Learning aids in Physics Education
(Oncoming presentation at BU Physics Department)
Before
starting the talk on the learning aids specifically, I would like to say a couple
of words on education in general. Of course, at any moment you can stop me and
ask a question or start a discussion.
And I
want to apologize for all the grammar and pronunciation mistakes I am gona
make.
There
is an old joke: those who can do something are doing it, those who can’t do
anything are teaching how to do something.
Every
joke has a portion of a joke.
The
reason that people have created this joke is simple; for many years teaching
job has not been considered as a real job. Indeed, what kind of a job is
repeating something from the textbook to the bunch of kids and then demand from
them to repeat. Anybody can do that! The hardest part of the job is just
keeping the kids at the desks and making them quiet.
However,
the view on what teaching is has been changing for the last couple decades. And
the reason for this change is that the view on what learning is has been changed. More and more politicians,
parents and even school teachers start thinking that learning is something more
then merely memorizing facts and procedures.
What
is it? What is learning?
There
are many different answers on this question, and I am not gona dig in this
discussion. But what I want to underline is that if you are a teacher, your
teaching stile, your teaching technique bases exclusively on your understanding
of what learning is. Your definition of learning defines your work as a
teacher. It means, the better you understand what learning is, the more
successful teacher you are.
Nowadays
a teacher has to have the own teaching/learning philosophy. “The own” does not
mean “so unique, nobody on Earth has the same philosophy”. No, “the own” means
“this is what I stand on; what I think about learning and teaching,
textbooks and assignments, students and parents, and everyone else”.
I have
my teaching philosophy. But the source for my philosophy is not the books on
educational research; even though I have PhD in Education. My source for my
teaching philosophy is my teaching experience. When I was studying theoretical
Physics at University I never saw myself as a teacher. But when I started
teaching it turned out I like it. I liked it so much I was teaching 35 – 40
lessons a week (plus, it helped for getting some money too). I was teaching to
middle school students, high school students, and college students and later to
school teachers. This situation of intense teaching forced me into thinking
about what am I doing, then into talking and finally writing about what I was
doing.
I find
the own teaching practice is the best source for building up a teaching
philosophy. Books or scientific publications or even lectures of people with
PhD in Education all are just secondary sources for that.
The
first question I am asking myself when I start teaching a class is always “How
will I know at the end of the course that I am giving a good teaching to my
students?” Luckily, in Physics the answer can be easy formulated as the list of
problems students have to be able to solve after the course gets finished. Those
could be experimental problems or theoretical problems, but in principle we can
always make the complete list of such problems. Now, when the teaching goal is
formulated, we can make an account of the time we can spend on the teaching –
just take the schedule and count all the classes excluding holydays.
The
time is most important factor when we are developing our teaching strategy and
tactics. Usually when planning the course we think something like this “This
day am gona give a lecture on
The
reason of that is that any teaching action has to be based on the correspondent
learning action which students have to perform in order to learn a portion of a
subject. The effective teaching planning has to be based on the scheduling of sequence
of acts students have to make in order to achieve the understanding of specific
theoretical construct or the building up of the specific skill. And when we
start talking about student learning actions we see that such actions as
“listening to a teacher” or “reading the textbook” are not enough for making an
effective teaching planning. The truth is nobody really knows what kind of
specific learning actions has to be taken into an account because there is no
systematic research on this. But acting teacher always has at least an
intuitive understanding of this and usually his/her understanding is much
better then the one of an educational theoretician.
This
is actually is what a good teacher differs from a not so good one. The good
teacher knows or feels what physical or mental action a specific student has to
perform in order to obtain the specific portion of a subject.
OK.
Let’s say we have the complete list of testing problems the students have to be
able to solve at the end of the course, and we are working on the perfect
planning for each lesson.
First
of all the number of testing problems is more then we used to think. For
example, when making the list of the problems we have to treat as different the
following ones:
1. A plain
needs to get the speed of 100 m/s to make a takeoff. The engines produce total
acceleration of 8.33 m/s2. Find the
time it takes for the plain to reach the speed.
2. A
plain needs to get the speed of 100 m/s to make a takeoff. The engines produce
total acceleration of 8.33 m/s2. Find the distance it takes for the plain to reach the speed.
