Poster
at 2006 AAPT Summer Meeting
Transition from
“I don’t
know it”
to “I know it”
is memorizing
Transition
from
“I can’t
do it”
to “I do it”
is training
Transition from
“I don’t understand
it”
to
“I get
it”
is thinking
Constructing Learning
Aids
for
Teaching
Algebra Based Physics
Dr. Valentin Voroshilov, Physics Department
Physics teachers experience occasional difficulties in helping students
understand the reasons behind selecting formulas used in constructing a
solution to a particular problem in Physics.
A set of specific exercises is a resourceful tool helping teachers
develop better explanatory skills and be able to identify students’ setbacks
during the actual process of solving a physics problem.
The same exercises can be used by teachers as a learning aid (teaching tool) to help students
master their problem solving skills.
The presented below learning aids are applicable for
solving problems in Kinematics; however, after the specialised training a
teacher becomes capable of developing similar aids for any part of Physics.
All exercises are based on the fact that, when a student gets into a
problematic situation, the brain starts constructing a solution from a recognition (i.e., it tries to
recognize the situation first).
To help teachers develop a technique that an experienced physicist
applies when developing a solution to a given problem, the
set of learning aids are being constructed by teachers as an exercise
(with the help of a facilitator).
1.
A terminological dictionary that connects an everyday lexicon to physics
terminology.
2. A classification table of typical physical models matching a situation
described in a problem.
3.
A correspondence table between models and physical quantities needed for
qualitative description of the models.
4.
A correspondence table between the models and formulas needed for quantitative description of the models.
5.
A schemata of logical and procedural connections between categories involved in
the analysis of the physical situation described in a problem.
Two main obstacles need to be overcome
by students in order to recognize a specific physical situation described in a
given problem.
The first obstacle represents a lack of
ability of a student to convert written text of a problem from an everyday
language to a specific physical language. For example, a situation “a car
starts from rest” and a situation “a stone is dropped from a height” are two
different situations for students. Students do not recognize that both of these
real world situations describe the same physical situation, i.e.,” an object
accelerates from rest and starts a linear motion”.
A terminological dictionary or a table
of a correspondence between an everyday lexicon and a subject terminology can
be used to help students perform a necessary interpretation of the problem.
1. Terminological
Dictionary
Empirical Term (Everyday Word) 
Theoretical Term;
Category 
Physical Quantities Describing
the Category (and
the common notations) 
A car; a stone; a rock; an arrow; a plane; a rocket; a box; a man 
A body; An
object 
coordinates (x, y, z); mass (m); volume (V); density (D) 
Goes; drops; flies; rolling; sliding; pushed; pulled; 
Moving; at a motion 
displacement (S); distance (L); velocity (v); acceleration (a); time taken for the motion (t) 
Getting at rest; moving from rest; starts; stops; making a turn 
Changing the velocity; Accelerating 
displacement (S); distance (L); average velocity (v_{av});
initial velocity (v_{i}); final velocity (v_{f});
time taken for the motion (t); acceleration (a) 
Lies; hangs; sits; stands 
At rest;
does not move 
the speed is 0; v = 0; no acceleration 
The second obstacle is that students
cannot recognize the physical model (models) needed to investigate a situation
described in a given problem.
The process of recognition is always
based on some classification parameters and their values.
In Kinematics, to identify the model
needed to solve a problem, we deal usually with the following parameters and
their values (within the framework of a physics school curriculum):
The form of the trajectory:
a) STRAIGHT LINE; b) CIRCLE.
The
behavior of the speed:
a) DOES NOT VARY (constant); b) VARIES.
Four main kinematical models can be
used in relation to values of these parameters:
2. Classification Table of
Typical Physical
Models
The Form of a Trajectory The
Behavior
of a Speed 
STRAIGHT LINE 
CIRCLE 
DOES
NOT VARY 
Linear
motion with constant speed 
Uniform circular motion 
VARIES 
Linear
motion with constant acceleration (Remember,
it is not an exact case, but for 99 % of problems it is true!) 
Circular
motion with constant acceleration (Remember,
it is not exact case, but for 99 % of problems it is true!) 
