Download What General Chemistry Students Know (and Don`t Know) About

Students’ Understanding of
Quantum Concepts During
Their First Introduction in a
General Chemistry Course
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
1
Exploring Quantum Concepts in
Chemistry:
The Team
Peter Garik (presenting), Boston University
([email protected])
Luciana Garbayo
School of Education
Alan Crosby, Dan Dill, Alexander Golger, Morton
Hoffman
Department of Chemistry
Peter Carr
Science and Mathematics Education Center
Boston University
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
2
Exploring Quantum Concepts in
Chemistry
This project is funded by the U.S
Department of Education’s
Fund for the Improvement of Post
Secondary Education (FIPSE)
(Award No. P116B020856.)
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
3
Quantum Concepts in Chemistry
The objectives of our FIPSE project are
• to find ways to introduce quantum
concepts into the chemistry curriculum;
• to design software that will support the
teaching of quantum concepts; and,
• to evaluate the success of our software
and curricular activities in supporting
student learning of quantum concepts.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
4
Quantum Concepts in Chemistry
Why teach quantum concepts at an early
stage in the chemistry curriculum?
The epistemology of a mature science relies
upon foundational models for its research
program.
Such models provide a unifying perspective
on the physical world and support the best
insights and reasoning that we can
currently achieve.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
5
Quantum Concepts in Chemistry
For cosmology, it is the inflationary theory of
the universe.
For geology, it is plate tectonics.
For biology, it is Darwinian evolution.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
6
Quantum Concepts in Chemistry
For chemistry, one of the foundational models is
unarguably the quantum theory of atomic
structure and electronic behavior.
The pedagogical issue is where does it belong in
the curriculum?
Quantum concepts appear burdened with
additional abstractions (including mathematics)
that make them first appear forbidding to teach.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
7
Quantum Concepts in Chemistry
We argue that the unifying power of
quantum concepts is so great, and their
utilization for modern chemistry so
extensive, that finding ways to
successfully introduce them at an early
point in chemistry education is our
obligation to the students.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
8
Quantum Concepts in Chemistry
What are quantum concepts in chemistry?
The principal quantum topics in chemistry
are:
1) The description of electrons and how
they behave in the presence of other
charges.
2) The description of the interaction of
radiation with matter, and primarily with
electrons.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
9
Quantum Concepts in Chemistry
Historically quantum concepts grew out of
analogies to electromagnetic theory. Since
the interaction of radiation with matter is a
key concept in chemistry (spectroscopy), it
is traditionally taught.
The properties of electromagnetic waves
provide an early access point for what we
refer to as “Quantum Readiness.”
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
10
Quantum Concepts in Chemistry
•
•
What is a wave?
What is an electromagnetic wave?
– Is there an associated electric field?
– Is there an associated magnetic field?
•
•
What is the relationship between
amplitude and intensity?
What is constructive and destructive
interference?
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
11
Quantum Concepts in Chemistry
• How does the phase of a wave vary with
time and space?
• How does a light wave interact with a
charged particle?
• What is a photon?
• How do charged particles interact?
Students prepared with these concepts
should have analogies for understanding
quantum phenomena.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
12
Quantum Concepts in Chemistry
What are the quantum concepts that we
would like students to master?
• The delocalization of the electron and its
description by a probability amplitude.
• The quantization of energy levels.
• The pairing of a wave function with an
energy.
• Constructive and destructive interference.
• The Pauli Exclusion Principle.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
13
Quantum Concepts in Chemistry
• The transition in energy levels associated
with absorption and emission of radiation.
•The geometry of atomic and molecular
orbitals.
• The atomic structure that arises from the
Aufbau Principle.
• The molecular structure that arises from
bonding orbitals and hybridization.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
14
Evaluating Students’ Conceptual
Understanding of Quantum
Concepts
As a first step to determining how students
learn quantum concepts, we engaged in
a qualitative research project.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
15
Design and Procedures
1) We interviewed students during the
outset of their instruction on quantum
concepts.
2) Students were selected from a pool of
volunteers taking the honors general
chemistry course at a research
university.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
16
Design and Procedures
• The students were all freshman in their
second semester.
• This was an elite group of students: they
had passed a placement test to enroll in
the honors course for science majors.
• Most students were chemistry or science
concentrators.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
17
Design and Procedures
• Students were selected for the interviews to
produce an even grade distribution.
• Each interview was conducted based on the
same set of questions (an interview guide
approach).
