The league is taking it easy on the 49ers. | Page 2

and now, an interesting, but short write-up on Quantum Physics by mod.

"Fig. 3: Electron diffraction.
The inverse wavelength (assigned to the pattern on the screen) plotted against
the electrons'
momentum
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
2,4
2,6
2,8
3
3,2
3,4
3,6
3,2
3,4
3,6
3,8
4
4,2
4,4
4,6
4,8
5
5,2
5,4
Momentum p in 10
-23
kg · m/s
1/ in 10
10
· 1/m
λ
Intensity
distribution
on
the
screen
Electrons
S1
S2
Fig. 4: Double slit experiment with electrons
There are
interferences! This looks like Newton's rings.
Electrons obviously move wavelike.
One particle activates the next.
(
Counterargument of another student:
Actually, the tube is evacuated.)
If the electrons are not waves before hitting the
crystal they couldn't cause
interferences.
Electrons and light are different things. For
me, these rings cannot be explained.
It is plausible to assign a wavelength
λ
to these
rings. It is not necessary to speak of electron
waves. The variation of the accelerating potential
difference in the tube results in the De Broglie relation p = h/
λ
, p is momentum of the electrons treated
classically before hitting the crystal,
λ
is wavelength related to the luminous phenomenon in the electron
tube, if being interpreted as an interference pattern (Fig. 3).
The 'double-slit' experiment with electrons cannot be demonstrated in reality. There are several good
films available.
High intensity: the distribution of the intensity is similar to interference patterns with light. Therefore one
can conclude: electrons are not
classical particles.
Low intensity:
statistically distributed singular
events. Therefore electrons cannot be
described as a wave. Electrons are
quantum objects (Fig. 4).
An interesting experiment with
classical particles is a part of the
teaching unit: Thousands of small
pellets pass a double slit and fall into
segments where the distribution can
be observed (Fig. 5). Students'
statements show that they now
attribute
STUDENTS' STATEMENT
S PRIOR TO THE EXPERIMENT
I expect an interference structure.
If this model is correct, then an
interference pattern must appear.
•
Actually, I expect an
interference pattern. Why
otherwise one should have
constructed this model?
Actually, electrons are particles
,
therefore these particles should be
36
comparable with
electrons.the electrons'
behaviour also to classical particles. For them, electrons are still
classical particles, so pellets have to have the same
behaviour.
EVALUATION OF THE TEACHING UNIT
The teaching unit was tested in a total of eleven physics courses of several high schools in Berlin. It was
a central decision for the evaluation process to choose a multidimensional
approach which allowed to trace
a single student's learning processes as well as learning outcomes of groups. Therefore, research followed
the steps below:
A questionnaire was given to students in all 11 courses, and interviews were carried out on two courses
before the start of the lessons to find out what conceptions the students then held.
Video recordings were taken of all 32 lessons in six courses in order to discover
correlations between
students' conceptions and their answers given during the lessons, and to obtain additional verifications for
the
conceptions which had been collected from the students.
Five weeks after the end of the teaching unit a second questionnaire was given. From these data the
conceptions which students held after the end of the lessons were worked out. With the help for students'
interviews from three courses we wanted to make sure the information gathered in this way was correct.
We gave the same questionnaire to the students before
and after the teaching unit in 14 further courses (control
group), which introduced quantum physics in the
conventional way of the Berlin syllabus. This was done to
help us correctly value the conceptual patterns shown in
the courses in which the new teaching concept had been
tested.
All questions were assigned to the range of topics which
make up the
subject-matter for teaching quantum physics
in school: light, atom-electron, particle-body, and
students' ideas on the philosophy of science. The
questions themselves were different in type: open
questions, e.g. 'What really is light?
'; word-pair
associations, e.g. 'electron-real body'; drawings, e.g.
'What do you think a real hydrogen atom looks like?
In total, written statements were gathered from 270
students of
which just under 150 belonged to the test group
(taught through the new teaching unit) and more than 120
belonged to the control group (taught along customary
lines). The verbal answers given by the students during the
teaching unit and in the interviews were transcribed from the videotapes. The transcripts also include notes
on students' play of features and gestures as remarks.
The results of the research consisted of four steps:
Overview of students' conceptions before the beginning of the teaching unit.
Comparison of students' conceptions of the two groups (test and control group) five weeks after the
lessons.
Perceptions in the process of change: a comparison of students' conceptions before and after the teaching
unit (whole data of all students).
Design of ideas' networks from all data of one student from the beginning of the teaching unit up to the
second questionnaire and interview.
In the following, some examples will be given for each of the four steps.
STUDENTS' CONCEPTIONS BEFORE THE TEACHING UNIT
One of the items in the questionnaire referred to the topic 'atom-electron'. Some of the open answers
given by the students before the beginning of the actual lessons about the introduction to quantum physics
were:
...
because the electron is tightly placed on an atomic shell, i.e., there is a distance between the shell and
the nucleus so that the electron cannot get to the nucleus.
Fig. 5: Double slit experiment with
classical particles
37
Fig. 6: Change of students' conceptions of an atom's stability.
before...
five
weeks
after...
... the teaching
unit
control - group: 92
students
21%
9%
64%
7%
13%
10%
60%
"CIRCLE"
8
44
7
6
4
4
4
2
4
1
"CHARGE"
"SHELL"
"LOC."
test - group: 96
students
1%
1
2
2
5
3
2
53
11
8
"CIRCLE"
"CHARGE"
"SHELL"
"LOC."
69%
18%
7%
22%
4%
68%
The
electron is acted upon by the centrifugal force and the attractive force of the atom. Both forces are
in equilibrium (Bohr's atomic model).
The electron is separated from the nucleus by its high velocity (centrifugal force).
As a result of the high angular velocity of the electrons, the resulting centrifugal force prevents the
electron from falling into the nucleus under the influence of the attractive force.
Because the charges of electrons and protons neutralize each other.
