Benefits Of Discussion-based Learning Physics

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This article reports on an investigation of students learning physics during group discussions around context-rich problems in introductory physics courses at the university level. We present the results from video recordings of student groups solving three different problems.
1. Eurasia Journal of Mathematics, Science & Technology Education, 2008, 4(2), 121-134
Learning Physics in Small-Group
Discussions – Three Examples
Sylvia Benckert and Sune Pettersson
Umeå University, Umeå, SWEDEN
Received 27 April 2007; accepted 13 March 2008
This article reports on an investigation of students learning of physics during group
discussions around context-rich problems in introductory physics courses at university
level. We present the results from video recordings of student groups solving three
different problems. We found that group discussions around physics problems can lead to
stimulating and learning discussions of physics but we also observed situations when the
discussions did not work well. Misunderstandings of physics concepts reported in the
literature emerge in the discussions now and then but the students also detect new
„problems‟. In the discussions most misunderstandings and problems are treated and
solved either by the students themselves or by the students together with the teacher.
Factors that stimulate a good discussion are engaging problems and a teacher at hand to
answer questions and to discuss with the students. Factors that prevent a fruitful
discussion are too little knowledge of the actual physics among the students and bad
functioning of the groups.
Keywords: Context-rich Problems, Group Discussion, Physics Education, Problem Solving
BACKGROUND working on understanding is through talk. When
students talk with each other they rephrase their own
Many physics students do not find physics ideas, obtain another perspective from their peers and
interesting and many of them pass physics courses even can eventually reach an improved understanding. Barnes
at university level without an acceptable conceptual and Todd introduce the notion of “exploratory talk”
understanding of physics. Small-group learning seems to when speakers think aloud, a talk that includes
promote both interest and understanding of physics hesitations and changes of directions, assertions and
concepts and principles. Springer, Stanne, and Donovan questions, self-monitoring and reflexivity. This way of
(1999), for example, showed in a meta-analysis that talking often occurs in group discussions and so these
students in undergraduate courses in science, could be promising milieus for learning.
mathematics, engineering and technology who learn in
small groups in general show a greater academic Group discussions in physics
achievement and express more favourable attitudes
toward learning than students that have been taught in a Group discussions around context-rich problems in
more traditional setting. physics were introduced at the University of Minnesota
In a socio-cultural perspective meaning making is (Heller, Keith & Anderson 1992; Heller & Hollabaugh
seen as a dialogic process (Barnes & Todd 1995; Lemke 1992). The context-rich problems are written as short
1990; Mortimer & Scott 2003). We agree with the stories about real objects or events including a reason
philosophy of learning expressed by Barnes and Todd for calculating a specific quantity (Heller & Hollabaugh
(1995, p. 10) that one of the most important ways of 1992). The student is the principal figure in the story
and the personal pronoun "you" is used throughout the
Correspondence to: Sylvia Benckert, Senior Lecturer problem. The problem statement does not always
Department of Physics, Umeå University specify the unknown variable. More information may be
SE-901 87 Umeå, Sweden available than is needed to solve the problem or some
E-mail: [email protected] necessary information may be missing. The students
solved these problems in cooperative groups. In a
Copyright © 2008 by Moment
E-ISSN: 1305-8223
2. S. Benckert & S. Pettersson
review of research on small group learning, Cohen students‟ performance on test afterwards. These studies
(1994) found that small group learning can be are of the type “black box approaches” in which they
productive for conceptual learning if certain conditions compare a cooperative method to a traditional teaching
are fulfilled. The most important of these conditions is method on outcome measures only.
that the task is a real group task. The context-rich
problems seem to fulfil these requirements. Heller et al. Problem solving in physics
(1992) also found that in well-functioning cooperative
groups a better problem solution emerged than was Problem solving is seen to be an essential part of
achieved by individuals working alone and the physics learning. Traditional end-of-chapter problems
instructional approach improved the problem-solving are, however, often criticized because students have a
performance of students at all ability levels. tendency, when they solve these problems, to just grab
Advice for instruction of cooperative groups is given an equation and plug in numbers. Why students act in
by Johnson, Johnson and Smith (1998) and much of this this way is explained by Larkin, McDermott, Simon and
advice is applied in small group-learning in physics by Simon (1980). Students often start with the goal of the
Heller and Hollabaugh (1992). They found that groups problem and work backwards. They identify the goal as
with three students of mixed abilities functioned well finding a specific numerical value and the most
together. If a group consisted of two students, they reasonable and efficient way to reach that goal is to find
often did not produce enough good ideas to solve the an equation. This behaviour is understandable but it
problem and if the group consisted of four students, does not enhance learning in physics.
one student was invariably left out of the problem- Maloney (1994) gives an overview of research on
solving process. Also in three-member groups there problem solving in physics. He finds that several studies
could be problems of dominance and conflict. To avoid argue that standard problems are not effective tools for
these problems they used rotating roles as Manager, helping students learn relevant concepts and principles
who keeps the group on task, as Sceptic, who helps the of physics. Is it possible for students to develop solid,
group to avoid quick agreement and asks questions that thorough declarative knowledge bases before they are
will lead to understanding and as Checker/Recorder given problems to solve or does solid understanding
who checks for consensus and writes down the group require that they attempt to apply the knowledge from
solution. the domain? Maloney finds studies that imply that
Gautreau and Novembsky (1997) used small group working with problem examples is an important part of
learning in introductory physic courses at the university. learning declarative knowledge, but other studies imply
They let students work in groups of three or four after a that students need to have a solid knowledge base to be
short lecture. They describe this as a first teaching by able to solve problems effectively. Maloney also states
the lecturer who introduces concepts followed by a that many studies show that making students adopt a
second teaching where students in small groups digest definite problem-solving strategy results in better
initially brittle ideas into workable knowledge that problem solving. He also concludes that if we expect
students own themselves. Molly Johnson (2001) students to learn concepts and principles we may need
introduced problem solving in small groups in to alter the form of the assigned problems. There are
introductory courses in physics at university level. different suggestions of the type of tasks to be used to
Students worked in groups of two to four and the group replace standard problems and one of the suggestions is
members took on roles as writer, leader and sceptic. The context-rich problems.