• To the extent possible, the interviews were
clinical in nature – in a Piagetian fashion. The
interviewers flexibly probed the individual
student’s responses to elicit deeply held
convictions.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
18
Design and Procedures
• As an aid to better elicit explanations from the
participants, experiments were done during the
interview (double slit interference pattern,
hydrodgen discharge tube with grating, strong
magnets).
• In conducting the interviews early in the
students’ instruction, an assumption was made
that students would have had exposure to
quantum concepts in their high school chemistry
courses.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
19
What is waving?
We asked students to answer the questions:
1. What is light?
2. It is said that light propagates as a wave.
What is it that is waving?
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
20
What is waving?
Student2’s response: It’s energy.
• S: Light, as far as I know, is made up of photons, and photons
are little packets of energy without mass. That's the key part
about photons. They move in waves, defined by wave
functions. They're just perceptions of light you and I are seeing
now is what our eyes are perceiving and then transferring into
what our brain can tell us what we're seeing. That’s why, people
who are colorblind, their perception is different than yours and
mine.
• P: What is electric and what is magnetic about electromagnetic
radiation?
• S: Well, anything that moves in a wave produces a magnetic
field, I want to say. What is electric? It's just energy that’s
moving, and as the energy moves it creates a corresponding
magnetic wave.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
21
What is waving?
Student3’s response: The sinusoidal wave is a trajectory.
P: Now you say that light can be either considered as
particles or waves. How does the particle of light travel?
S: In a sinusoidal curve.
P: Could you, perhaps, draw for me what you mean by
that?
S: Sure. …Something, I guess you'd say… I mean, I
guess, on an xy axis, I assume starts off and it just keeps
traveling like that.
P: Okay, could you label the axes?
S: Sure.
P: Okay, so y and x and, so, this is, then, a trajectory?
S: This is the amplitude.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
22
What is waving?
(Student3 continues)
P: Oh, amplitude, okay.
S: This is the amplitude, so I guess I could just label that
amplitude.
P: Amplitude of what?
S: Amplitude of the wave… Of the particle in space,
traveling up and down.
P: The amplitude of the particle traveling up and down.
Can you draw for me the particle on this? Or…
S: I mean, this would be basically like the trajectory of it, I
would assume. So it would just start off here, I guess, at
the zero, at the origin, and just travel along this path.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
23
What is waving?
Student5: Packet of energy with wave trajectory
P: Okay. You drew a packet of energy. How does that
packet of energy travel?
S: Like a wave does in a transverse version. Like a science
of the wave does.
P: So could you draw for me a trajectory or how this packet
of energy is traveling?
S: So, I mean, if this was the energy, it would travel in…
This is very abstract, I don’t… I can’t think of light
traveling, per se. I only know the diagrams that I was
taught, that I've seen before, and this is how I've seen it.
Like, there's a little packet of energy, and it’s going along
to a source, and you see it. This is the eye. (In the
drawing, the student has drawn an eye at which the
waving trajectory terminates.)
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
24
What is waving?
Student5 continues
P: Okay, so this is the trajectory, then?
S: I think so.
P: Of the packet of energy?
S: Yeah.
P: Is there a name for this packet of energy?
S: Photon.
P: Okay. So this is, then, a photon?
S: Yeah, a packet of energy, this packet of energy
is a photon, and the photon travels in a wavelike motion through space.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
25
What’s waving?
Student5 continued
• Later, in the context of discussing interference of
waves, Student5 said:
• S: I think I should look at the book more closely.
Energy. It has to be energy. I don’t know why,
but I think it’s energy.
• P: And what's along this axis?
• S: Distance.
• P: Distance.
• S: No, no, no. Yeah, it has to be, because this is
wavelength, and wavelength is measured in
meters, so this is distance. Yeah.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
26
What’s waving?
Student6: Confused by amplitude.
P: What are photons?
S: They're particles with light. And transfer momentum like
a particle.
P: Could you perhaps draw for me what you mean by a
wave-like motion?
S: Yeah. A classic sine wave.
P: And this represents the light wave?
S: Mm-hmm.
P: What's on the y-axis and what's on the x-axis?
S: X-axis is position… I think it would be position over here,
too. The real fundamental questions are the ones that
mess you up, but you can solve if you have your
amplitude.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
27
What is waving?
Student6 continues.
P: So this is an amplitude of what?
S: Of distance from the y-axis…or…x-axis, I'm
sorry. And that's squared when there's an
interference. I think we just learned that. I'm not
sure if that's right or not. But…
P: Now this is the wave-like motion of light, but you
said something about photons.
