Appendix-1: A gedanken PBL-cycle
The 8 ESRs
convene on the Monday, for a first session on a new PBL-task. The four women
and four men have quite different personalities and have also some difference
in English proficiency. Claus, Giuseppi and Mary are quite extrovert, Balazs is
rather shy, Maria is very social but have some difficulties in expressing
herself in English, Gunhild and Ana are rather similar with a good
undergraduate knowledge and soft spoken. Antonio tends to want to dominate the
meetings.
The supervisor
distributes the text and figure describing the situation to address, and asks
Ana to read it out load. Ana reads:
A team has made a set-up to
measure the performance of a silicon detector. The set-up is shown in the
attached figure.
The detector is exposed to a 10
GeV/c beam of p-s from an
accelerator. The scintillator detectors, S1 and S2, before and after the
silicon detector is used to trigger in an experiment to measure the collected
charge from the silicon detector. The coaxial cable between S1 and the
coincidence unit is 10 metres while the corresponding cable for S2 is 14
metres.
The output from the amplifier is
first connected to an oscilloscope but no signals are observed. Both cables
from S1 and S2 are connected to the oscilloscope and a decision is taken
concerning the cable-lengths. The system is reconnected and a signal from the
silicon-detector is now observed on the oscilloscope.
The output from the amplifier
from the silicon detector is now connected to an ADC, gated by the S1-S2
coincidence, and read by a computer when triggered by the S1-S2 coincidence to
do so. Three parameters are varied for
these measurements: The beam momentum, the high voltage over the silicon
detector, the number of beam-particles to accumulate for each histogram.
The group
spends five minutes in thinking about text, and the supervisor then asks if
there is something unclear about the text or some words that have to be
explained. Mary asks about ADC and gated, and the supervisor explains that
it stands for Analogue to Digital Converter, an electronic unit that transforms
an analogue electrical signal to a digitized number that can be read by a
computer. With gated is meant that the ADC measures the signal only when a
level is set by the S1-S2 coincidence to do so. The supervisor asks who is in
line to chair the meetings, and Ana volunteers. She asks Claus to be secretary,
and he draws a table on the black-board. The columns are: The facts, Problems, “Brainstorm output”, Attempts to explain, Learning
Objectives. He also projects the figure of the set-up on the screen. The
supervisor moves back a bit from the table, but will continue to follow closely
the discussion and through small signs demonstrate that he does so.
Jump-1
Ana starts by
stating that they should now write up the facts from the described scenario,
and asks who would like to start.
Antonio jumps
in immediately. He starts to explain the set-up using the figure as basis, and
demonstrated clearly how well he understands how it is working. He lines up the
facts: Signals from S1 and S2 must arrive simultaneously at the coincidence
unit and the cable lengths matter, the silicon works differently at different
tensions, all particles from the beam are of the same type and momentum, … .
Ana interrupts
after a while to let other people put forward their observations.
Maria points
out that the set-up that worked at 10 GeV/c stops working at 0.1 GeV/c.
Antonio comes
in and says that is irrelevant, he knows that now and then equipment stops
working because of bad contact etc. It is obvious that this is an irrelevant
fact that should be ignored. He then moves on and start lining up another set
of facts and moves over to how he interprets the situation.
The supervisor
asks the chairperson for the word.
- It seems as if you need to discuss a bit
what this group is for. What is the purpose of our work here and in this form?
Ana picks up on that, and after some
discussion they recollect that the purpose is to understand the described
situation, learn to collaborate and profit from each others ideas and thoughts.
- Is that all that has happened during the
last minutes? says the supervisor.
- I understand, I have tried to dominate the
situation too much and this may have hindered the group to work as such. I will
restrain myself a bit. says Antonio.
The meeting can
now continue and by the guidance of Ana all members contribute to build up the
column of facts. It becomes quite large. Ana asks if the group thinks that all
facts have been stated, she glance at the supervisor who discretely nods the
head. She then suggests that they move over to jump-2.
Jump-2
- We should now state the problems. I remind
you that what we mean with problems are things we need to get explained or if
there are unsatisfactory things in the situation that we need to do something
about. says Ana.
She observes
that Balazs has been very silent and looks at him.
- You want me
to say something? I will try. I think there is a problem in that the silicon
works with one polarity and not with another. It also works different with
different tensions at the good polarity. What is happening in the silicon and
how does that affect what happens after a p
has traversed it? What does the diagram they draw look like and how does it
help them to decide which tension to apply?
Giuseppi raises
his hand and says:
- A central
thing we need to understand is how these histograms look like. Clearly the ps ionizes the silicon and it is this ionization
that is measured. The histogram shows how this ionization fluctuate
particle-by-particle. They think this distribution look peculiar, so this we
have to explain. There is also some basic statistics here, the uncertainty in
average and variance. I’m also not sure of what they mean with higher moments,
and in which way that is relevant.