problems were similar to those in textbooks focusing on Heller et al. (1992) were interested in what way
conceptual and problem solving skills. Johnson presents problem solving was best learned and formulated a
the implementation and difficulties with this approach. problem-solving strategy which included a detailed five-
She notes that the students during the group discussions step procedure to solve real-world context-rich physics
raise questions that have been identified in the literature problems. The first step is to make a translation of the
as important difficulties for students, often overlooked problem statement into a visual and verbal
by texts and instructors. Enghag, Gustafsson and understanding of the problem situation. The second
Jonsson (2007) found that students reach consensus in step requires the students to use their understanding of
group discussions using exploratory talk and that physics concepts and principles to analyze the problem
individual questions are formulated in the process of in physical terms. The third step is to plan the solution,
meaning making and that these questions recur during the fourth step to execute the plan, and the fifth step to
the conversations. evaluate the reasonableness of their answer. Heller et al.
Booth and James (2001) and Samiullah (1995) say that they have reason to believe that teaching this
investigated the effects of student-student interaction on problem-solving strategy to solve context-rich problems
learning physics at university level. They found that the enhances students‟ conceptual understanding.
cooperative learning did not have any effect on the
122 © 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134
3. Small-group Discussions
Huffman (1997) investigated if students in high understand from the p-prim perspective than from the
school who were taught to use an explicit problem- misconception perspective.
solving strategy exhibited greater improvement in As Driver, Asoko, Leach, Mortimer and Scott (1994)
problem-solving performance and conceptual write, the constructivist position is shared by a wide
understanding of physics than students who were taught range of different research traditions related to science
to use a textbook problem-solving strategy. The results education. One tradition focuses on individual
indicated that the explicit problem-solving instruction construction of meanings while another tradition
helped improve the quality and completeness of describes knowledge construction as a social
students‟ problem representations but it did not seem to construction of knowledge. Leach and Scott (2003)
significantly affect students‟ understanding of concepts. present a view of science learning drawing on both
Leonard, Dufresne and Mestre (1996) on the other hand socio-cultural and individual views. They conclude that
introduced qualitative problem-solving strategies to learners must reorganise and reconstruct the talk and
highlight the role of conceptual knowledge and they activities on the social plane and so Vygotskian theory
found that these strategies were valuable for focusing through the process of internalisation brings together
students‟ attention on the role conceptual knowledge social and individual views. Even if Leach and Scott see
plays in solving problems. limitations in the individual views of learning, they think
that the so-called „alternative conceptions literature‟
Learning physics concepts does offer useful resources for those interested in
improving science education.
Findings from many studies show that students An important background when studying students‟
come to science courses with knowledge and beliefs problem solving is identified conceptual and reasoning
about the phenomena and concepts to be taught and in difficulties that students encounter. In our study
many cases students‟ ideas are not in accordance with students solve one problem in special relativity and
science views. Commonsense beliefs about motion and there are a few studies of problems that students
force are for example incompatible with Newtonian encounter in their study of relativity. Posner, Strike,
concepts in most respects and traditional physics Hewson and Gertzog (1982) in a classic study of
instruction produces little change in these beliefs conceptual change interviewed students and physics
(Halloun & Hestenes, 1985; Hake, 1998). There are instructors about problems in special relativity. The
many studies identifying and analysing students‟ central metaphysical belief that contrasts special
difficulties in different areas of physics. McDermott and relativity with classical mechanics is its rejection of
Redish (1999) give an overview of this type of research. absolute space and time. Posner et al. found that if a
Many researchers have seen students‟ difficulties student requires objects to have fixed properties such as
with physics phenomena as rather strongly held lengths, he or she may explain length contraction by
misconceptions or alternative conceptions that have to saying that the rod does not shrink; it is just a perceptual
be addressed by instruction. The idea of strongly held problem. Hewson (1982) interviewed a graduate student
misconceptions, however, has also been challenged. It as a case study about the propositions that moving
can be argued that students do not have coherent clocks runs slow and that moving rods shrink and this
frameworks and that there is a variation of students‟ student also saw length contraction as a question of
reasoning across different contexts. Misconceptions perception. Scherr, Shaffer and Vokos (2001) report on
could appear as an act of construction of knowledge. an investigation of student understanding of time in
DiSessa (1993) suggested that students‟ intuitive physics special relativity. They found that students most often
knowledge is built by explanatory abstractions of do not spontaneously recognize that simultaneity is
experiences in the day-to-day physical world called relative. Frames of reference are important in special
phenomenological primitives. “Closer means stronger” relativity and Panse, Ramadas and Kumar (1994)
and “force as a mover” are examples of such p-prims. investigated how students handled these conceptual
One conclusion from this work is that the intuitive tools.
knowledge does not need to be replaced but should be The second group discussion that we report deals
developed and refined. Hammer (1996) analysed how a with sound. There seems to be very few studies of
teacher may perceive students‟ participation from the students‟ acquisition of concepts related to sound.
two perspectives, misconceptions and p-prims, and he Published studies focus on students‟ thoughts about
found both valuable. The misconceptions perspective factors affecting the sound velocity (Linder, 1993) and
was more valuable to help students become aware of about a common misconception that sound waves have
their reasoning, while the p-prim perspective motivated object-like properties (Wittmann, Steinberg, & Redish,
the teacher to discuss and refine definitions and 2003).
students‟ ideas. Hammer also points out that the context The third group discussion is about a problem in
sensitivity of students‟ discussions was easier to mechanics where knowledge of energy of rotating rigid
© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 123
4. S. Benckert & S. Pettersson
bodies and moment of inertia is necessary. There are lot This study was done during two introductory physics
of studies of problems that students encounter when courses, Mechanics, relativity and experimental
studying mechanics, but we have not found any studies methods, and Electricity and waves. The class consisted
dealing with rotating bodies. of 16 students, 10 aiming for a major in physics, 3 pre-
service teachers and 3 other students. The students
Research questions worked with just one course at a time, which is the
traditional way of studies at Swedish universities. In the
We have for some years, inspired by the work at the courses there were lectures, laboratory work and group
University of Minnesota, used group discussions around discussions and the students had lectures almost every
context-rich problems in the first courses in physics at day and group discussions about two times a week.
