You should be very proud of yourself if you are a Nobel Prize Laureate,
but you should be even more proud of
yourself
if you are the teacher of a Nobel Prize
Laureate.
Some
useful learning aids
|
An inclined plane problem solution |
General algorithm of problem solving Introduction of the category “Work” Do you understand Newton’s laws? |
I have developed a number of tools that
allow the teacher to help the student without replacing the student's thinking,
but motivating him to perform the logical steps that gradually lead to the
completion of the task. Such tools involve the
system of operationally-connected categories (SOCC helps to visualize a
students’ knowledge structure), the table of correspondence between everyday
lexicon and subject terminology (helps to interpret the text of the problem),
the classification table of typical subject models (helps to recognize the
model that useful for the problem), generalized algorithm of reasoning (helps
to make a correct sequence of actions), educational games and puzzles (help
motivate students and to develop their ability to think), and others.
Please, keep in mind there are two main
ways for using the learning aids. The first one is using them as learning
crutches. It means, a teacher creates them, gives out to the students and
explains how to use them for the problem solving.
But there is the second way, which is
more efficient, when these learning aids are learning indeed. The teacher
introduces the aid once, and then students keep creating them during studying
of the Physics.
I have had no English classes neither
in a school nor in a university, I have taught English by myself, hence, there
are a lot of mistakes in my texts. However, I am sure that you, the Reader,
will understand the sense/meaning of the texts of this site. If not, just send
me an email on mathhealth@beaplus.com
Example of the terminological dictionary on kinematics (9th
grade)
This
is the table of correspondence between everyday lexicon and subject terminology
(helps to interpret the text of the problem)
|
Empirical
term (everyday word) |
A theoretical term,
category |
Physical quantities describing the category (and the common notations) |
|
A car, a stone, an arrow, … |
A body, an
abject |
A mass (m),
coordinates (x, y, z), a volume (V), etc |
|
Goes, drops, rolling, pulling, flies, … |
Moving, at a motion |
Displacement
(S), distance (L), velocity (v), acceleration (a), time taken for the motion
(t), etc |
|
Getting at rest, moving from rest, doing a turn,
changing the velocity, … |
Accelerating |
Displacement
(S), distance (L), average velocity (vav),
initial velocity (vi), final/terminal velocity (vf), , time taken for
the motion (t), acceleration (a), etc |
|
Lies, hangs, sits, … |
At rest |
The speed is
0, v = 0 |
The below are
the classification tables of typical subject models (helps to recognize the
model that useful for the problem)
Example of the generalized classification table (physics)
|
Indications of a situation |
Section of physics (phenomena studied) |
|
Objects change
positions |
KINEMATICS (describing of motion) |
|
Objects are acting no each other, have an obviously
observed influence on each other (a
body in a liquid; springs; two surfaces at a contact; one body presses or
pulls the other; two bodies are attracting or repelling each other) |
DYNAMICS
(forces between objects) |
|
An oscillating body (on a spring, on a thread,
about a pivot point) |
OSCILLATIONS
(moving periodically back and force) |
|
The motion of many molecules has to be considered |
KINETIC
THEORY OF MATTER |
|
Processes on a gas (usually the change in volume,
pressure or temperature has to be considered) |
THE GAS LAWS
|
|
Bodies are heated or cooled up and it is important
that their internal energy varies |
THERMODYNAMICS |
|
Charged objects (without a motion) |
ELECTROSTATICS |
|
Moving charged particles (usually along with the
consideration of wires, EMF or generators) |
DIRECT CURRENT or ALTERNATE CURRENT |
|
Wires with a current (linear or in loops) and/or a
number of magnetic arrows |
MAGNETISM |
|
Light is transferring or reflecting or refracting
(there are bulbs, mirrors, prisms etc.) |
OPTICS |
|
Very fast moving objects, processes with atoms and
nucleuses, photons and other unusual words |
NONCLASSICAL
PHYSICS |
The example of the classification table on a theme
"kinematics"
To make a correct choice of a
kinematics model necessary to solve a problem we have to determine the value of
two main parameters of classification: 1. the form of
a trajectory; 2. the behaviour of a speed. Within the
framework of school physics curriculum for 99 cases from 100 we deal with the
following values of these parameters:
The form of a trajectory –
a) A STRAIGHT LINE; b) A CIRCLE.
The behaviour of a speed –
a) DOES NOT VARY (constant);
b) VARIES (changing).
In the correspondence to the
values of the parameters, three main kinematics models we meet in a school
(within the framework of the school standard). After choosing the correct model
we can make the next two steps, i.e. choose important
quantities and, finally, choose correct equations. For
dealing with complex problems SOCC can be helpful to make the two last steps.
|
The behaviour of a speed |
A STRAIGHT
LINE |
A
CIRCLE |
|
DOES NOT VARY |
A linier motion with a constant speed |
A uniform
circular motion |
VARIES
|
A linier motion with a constant acceleration
(remember, it is not exact definition, but for 99 % of problems it is true!) |
|
After the correct
identification of the model we can make the next step that is choosing the
correct equations to describe the physics situation we have met in the problem.
Example of the table of the correspondence of models and concepts
(kinematics)
|
MODEL |
MAIN PHYSICS MAGNITUDES |
|
A linier motion with a constant speed |
Displacement
(initial point, final point), distance, trajectory, velocity, speed, time
taken |
|
A linier motion with a constant acceleration |
Displacement (initial point, final point),
distance, trajectory, time taken, initial velocity, final/terminal velocity, (initial
instant, final instant), acceleration. |
|
A uniform circular a motion |
Displacement (initial point, final point),
distance, velocity, time, angle, angular displacement, amount of revolutions,
frequency, angular velocity, period, centripetal acceleration. |
|
The mixed model |
Concepts of parents models
and interval of motion, average velocity, average speed. |
Example of the table of the
correspondence of
physical models and formulae
(kinematics)
|
The
Model |
The
Formulas |
|
A linier motion with a constant speed |
v = s/t; s = x – xo |
|
A linier motion with a constant acceleration |
v = vo
+ at; s = x – xo s = vot
+ at2/2 |
|
A uniform circular motion |
n = 1/T; ac = v2/R; |
All
textbooks start solutions from writing down the necessary equations, which then
get applying to solve the problem. While reading that students keeping be
curios; how does the author know what equations have to be chosen? I teach my students that writing down the necessary equations is the
final step of analysis! Physics is done after that! Math is starting. The main
cause of misunderstanding Physics and of disability to solve Physics problem is
lack of experience of making the analysis which leads
to necessary equations! This is the focus, the main goal and the most valuable
result of Physics education.