We cannot use
this table to solve every problem in
Kinematics, but we can use the principle! 



For some
problems a combination
of models should be used. 

When the two main steps are completed and the necessary models
are identified; then, the set of the most important physical quantities needed
to investigate the problem can be useful (Refer to Table 3. “Physical
Quantities” (school Kinematics)).
Finally, a set
of formulae needed to analyze the model can be constructed. The table of the
correspondence between the models and the formulae can be used for this step
(Refer to Table 4.“Main Equations”).
At this point,
it is important to emphasize that this step – choosing the equations
– is the last step of the
analysis of a physics problem. After this step, mainly the mathematical
calculations are left.
3. Physical Quantities
MODEL 
MAIN PHYSICAL QUANTITIES 
Linear motion with constant speed 
Displacement
(initial and final points), distance, trajectory, velocity, speed, time taken 
Linear motion with constant acceleration 
Displacement, distance, trajectory, time taken,
initial velocity, final/terminal velocity, (initial and final instant),
acceleration. 
Uniform circular motion 
Displacement, distance, velocity, time, angle,
angular displacement, number of revolutions, frequency, angular velocity,
period, centripetal acceleration, the radius of the circle. 
Uniformly accelerated circular motion 
Displacement (initial point, final point),
distance, velocity, time, angle, angular displacement, angular velocity,
angular acceleration, centripetal acceleration, tangential acceleration, the
radius of the circle. 
Mixed
model 
Concepts of parent models; intervals of motion,
average velocity, average speed; average acceleration. 
4.
Main Equations
Model 
Formulas 
Linear
motion with constant speed 
v =
s/t; s = x – x_{o}, a = 0 
Linear
motion with constant acceleration 
v = v_{o} + at;
s = x – x_{o} s = v_{o}t + at^{2}/2 
Uniform
circular motion 
w = j/t; wT = 2p
n = N/t; v = wR n =
1/T; a_{c} = v^{2}/R; j = s/R 
Uniformly
accelerated circular motion 
j = S/R; w = w_{o} + εt;
j = w_{o}t + ε t^{2}/2 v = wR; a_{c} = v^{2}/R; a_{t} = ε
R 
References:
1. Erich Mazur, “Peer Instruction”,
Prentice Hall, Inc., 1997).
2.
George Polya, “How to Solve It: a new aspect of
mathematical method”, (Princeton University Press, Expanded Princeton Science Library Edition,
2004).
3.
Mark Vondracek, “Improving Student Comprehension by
Thinking about a Topic in
4.
5.
Donald Scarl, “How to Solve Problems: For Success in
Freshman Physics, Engineering and Beyond”, (Dosoris
Press, 6^{th} Edition, 2003).
6.
Carl Wieman, Katherine Perkins, “Transforming Physics
Education”, Physics Today, November 2005.
7. David Hestenes,
“Modeling Methodology for Physics Teachers”, Proceedings of the International
Conference on Undergraduate Physics Education (College Park, August 1996)
(located at www.modeling.asu.edu).
8. Richard P. Feynman, “Six Easy Pieces”, Helix Books,
1994).
9.
F.K.L. Chit Hlaing (F. K. Lehman), “Cultural models
(and Schemata) and Generative Knowledge Domains: How are they related?”, Paper for the panel on Cultural Models and Schema Theory,
American Anthropological Association Annual Meeting, October, 2000, San
Francisco (located at real.anthropology.ac.uk/AAA2000SF).
10.
Valentin Voroshilov, “Universal Algorithm for Solving
Problems in School Physics”, (in the book “Problems in Applied Mathematics and
Mechanics”, Perm,
11.
Valentin Voroshilov, “Quantitative Indicators for the
Learning Difficulty of Physics Problems”, (in the book “Problems of Education,
Scientific and Technical Development and Economy of Ural Region”,
12.
Valentin Voroshilov, “Application of the System of
OperationallyInterconnect Categories for Diagnosing the Level of Student
Understanding of Physics”, (in the book “Artificial Intelligence in Education”,
part 1. 