university level. We introduced group discussions We constructed groups with three students and in
because we saw a need for more discussions about some cases four students. We formed the groups so that
physics concepts and principles but also about problem they were composed of students of different abilities as
solving. From the research literature we find that group shown by the results of a FCI-test (Hestenes, Wells &
discussions could be a promising milieu for learning Swackhamer, 1992) given to the students at the
physics. Most studies of group discussions are, however, beginning of the Mechanics course. The ideal was to
from secondary school and this is especially true for keep the assigned groups during the whole course, but
those which are not “black box approaches”. Therefore when one or more students were absent, new groups
it is a need for more in-depth studies of group were formed temporarily. Regrouping of the students
discussions at university level. was made once during the two courses and then the
We want to find answers to the following questions: teachers used their personal knowledge of the students
 How do students discuss and solve physics to guide the formation of new groups.
problems in group discussions? In this article we report the results from three group-
 What kinds of problems with physics concepts discussion occasions. We video recorded two study
and principles do the students encounter? groups at each of these three occasions. These three
 What does group communication mean for the group discussions were in some ways different from
problem solving to be successful? each other. In the first group all the students were active
and very enthusiastic about a problem in special
RESEARCH CONTEXT AND METHOD relativity. The second group discussion dealt with a
more qualitative problem. The second problem was
We introduced group discussions around context- included in order to study if the discussions would be
rich problems in our introductory physics courses at different for a qualitative problem compared with more
university level seven years ago and have used this ordinary context-rich problems. The teacher had in
teaching method since then. In our group discussions, previous classes had group discussions around questions
students have about two hours to solve one or two such as: “Explain the reasons for the rainbow”. He had
context-rich problems and the students are supposed to then observed that the group discussions tended to be
solve the problems within the allocated time. We rather shallow with these “Explain questions” and the
introduce a problem-solving strategy similar to the one questions did not seem to engage the students as much
described by Heller et al. (1992). After some of the as the context-rich problems did. In the third group
group discussions the groups were obliged to hand in a discussion the groups did not function so well. This
solution of the problem in which all steps should be discussion dealt with a problem in mechanics with
well motivated and should follow the steps in the rotational energy.
problem-solving strategy. These problem solutions were The students filled in a small questionnaire of Likert-
then given back to the students with comments. We type format at the end of the group-discussion sessions.
have also found that groups of three students are ideal The students answered three questions: How interesting
in our group discussions. We try not to have just one did you find the problem? How difficult did you find
female student in a group. Sometimes this can still be the problem? How much have you learned through
the case when groups are rearranged because some solving this problem? They could choose six different
students are missing. The group roles, Manager, Sceptic answers ranging from for example “Not at all
and Checker/Recorder are introduced at the start of a interesting” to “Very interesting”.
course. We have not stressed the use of group roles but At the beginning of the group-discussion session we
we have found it useful to start with. During the group selected groups for video recording and the members of
discussions the teacher is present the whole time and the groups all had to agree to be videotaped. We
intervenes when necessary. The groups are free to ask wanted to keep an authentic milieu for the group
the teacher for help and advice whenever they need. discussions that we recorded so we brought the
equipment to the location that the groups chose for
124 © 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134
5. Small-group Discussions
their work. A camera was mounted in front of each transformation and they must be aware that the
group and an external microphone was placed on the simultaneity is relative. We video recorded two groups
table in the middle of the group. It took some time when they tried to solve the problem given below. In
before the equipment was set up and the camera rolling one group there were four male students and in the
so the first minutes of the discussions were usually not other three female students.
caught on tape. The tapings of the group discussions on
A test of length contraction?
special relativity and on rotational energy all took place
in the lecture room where the other groups were Two of your friends decided, when they travelled
working. This led sometimes to disturbing noise from by train, to try to determine the length contraction
neighbouring groups that made it difficult to hear some of a very rapid train. They planned to sit at the two
utterances when we analyzed the films. One of the ends of a 100 m-long train with their watches
recordings of the second group discussion was made in properly synchronised. At the time t = 0 each of
the lecture room and the other took place outside the them should drop a bag through the window.
lecture room at a relatively quiet place found by the These bags should act as markers. When the train
students themselves. stopped at the next station they could go back and
We started the analyses by looking through the video measure the distance between the bags. Shouldn‟t
tapes from the group discussions and noted what the distance between the bags then be the length
happened. We then looked through the tapes several of the train as measured by observers on the
times, transcribed the records, and analysed the ground? Your friends ask you about this because
documented group talk. By studying the students‟ they know that you are very good at Lorentz
comments, questions and interplay we tried to achieve a transformations. Your friends tell you that they
picture of the students‟ lines of reasoning and their suppose that the velocity of the train is 0.7 c and
problem-solving process. We especially looked at the that you can neglect the time for the bags to fall to
students‟ handling of important physics concepts and the ground. We calculated the distance between
principles in their problem solving and if they showed the bags to 71 m, they say. Is this right?
some alternative conceptions or misunderstandings. We
In the group with three female students (Anne,
also looked at the group interaction by noting the
Susan and Tanya) Tanya starts the discussion: ”This
distribution of talk among the group members.
seems to be fun.” The first step in their problem
solution is to try to understand what the problem is
about. Then Anne tries to do as in another problem,
they have solved, with a car driving through a garage
which is open in both ends, and they stumble on a
The three examples are group discussions around a
dilemma. Anne uses the formula for length contraction
problem in special relativity, a more qualitative problem
and calculates the train to be 71 m. Tanya is not quite
about sound waves and a problem in mechanics and
convinced that this is the right way to start.
rotational energy. From the questionnaires given to the
Tanya: Is this really applicable here?