The electron is negatively charged while the nucleus is positively charged. Again, the electron is subject
to a kind of centrifugal
force which keeps it in its orbit. Therefore they rather repel each other.
Electrons are fixed in their shells.
From these answers, typical patterns could be constructed which show students' conceptions:
Circle
(circular orbit): conceptions of
electrons which fly round the nucleus with (high) velocity in fixed,
prescribed orbits. In this conception the centrifugal force and the Coulomb (electric) force are brought into
equilibrium. The students use their experience with roundabouts first to explain the movement of the
planet, and then second to explain the process in atomic shells, without regard to reference systems (63% of
240 students in both groups).
Charge
: students have a fixed conception of the repulsion between charges. They often explain the
properties of charges incorrectly. The charges of both the proton and the electron cause a distance between
the two particles (23% of 240 students in both groups).
Shell
: conception of a firm casing (shell, ball) on which the electrons are fixed or move (8% of 240
students in both groups).
In conclusion it can be noticed that the students already possessed a fixed idea of an electron in an atom,
being strongly based on a mechanistic conception. The question is
, therefore, whether normal teaching,
including the treatment of Bohr's atomic model as an explanation of the
quantization of energy levels, does
imply the reinforcement of already existing thought patterns.
CHANGE OF STUDENTS' CONCEPTIONS
A comparison of the conceptions of the students from the two groups (test and control group) after the
lessons demonstrates that different changes in conceptions have taken place. First of all, another conceptual
pattern could be constructed from
students' answers:
Loc. (localization energy)
: the
stability of atoms was regarded by the
students as connected with the
Heisenberg uncertainty principle.
According to this conception, the mere
restriction of space results in a rise of the
kinetic energy of the electrons, the loci
of which are subjected to a statistical
distribution. At the same time the
students dispensed with statements about
singe electrons which they thought of as
inconceivable.
In Fig. 6 the changes in students'
conceptions concerning the stability of
an atom are given.
Within the range of topics discusses
here, a clear dependency on the teaching
experienced by the students can be observed: 68% of the students in the test group oriented themselves
toward the conception of localization energy
(Loc.)
while the students of the control group persisted in the
conception of
circle
and
shell
.
38
Fig.7: Comparison of conceptual changes between test and control group.
.
control-group: 108 students test-group: 116 students
71%
6%
27%
27%
2%
47%
0%
20%
none
little
satisfactory
complete
SUMMARY OF THE EVALUATION
The example given illustrates the trend of the results of the investigation.
A teaching approach, for
example like the one introduced here, which, from the outset, considers possible conceptions of students in
detail and consciously provides room for these conceptions to develop in class, will achieve an increased
cognitive conflict situation which will then, in turn, lead the students to grapple with the subject. In this
way, the students became conscious of their own conceptions and began to question them. The students
became conscious of their own conceptions and began to question them. The results of the control group
pointed to an incorporation of the 'new' phenomena into the 'old' mechanistic ideas. Here, the different
ideas in quantum physics were merely acquired verbally and were forgotten again afterwards. This
statement is supported by
Fig. 7. Here, for all items
of the various topic areas,
the conceptual changes are
rated, summarized, and
reproduced separately for
test group and control
group.
STUDENTS'
NETWORK
STRUCTURES
Students "react to things
on the basis of meanings
which these things have
for them" (
Blumer 1976,
p. 81
; translation by the
author of the present paper). This approach proceeds from the theory of symbolic
interactionism (adapted
from Mead,
Schütz), according to which, meanings are built up on the basis of a correlation between a
"stock of commonplace knowledge" and "situational experience" (
Schütz/
Luckmann 1979; p. 133;
translation by the author of the present paper).
On the basis of this interaction, a research approach is formulated, which constructs cognitive networks
of students from the interpretation of students' ideas together with their meanings. These networks
themselves, according to this assumption, reflect students' conceptions.
The following figures point out network structures of two students
, both constructed before and after
the lessons. The initial sets of single ideas were deduced from the total data set of all students' answers
before and after the lessons. The single answers show students' main ideas. The ideas themselves are
interconnected through various features demonstrating the connection of meanings (following
Klix 1976,
his adaptation by Norman and
Rumelhart 1975):
R:
represents a relation between general ideas and sub-ideas. Features which form a general
idea can be transferred to the sub-idea (
..is a..).
CM:
typifies characteristic features of an idea through the use of other ideas (
..
heard
..;..
has..).
AM:
typifies active features which characterize an idea (
..can..).
N:
points out that a character of an idea consists in establishing another
idea (shown with
..).
ZO:
illustrates a relation between two ideas without itself being a characteristic feature (
..will
be assigned..).
TI:
signifies partial identity of two ideas (
..is like..).
WI:
contradiction: no further relation between both ideas (
..it cannot be..)
Fig. 8 and 9 show the networks of a student from the group which throughout the lessons received an
introduction to quantum mechanics according to the new concept (see Berg et al. 1989); whereas Fig. 10
show the networks of a student who was enrolled in a course which followed the regular Berlin syllabus.
In Fig. 8 and 9 the two networks give an impression of the development of ideas and their meanings. The
students was able to change his basic ideas in atomic-physics (see Fig. 8) to the new idea of the quantum
(see Fig. 9). For him the quantum is something new without a relation to the classical wave or real particle.
In the other case (see Fig. 10) the student was fitting the new ideas into the old network. The photon
39
became a real particle, and the electron is still on a fixed prescribed orbit around the nucleus now under
oscillation.
R
TI
N
ZO
R
ZO
R
CM
CM
R
TI
CM
40
REFERENCES:
Berg, A.,
Fischler
, H.,
Lichtfeldt
, M.,
Nitzsche
, M., Richter, B., &
Walther
, F. (1989).
Einführung in die
Quantenphysik.
Ein
Unterrichtsvorschlag
für
Grund
-
und
Leistungskurse
.
Pädagogisches
Zentrum
Berlin.
