when misconceptions observed.
• Provides guidance when student doesn’t know how to

proceed.

Andes II, an ITS for Intro Physics

Andes components

• Problem solver: Generates methods of solution and

``canonical’’ equations

• Algebra System:
• Equation solver: solves systems of equations
• Dependency checker
• Equation checker
• Workbench: provides interface for communicating with

student

• Help system:
• Tracks student progress
• Explores for possible corrections of wrong entries
• Provides guidance for stuck students

Opening problem presentation

Andes in mid-solution

Equation for hanging body

ab and Ftb represent the magnitudes of the acceleration and tension, so the student might reasonably write the equation:

Equations hard to identify

See latex version

Make a list of all derived equations

One way to do equation checking and derivation is to try to compile a list of all equations derivable from the canonical equations.

• A student equation is correct if it is equivalent to one on the list
• Each equation on the list has associated with it a list of sets of

equations from which it can be derived. Presumably the student used one of these sets.

Problems with using a list

• Need a set of manipulation rules which determine what gets

derived.

• If rules are too strong, too many, or infinitely many,

equations will be derivable

• If rules are too weak, reasonable correct equations will not

be recognized

• Andes I used this approach. In practice, it was found that only

simple problems could be done this way – for more complex problems, the computer crashed before finishing the list.

Alternate method

• The correctness of equations can be judged by

whether or not they are true whenever the canonical equations are. [Called ``color by numbers’’]

– This is easy to check, and is equivalent to algebraic derivability

• Dependency on a subset can be ascertained if the

equation is true whenever the subset is.

– This is easy to check for linear equations, or for the linear expansion of the equations about the solution point.

Pros and cons of color by numbers

Pro: powerful – works for all problems tried, and quickly, too. Cons:

• Algebraic correctness is more inclusive than pedagogic

correctness [slide to follow]

• Independent equations can be dependent in the linear

approximation about the solution point.

• This can be fixed for the common and simple cases, but is a

weakness in principle to the method.

Pedagogic vs. algebraic correctness

See latex version, slide13

Pedagogic != algebraic

See latex version, slide14

References on the Web

• Algebra Subsystem for an Intelligent

Tutoring System, Joel A. Shapiro,

– http://physics.rutgers.edu/~shapiro/algsys.pdf – Submitted to International Journal of Artificial Intelligence in Education

• Andes home page:

http://www.pitt.edu/~vanlehn/andes.html

• My email:

shapiro@physics.rutgers.edu