S: Mm-hmm. Let's see, how do I explain that. I'm
not sure if I could really put that into words. No, I
don’t think I know how to answer that.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
28
What is waving?
Superficial Comments
• The students were baffled by how to resolve the
particle-like nature of light with its presumptive
wave-like property.
• They were uniformly unaware that it is the
electric and magnetic fields’ oscillations that give
rise to the wave-like character of light.
• Not a single student could properly label the yaxis of their graph as a field strength.
• Our subsequent studies with junior physical
chemistry students have found this same pattern
of ignorance (pardon, but it’s true) about
radiation.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
29
How does light interact with
matter?
The researchers asked the participants:
If an H-atom is exposed to radiation, what
may happen to the electron?
During the interview, the researcher also
took care to find an opportunity to ask
what the interaction is tetween a charged
particle and radiation.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
30
How does light interact with
matter?
Student2:
P: Would light interact with a charged particle?
S: In theory, yes, because it's energy reacting with energy.
Well, energy reacting with something that's charged.
Since light creates a magnetic field on its own,
something that would have a charged particle would, in
some way, be affected by it.
Student5:
P: Okay. What would happen if that light or that packet of
energy were to go by a charged particle?
S: I don’t know. If it was negatively charged, I assume that
it would be attracted, or repelled. I mean, the charge
would… It would depend on the charge. It would
probably go to it or not go to it, I think. I don’t know.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
31
How does light interact with
matter?
Student3:
Well, from what we just went over lately, which we just started a light
and electromagnetic waves and stuff, I would say it's
electromagnetic radiation. You know, it’s in a wave, and according
to what we've read in our chem books so far, it's actually …Also
consists of…It has particle-like and wave-like characteristics. When
it's alone, it's more particle-like, and when it's a whole group of
photons, it's more wave based, and so it's basically electromagnetic
radiation in space.
P: What is electromagnetic radiation?
S: It's a… It's a…In a sinusoidal curve, just electric, and a magnetic
field.
P: An electric…And what would happen if electromagnetic radiation
was to pass by a charged particle?
S: It would actually…Depending on the particle's behavior to it, it
would…It might actually knock up an electron to a higher energy
level and make it, let it emit a photon, which is a charged particle.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
32
How does light interact with
matter?
Student6:
P: Okay, suppose that I had a charged particle and a light
wave came by my charged particle. What would happen
to the charged particle?
S: …it would transfer momentum to the charged particle.
P: Can you explain to me the mechanism by which this
momentum is transferred?
S: Okay…I'd say that the photon, the photon is a particle
that, without mass, can't transfer momentum and so it
transfers momentum to the charged particle.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
33
How does light interact with
matter?
Student6 continues
P: Photon is without mass, did you say?
S: Mm-hmm, yeah .
P: And so it transfers momentum to the particle.
S: Which is odd, because momentum is mass times
velocity. So that's why quantum is so confusing.
P: So how does the photon then transfer the momentum?
S: I don't really know, actually. I think I understand the
mechanics of what happens. That's what we've been
studying lately. But how it actually transfers it, I don’t
think I really know.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
34
How does light interact with
matter?
Student8: Momentum transfer.
P: When a photon interacts with an electron can you tell me
a little bit more about how it interacts.
S: There is a transfer of energy from the photon packet,
which is the packet of energy, and the light strikes the
electron, the electron gains energy and this energy is
transferred into kinetic energy, or energy of motion. And
in doing so, the electron gains a certain momentum. And
so, in a way when the light hits it, it hits it with a certain
momentum that is transferred into the electron and the
electron behaves with a certain kinetic energy and this
explains the particle-like theory.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
35
How does light interact with
matter?
Superficial Comments
Students do not know the force relationship
between a charged particle and the electric and
magnetic fields of a light wave.
The object view of a photon has completely
occluded the field nature of the light wave.
In the absence of an understanding of the
electromagnetic nature of light, the mechanism
for exchange of energy is reduced to a contact
problem.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
36
Reconciling particle- and wave-like
characters of an electron orbital
We asked the students: “Describe in your own words what
a hydrogen atom is. Please draw a picture that you feel
assists with your description.”
We have conducted interviews with high school students in
the past and categorized their response to this question
(Eshach & Garik 2001). This cohort of students was an
elite group and their responses tended to be more
uniform and restrained. Little remained of the Bohr
planetary model in the descriptions provided by the
students; there was more of an attempt to integrate
particles with a probability density interpretation.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
37
Reconciling particle- and wave-like
characters of an electron orbital
Student2: The speedy electron.