Blumer
, H. (1976).
Der
methodologische
Standort
des
symbolischen
Interaktionismus
. In
Arbeitsgruppe
Bielefelder
Soziologen (Eds.),
Alltagswissen,
Interaktion
und
gesellschaftliche
Wirklichkeit. Bd. 1:
Symbolischer
Interaktionismus
und
Ethnomethodologie
(pp. 80-176). Hamburg:
Rowohlt.
Brachner
, A., &
Fichtner
, R. (1974).
Quantenmechanik
im
Unterricht
.
Physik
und
Didaktik
, Vol. 2, part I
(pp. 81-94), part II (pp. 249-275).
Feynman
,
R.P.
, Leighton, R.B., & Sands, M. (1965). Lectures on Physics, Vol. III,
Quantum Mechanics
.
London: Addison-Wesley.
Klix
, F. (1976).
Über
Grundstrukturen
und
Funktionsprinzipien
kognitiver
Prozesse
. In F.
Klix (Ed.),
Psychologische
Beiträge
zur
Analyse
kognitiver
Prozesse
. Berlin:
Deutscher
Verlag
der
Wissenschaften.
Norman,
D.A.
, &
Rumelhart
,
D.E.
(1975).
Explorations in Cognition. San Francisco: Freeman and
Company.
Schütz
, A., &
Luckmann
, T. (1979).
Strukturen
der
Lebenswelt
. Bd. 1, Frankfurt:
Luchterhand.
Squires, E. (1986).
The Mystery of the Quantum World. Bristol: Adam
Hilger.
41
THE INFLUENCE OF STUDENT UNDERSTANDING OF CLASSICAL
PHYSICS WHEN LEARNING QUANTUM MECHANICS
Richard
Steinberg, Michael C.
Wittmann, Lei
Bao, and Edward F.
Redish
Department of Physics, University of Maryland, College Park, MD, 20742-4111
[email protected], [email protected]
[email protected]
,
[email protected]
INTRODUCTION
Understanding quantum mechanics is of gro
w
ing importance, not just to future physicists, but to
future engineers, chemists, and biologists. Fields in which understanding quantum mechanics is important
include
photonics,
mesoscopic engineering, and medical diagnostics. It is therefore not surprising that
quantum is b
e
ing taught more often to more students starting as early as high school. However, quantum
mechanics
is difficult and abstract. Furthermore, understanding many classical concepts is prerequisite to a
meaningful understanding of quantum systems.
I
n this paper, we describe research results of two examples of the influence of student
understanding of classical concepts when learning quantum mechanics. For each example, we describe
difficulties students have in the classical regime and how these difficulties seem to impair student learning
of quantum concepts. We briefly discuss how these difficulties can be addressed.
Obviously the examples described in this paper are not intended to be exhaustive. Instead, we have
two objectives. The first is to highlight the importance of having a strong conceptual base when learning
more advanced topics in physics. The second is to illustrate the importance of continuously and
systematically probing student learning by using the tools of physics education research.
PHYSICS EDUCATION RESEARCH
The results described in this paper come from systematic investigations of how
student learn
physics. Research tools include classroom observations, free response and multiple-choice diagnostics,
videotaped and transcribed individual demonstration interviews, and many other methods. Due to space
limitations, we will only cite the results of a few studies and provide references where further details can be
found. An overview of the field of physics education research can be found in a recent issue of
Physics
Today
(
Redish &
Steinberg, 1999).
FROM PHYSICAL OPTICS TO PHOTONS
Before studying modern physics and quantum mechanics, students first typically study mechanical
waves and then physical optics. The reasons behind this are logical. The wave properties of matter, wave-
particle duality, and atomic spectroscopy make no sense if one does not understand superposition, wave
representations, and diffraction. In this section, we describe how student difficulties interpreting the wave
nature of light can propagate when they are introduced to the concept of a photon.
Students struggle with learning physical
optics ...
Difficulties that students have learning models of light have been reported (
Ambrose
et al., 1999).
Clearly, most students do not develop a reasonable wave model for the behavior of light. For example,
about half of the students who had just completed the introductory calculus-based physics course believed
that the amplitude of a light wave is spatial (as opposed to electromagnetic). Many students speak of waves
"fitting" or "not fitting" through a narrow slit while trying to describe diffraction. Fig. 1a shows a student
response in an interview when asked to describe the behavior of light passing through a narrow slit. His
response was typical.
...
and then they study photons
When studying more advanced topics in physics that follow physical optics, students appear to
take with them difficulties such as the one exemplified in Fig. 1a. This can lead to misinterpretations of,
among other things, the quantum nature of light (
Steinberg,
Oberem, & McDermott, 1996). Instead of
correcting the way they think about light, many students incorporate the new physics they are learning into
their faulty model. Many introductory students think of the amplitude of light as a spatial quantity. It
appears that these students then simply have photons moving along sinusoidal paths when they learn about
42
the particle nature of light. Fig. 1b shows an example of how a student who had just studied about photons
describes the behavior of light as it passes through a slit. Other students had photons traveling up and down
along the sinusoidal path.
FROM CIRCUITS TO BAND DIAGRAMS
In teaching elementary quantum mechanics, band diagrams, and the fascinating
properties of
semiconductor devices, instructors typically assume that their students have a reasonable model of
conductivity. After all, what sense can a MOSFET make if students do not have a functional understanding
of current and voltage? In this section, we describe some of the difficulties that many students have when
they study current and voltage in a college physics class and how these difficulties can limit understanding
of students who are studying more advanced models for conductivity.
Students struggle with learning current and
voltage ...
"electric flux"
"magnetic part"
For slit width >
λ
λ
: Geometrical optics applies:
"The waves are still making it though the slit."
For slit width >
λ
λ
: A diffraction pattern occurs
:
The magnetic part will not "be affected" but the
electric part "will be affected ... [the slit]
knocks
it out of whack."