students after each group-discussion we found that the
Susan: If you look at the train, you see the train
problem in special relativity was seen as the most
going by as being shorter.
interesting, the most difficult and the problem from
Tanya: But the thing is that you don‟t do that.
which they learnt the most. The other two problems
You go back and measure the distance.
were judged to be rather interesting and difficult but less
Is the train 100 m or 71 m? Anne makes their
so than the problem in relativity. The students also said
dilemma clearer.
that they learned physics from these two problems but
Anne: Shouldn‟t the distance between the bags be
less so than from the problem in relativity.
the length of the train that is measured by the
observers on the ground? The train goes by with
Group-discussion around a problem in special
0.7 c. And then they look at the train and think it
is 71 m. And I think that the bags should end up
Before this group discussion the students had 100 m from each other because the train is 100
attended one lecture on Time dilation and length m, but if you look at it, it is 71 m.
contraction and in the morning the same day a lecture Then they go on and discuss this dilemma, compare
on the Lorentz transformation. The teacher‟s purpose with other problems and expound the problem with
for including a group discussion with this problem was other examples. They once again compare with the
to give the students a possibility to discuss and realize garage problem and Tanya wonders if their dilemma
that it is not enough to know the length-contraction could be explained if the length contraction could be
formula, they also have to be able to use the Lorentz seen as an optical illusion.
© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 125
6. S. Benckert & S. Pettersson
Tanya: Optical illusion. I know I shouldn‟t call it one at the back comes first, then it could very
an optical illusion, but I do so. The optical well be 100 m between them.
illusion is still there when the car has stopped; Susan and Tanya then discuss what it means that the
otherwise the optical illusion wouldn‟t be there bags are not dropped at the same time and Tanya
when the bags have stopped because they go explains for Susan that if the person at the end of the
straight down. But perhaps that is just what I train drops his bag first the distance between the bags
think. on the ground could be 100 m. If the person at the
Susan: That is tricky. When they land they have 0.7 front of the train drops his bag first the distance will be
c. What is happening just when they land? shorter. They go on and discuss what this means and if
They go on and discuss what happens when the bags the distance between the bags might be 100 m.
fall down and if the distance between the bags is 100 m So they are able to solve the problem. Ann writes
or 71 m. down the Lorentz transformation for time and they
Anne: It has to be the same way from the other calculate the time t when the bag at the front of the
side. It is the same thing from the train as from the train is dropped. They calculate the distance travelled by
ground. the train since the bag at the end of the train was
Tanya: But I can absolutely not explain why it dropped. They hope this distance will be 29 m, so that
should be 100 m between them. I don‟t know what the distance between the bags should be 100 m. The
to call the 71 m, because in reality the train is 100 result they arrive at is however 68 m so the distance
m. between the bags must be 139 m. They discuss the
Anne: In reality and in reality? That is tricky. result with the teacher and they then also realize that the
Tanya: I think.. I think it is peculiar. I want to see distance between the bags as measured from the train is
the contraction more as an optical illusion. still 100 m and that a distance 139 m at the ground is
Here the idea of length contraction as an optical seen as 100 m from the train. They end the discussion
illusion turns up again. Then Susan discusses what by reflecting on their work.
happens when you go by the train and you see two Anne: On the train they still think that the
stones on the ground 100 m from each other. She distance is 100 m.
concludes that you see the distance between the stones Tanya: Everything that we discussed was very
as 71 m from the train. So she finds that the length logical.---
contraction is the same seen from the train as seen from Susan: It was a very good problem. It was fun
the ground. They go on and make up more examples really.
that resemble the actual problem. All three students in this group participated in the
Eventually time and simultaneity comes into the discussion to the same extent. They started to discuss
discussion. The word simultaneity comes into the what the problem was about. They compared with
discussion for the first time when Anne says: “We could another problem and they constructed new examples to
just answer that there is no simultaneity.” The illustrate the problem. The discussion eventually led
discussion goes on. Susan points to something in her them to the solution of the problem. They listened to
notes and Anne answers that she thinks that time each other and asked questions, when they didn‟t
shouldn‟t be of any importance. “Shouldn‟t it?” Tanya understand.
asks and in a while Anne has a suggestion. Probably she The second group discussing this problem went on
has thought of the importance of time and also heard in about the same way as the first group. They started to
something from a discussion between the teacher and discuss length contraction and how this phenomenon
some other group. should be interpreted. Also in this group one student
Anne: I think, as I heard now and I have been suggested that the length contraction could be explained
sitting here and thinking. When we look at them as an optical illusion. This group asked the teacher for
from the ground, they don‟t do it at the same help several times and they needed this help to realize
time (Drop the bags.). that the bags were not dropped at the same time as seen
Tanya: Don‟t they? from the ground. Then they concluded that the person
Anne: I don‟t think so. at the end of the train must drop his bag first and they
Tanya: Will we first see one of them, poff, and could calculate the distance between the bags on the
then the other, poff? ground.
Anne: Yes. In this group as in the first group all the students
Tanya: But which comes first? seemed to enjoy the discussion but two of the students
Anne: I think it is… talked more than the other two and sometimes there
Tanya: First one of them, poff, and then the was a discussion going on in two subgroups. At some
other, poff. Which comes first? Because if the occasions one of the students seemed to dominate the
discussion and he was also the group member who most
126 © 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134
7. Small-group Discussions
eagerly wanted to hear the explanations from the discussion if it is possible to fall from one reference
teacher. system to another.