S: It would be, like, nucleus which we knew where it was and it would sort of
be, like, a mess around it, and in that scribbled mess would be where you
find the electron, somewhere in there.
P: Mm-hmm. When you say where we would find it, what do you mean? I
mean, is there a difficulty with finding the electron?
S: Again, to measure the exact location of an electron, I would imagine it would
require something like stopping it from moving, because they're moving at
extremely high speeds and it's…I can't think of a way… There may be, that
I don't know, but I can't think of a simple way to pinpoint the exact location
of an electron over any given period of time. We can't necessarily tag them
and attract them. We can't slow them down enough because I don’t think…
Again, if you stop an electron, I want to say that part of the reason an atom
stays the way it is and keeps its structure is because electrons are moving.
And that if you stop that electron then, you know, what's to keep it from
rushing towards the nucleus, because it's a positive nucleus and negative
electron? What's to stop them from coming together?
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
38
Reconciling particle- and wave-like
characters of an electron orbital
Student2 continues
S: I know there's a strong force and a weak force. We
glazed over that in high school. We really never talked
about what it was or about what it did. That's what kept
the atom from collapsing on itself. But I can’t… Back to
the original question, I can't think of a way that you could
possibly measure exactly where the electron would be.
You can make… You can measure it, the area, because
you would be able to see a charge moving around. I
don't know how to describe this. If you looked at it long
enough, like if you put it on something that would detect
a charge, a change in charge, you would see… You
know, there's obviously a dark spot in the center, where
the positive charge is, and then you would see sort of a
haze around it, because it's moving so fast. You couldn't
take a picture fast enough to see exactly where the
electron is.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
39
Reconciling particle- and wave-like
characters of an electron orbital
There is much to be commended in the
causal reasoning of Student2. Indeed, the
electron does have substantial kinetic
energy.
A product of the student’s reasoning is the
liberated conviction that there must be a
reason why the electron does not collapse
into the nucleus. Even expert quantum
chemists can baffled by this (Eshach &
Garik 2002).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
40
Reconciling particle- and wave-like
characters of an electron orbital
Student3
P: So you say the electron is whizzing around the
proton?
S: Yes. There's mostly empty space between the
nucleus and the trajectory of the electron.
P: Do you think you could show me what trajectory,
roughly, the electron is following?
S: … I couldn't tell you what trajectory it really follows,
but I know it's not circular, per say.
P: Uh-huh. But you said there was empty space…
S: Uh-huh. The probability of finding the electron is,
you know, somewhere in a circular pattern around
the nucleus, there's a probability of finding it there.
There’s… You can't really pinpoint the location of the
electron.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
41
Reconciling particle- and wave-like
characters of an electron orbital
• P: Okay.
• S: But there's a probability of, you know,
finding, like, a 90% probability of finding it in
a certain area around the nucleus.
• P: You're referring to a circular area.
• S: Yes.
• P: It is a two-dimensional?
• S: No. It's a three-dimensional.
• P: Three, so do you mean circular, or would
you…?
• S: Spherical.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
42
Reconciling particle- and wave-like
characters of an electron orbital
From this response we can truly conclude that we
have met the enemy, and it us (Kelly, comic
communication).
The 1s orbital has spherical symmetry. But like all
the other orbitals, it has no shape. We impose
shape upon the orbitals in our diagrams by
emphasizing regions of higher density and their
symmetry. Despite the potential causal pitfalls
(bouncing around inside a sphere), Student3
has done an admirable job of avoiding arriving at
the worst of the misconceptions that can be
imagined.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
43
Findings
Our findings in our pre-instruction interviews are
confirmatory of prior physics education research, and some
echo our earlier findings with high school students (Eshach
and Garik 2001).
• 1) In describing the structure of the hydrogen atom, most
students began with descriptors reminiscent of the Bohr
model (orbit, circular region) but in further conversation
they described and drew pictures with elements of an
electron cloud model, albeit one frequently characterized
by a rapidly moving particle. Such transitional descriptions
of the H-atom agree with the reports of Petri and Niedderer
(1998), Müller and Wiesner (2002), Mashhadi (1996), and
Ireson (2000).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
44
Findings
2) Students knew that both light and electrons
possessed wave-like properties. However, some
believed that this referred to the trajectory of
these as particles in space, a previously
described cognitive attractor (Ireson 2000;
Müller and Wiesner 2002; Olsen 2002).