(
a)
"part of the amplitude
is cut off"
(
b)
Figure 1. Typical student descriptions of light passing through a narrow slit: (a)
Diagram and explanation given by
a student who just completed introductory calculus-
based physics. (b) Diagram drawn by student who just studied the photon.
Figure 2. Part of an examination question given to introductory calculus-based
physics students after they had finished studying dc circuits. Only 16% of the 94
students in the class gave the correct ranking (A=D=E>B=C).
A
B
C
D
E
EMF
Rank the brightness of the five identical bulbs shown in the
diagram. Explain your reasoning.
43
McDermott &
Shaffer (1992) have documented difficulties students have when they study current
and voltage in college physics. They found that many students do not know what a complete circuit is, do
not have a model for current as a flow, and do not have a functional understanding of voltage. At the
University of Maryland, in an introductory calculus-based physics class dominated by sophomore
engineering
majors (many of them in electrical engineering) we reproduced these findings. For example, in
a class of 94 students that had just studied dc circuits, equivalent resistance, Ohm's law, and
Kirchoff's
laws, only 16% correctly answered the final examination question shown in Fig. 2. Student difficulties,
such as the current being "used up" in bulb B before getting for bulb C, were essentially the same as those
described by McDermott &
Shaffer.
...
and then they study semiconductor physics
At the University of Maryland, we are exploring student understanding of m
icroscopic models for
conductivity after having taken several more advanced courses, including intermediate undergraduate
electrical engineering courses. After all, it is often assumed that students overcome their difficulties as they
revisit the same concepts in progressively more advanced contexts. We decided to administer one
-on
-one
interviews using the protocol outlined briefly in Fig. 3. We thought this was a reasonable set of questions
for this set of students. Unfortunately, of the 12 or so students we have interviewed so far, none of them
have had a model for current suitable for accounting for the differences between conductors, insulators, and
semiconductors
. For example, about half of the students described conductivity similar to the student in
Fig. 4. In explaining conduction in a wire, this student said that there is a "minimum voltage" necessary for
there to be any current. (Note the qualitative similarities here with electrons being removed from a metal
via the photoelectric effect.) Unfortunately, with this model, current first "kicks in" when there is a finite
voltage and there is no mechanism to account for semiconductor physics. Other students describe
differences in conductivity by the size of physical constrictions the electrons move through at the atomic
level. Very few of the students interviewed invoked any kind of a drift velocity mechanism, charge carrier
density, or band diagram. This is of particular concern since many of these students had studied how diodes
and transistors work in great detail.
RESEARCH BASED CURRICULUM DEVELOPMENT
At the introductory level, physics education research has guided the development of curriculum
and instructional strategies with encouraging results (e.g.
Redish &
Steinberg, 1999). For example, having
students work through materials where they can build their own models, strengthen their conceptual
understanding, and exercise their reasoning skills has yielded marked improvement in instruction in both
physical optics (
Ambrose et al., 1999) and simple circuits (
Shaffer & McDermott, 1992). We are now using
this same paradigm in developing materials at the quantum level. Our preliminary results are encouraging
(e.g.,
Steinberg &
Oberem, 1999).
Figure 3. Brief outline of interview protocol administered to students who had finished
introductory calculus-based physics and at least one more advanced course in physics
or electrical engineering. In
qbout
a dozen 45-minute interview, we often have not
gotten past question 3 and have never gotten to question 6.
1.
Describe the behavior of resistor wired to battery (real circuit elements
in hand).
2.
Contrast the behavior in the resistor and in the wire.
3.
Contrast the behavior when the resistor is replaced with one of a
different value. Explain why the 2 behave differently.
4.
Repeat for insulator.
5.
Repeat for piece of semiconductor.
6.
Repeat for diode.
7.
Repeat for MOSFET. (Have one in hand and let student do what s/he
wants with the three leads.)
44
CONCLUSIONS
Clearly there are many good reasons to teach quantu
m mechanics to a broad audience. However,
the goal is not merely to turn this instruction into a vocabulary lesson or a mathematics exercise for the
students. Instead, it is possible to have instruction in quantum mechanics be much more meaningful. In this
paper, we have tried to show how recognizing what students understand about relevant classical concepts
and how they build an understanding of quantum ideas can inform instruction.
ACKNOWLEDGEMENTS
This work has been funded in part by the National Scie
nce Foundation (DUE 9652877) and the
Department of Education (FIPSE grant 116B70186). We thank Dean Zollman for his work setting up this
important session.
REFERENCES
Ambrose,
B.S.,
Shaffer, P.S.,
Steinberg, R.N., & McDermott, L.C. (1999). An investigation of
student understanding of single-slit diffraction and double-slit interference. American Journal of Physics
67, 146-155.
McDermott, L.C., &
Shaffer, P.S., "Research as a guide for curriculum development
: An example
from introductory electricity. Part I
: Investigation of student understanding," American Journal of Physics
60, 994-1003 (1992); erratum,
ibid.
61,
81 (1993).
Redish
, E.F. &
Steinberg
, R.N.
(
1999). Teaching physics: Figuring out what works.
Physics
Today, 52(1), 24-30.
Shaffer, P.S., & McDermott, L.C., "Research as a guide for curriculum development: An example
from introductory electricity. Part II: Design of an instructional strategy," American Journal of Physics 60,
1003-1013 (1992).
Steinberg
, R.N.,
Oberem
,
G.E.
, & McDermott, L.C. (1996).
Development of a computer-based
tutorial on the photoelectric effect.
American Journal of Physics,
64, 1370-1379.
Steinberg, R.N., &
Oberem,
G.E., (1999). Research based instructional software in modern
physics.
To be published.
e
-
e
-
e
-
a minimum voltage is
needed to remove
electrons from atoms so
that they can participate
in conduction
Figure 4.
Typical student explanation about conductivity in the wire. This student
explains that at some "minimum voltage" the electron is removed from the atom and
contributes to conduction. The student was notable to contrast the behavior of
conductors, insulators, and semiconductors using his model.35
Fig. 3: Electron diffraction.
