A Computer Tutorial System for Introductory Physics Courses

Joel A. Shapiro

Instructional Seminar

November 15, 2001

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

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!

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!

Andes II, an ITS for Intro Physics

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.

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.

Topics covered•Vectors

•Statics (no torques)

•Translational Kinematics

•Translational Dynamics

•Linear momentum

•Rotational Kinematics•Circular motion

•Torque

•Angular Momentum

•Work

•Energy

Andes topics (currently)

Select problem within topic

Problem choosing (blowup)

Opening problem presentation

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.

An example problem

Problem decomposition• Draw the free body diagram for the block on the slope• Apply Newton’s 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.

Selecting a body

Selecting body (blowups)

Defining a force, part 1

Specifying force’s agent

Specify type

Note wrong angle

Finishing up force

Note angle adjusted

Note variable name changed Note hint to draw axes

Defining axes (blowup)

Axes tool

New axes

Defining axes

Mistaken force

Normal straight up?

Asking what’s wrong

What’s wrong (blowup)

Hints on normal forces

Hints (blowup)

Defining an acceleration

Acceleration dialog

Entering equations

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_x+Fw_x+Fn_x=ma*aa_xFta_x=FtaFw_x=-Fw*sin 25 degFn_x=0aa_x = aa

The second body

Dialog

Andes solves equations

Solving for the acceleration

Undefined variable

Answers need correct units

Right answer

Problem Closed

Send log of session

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.

Andes structure

Andes contains:

• a physics knowledge database, which contains basic physical principles such as Newton’s 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.

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")

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|)) t = 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

PowerPoint Instructions