The students in both groups gradually evolved their The problem formulation led the students to
understanding. They compared with problems they had interesting discussions. When the students tried to solve
solved earlier and they made up their own problems to the problem, lead by the problem formulation, they
clarify the situation. They discussed back and forth. The used their knowledge of length contraction and
second group got explanations from the teacher several calculated the distance between the bags to be 71 m, but
times and they then repeated with their own words, at the same time they thought that the distance ought to
what the teacher had said. be 100 m. It became a paradox for them and it was very
In this problem the students were lead by the interesting for them to go on and discuss the problem.
problem formulation to discuss length contraction and We have in another study (Benckert, Pettersson, Aasa,
the students thoroughly investigated what length Johansson & Norman 2005) also found that students
contraction might be before they could solve the find it interesting to solve problems where they have to
problem. Tanya wanted to call the length contraction an determine if something is true or not. This is more
optical illusion and so did a student in the second group. interesting than to just be asked to calculate for example
This misunderstanding is in accordance with the results a certain velocity or distance. The formulation of the
found by Hewson (1982). From these group discussions problem with the question “Is this right?” may be
we can, however, see that the view of length contraction another factor, besides the paradox, that makes this
as a form of perception is not a firm misunderstanding. problem interesting for the students and makes it a real
It is rather a suggestion when the students tried to find group problem.
an explanation to their peculiar results. Even if this is
not really misunderstandings it is useful for the teacher The helium problem
to know that the students discuss in this way and it
could be valuable to discuss it in class after the group We studied two groups that discussed why the voice
discussion to make the students aware of the problems of people changes if they inhale helium gas. This was a
with such an interpretation. part of the combined course in electricity and waves.
Scherr et al. (2001) report on an investigation of Before this group discussion the students had attended
student understanding of time in special relativity. They three lectures on mechanical waves, one of these, about
found that students most often do not spontaneously sound waves and resonance, was given the same
recognize that simultaneity is relative and from the morning as the group discussion.
beginning our students did not realize this either. They Changing the pitch by inhaling helium
needed a lot of discussion and for one group help from If you inhale helium gas you will get a completely
the teacher to really understand and accept it. Of course different voice. What is the reason for this and
these students have in the lecture heard that the how will the pitch change? Note that it can be
simultaneity is relative and they have also in lectures dangerous to inhale large quantities of helium gas.
been told that length contraction is a consequence of The lungs will normally prevent suffocation by
the fact that the simultaneity is relative, but this is not detecting a surplus of carbon dioxide, but with
the same thing as understanding it and being able to use helium gas you don‟t experience any suffocation
the knowledge in problem solving. This group discomfort.
discussion shows that students need to discuss such The teacher had expected the students to discuss
phenomena at length to really understand what it is which frequencies that would dominate by comparing
about. As there are many aspects of special relativity with standing waves in a pipe. Since the size of the
that are counterintuitive it seems to be especially organs of speech is not changed by inhaling helium the
important for the students to be able during discussions standing waves must have the same wavelength. The
to find out all contradictions in their reasoning. relation between the speed of sound, v, the frequency, f,
The discussions in the groups also indicate that the and the wavelength, λ, is given by v = fλ for all
students can have problem understanding what a periodic waves. By comparing the speed of sound for air
reference system is. One student said, “They leave this and helium the students were supposed to draw the
system and the earth is the other system, isn‟t it?” This conclusion that standing waves in helium will
is a misunderstanding also described by Panse et al. correspond to higher frequencies than in the case with
(1994). In this group discussion it can be discussed if air.
this really is a misunderstanding or if the student just did We video recorded two groups when they tried to
not express himself in a correct physical manner. The solve the helium problem. The first group consisted of
group did not discuss the question; it was just one four men, David, Ron, Ken and Bill. The second group
student that talked in this way. In this case it could also consisted of three men, Charlie, John and Ben. Both
be valuable to discuss in a lecture after the group groups start off by looking for formulas with which they
© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 127
8. S. Benckert & S. Pettersson
can calculate the sound velocity in helium gas. The physical picture of the situation by beating his pen
teacher intervenes and shows that they can find the against the table top to illustrate what will happen at the
sound velocity for helium gas in their textbooks. He interface between helium and air.
intervenes at an early stage since he has experience from Ken: The frequency is higher, though. It will hit
the year before that students tried to find ways to more often against the air when it arrives there.
calculate the velocity instead of finding a tabulated (He is beating his pen rapidly against the
value. The sound velocity of helium is tabulated to 999 tabletop) Can the frequency be different?
m/s which is about three times higher than the sound Ron: No.
velocity in air, 340 m/s. After the groups have found Ken: It must be like that…If you hit something…
the value of the sound velocity of helium they started to Ron: It is this that will be changed.
discuss the reason for the higher pitch of the person‟s Ken: Then the wavelength will be changed.
voice. Both groups start off with the assumption that Ron: The frequency is formed here. It must be
the vocal cords produce a certain frequency regardless the same, though? Then it is the wavelength that
of which gas that is surrounding them. This assumption changes.
is taken for granted and is never questioned until the Ken: Yeah, it is the wavelength that changes when
teacher intervenes. This leads to much discussion about it comes out.
how the frequency changes when the sound goes from
Ron seems to accept that the frequency is constant.
one medium to another.
However, the group decides to be very explicit and
The teacher approaches the first group and asks
writes down what is known before and after the sound
them to tell him what tey have found out.
passes the interface. They put numbers into their
Bill: When the sound is created in the throat
equations and find that the wavelength in air will be
then…then the vibrations in the vocal cords are
shorter than in helium. However, Bill is puzzled why the
transmitted to the helium gas and these vibrations
frequency does not change. Then Ken makes an analogy
must be…
with light. He knows that when light enters into glass
David: …the same.
the light will have a different wavelength inside the
Bill: Yes. It can‟t depend on the helium gas itself
Ron once again accepts Ken's explanation but Bill is
David:…that the vocal cords….that there will be
now becoming more confused. He does not understand
other vibrations in the vocal cords. That must be
what decides whether wavelength or frequency will
the same for both gases.
remain constant when the sound wave travels between
Bill: Instead the change is when the sound is
media with different speeds of sound. Ron agrees with
transferred from the helium gas to the air.
Bill and he quickly forgets the arguments from Ken.