The inverse wavelength (assigned to the pattern on the screen) plotted against
the electrons'
momentum
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
2,4
2,6
2,8
3
3,2
3,4
3,6
3,2
3,4
3,6
3,8
4
4,2
4,4
4,6
4,8
5
5,2
5,4
Momentum p in 10
-23
kg · m/s
1/ in 10
10
· 1/m
λ
Intensity
distribution
on
the
screen
Electrons
S1
S2
Fig. 4: Double slit experiment with electrons
There are
interferences! This looks like Newton's rings.
Electrons obviously move wavelike.
One particle activates the next.
(
Counterargument of another student:
Actually, the tube is evacuated.)
If the electrons are not waves before hitting the
crystal they couldn't cause
interferences.
Electrons and light are different things. For
me, these rings cannot be explained.
It is plausible to assign a wavelength
λ
to these
rings. It is not necessary to speak of electron
waves. The variation of the accelerating potential
difference in the tube results in the De Broglie relation p = h/
λ
, p is momentum of the electrons treated
classically before hitting the crystal,
λ
is wavelength related to the luminous phenomenon in the electron
tube, if being interpreted as an interference pattern (Fig. 3).
The 'double-slit' experiment with electrons cannot be demonstrated in reality. There are several good
films available.
High intensity: the distribution of the intensity is similar to interference patterns with light. Therefore one
can conclude: electrons are not
classical particles.
Low intensity:
statistically distributed singular
events. Therefore electrons cannot be
described as a wave. Electrons are
quantum objects (Fig. 4).
An interesting experiment with
classical particles is a part of the
teaching unit: Thousands of small
pellets pass a double slit and fall into
segments where the distribution can
be observed (Fig. 5). Students'
statements show that they now
attribute
STUDENTS' STATEMENT
S PRIOR TO THE EXPERIMENT
I expect an interference structure.
If this model is correct, then an
interference pattern must appear.
•
Actually, I expect an
interference pattern. Why
otherwise one should have
constructed this model?
Actually, electrons are particles
,
therefore these particles should be
36
comparable with
electrons.the electrons'
behaviour also to classical particles. For them, electrons are still
classical particles, so pellets have to have the same
behaviour.
EVALUATION OF THE TEACHING UNIT
The teaching unit was tested in a total of eleven physics courses of several high schools in Berlin. It was
a central decision for the evaluation process to choose a multidimensional
approach which allowed to trace
a single student's learning processes as well as learning outcomes of groups. Therefore, research followed
the steps below:
A questionnaire was given to students in all 11 courses, and interviews were carried out on two courses
before the start of the lessons to find out what conceptions the students then held.
Video recordings were taken of all 32 lessons in six courses in order to discover
correlations between
students' conceptions and their answers given during the lessons, and to obtain additional verifications for
the
conceptions which had been collected from the students.
Five weeks after the end of the teaching unit a second questionnaire was given. From these data the
conceptions which students held after the end of the lessons were worked out. With the help for students'
interviews from three courses we wanted to make sure the information gathered in this way was correct.
We gave the same questionnaire to the students before
and after the teaching unit in 14 further courses (control
group), which introduced quantum physics in the
conventional way of the Berlin syllabus. This was done to
help us correctly value the conceptual patterns shown in
the courses in which the new teaching concept had been
tested.
All questions were assigned to the range of topics which
make up the
subject-matter for teaching quantum physics
in school: light, atom-electron, particle-body, and
students' ideas on the philosophy of science. The
questions themselves were different in type: open
questions, e.g. 'What really is light?
'; word-pair
associations, e.g. 'electron-real body'; drawings, e.g.
'What do you think a real hydrogen atom looks like?
In total, written statements were gathered from 270
students of
which just under 150 belonged to the test group
(taught through the new teaching unit) and more than 120
belonged to the control group (taught along customary
lines). The verbal answers given by the students during the
teaching unit and in the interviews were transcribed from the videotapes. The transcripts also include notes
on students' play of features and gestures as remarks.
The results of the research consisted of four steps:
Overview of students' conceptions before the beginning of the teaching unit.
Comparison of students' conceptions of the two groups (test and control group) five weeks after the
lessons.
Perceptions in the process of change: a comparison of students' conceptions before and after the teaching
unit (whole data of all students).
Design of ideas' networks from all data of one student from the beginning of the teaching unit up to the
second questionnaire and interview.
In the following, some examples will be given for each of the four steps.
STUDENTS' CONCEPTIONS BEFORE THE TEACHING UNIT
One of the items in the questionnaire referred to the topic 'atom-electron'. Some of the open answers
given by the students before the beginning of the actual lessons about the introduction to quantum physics
were:
...
because the electron is tightly placed on an atomic shell, i.e., there is a distance between the shell and
the nucleus so that the electron cannot get to the nucleus.
Fig. 5: Double slit experiment with
classical particles
37
Fig. 6: Change of students' conceptions of an atom's stability.
before...
five
weeks
after...
... the teaching
unit
control - group: 92
students
21%
9%
64%
7%
13%
10%
60%
"CIRCLE"
8
44
7
6
4
4
4
2
4
1
"CHARGE"
"SHELL"
"LOC."
test - group: 96
students
1%
1
2
2
5
3
2
53
11
8
"CIRCLE"
"CHARGE"
"SHELL"
"LOC."
69%
18%
7%
22%
4%
68%
The
electron is acted upon by the centrifugal force and the attractive force of the atom. Both forces are
in equilibrium (Bohr's atomic model).
The electron is separated from the nucleus by its high velocity (centrifugal force).
As a result of the high angular velocity of the electrons, the resulting centrifugal force prevents the
electron from falling into the nucleus under the influence of the attractive force.
Because the charges of electrons and protons neutralize each other.