3. A
plain is taking off after 12 seconds of the motion with the acceleration of
8.33 m/s2. Find the distance it
takes for the plain to reach the speed.
All
these problems have to be considered as different
because the sequences of the
elementary mental operations which have to be performed in order to solve the
problems are different (in part,
but still!).
However,
the problem:
4. A
car starting from rest gets the speed of 18 m/s, moving with the constant
acceleration of 6 m/s2. Find the
time it takes for the car to reach the speed.
- has
to be considered as equal to the problem 1.
When
we get the list of ALL testing problems, we see that it is just impossible to
go through each of them in order to show the all solutions to students; we
don’t have a time for that. And even if we could do this, there is a big
question on is it really a good thing to do? I don’t want to discus this
question now. For me it is enough to say that it is just technically
impossible.
Now we
have a contradiction.
The
number of the problems we can teach students how to solve is less (usually,
significantly less) than the number of problems we need to teach them how to
solve.
We
need to teach students haw to solve problems do not teaching them haw to solve those problems (in common meaning
of teaching)!
The
solution of the contradiction is simple (in principle): while teaching how to
solve a specific problem we have to use
the instruction in a way allowing students to learn how to solve the class (the
set) of problems, which are in some way adjacent to the instructed one.
What
are the possible main features of that kind of instructions?
Again,
there are many possible answers on this question.
My way
is this.
We
need to understand, there are two different ways to find the solution of a problem.
The
first way is making a search in a
database of solutions (i.e. in a memory, in a book, on the Internet, ask
another person) and literally find the solution of the given problem.
The
second way is creating the solution,
building it up step by step on the basis of the given information. Of course,
creating a solution is a more difficult task then searching for a solution
(plus, in many cases the search can be viewed as the first step of the
creating).
When a student gets the skills
necessary for creating the solution of a problem, he/she gets the necessary
ability to solve a set (a class) of problems.
This
is the way to solve the contradiction between the number of problems students
have to be able to solve and the number of problems a teacher can show how to
solve. Every problem in a class has to
be considered not as a specific Physics problem but as an example for
illustrating of the general way for constructing the solution of any Physics
problem. (By the way, we can say the same about teaching labs too)
The
first thing to do for a teacher is to visualize for students some hidden
difficulties, which they can meet while a problem solving situation, and which do
not depend on the specific physical situation given in the problem, but rather
derived from the general ways of how a human brain works in this situation.
After
that the teacher can give them an aid, which wouldn’t replace the students work
but would give them the clue, the hint, the possible lead in the right
direction on the way of getting the solution of a problem.
Now it
is a time to start the talk on the learning aids in Physics.
Every
learning aid is to be helpful to overcome a specific difficulty that student
can meet while a problem solving.
The
first possible difficulty is misunderstanding the problem, or wrong
understanding it, or just does not understanding the one.
Now I
have to make a remark about understanding. There are different kinds of understanding.
You can see it every day in your class. For example, a student read the text of
the problem #1 (on the plain). “Do you understand it?” “Yes” “Do you know how
to solve it” “No”.
It
means simply that the student didn’t meet in the text of the problem any
unknown word. This is the understanding of the text. But he/she does not know
what to do with all these words. This is un-understanding (no-understanding) of
the physical nature of the situation described in the text.
The
first difference between that student and a physicist is the student does not
know how to interpret the text of the problem in terms of Physics, the student
cannot translate the problem from an everyday life language into the language
of Physics.
What
kind of a learning aid a teacher can use in this situation?
Let’s
take again the problem with a plain.
A
plain needs to get the speed of 100 m/s to get takeoff. The engines produce
total acceleration of 8.33 m/s2. Find the time it takes for the
plain to reach the speed.
When we read this problem we do translate it
immediately and intuitively into the following text.
A
body moves from rest with a given constant acceleration and at unknown instant
of time has a given speed.
For
many of us the ability of making this kind of translation is the result of a
pure luck we got when we were kids. We got good parents, they gave us good
genes, we used to read books, and we got good teachers (maybe they were not
school teachers, but we definitely had them somewhere).
Now it
is our turn to be a good teacher to our students.
We can
actually teach them how to translate the text of the problem from everyday
language into our language.