The teacher understands that the group has been on The discussion has now focused for a long time on what
the wrong track and suggests that the group make a happens to the frequency and the wavelength at an
comparison with an organ pipe that is filled with helium. interface. At least some members of the group seem to
Bill draws a picture of a pipe with a standing wave on have forgotten that they had found that the frequency is
the whiteboard. The group argues that the wavelength higher already when it is produced in the throat. They
should be the same if air is replaced with helium in the have now returned to their original question on how the
pipe and they conclude that the frequency must then be frequency can increase at the interface.
three times higher. The group returns several times to the question if we
The group seems to have solved the problem with hear differences in wavelength or in frequency. They
the help of the analogy with the pipe but Ron is not quickly agree that it is frequency that we perceive with
satisfied with this solution. He still worries about what our ears. However, the question is still raised several
will happen when the sound leaves the helium and times during the discussion. This might be a way for
enters the air. Ron then examines the relation between them to find another opening since they cannot get an
speed, frequency and wavelength that they have written increased frequency.
down. Since the speed of sound decreases when the Ken: If we say that we have a boarder here. Here
sound leaves the helium in the mouth he thinks that the the waves are rather far apart. Then we come to
frequency should also go down. Bill agrees with him and this boarder.
says that the high frequency that was produced must Ron: Then it will be a different medium.
return to normal when the sound comes out in the air. Ken: Then we will get a shorter wavelength. Then
Ken, on the other hand, acknowledges that the it will become a different frequency also?
frequency is higher already when it is produced in the Ron: Yes.
throat and he questions that the frequency will change at Bill: No, not if the velocity is increased here. It
the interface between helium and air. He makes a still will have time to do the same number of
128 © 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134
9. Small-group Discussions
vibrations. It travels much quicker. What do we calculation so the teacher quickly made sure that the
perceive? Is it wavelength or frequency? students did not spend time on this calculation. Second,
David: Frequency, I think. the students incorrectly assumed that the vocal cords
produce a certain frequency and therefore they focused
The first group does not find a way to explain the
on the transition of the sound from helium to air. They
phenomena. They become stuck in the discussion on
spent a lot of time discussing whether frequency or
what happens at the interface between helium and air.
wavelength is preserved in such a transition. This was
They have to ask the teacher if it is the wavelength or
another unexpected discussion but it dealt with
frequency that changes at the interface. The teacher
important concepts. That the frequency must be
gives some arguments to why the frequency cannot
constant for a wave travelling between different media
change which is accepted by the students and they
was neither brought up during lectures nor discussed in
continue directly to write down the solution that they
the textbook for sound waves. It is very briefly
were required to hand in.
mentioned in the case of light travelling into another
In this group, Ron and Bill talk twice as much as
material but this had not been covered in the course yet.
Ken and David. Ron and Bill lead the discussion and
In both groups, there were questions that popped up
write down the solution in the end. Ken does not say so
over and over again during the discussions. One
much but he brings new (and correct) ideas into the
example is the question whether we perceive frequency
discussion. Ron and Bill listen to Ken's ideas but they
or wavelength with our ears. This question was raised
do not really include them in their own reasoning. The
several times in the first group and each time the group
contributions from David consist of obvious
quickly agreed that it is the frequency that we perceive,
conclusions and questions that do not belong to the
but as they did not find a solution to the problem they
main discussion.
returned to this question several times. This is an
The second group also focuses on what will happen
example of how the discussion went back and forth
to the frequency when the sound leaves helium and
between different parts of the problem. The solution
enters air. They realise that they need the speed of
did not evolve in a stable linear pace.
sound in helium and they use quite a long time to
Wittman et al. (2003) found that many students tend
discuss how to get the sound velocity until they finally
to think of sound in terms of objects. This might be a
find a value for it in the text book. Like the first group,
reason why our students were not sure that the
they assume that the vocal cords produce a certain
frequency of the wave should be unchanged when the
frequency and they try to find a way to get an increased
wave passes from one medium to the other. By treating
frequency at the interface between helium and air by
the sound wave as an object, frequency is a property
manipulating the equation v = fλ. The teacher gives
that could change like the speed of an object. If instead
them the same hint as he gave to the first group and
the wave is seen as a series of events it ought to be clear
asks them to make a comparison with an organ pipe
that the frequency cannot change by passing an
filled with helium. After a short while John has a clear
interface. It seems that our students alternated between
picture and can explain for the others that the high pitch
treating the sound as an object and as a series of events.
is produced in the throat in the same way that helium
We can notice that the students had a strategy when
would produce a higher pitch in an organ pipe. The
they manipulated their equations, namely that in a
group is completely satisfied with this explanation and
relation between three physical quantities one should be
does not return to the discussion about what will
held constant while the other two will depend on each
happen at the interface between helium and air.
other. They had no physical arguments to their
In the second group Charlie talks a lot, commenting
assumption that either wavelength or frequency should
on all ideas that are brought forward. John talks less but
be constant but the students start from this fundamental
he introduces most ideas in the discussions. Many of
strategy. This strategy is often useful when solving
them are incorrect which John realizes himself after a
physical problems but it is not always valid.
while. Ben talks less than John but he poses short
Students normally accept without any questioning
relevant questions for the discussion.
that the frequency is constant when a wave enters a
The teacher had anticipated that the students should
medium with different wave speed. This is the case for
discuss the conditions for producing sound when
light entering a material with different index of
helium fills the vocal organs. Instead the students in
refraction and water waves that enter a region with
both groups discussed other things. First, they tried to
shallower water. That these students started to discuss
calculate the speed of sound in helium by referring to
that the frequency of the sound should change at the
theories for sound velocity in gases. This was not the
interface between air and helium should not be seen as a
intention of the teacher since it is easy to find a
misconception, this discussion was provoked by the
tabulated value of the sound velocity and using theories
question that they could not find the answer to. This is
for sound velocities would require other data that are
similar to the discussion by Hammer (1996) of students‟
much harder to find. It would be a too difficult
© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 129
10. S. Benckert & S. Pettersson
explanations to why it is hotter in the summer. group three male students and one female student
Depending on the situation the students could come up (Marvin, Ted, Ann and Alfred).
with different answers to the question. Who wins?