The electron is negatively charged while the nucleus is positively charged. Again, the electron is subject
to a kind of centrifugal
force which keeps it in its orbit. Therefore they rather repel each other.
Electrons are fixed in their shells.
From these answers, typical patterns could be constructed which show students' conceptions:
Circle
(circular orbit): conceptions of
electrons which fly round the nucleus with (high) velocity in fixed,
prescribed orbits. In this conception the centrifugal force and the Coulomb (electric) force are brought into
equilibrium. The students use their experience with roundabouts first to explain the movement of the
planet, and then second to explain the process in atomic shells, without regard to reference systems (63% of
240 students in both groups).
Charge
: students have a fixed conception of the repulsion between charges. They often explain the
properties of charges incorrectly. The charges of both the proton and the electron cause a distance between
the two particles (23% of 240 students in both groups).
Shell
: conception of a firm casing (shell, ball) on which the electrons are fixed or move (8% of 240
students in both groups).
In conclusion it can be noticed that the students already possessed a fixed idea of an electron in an atom,
being strongly based on a mechanistic conception. The question is
, therefore, whether normal teaching,
including the treatment of Bohr's atomic model as an explanation of the
quantization of energy levels, does
imply the reinforcement of already existing thought patterns.
CHANGE OF STUDENTS' CONCEPTIONS
A comparison of the conceptions of the students from the two groups (test and control group) after the
lessons demonstrates that different changes in conceptions have taken place. First of all, another conceptual
pattern could be constructed from
students' answers:
Loc. (localization energy)
: the
stability of atoms was regarded by the
students as connected with the
Heisenberg uncertainty principle.
According to this conception, the mere
restriction of space results in a rise of the
kinetic energy of the electrons, the loci
of which are subjected to a statistical
distribution. At the same time the
students dispensed with statements about
singe electrons which they thought of as
inconceivable.
In Fig. 6 the changes in students'
conceptions concerning the stability of
an atom are given.
Within the range of topics discusses
here, a clear dependency on the teaching
experienced by the students can be observed: 68% of the students in the test group oriented themselves
toward the conception of localization energy
(Loc.)
while the students of the control group persisted in the
conception of
circle
and
shell
.
38
Fig.7: Comparison of conceptual changes between test and control group.
.
control-group: 108 students test-group: 116 students
71%
6%
27%
27%
2%
47%
0%
20%
none
little
satisfactory
complete
SUMMARY OF THE EVALUATION
The example given illustrates the trend of the results of the investigation.
A teaching approach, for
example like the one introduced here, which, from the outset, considers possible conceptions of students in
detail and consciously provides room for these conceptions to develop in class, will achieve an increased
cognitive conflict situation which will then, in turn, lead the students to grapple with the subject. In this
way, the students became conscious of their own conceptions and began to question them. The students
became conscious of their own conceptions and began to question them. The results of the control group
pointed to an incorporation of the 'new' phenomena into the 'old' mechanistic ideas. Here, the different
ideas in quantum physics were merely acquired verbally and were forgotten again afterwards. This
statement is supported by
Fig. 7. Here, for all items
of the various topic areas,
the conceptual changes are
rated, summarized, and
reproduced separately for
test group and control
group.
STUDENTS'
NETWORK
STRUCTURES
Students "react to things
on the basis of meanings
which these things have
for them" (
Blumer 1976,
p. 81
; translation by the
author of the present paper). This approach proceeds from the theory of symbolic
interactionism (adapted
from Mead,
Schütz), according to which, meanings are built up on the basis of a correlation between a
"stock of commonplace knowledge" and "situational experience" (
Schütz/
Luckmann 1979; p. 133;
translation by the author of the present paper).
On the basis of this interaction, a research approach is formulated, which constructs cognitive networks
of students from the interpretation of students' ideas together with their meanings. These networks
themselves, according to this assumption, reflect students' conceptions.
The following figures point out network structures of two students
, both constructed before and after
the lessons. The initial sets of single ideas were deduced from the total data set of all students' answers
before and after the lessons. The single answers show students' main ideas. The ideas themselves are
interconnected through various features demonstrating the connection of meanings (following
Klix 1976,
his adaptation by Norman and
Rumelhart 1975):
R:
represents a relation between general ideas and sub-ideas. Features which form a general
idea can be transferred to the sub-idea (
..is a..).
CM:
typifies characteristic features of an idea through the use of other ideas (
..
heard
..;..
has..).
AM:
typifies active features which characterize an idea (
..can..).
N:
points out that a character of an idea consists in establishing another
idea (shown with
..).
ZO:
illustrates a relation between two ideas without itself being a characteristic feature (
..will
be assigned..).
TI:
signifies partial identity of two ideas (
..is like..).
WI:
contradiction: no further relation between both ideas (
..it cannot be..)
Fig. 8 and 9 show the networks of a student from the group which throughout the lessons received an
introduction to quantum mechanics according to the new concept (see Berg et al. 1989); whereas Fig. 10
show the networks of a student who was enrolled in a course which followed the regular Berlin syllabus.
In Fig. 8 and 9 the two networks give an impression of the development of ideas and their meanings. The
students was able to change his basic ideas in atomic-physics (see Fig. 8) to the new idea of the quantum
(see Fig. 9). For him the quantum is something new without a relation to the classical wave or real particle.
In the other case (see Fig. 10) the student was fitting the new ideas into the old network. The photon
39
became a real particle, and the electron is still on a fixed prescribed orbit around the nucleus now under
oscillation.
R
TI
N
ZO
R
ZO
R
CM
CM
R
TI
CM
40
REFERENCES:
Berg, A.,
Fischler
, H.,
Lichtfeldt
, M.,
Nitzsche
, M., Richter, B., &
Walther
, F. (1989).
Einführung in die
Quantenphysik.
Ein
Unterrichtsvorschlag
für
Grund
-
und
Leistungskurse
.
Pädagogisches
Zentrum
Berlin.
Blumer
, H. (1976).
