A Computer Tutorial System for Introductory Physics Courses

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A Computer Tutorial System for Introductory
Physics Courses

• Joel A. Shapiro
• Instructional Seminar
• November 15, 2001

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Intelligent Tutoring Systems

• Interactively helps students while they try to
  solve physics problems
• Not a homework grader
• Not just right or wrong
• Models student understanding

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Learning by Solving Problems

• Learning physics without trying to solve problems
  will not produce deep understanding. Independent
  problem solving teaches the student to
• Analyze a situation
• Decompose into semi-independent pieces
• Examine which fundamental principles apply
• Utilize these principles to find appropriate
  equations
• Construct from these a solution to the problem
• Unfortunately, these are hard to learn!

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What not to learn

• Problem analysis is hard students try to use a
  primitive problem solving method find the right
  equation to plug into.
• On problems too hard for that technique, without
  help students may give up.
• Do we give in by assigning only one-step
  problems? This only reinforces their poor attack
  strategy, and is not what we want!

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Andes II, an ITS for Intro Physics
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Andes Developers

• Prof. Kurt VanLehn of the Learning Research and
  Development Center, Univ. of Pittsburgh, and his
  group. This currently consists of Anders
  Weinstein, Collin Lynch, and Linwood Taylor, but
  has included Abigail Gertner and Christina Conati
  and others. Including me.
• Members of the Physics and Computer Science
  Departments of the U. S. Naval Academy, including
  Bob Shelby, Don Treacy, Mary Wintersgill and Kay
  Schulze.

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Andes

• Used in a general introductory physics course at
  the US Naval Academy
• Currently covers mechanics through angular
  momentum (rotation in a plane only)
• Has 115 problems of varying complexity
• Problem specification requires only a small
  amount of programmer-style entry --- the system
  itself solves the problems and generates the help.

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Andes topics (currently)

• Topics covered
• Vectors
• Statics (no torques)
• Translational Kinematics
• Translational Dynamics
• Linear momentum
• Rotational Kinematics

• Circular motion
• Torque
• Angular Momentum

• Work
• Energy

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Select problem within topic
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Problem choosing (blowup)
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Opening problem presentation
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An example problem
An inclined plane making an angle of 25.0 degrees
with the horizontal has a pulley at its top. A
30.0 kg block on the plane is connected to a
freely hanging 20.0 kg block by means of
a cord passing over the pulley. Compute the
distance that the 20.0 kg block will fall in 2.00
seconds starting from rest. Neglect friction.
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Problem decomposition

• Draw the free body diagram for the block on the
  slope
• Apply Newtons second law to that block
• Draw the free body diagram for the hanging block
• Apply Newton II to the hanging block
• Recognize that the tensions are the same, and
  that the accelerations are correlated
• Use all the above to find the acceleration
• Use the kinematics of constant acceleration to
  find the distance the hanging mass falls.

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Selecting a body
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Selecting body (blowups)
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Defining a force, part 1
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Specifying forces agent
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Specify type
Note wrong angle
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Finishing up force
Note angle adjusted
Note variable name changed
Note hint to draw axes
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Defining axes (blowup)
Axes tool
New axes
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Defining axes
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Mistaken force
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Normal straight up?
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Asking whats wrong
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Whats wrong (blowup)
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Hints on normal forces
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Hints (blowup)
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Defining an acceleration
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Acceleration dialog
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Entering equations
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Equations for block on incline
Stricter scaffolding would require writing the
first equation in terms of components, and then
giving the components in terms of magnitudes and
directions. The scaffolding should fade as a
student demonstrates competence.
Fta_xFw_xFn_xmaaa_x Fta_xFta Fw_x-Fwsin 25
deg Fn_x0 aa_x aa
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The second body
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Dialog
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Andes solves equations
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Solving for the acceleration
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Undefined variable
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Answers need correct units
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Right answer
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Problem Closed
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Send log of session
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To do next?
To do next?

• Describe what it takes to specify a problem in
  Andes.
• Switch to Andes itself, and watch
• one of you
• all of you collectively
• try one of the other problems.

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Andes structure

• Andes contains
• a physics knowledge database, which contains
  basic physical principles such as Newtons Laws,
  and also rules about when various constraints
  apply.
• a database of problem specifications
• A workbench for interacting with the student
• A problem solver, for finding all solutions to a
  specified problem.
• An algebra subsystem, for analyzing and solving
  equations.
• A help system, for organizing dialog with the
  student.

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Problem Description(just comments)

• (defproblem exdt2a
• "with the horizontal has a pulley at its
  top."
• "A 30 kg block on the plane is connected to
  a freely hanging 20 kg block"
• "by means of a cord passing over the
  pulley."
• "Compute the distance that the 20 kg block
  will fall in 2.00 seconds"
• "starting from rest. Neglect
  friction.")
• features (working Andes2 dynamics)
• comments (
• "Should return 60 states 2 axes for blk30
  (0 degrees 25 degrees)"
• "and 2 orders for the x and y axes if the 0
  degree axis is used."
• "crossed with resolving forces on blk30
  first or blk20 first"
• "crossed with 10 ways to solve the
  kinematics sub-problem")

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Problem Description, cont.
soughts ((answer(at (mag (displacement block2))
(during 1 2)))) givens ( (time 1) (time
2) (time (during 1 2)) (given (duration
(during 1 2)) (dnum 2 s))
Dt 2 s (object block1) (given (mass
block1) (dnum 30 kg))
m1 30 kg (supports plane block1
(during 1 2) (dnum 25 deg)) (tied-to
string block1 (during 1 2) (dnum 25 deg))
(motion block1 (during 1 2) (straight speed-up
(dnum 25 deg))) for now, just tell that
accel is constant so LK applies (constant
(accel block1) (during 1 2)) (near-planet
earth) (object block2) (given (mass
block2) (dnum 20 kg))
m2 20 kg (tied-to string block2
(during 1 2) (dnum 90 deg)) (motion
block2 1 momentarily-at-rest) (motion
block2 (during 1 2) (straight speed-up (dnum 270
deg))) for now, just tell that accel is
constant so LK applies (constant (accel
block2) (during 1 2)) (motion block2 2
(straight NIL (dnum 270 deg))) ))
Answer magnitude of displacement
Time points and intervals
Objects need declaring
Block is on plane at 25 deg tied to string at 25
deg and moves straight at 25
Acceleration is constant. Need to consider gravity
String is vertical on block 2 Block starts from
rest, then it moves downward
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PowerPoint Instructions