We can
tell them the secret, that for us a
plain, a rocket, a stone, a rock, an arrow, a car, a particle, the Sun, a train,
etc, etc is just a body or an object. And when we read such words as “flying,
dropping, starting, shoot, thrown, driving” etc we read actually just “moving”.
The word “rest” translates as “zero velocity”. The words “starting” or
“stopping” translates as “velocity is changing”. We can even show to students a
dictionary we use for the translation. It can look like this, for example.
|
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, making 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
first column lists the everyday words students can meet while reading the text
of a problem; the second column gives the translation from an everyday language
into Physics language; and the third column lists the usual physical quantities
which can be used in order to describe the corresponded object or process.
When we’ve done with the translation part we meet the next obstacle on
our way to create the solution of the problem. We need to recognize the
physical model which we can use to describe the physical situation we are
having.
First of all it does not hurt to say to students that Physics has many
parts, and if we do not read in the text of the problem such words as “a
charge” or “an electric field” we do not need to use any conceptions from the
electrostatics. Even when students just start to study Classical Mechanics they
have some ideas about electricity and magnetism and optics from everyday life
and we can use it. We can even tall them there are many parts in Physics we are
going to study and show them the brief description of these parts.
The table below set up the context of main possible situations we can
meet when study Physics.
|
Indicators of a situation |
Section of physics (phenomena studied) |
|
Objects change positions |
KINEMATICS (describing of motion) |
|
Objects are acting on
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 |
When working on a certain problem we need to use more specific
classification in order to figure out (i.e. to recognize) the physical model we
have to use to solve the problem.
For example, when working on a
problem in Kinematics, in many cases 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).
Corresponding to the values of the parameters, three main kinematics
models we meet in a school Physics (within the framework of the school
standard).
|
The form of a trajectory 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, and it is always worth to check it out) |
Outside the school curriculum |
Of course, we cannot use this table to solve any problem in kinematics, but we don’t
need it! We use this table just to get students a main idea how does our brain
works.
After the correct
identification of the model we can make the next steps, which are fixing the
physical quantities and choosing the correct equations we need to use to
describe the physical situation we have met in the problem.
To do that two following
learning aids can be useful.
The table of the
correspondents between a kinematical model and the usual physical quantities
needed to give the quantitative description of the model.
|
MODEL |
MAIN PHYSICAL QUANTITIES |
|
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
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 parent
models and interval of motion, average velocity, average speed. |
The table of the correspondence between a kinematical
model and formulae needed to give the quantitative description of the model.
|
Model |
Formulas |
|
A linier motion with a
constant speed |
v
= s/t; s = x – xo, a = 0 |
|
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 |
One of the most effective learning aids that give
students the understanding of how the brain of a physicist works while working
on a problem is a System of Operationally Connected Categories (SOCC).
The main idea for this aid is that a real
knowledge is always a network of concepts; it is a complex of interconnected
terms, categories, meanings, senses. Moreover, connections in fact make a
knowledge being knowledge. We know in Physics; even the smallest interaction
can drastically change the property of a system. Same is true for a system of
knowledge. Without connections all the words in our memory are just the names
for some objects we can point to: “The table”, “The chare”. Without connections
a generalisation does not exist (there is no “Furniture”). Connections make the
combination of words being sensible.
In Physics all our work actually is looking for
connections, even on such a simple level as solving high school or undergraduate
physics problems .
To build an example of SOCC first we have to choose the most important
terms, categories, names of physical quantities within a specific part of a
subject. While doing that, we have to make sure that each of the terms has a
direct logical connection with at least one of the others. In Physics any
direct connection means there is a formula (at least one) which both quantities
go in (a direct logical connection can
be also a verbal statement; for example, a definition of straight line connects
terms as “an object”, “dimension”, “infinitely”).
Now we can make a simple graph.
Each
important concept/term/category/name we can indicate by a circle with a number
(or name) inside
(for
example, the circle with number 33 inside it - 
- indicates the
term «an angular speed»).
Each important
direct logical connection between two terms we can indicate by a line that
connects them.
Let’s say one more
time; a direct logical connection is a verbal statement (like a definition) or
a formula (like a definition, a law or an important formula derived from them).
