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 |
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.