Der
methodologische
Standort
des
symbolischen
Interaktionismus
. In
Arbeitsgruppe
Bielefelder
Soziologen (Eds.),
Alltagswissen,
Interaktion
und
gesellschaftliche
Wirklichkeit. Bd. 1:
Symbolischer
Interaktionismus
und
Ethnomethodologie
(pp. 80-176). Hamburg:
Rowohlt.
Brachner
, A., &
Fichtner
, R. (1974).
Quantenmechanik
im
Unterricht
.
Physik
und
Didaktik
, Vol. 2, part I
(pp. 81-94), part II (pp. 249-275).
Feynman
,
R.P.
, Leighton, R.B., & Sands, M. (1965). Lectures on Physics, Vol. III,
Quantum Mechanics
.
London: Addison-Wesley.
Klix
, F. (1976).
Über
Grundstrukturen
und
Funktionsprinzipien
kognitiver
Prozesse
. In F.
Klix (Ed.),
Psychologische
Beiträge
zur
Analyse
kognitiver
Prozesse
. Berlin:
Deutscher
Verlag
der
Wissenschaften.
Norman,
D.A.
, &
Rumelhart
,
D.E.
(1975).
Explorations in Cognition. San Francisco: Freeman and
Company.
Schütz
, A., &
Luckmann
, T. (1979).
Strukturen
der
Lebenswelt
. Bd. 1, Frankfurt:
Luchterhand.
Squires, E. (1986).
The Mystery of the Quantum World. Bristol: Adam
Hilger.
41
THE INFLUENCE OF STUDENT UNDERSTANDING OF CLASSICAL
PHYSICS WHEN LEARNING QUANTUM MECHANICS
Richard
Steinberg, Michael C.
Wittmann, Lei
Bao, and Edward F.
Redish
Department of Physics, University of Maryland, College Park, MD, 20742-4111
[email protected], [email protected]
[email protected]
,
[email protected]
INTRODUCTION
Understanding quantum mechanics is of gro
w
ing importance, not just to future physicists, but to
future engineers, chemists, and biologists. Fields in which understanding quantum mechanics is important
include
photonics,
mesoscopic engineering, and medical diagnostics. It is therefore not surprising that
quantum is b
e
ing taught more often to more students starting as early as high school. However, quantum
mechanics
is difficult and abstract. Furthermore, understanding many classical concepts is prerequisite to a
meaningful understanding of quantum systems.
I
n this paper, we describe research results of two examples of the influence of student
understanding of classical concepts when learning quantum mechanics. For each example, we describe
difficulties students have in the classical regime and how these difficulties seem to impair student learning
of quantum concepts. We briefly discuss how these difficulties can be addressed.
Obviously the examples described in this paper are not intended to be exhaustive. Instead, we have
two objectives. The first is to highlight the importance of having a strong conceptual base when learning
more advanced topics in physics. The second is to illustrate the importance of continuously and
systematically probing student learning by using the tools of physics education research.
PHYSICS EDUCATION RESEARCH
The results described in this paper come from systematic investigations of how
student learn
physics. Research tools include classroom observations, free response and multiple-choice diagnostics,
videotaped and transcribed individual demonstration interviews, and many other methods. Due to space
limitations, we will only cite the results of a few studies and provide references where further details can be
found. An overview of the field of physics education research can be found in a recent issue of
Physics
Today
(
Redish &
Steinberg, 1999).
FROM PHYSICAL OPTICS TO PHOTONS
Before studying modern physics and quantum mechanics, students first typically study mechanical
waves and then physical optics. The reasons behind this are logical. The wave properties of matter, wave-
particle duality, and atomic spectroscopy make no sense if one does not understand superposition, wave
representations, and diffraction. In this section, we describe how student difficulties interpreting the wave
nature of light can propagate when they are introduced to the concept of a photon.
Students struggle with learning physical
optics ...
Difficulties that students have learning models of light have been reported (
Ambrose
et al., 1999).
Clearly, most students do not develop a reasonable wave model for the behavior of light. For example,
about half of the students who had just completed the introductory calculus-based physics course believed
that the amplitude of a light wave is spatial (as opposed to electromagnetic). Many students speak of waves
"fitting" or "not fitting" through a narrow slit while trying to describe diffraction. Fig. 1a shows a student
response in an interview when asked to describe the behavior of light passing through a narrow slit. His
response was typical.
...
and then they study photons
When studying more advanced topics in physics that follow physical optics, students appear to
take with them difficulties such as the one exemplified in Fig. 1a. This can lead to misinterpretations of,
among other things, the quantum nature of light (
Steinberg,
Oberem, & McDermott, 1996). Instead of
correcting the way they think about light, many students incorporate the new physics they are learning into
their faulty model. Many introductory students think of the amplitude of light as a spatial quantity. It
appears that these students then simply have photons moving along sinusoidal paths when they learn about
42
the particle nature of light. Fig. 1b shows an example of how a student who had just studied about photons
describes the behavior of light as it passes through a slit. Other students had photons traveling up and down
along the sinusoidal path.
FROM CIRCUITS TO BAND DIAGRAMS
In teaching elementary quantum mechanics, band diagrams, and the fascinating
properties of
semiconductor devices, instructors typically assume that their students have a reasonable model of
conductivity. After all, what sense can a MOSFET make if students do not have a functional understanding
of current and voltage? In this section, we describe some of the difficulties that many students have when
they study current and voltage in a college physics class and how these difficulties can limit understanding
of students who are studying more advanced models for conductivity.
Students struggle with learning current and
voltage ...
"electric flux"
"magnetic part"
For slit width >
λ
λ
: Geometrical optics applies:
"The waves are still making it though the slit."
For slit width >
λ
λ
: A diffraction pattern occurs
:
The magnetic part will not "be affected" but the
electric part "will be affected ... [the slit]
knocks
it out of whack."