The statement or the formula must include BOTH the terms linked by the
corresponded line.
For example, the line connecting circles 33 and 30,
represents the formula (or the statement), relating a radius of a circle
(R, number 30) with an angular speed (w, number 33).
After finishing our work we have the set of vertexes connected by the set
of lines (see Fig. 1).
Fig. 1
Each vertex answers a question “what kind of physics quantity can be used
to describe the situation within a given part of a subject”.
Each line answers questions “is there a direct connection between two
given physical quantities”; or we can say in other words “does the value of this
quantity affects the value of that”?
In addition, we can
give students an actual formulation of each link. For example, the line 33 – 30
represents the formula v = wR (the same formula is represented also by the lines 33 –
32 and 30 – 32, where the vertex 32 represents the linear speed of a body under
a circular motion).
The schematics above (Fig. 1) visualises the main connections/terms, and
relations/connections/dependencies between physical quantities within the
school Kinematics.
When necessary, we can provide a brief explanation of main vertexes and
links. For example:
1. Object is a body (a car, a spacecraft, a stone etc.).
2. A point mass is a body, which sizes are not essential for the given
problem. Usually it is right for small objects, particles, which are placed in
the vicinity of large objects (a stone falls to the surface of Earth; a train
goes from one city to another etc.).
5. Circular motion is a motion when all points of a body lie on circles,
which centres belong to one axis (line), and the planes of the circles are
mutually parallel.
7. Distance is the length of a trajectory. To find a distance it is
necessary to put a thread along a trajectory, then to stretch this thread into
strait line and to apply to a ruler and read the number.
8. Displacement is a vector connecting an initial and final position of a
body.
28. The displacement of the body undergoing a linear motion with a
constant acceleration is 
The given formula is
represented by the lines 16 - 28 and 23 - 28.
33. An angular speed is a physical quantity describing the rate of
changing of angular displacement during the time. The angular speed is defined
by the formula w = j/t, which is represented
by lines 16 - 33 and 31 - 33. The angular speed also is connected to the speed
by the formula v = w R, which is represented
by a line 19 - 33.
I don’t show here the full list of the quantities
and equations because it is the matter of a teacher’s choice. There is no ideal
graph; the structure of course depends on a teacher’s preferences.
The smaller version of the SOCC can be drown
quickly for any given problem a teacher is going to explain to students. The
visualisation of logical connections between quantities helps very much to get
students the understanding of the general way of how our brain works while
working on the solution of a problem.
But more important, it gives students the
understanding that any problem solving is always just a finding the necessary
connections between necessary quantities.
There is one more learning aid
I am going to talk about, but first I want to say, a teacher doesn’t have to
use every aid every time when students are having troubles for solving a
problem. There is no fixed rule when it is appropriate to use an aid and when it
isn’t.
Usually, when you see a
student got stuck or when a student is asking a question, you can ask first if
he or she tried to use any aid already, and one of the easiest ways to get rid
of the student and buy a some time for yourself is to say “show me the SOCC for
this problem” or “give me the list of the quantities involved in the situation”
or so. The main idea is trying to work as little as possible but keeping
students working on a problem. Of course in a class of 30 people having one
hour discussion section it is very hard balancing your work and students work,
but on the other hand it is also an interesting problem.
Finally, let’s talk out the
last learning aid worth to be used in a class.
I am talking about an
algorithm for constructing the solution of a problem from a specific class of
problems. It is not something new for us. In many books we can find an
algorithm for solving a problem on one-dimensional Kinematics:
- Read the text; make sure you understand each word
- Make a sketch; mark on the sketch all the important moments of time,
intervals of motion; locations of a body (bodies); displacements of a body
(bodies); velocities; accelerations
- Write for each interval of the motion the equation by using the
notations
- Substitute into the formulas all known magnitudes
- Solve the obtained set of equations
There are examples on Dynamics problems etc.
I find very useful for a teacher is keeping in
mind the general algorithm of reasoning which is executing while solving any
Physics problem.
The outstanding book “How to Solve IT” of the
outstanding author Gorge Polya gives an example of a general algorithm for
problem solving. The first edition of the book is dated 1945. I believe, if
departments of education (I mean Russian or American or any) would take this
book seriously 60 years ago, they could save tons of money on useless research
and get a good education to tons of people. But …
Anyway.