3) In discussing interference of light waves,
students treated the sinusoidal representations
of the waves as if they were objects, as opposed
to being processes (Wittmann 2001). Ironically, it
would be correct to treat the field as an object,
as opposed to graph representing the value of
the field at a single instant of time.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
45
Findings
• 4) The confusion of students about the
properties of electromagnetic waves is
apparent from the fact that they were
unaware that there is an electric field
component to radiation. This was
uniformly true in our pre-instruction
interviews.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
46
Theoretical Background and
Methodology
• We base our qualitative research
approach of using interviews on the
empirical result from misconceptions
research that, in assessing a population of
students’ understanding of a scientific
phenomenon, the number of different
conceptions observed saturates quickly
(Wanderse, Mintzes and Novak 1994).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
47
Theoretical Background and
Methodology
• For our interpretive work reading the
interviews, we adopted a perspective
based on a dynamics systems approach
proposed by Smith, diSessa and
Roschelle (1993), diSessa and Sherin
(1998), and by Petri and Niedderer (1998).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
48
Theoretical Background and
Methodology
– We look for phenomenological primitives or
cognitive elements/tools that students employ
in order to construct their understanding.
– We expect to find cognitive attractors –
recurring misconceptions expressed by the
students.
– We further expect to find stable cognitive
elements, the deep seated convictions upon
which students rely for their interpretations.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
49
Theoretical Background and
Methodology
To further understand students’ reasoning, we
adopt a modified ontological categorization
scheme following Chi, Slotta and de Leeuw (1994).
They categorize entities as matter (objects),
processes, and mental states. This can be useful.
For example, if a student thinks that a photon is an
“object”, then with it comes a host of associations
such as the photon energy object can collide with
an electron and knocks it to another orbital.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
50
Extending Chi et al’s Ontological
Categories
The ontological categories proposed by Chi
for analyzing science learning are broad
and general.
The underlying epistemology subscribes to
specific scientific model.
But (!), an epistemology must be specified
prior to discussing ontology.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
51
Extending Chi et al’s Ontological
Categories
As written by diSessa and Sherin (1998)
“…the comment is often made that every
observation is theoretically based, as well
as empirical. The notion of pure and
indubitable ‘data’ is no longer regarded as
a serious possibility in the philosophy of
science, nor is it commonly used in the
avowed warrants of professional science.”
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
52
Models of the
Physical Universe
As
realized
by
Aristotelian
Matter
As
realized
by
As
realized
by
As
realized
by
Quantum Mechanics/
Einsteinian Special
and General
Relativities
Biblical basis
Divine
Matter
Processes
Classical
Dynamics
Newton/Maxwell
Divine
Processes
Matter
Fields/
Energy
Proces
ses
Figure 1: Epistemology determines ontological categories and subsequent trees modeled after Chi et al (1994). (N.B.: The States of
Mind ontological category is missing due to lack of space.)
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
53
Quantum and
Relativistic
Model
Energy/
Matter
Macroscopic
Mesoscopic
Elementar
y
Particles
Processes
Elementar
y
Level
Macroscopic
Mesoscopic
Elementar
y
Level
Elementar
y
Fields/
Excitations
Figure 2: Beginning of ontological tree for modern quantum and relativistic science. Note the lateral separation of elementary
particles and elementary field excitations. (N.B.: The States of Mind ontological category is missing due to lack of space.)
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
54
Ontological Categories, Trees, and
Wave-Particle Duality
In order to adequately describe the
ontological categories of classical and
modern physics, we have added the field
ontology to a branch on Chi’s trees.
In terms of these ontological categories, we
can say that students have great difficulty
with quantum concepts because of the
ontological blur between particles and fields.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
55
Duality and Crossing Trees
In Creativity: Shifting Across Ontological
Categories Flexibly, Chi (1997) writes that:
“…it is possible to cognitively change the
representation of a concept through
cognitive operations if the changes do not
require the concept to be re-represented
across branches or trees…”
Wave-Particle duality explicitly requires the
student to move between branches, and
when considering processes, between
trees.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
56
Conclusions
1. Currently, the field ontological category is not
adequately recognized, taught or explained. It
must be added to the curriculum in the form of
an explanation of electric and magnetic fields.
It must be recognized as an object that can be
strictly imaginary and unobservable as for an
orbital.
2. After all this analysis, we return to the waveparticle oxymoron with a new insight into
Born’s creativity and the realization that
students must be informed of the integration
task they face.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
57