(
a)
"part of the amplitude
is cut off"
(
b)
Figure 1. Typical student descriptions of light passing through a narrow slit: (a)
Diagram and explanation given by
a student who just completed introductory calculus-
based physics. (b) Diagram drawn by student who just studied the photon.
Figure 2. Part of an examination question given to introductory calculus-based
physics students after they had finished studying dc circuits. Only 16% of the 94
students in the class gave the correct ranking (A=D=E>B=C).
A
B
C
D
E
EMF
Rank the brightness of the five identical bulbs shown in the
diagram. Explain your reasoning.
43
McDermott &
Shaffer (1992) have documented difficulties students have when they study current
and voltage in college physics. They found that many students do not know what a complete circuit is, do
not have a model for current as a flow, and do not have a functional understanding of voltage. At the
University of Maryland, in an introductory calculus-based physics class dominated by sophomore
engineering
majors (many of them in electrical engineering) we reproduced these findings. For example, in
a class of 94 students that had just studied dc circuits, equivalent resistance, Ohm's law, and
Kirchoff's
laws, only 16% correctly answered the final examination question shown in Fig. 2. Student difficulties,
such as the current being "used up" in bulb B before getting for bulb C, were essentially the same as those
described by McDermott &
Shaffer.
...
and then they study semiconductor physics
At the University of Maryland, we are exploring student understanding of m
icroscopic models for
conductivity after having taken several more advanced courses, including intermediate undergraduate
electrical engineering courses. After all, it is often assumed that students overcome their difficulties as they
revisit the same concepts in progressively more advanced contexts. We decided to administer one
-on
-one
interviews using the protocol outlined briefly in Fig. 3. We thought this was a reasonable set of questions
for this set of students. Unfortunately, of the 12 or so students we have interviewed so far, none of them
have had a model for current suitable for accounting for the differences between conductors, insulators, and
semiconductors
. For example, about half of the students described conductivity similar to the student in
Fig. 4. In explaining conduction in a wire, this student said that there is a "minimum voltage" necessary for
there to be any current. (Note the qualitative similarities here with electrons being removed from a metal
via the photoelectric effect.) Unfortunately, with this model, current first "kicks in" when there is a finite
voltage and there is no mechanism to account for semiconductor physics. Other students describe
differences in conductivity by the size of physical constrictions the electrons move through at the atomic
level. Very few of the students interviewed invoked any kind of a drift velocity mechanism, charge carrier
density, or band diagram. This is of particular concern since many of these students had studied how diodes
and transistors work in great detail.
RESEARCH BASED CURRICULUM DEVELOPMENT
At the introductory level, physics education research has guided the development of curriculum
and instructional strategies with encouraging results (e.g.
Redish &
Steinberg, 1999). For example, having
students work through materials where they can build their own models, strengthen their conceptual
understanding, and exercise their reasoning skills has yielded marked improvement in instruction in both
physical optics (
Ambrose et al., 1999) and simple circuits (
Shaffer & McDermott, 1992). We are now using
this same paradigm in developing materials at the quantum level. Our preliminary results are encouraging
(e.g.,
Steinberg &
Oberem, 1999).
Figure 3. Brief outline of interview protocol administered to students who had finished
introductory calculus-based physics and at least one more advanced course in physics
or electrical engineering. In
qbout
a dozen 45-minute interview, we often have not
gotten past question 3 and have never gotten to question 6.
1.
Describe the behavior of resistor wired to battery (real circuit elements
in hand).
2.
Contrast the behavior in the resistor and in the wire.
3.
Contrast the behavior when the resistor is replaced with one of a
different value. Explain why the 2 behave differently.
4.
Repeat for insulator.
5.
Repeat for piece of semiconductor.
6.
Repeat for diode.
7.
Repeat for MOSFET. (Have one in hand and let student do what s/he
wants with the three leads.)
44
CONCLUSIONS
Clearly there are many good reasons to teach quantu
m mechanics to a broad audience. However,
the goal is not merely to turn this instruction into a vocabulary lesson or a mathematics exercise for the
students. Instead, it is possible to have instruction in quantum mechanics be much more meaningful. In this
paper, we have tried to show how recognizing what students understand about relevant classical concepts
and how they build an understanding of quantum ideas can inform instruction.
ACKNOWLEDGEMENTS
This work has been funded in part by the National Scie
nce Foundation (DUE 9652877) and the
Department of Education (FIPSE grant 116B70186). We thank Dean Zollman for his work setting up this
important session.
REFERENCES
Ambrose,
B.S.,
Shaffer, P.S.,
Steinberg, R.N., & McDermott, L.C. (1999). An investigation of
student understanding of single-slit diffraction and double-slit interference. American Journal of Physics
67, 146-155.
McDermott, L.C., &
Shaffer, P.S., "Research as a guide for curriculum development
: An example
from introductory electricity. Part I
: Investigation of student understanding," American Journal of Physics
60, 994-1003 (1992); erratum,
ibid.
61,
81 (1993).
Redish
, E.F. &
Steinberg
, R.N.
(
1999). Teaching physics: Figuring out what works.
Physics
Today, 52(1), 24-30.
Shaffer, P.S., & McDermott, L.C., "Research as a guide for curriculum development: An example
from introductory electricity. Part II: Design of an instructional strategy," American Journal of Physics 60,
1003-1013 (1992).
Steinberg
, R.N.,
Oberem
,
G.E.
, & McDermott, L.C. (1996).
Development of a computer-based
tutorial on the photoelectric effect.
American Journal of Physics,
64, 1370-1379.
Steinberg, R.N., &
Oberem,
G.E., (1999). Research based instructional software in modern
physics.
To be published.
e
-
e
-
e
-
a minimum voltage is
needed to remove
electrons from atoms so
that they can participate
in conduction
Figure 4.
Typical student explanation about conductivity in the wire. This student
explains that at some "minimum voltage" the electron is removed from the atom and
contributes to conduction. The student was notable to contrast the behavior of
conductors, insulators, and semiconductors using his model.
35