Poster at 2006 AAPT Summer Meeting

Syracuse University, Syracuse, NY


July, 24, 2006


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

Boston University,


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;


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 (vav); initial velocity (vi); final velocity (vf); 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:                                                                               


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





Behavior of

a Speed












Linear motion with constant speed

 Uniform circular motion




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




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





Linear motion with constant speed


v = s/t;     s = x – xo,


a = 0



Linear motion with constant acceleration



v = vo + at;   s = x – xo


s = vot + at2/2


Uniform circular




w = j/t;      wT = 2p


n = N/t;      v = wR


n = 1/T; ac = v2/R; j = s/R




accelerated circular




j = S/R;  w = wo + εt;


j = wot + ε t2/2


v = wR; ac = v2/R;


at =  ε R





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 Multiple Ways”, (The Physics Teacher, November 2005, Volume 43, Number 8).

4. Arnold Arons, “A Guide to Introductory Physics Teaching”, (Wiley, New York, 1990).

5. Donald Scarl, “How to Solve Problems: For Success in Freshman Physics, Engineering and Beyond”, (Dosoris Press, 6th 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

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

10. Valentin Voroshilov, “Universal Algorithm for Solving Problems in School Physics”, (in the book “Problems in Applied Mathematics and Mechanics”, Perm, Russia, 1998).

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”, Berezniki, Russia, 1996).

12. Valentin Voroshilov, “Application of the System of Operationally-Interconnect Categories for Diagnosing the Level of Student Understanding of Physics”, (in the book “Artificial Intelligence in Education”, part 1. - Kazan, Russia, 1996).