I tried to find the general algorithm for processes
which are usually going on in our head while we are looking for the solution of
a problem. Of course, “an algorithm” is a wrong word. During the real process of
creating of a solution many parallel processes are happening simultaneously. We
can say that in a real life all the parts of the algorithm are proceeding
simultaneously. There is an overlapping of the thinking processes and of
course, the extracting and arranging the mental operations performing in our
mind is kind of a subjective work.
But I find it’s very helpful to get a better
understanding of our way of working problems out, because we can better
understand the difficulties students experience in the same situation. This
algorithm is not a learning aid. It is useless to try to give this algorithm to
students in a direct way. But keeping this algorithm in a head helps to
understand the way a student has done and the possible reason the student get
stuck and to find the learning aid that could help the student to get out from
the frustrating situation.
The Algorithm has four parts:
I. Psychology of creating of a solution
II. Technique for creating a solution
III. Logic of creating a solution
IV. Reflection of the process of the creating of a
solution
Usually we can meet algorithms which describe
technique and/or logic has to be applied to get the solution. But I think the
first part (Psychology of creating of a solution) and the last part (Reflection of
the process of the creating of a solution) are more important for getting
students a feeling of what the process of creating the solution of a problem really is.
We never start solving a problem until we feel ourselves confident enough
that we can solve it. And when we get stuck it is very important to know that
we are capable to get through this if we know right questions we can ask to
ourselves. Emphasizing the psychological side of the problem solving process
helps student become more confident about their problem solving skills.
And finally, the last remark.
All the textbooks start the solutions from
writing down the necessary equations, which then get applied to solve the
problem. Reading this way to solve a problem, students keep being curios, how
did the author know what kind of equations to choose? The same situation
usually is happening in a class when we are doing the explanation on how to
solve a specific problem.
I think that writing down the necessary equations
is the final step of analysis! Physics is done after that! Math is starting.
The main cause for misunderstanding Physics and for disability to solve Physics
problems is the lack of experience of making the analysis which leads to the
necessary equations! This is the focus, the main goal and the most valuable
result of Physics education.
General algorithm for creating the solution of a
problem in Physics
I. Psychology of creating of a solution
1. Convince yourself that the problem has a solution
2. Convince yourself that you can find/create the solution of the
problem; it is not really important can you do it absolutely independently or
with engaging of somebody’s help (teacher’s, friend’s)
3. Formulate some simple to perform operations/actions, from which it
would be possible to begin a solution, something that is possible to proceed in
conditions of a problem
4. Make a chose what the action are you going to do right now and do it
("enter into a cold water"), convince yourself that it is possible to
reflect the problem, to think about the problem and to do some actions on the
problem
5. Keep acting and acting, make different attempts to obtain any new
information from the text of the problem, try various variants of operations,
fix their outcomes. If the problem is still not solved, proceed to the
algorithm of creating a solution
6. Fix/record the specific gap between the goal of the problem (unknown)
and the state achieved in the solution of the problem
7. "Convert your ignorance (lack of knowledge) into a key to a
solution ":
- Analyse the reasons/premises for organization of your previous
activities, think about why you have been acting like you have been acting
(what has forced you to act in that way). The reason for errors were made or
for you got stuck lies either in an inaccuracy of your premises, or in their
insufficiency (you have made a mistake at some step or you do not have all the
necessary information)
- Formulate the new question to the problem, the answer on which could
allow you to make a new step in a solution of the problem;
- Locate search areas to find the answer on the question, formulate
methods of searching of the answer
- Find the answer on the raised question, formulate additional obtained
information
- Formulate a hypothesis on a method of a solution of the problem
(determine the sequence of steps which could lead to the solution)
- Check up the hypothesis; proceed the (hypothetical) method of the
solution
- Get the result, if not yet, ask yourself the set of questions: Am I
really want to solve this problem, Am I sure in my success, Who can assist me
in my work, Am I ready to start, Do I get myself in circles doing again and again
the same attempts/steps, Why have I started to do this, not that, Because of
what premises I proceed my reasoning in this way, How can it be done in a
different way, What can I try to do instead of doing this, What is it possible
to try to do in order to bypass or to remove an obstacle and why is this?