All students in these groups took part in the In an amusement park there is a racer track
discussions and they were focused on the problem where competing persons go down the track in
solving, they did not talk about other things. It was, small carts with big wheels. The incline of the
though, a difference in how much each group member track is 30 to the horizontal plane. The carts
participated in the discussion. It is an interesting have four wheels and every wheel has a mass of
observation that although Ken, in the first group, gave 20 kg and a diameter of 1 m. The total mass of a
correct explanations to what will happen at the interface cart is 100 kg and the total length of the track is
between helium and air his ideas were never really 60 m.
accepted. One reason could be that he did not have the You visit the amusement park together with a
required status in the group so that the others would boy. His mass is 30 kg. You two compete on this
trust what he said. Another reason, which is supported track several times and you always win. Do you
by observations from the video recordings, could be have nature on your side and the boy nature
that Ron and Bill were so occupied with their own against him? What final velocity do you reach?
problems that they did not take in what Ken said In the first group John and Mike sit beside each
although they let him speak. other at a table. Alan comes a little later and sits down
This group discussion shows that it is important that right opposite to John and Mike. Mike says in a while
the teacher is present and can guide the groups to a that the problem will involve potential energy and
correct explanation in the end. Several times, the first kinetic energy. He fetches the calculator and starts to
group made a correct description that the frequency calculate the potential energy for the different masses.
does not change at the interface between two different John comments that this means that the one with the
media. When the teacher came to the group they still biggest mass will reach the bottom first. Alan says,
had to ask the teacher if it is the frequency or the “Does it?”, but they don‟t discuss it any more. In a
wavelength that will be constant when the sound travels while John starts to talk about the moment of inertia.
across an interface. Probably none of the groups would John: But shouldn‟t we use the moment of
have come to the correct explanation by themselves. inertia?
This qualitative problem gave rise to lively Mike: Yes, we can do that.
discussions, even though our experience was that Mike looks into the textbook. John erases the
qualitative questions in general give rise to rather whiteboard and Alan looks in his notebook. Mike
shallow discussions. We had previously observed that finds something.
students did not work so hard with the question Mike: Perhaps. Force times the distance is equal
“Explain the reasons for the rainbow!”. They could just to the work.
note that different colours are refracted in different Alan: Mm.
ways in a raindrop and be satisfied with this short Mike: So it is in this way you will get to know the
explanation for the rainbow although there are many force. The moment of inertia for each wheel
more aspects of the rainbow that are hard to times the distance. Look!
understand. In the case with the helium problem, the Alan: Moment of inertia, is that force?
students did not find a solution that worked. In this way Mike: It is force.
they became eager to really try to understand what was Alan: Can‟t we do as we did in the lecture.
going on. Mike seems sure that moment of inertia is force, but
the other students ignore him. Then the teacher comes
Group discussion around a problem dealing by and Mike explains that they now talk about moment
with rotation of rigid bodies of inertia, but that his first thought was that the cart has
potential energy and loses it which becomes kinetic
The purpose of this group discussion is to give the energy. The teacher explains that this is part of the
students a possibility to discuss energy of rotating, rigid truth, but the moment of inertia should also be part of
bodies and moment of inertia. These are new concepts the solution. Mike asks again if moment of inertia is not
for the students. Before this group discussion the force and the teacher explains that moment of inertia is
students had attended three lectures on rigid bodies for rotational motion what mass is for translational
dealing with rotation of a rigid body, moment of inertia, motion. The rotational energy must in some way be part
torque and angular momentum. We video recorded two of the solution, the teacher says. Now John seems to
groups when they discussed and tried to solve the understand the problem and writes down that the
problem given below. In one group there were three potential energy is equal to translational energy plus
male students (John, Mike and Alan) and in the other rotational energy and so they find an expression for the
130 © 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134
11. Small-group Discussions
final velocity. John and Alan discuss if the velocity will their steps, dimension analysis and a discussion if the
be bigger if the mass is bigger and they find that it will result is reasonable. Alfred asks Ann to write up their
be so. John observes that they have solved the first part results. Ann, who hitherto has mostly tried to follow the
of the problem and says; “But then it is done.” discussion, is in this way drawn into the problem
John then points out that they also should calculate a solving. She starts to draw a picture and to write down
value for the final velocity but they miss a value for the the solution. Alfred gives her instructions on how to
moment of inertia. He has earlier heard the teacher write down the solution. The students also discuss
telling another group that one cannot know what the friction in the wheels and if it is friction just in the hub
moment of inertia is, as they do not know what the or somewhere else too. And so a discussion about how
wheels look like. Alan wants to suppose that the wheels to write down the solution and a discussion about
are cylindrical shells. John is doubtful if they may friction is going on in parallel for a while. They discuss
assume such a thing. The teacher comes and John asks rolling friction, sliding friction and air resistance but
him if you can calculate the velocity if you don‟t know they don‟t seem to have a clear picture of what rolling
what the wheels look like and the teacher answers that friction is. Their conclusion is that friction can be of
they can make some assumption. They then calculate importance but they don‟t know how to handle it. In
the velocity with the assumption that the wheels are their written solution they write without any
hollow cylinders. justification, that even if there is friction the greater
In this group the contributions to the discussion are mass is most important.
rather equally distributed among the participants but a In the first part of the discussion it is mostly Alfred
problem for the group is that they do not seem to rely and Ted who have contributed to the discussion.
on each other enough to be able to question the other Marvin has only asked one question and he has said
students‟ arguments and to suggest improvements to “Yes,” “Yes, it is so,” “Suitable” which shows that he is
them. Instead they want to hear what the teacher has to following the discussion. Ann has first been away
say. This group is also uncertain about the definition of discussing with another group and then she has tried to
many concepts and they have difficulties seeing what follow the discussion but she has not contributed to it.
their formulas imply. Mike certainly lacks knowledge Most of Ann‟s contributions come when she writes
about moment of inertia and the other students in the down their solution and then receives help from Alfred.
group are not sufficiently competent and influential to Neither of these two groups did function very well.
protest loudly. The problem solving and calculation take In the second group two of the students were more
a long time for them. active in the discussion than the other two. Ann was
In the other group Ted starts the discussion by very unsure of her knowledge about the actual physics.
