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” Method
of determination of difficulty 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 |
|
|
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 |
w = j/t; wT
= 2p;
n = N/t; v = wR n = 1/T; ac = v2/R; j
= s/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.