- Get the result, if not yet, go back to #6
II. Technique for creating a solution
1. Analysis of a situation:
Select (and formulate the reasons for your selection):
- Key objects
- Main interactions between objects
-
- Have you met the similar situation before?
2. Abstractization and schematisation:
- Determine main empirical terms used for the description of the physics
situation of the problem
- Make the visual image of the situation (draw a detailed picture)
- Link empirical terms to appropriate physics concepts (locate the
appropriate region of physics);
3. Statement of a problem in theoretical language
- Find the correspondence between empirical terms and theoretical terms
(“a car” = “an object”, etc)
- Translate the text of the problem from empirical language into
theoretical
4. Determination of a model:
- Select main parameters describing the objects and processes (formulate
the reasons for the selection)
- Select key parameters describing a situation as a whole
- Determine variables for chosen parameters
- Correlate/compare the chosen variables with the variables for similar
physical models
- Determine classes of the phenomena most relevant to the situation
described in the problem
- Select models closest to the situation considering to the set of
variables standing for key parameters
5. Mathematical description
- Define the correspondence between specific objects, processes,
quantities essential to the considered situation and the general (abstract,
theoretical) objects, processes, quantities describing the chosen classes of
the phenomena and models
- Determine the set of main categories essential to the description of
selected classes of the phenomena and corresponding models
- State main laws and definitions relevant to classes of the selected
phenomena and models
- Fix/write main algebraic statements/expressions corresponding to the
laws and definitions
6. Solution:
- Substitute the given numbers in the stated equations
- Perform the mathematical transformations necessary for determination of
the values of the quantities
- Analyze the obtained results in point of view of their reasonableness,
naturalness, consider the possible limiting cases
III. Logic of creating a solution
Corresponding to the algorithm described above, the below is mental
operations which have to be realised at each stage of the solution; this part
of mental work consists of the answers to the following questions:
1. Analysis of a situation:
- What can we say about objects (bodies, things) in the condition of a
problem?
- What is happening to the objects, in what processes they are
participating, do they experience any changes
- What is having an influence on the objects, do some objects act on
another, are there some interactions
2. Abstractization and schematisation:
- What words (usually they are nouns) are used to name the objects/bodies
- What words (usually they are verbs) are used to describe the processes
(what is happening to the objects)
- What words (usually they are adjectives) are used to describe/indicate
properties of both bodies and processes
- What is the way to represent each object and what is happening to it on
a sketch
- What theoretical categories/terms Physicists use to describe the
similar objects and processes
- What is a possible "translation" of the text of the problem
into a theoretical language?
3. Determination of the type of a model:
- What are main physical quantities (terms, categories) are used for the
description of a situation
- What physical phenomena can be described by using the same physical
quantities (terms, categories)
- What are main parameters of classification are used to select
appropriate model
- What are values of these parameters for our problem?
- What is the name of the physics model/models which have the same values
of the same parameters?
4. Mathematical description:
- What are main physical quantities are used for the description of the
selected models
- What are main physical quantities from above connected by some physical
relations/dependents?
- By what kind of equations are the physical quantities connected
5. Solution:
- What are physical quantities used in the equations which a relevant to
the selected model/models
- Can we stand appropriate variables (letters) for the physical
quantities using in the model and can we write the equation corresponded to
connections between them
- What numerical values can be substituted in the equations for the
labels/letters of the quantities (corresponded variables)?
- How many unknowns and algebraic equations are obtained as the result of
the substitution?
- How can we solve the obtained set of equations?
- Ether the obtained solutions are reasonable or they contradict to our
experience.
IV. Reflection of the process of the
creating of a solution
- Analyse the process of the creating of a
solution: - about what, in what sequence, for what reason, with what outcome it
was necessary to think during a creating a solution; what happened during the
reasoning; what problems were overcame; what kind of emotions have been
experienced
- Analyse the solution found: - is the method of the creating of the
solution applicable to the given problem only or it can be generalized for the
class of problems; what indicators determine this class of problems (by using
which indicators can a problem been assigned to the given class)
- State a general method for problem solving of the problem from the
given class/set of problems.