- I want to
come back to that it stops working at 0.1 GeV/c. I think this should be listed
as a problem. says Maria.
The group
continues until all unsatisfactory issues, things that have to be explained,
and things that require actions have been listed in column 2. Ana suggest a
short break before they move over to jump-3.
Jump-3
The group
reconvenes and it is now time to discuss the problems and try, in a brainstorm
manner, to suggest different relations and hypotheses.
- Who wants to
start? says Ana, who is chairing the meeting.
Antonio raises
his hand.
- The silicon must be a diode, which must be why it cannot operate as a
detector with one polarity.
- The charges
that have been liberated by the ionization, produced by the p, are what is measured. says Maria.
- The
measurement is done when there is a simultaneous signal in S1 and S2, i.e. one
measure that a particle has gone through them. says
Balazs.
- Yes, but the
velocity is different for the different momenta. Why
don’t they have to change the cable lengths for each beam momentum? asks Gunhild.
- The particles
are relativistic of course; they are all at the edge of light-speed. explains Claus.
- Also at 0.1
GeV/c? asks Maria.
- Maybe that's
why it did not work! Or, maybe they decayed. says
Claus.
- They measured
the signals in the silicon and studied two things: The signal-distribution for
a given momentum and the averages of these distributions for different momenta. I remember having read about this in the
undergraduate course in nuclear physics. I think it was about the average value
as a function of velocity, not momentum. remembers
Giuseppi.
The group
continues to try to express relations and remember from what they already know
from different undergraduate courses. In the end they have noted a series of
hypotheses in the third column on the blackboard.
Ana sense that
it is time to move on:
- Friends, let us now move to jump-4 and try to group and systematize the
relations that we have come up with.
Jump-4
Gunhild take
the word and says:
- I think we
need to classify the relations, since there are several different sub-issues in
the scenario. We have the coincidence S1-S2 with its cable lengths, then there
is the physics inside the silicon and what happens at different voltages, … .
- Yes, and then
there is how the p ionizes in the silicon, and how that
depends on the momentum. interrupts Antonio.
- Velocity, not
momentum. corrects Giuseppi.
The group
continues along this line until they arrived at a fourth column with the
content:
The group looks
at the blackboard and seems satisfied. Ana suggests that they move on to
jump-5.
- Can I say
something? asks the supervisor.
- Yes, please
go ahead. says Ana.
- Well, there
is the last point in the scenario. They talk about electrons, pions and protons in the beam. Could there be something
else that could ionize in the silicon? asks the
supervisor.
This prompts
the Claus to write a 7th item in the column: There may be other
particles in the beam.
Jump-5
- Ok, what do
we need to learn until the next meeting? asks Ana.
- Relativity,
says Gunhild. How varies the velocity at different momenta.
Does the ps decay, and how often? Does that vary
with velocity; I remember something about time dilation?
- We need to
learn about the speed of the signals in the cables.
- How does a
silicon detector function? What is the physics at the different voltages, and
how does that effect the measured ionization?
The group
continues until the study plan in the fifth column is filled. It spans issues
of relativity, electrodynamics, condensed matter physics, statistics, mathematical
methods for fitting procedures and particle physics.
Before
adjourning the meeting to enter a several days of studies, the group evaluates
its performance as a group during this session. They agree of the importance to
be part of the group, and not communicate as an outsider, Ana get some feedback
on how she has functioned as chairperson, etc. In general they are quite
satisfied with how they have functioned.
The supervisor
notes in his log-book how the individual participants have contributed to the
group. He is happy to note that none have been just a passive observer.
Jump-6
The
participants spend now some days on studies and calculations; some of them
individually while a few others work together. They use the supplied literature
lists but also searches on the web and picks up their old undergraduate
literature. They discover that the scenario has opened up large areas that they
are not familiar with, and also have to prioritize what they should focus on.
Jump-7
The group
reconvene on the Thursday. Ana asks if the ordering, or grouping, of the issues
in the fifth column needs to be revised. This is not the case. The presentation
of the weeks findings are now gone through. They go through all problems they
previously identified and verify that they can now address and understand them.
The group has learned:
They agree on
the table of content of their report and distribute the writing-work among
them. Claus should collect the contributions, merge them and send to Ana. She submits
the report on the Friday afternoon to the supervisor.
Finally the
group evaluates again how they have functioned with feedback to each other and
on the group dynamics.
After the group
has adjourned the supervisor continues to log his observations.
An independent
examiner will after two months individually discuss with each member on the
basis of the reports they produced from the PBL-cycles.