telling that he is not so familiar with this stuff. “I know my shortcomings,” she said. Though this group
Ted: Is there somebody who has a good idea? I was not functioning well in every way, Alfred asked Ann
have not had enough time to solve so many to be the secretary and so he drew her into the problem
problems, so I‟m not so familiar with this. solving discussion. In the first group Alan and John
In this group there is another student, Marvin, who sometimes had productive discussions but overall it was
has ideas about how the problem should be solved. He difficult for this group to advance their solution on their
suggests that they can use energy conservation and that own. They had to and wanted to receive help from the
they have to take care of the rotation of the wheels. teacher. Mike was ignorant of certain physics concepts,
They go on and discuss what the wheels do look like but he did not question his own knowledge in the way
and if the wheels can be seen as solid cylinders or if Ann did.
there are spokes in the middle. They give examples of Some of the students in these two groups seemed to
different types of tyres and Marvin suggests that they be rather uncertain about important concepts and it was
can take ordinary Opel rims, because then the centre is difficult especially for the first group to solve the
quite heavy. After some more discussion they agree that problem. For the group discussions to function well the
the wheels can be seen as solid cylinders. They write students have to be rather well prepared on the subject.
down the relation between potential energy, This type of group discussions is intended to give the
translational energy and rotational energy. They take the students an opportunity to discuss, interpret and apply
moment of inertia for the wheels to be a constant and physics concepts and principles and so deepen their
so they receive an expression for the velocity and they understanding. It is not intended to be an opportunity
argue that a larger mass will give a larger velocity. They to learn totally new concepts as for example in problem
go on and calculate the final velocity. The problem is based learning.
solved. The second group discussed thoroughly how to
They then start to write down the solution. They are present the solution and they then followed the taught
taught to write down the solution according to the steps problem-solving strategy. This discussion was also a
of the problem-solving strategy with motivations for all repetition of the problem solving and an opportunity
© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 131
12. S. Benckert & S. Pettersson
for Ann to get involved and perhaps understand the students‟ attention on the role of conceptual knowledge
solution. They also had a discussion on different forms when solving problems. This is important even if such a
of friction, although this discussion should preferably be strategy is not a golden rule for problem solving because
followed by a discussion in class. students for example can lack relevant knowledge or
This problem about carts going down a track was start with a wrong assumption.
not as engaging for the students as the problem in The students discussed physics concepts and
relativity. It is also rather unrealistic with the carts with principles nearly all the time in the group discussions.
very big wheels and where the child is allowed to go in Misunderstandings of physics concepts reported in the
his own cart. The students had occasional comments literature emerged in the discussions now and then.
about the big wheels and one student said that he However, when the students suggested that length
wouldn‟t like go by such a cart with the velocity 80 contraction can be seen as an optical illusion, this seem
km/h. The problem is ended with a question: What final to be just a suggestion on the way to a more profound
velocity do you reach? This question was added to give understanding, not a real misunderstanding. When the
the students a hint that they could use the energy students tried to solve the problem in relativity we find
principle, but this question made the problem more like as did Scherr et al. (2001) that the relative simultaneity is
an ordinary task than a good context-rich problem. The a difficult concept for the students and they need a lot
question could be left out. of discussion to realize that the simultaneity is relative.
The students can also „detect problems‟ that the teacher
RESULTS AND CONCLUSIONS and the textbook do not see as difficulties. An example
is what happens when the sound leaves helium and
The discussions in the groups went back and forth enters air. For the teacher it was rather obvious that it is
and the discussion did not evolve in a stable linear pace. frequency that is unchanged but this was not evident for
The students had to discuss examples and other the students. They needed a long discussion on this
possibilities to be convinced of what is true, they issue.
compared with other problems they had solved and they For the group discussions to function well the
used examples from everyday life. It was also important students have to be rather well prepared on the subject.
for the students to formulate conclusions and results If the students are too ignorant of the physics content
from the discussions in their own words to really they may just look in the textbook for formulas as they
understand what it meant. When the teacher explained did in one of the groups that solved the problem in
something for the students they often repeated the mechanics. This way of working does not lead to
conclusions with their own words and then they went productive discussions and this group also had to get a
on with their discussion. These group discussions show lot of help from the teacher. Maloney (1994) points out
that the students need to discuss physical phenomena, that there exist studies that imply that working with
as for example length contraction, at length to really problem examples is an important part of learning
grasp all aspects of it. It is also clear that there are a lot declarative knowledge but other studies imply that
of questions, which the teacher has not thought of as students need to have a solid knowledge base to be able
problematic, that can come up in the discussions. to solve problems effectively. Our conclusion from this
The students were introduced to and supposed to study is that the students need some knowledge of
follow a problem-solving strategy. Some groups relevant physics concepts and principles when they start
followed the problem-solving strategy when they began to solve problems in the group discussion but also that
their discussion making their own picture of the the group discussions are effective opportunities for
problem situation but others did not. A better use of the learning and understanding physics concepts and
problem-solving strategy could probably have helped principles.
the students to organize their attempts to solve the If the groups do not function well this can lead to
problem. However, the groups might get into trouble less productive discussions which was seen especially in
even if they start according to the problem-solving the groups solving the mechanics problem. In one
strategy. In the case of the helium problem, both groups group two of the students were more active than the
made the wrong assumption about the frequencies other two and in the other group they did not seem to
produced and the groups started to discuss a problem, rely enough on each other to be able to work on their
which was there only because of their erroneous understanding together. A more emphasized use of
assumption. In any case the students used the problem- group roles and more evaluations and discussions of the
solving strategy when they wrote down the solution they group work during the course, as suggested by Heller
were going to hand in and this gave them the and Hollabaugh (1992), might have made the group-
opportunity to talk through the solution once again and work more effective for all students.
to discuss the results. We agree with Leonard et al. It is also important that the teacher is present and
(1996) that teaching problem-solving strategies focuses can guide the groups. This was shown in the first helium
132 © 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134
13. Small-group Discussions
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