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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

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

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

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

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

RESULTS: LEARNING OF PHYSICS – THREE

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

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

RESULTS: LEARNING OF PHYSICS – THREE

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

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 = fλ 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

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 = fλ 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

glass.

that…

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

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

glass.

that…

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 = fλ. 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

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 = fλ. 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

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

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

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

group where the group several times had made a correct Cohen, E.G. (1994). Restructuring the classroom: Conditions

description but when the teacher came to the group for productive small groups. Review of Educational

they still had to ask if it is the frequency or the wave- Research, 64(1), 1-35.

length that will be constant when the sound travels DiSessa, A.A. (1993). Towards an epistemology of physics.

Cognition and Instruction, 10, 105-225.

across an interface. To listen to the questions of the

Driver, R., Asoko, H., Leach, J., Mortimer, E. & Scott, P.

students can be an important occasion for the teacher to (1994) Constructing scientific knowledge in the

learn about students‟ difficulties with physics. It is classroom. Educational Researcher, 23(7), 5-12.

important for the teacher to listen to the discussions to Enghag, M., Gustafsson, P. & Jonsson, G. (2007) From

be able to treat important questions raised in the group everyday life experiences to physics understanding

discussions in a following lecture. occurring in small group work with context-rich

Maloney (1994) says that if we expect students to problems during introductory physics work at

learn concepts and principles we may need to alter the university. Research in Science Education. Published online

form of the assigned problems. He mentions context- 11 January 2007.

rich problems introduced by Heller and Hollabaugh Gautreau, R. & Novembsky, L. (1997). Concepts first – A

small group approach to physics learning. American

(1992) as one possibility. Context-rich problems,

Journal of Physics, 65 (5), 418-428.

however, can differ in content and form. The problem Hake, R. R. (1998). Interactive-engagement versus traditional

in special relativity was very engaging and the problem methods: A six-thousand-student survey of mechanics

in mechanics less so. It is essential to put energy in test data for introductory physics courses. American

designing good problems. The qualitative helium Journal of Physics, 66 (1), 64-74.

problem gave rise to lively discussions, even though our Halloun, I. A. & Hestenes, D. (1985). Common-sense

experience was that qualitative questions in general give concepts about motion. American Journal of Physics, 53,

rise to rather shallow discussions. The conclusion is that 1056–1065.

qualitative questions as other context-rich problems Hammer, D. (1996). Misconceptions or P-Prims: How may

should be formulated so that they result in some alternative perspectives of cognitive structure influence

instructional perceptions and intentions? The Journal of

puzzling experience for the students.

The Learning Sciences 5(2), 97-127.

We find that group discussions around physics Heller P., Keith R. & Anderson S. (1992). Teaching problem

problems can lead to stimulating and learning solving through cooperative grouping. Part 1: Group

discussions of physics. The students discussed physics versus individual problem solving. American Journal of

concepts and principles and evolved their knowledge Physics, 60 (7), 627-636.

gradually. Misunderstandings known from the literature Heller P. & Hollabaugh M (1992) Teaching problem solving

came up in the discussions but the students also through cooperative grouping. Part 2: Designing

detected new „problems‟. In the discussions most problems and structuring groups. American Journal of

misunderstandings and problems were treated and Physics, 60 (7), 637-644.

solved either by the students themselves or by the Hestenes, D., Wells, M. & Swackhamer, G. (1992). Force

Concept Inventory. The Physics Teacher, 30, 141–158.

students together with the teacher. Factors that

Hewson, P. (1982). A case study of conceptual change in

stimulate a good discussion are engaging problems and a special relativity: The influence of prior knowledge in

teacher at hand to answer questions and to discuss with learning. European Journal of Science Education, 4, 61-76.

the students. A taught problem-solving strategy can also Huffman, D. (1997). Effect of explicit problem solving

in some occasions be valuable. Factors that can prevent instruction on high school students‟ problem-solving

a fruitful discussion are too little knowledge of the performance and conceptual understanding of physics.

actual physics among the students and bad functioning Journal of Research in Science Teaching, 34 (6), 551-570.

of the groups. Johnson, D. W., Johnson, R. T. & Smith, K. A. (1998).

Cooperative learning returns to college. Change, 30 (4),

REFERENCES 26 – 35.

Johnson, M. (2001). Facilitating high quality student practice

Barnes, D. & Todd, F. (1995). Communication and Learning in introductory physics. Phys. Educ. Res. American Journal

Revisited. Portsmouth: Boynton/Cook Publishers. of Physics Suppl. 69 (7), S2-S11.

Benckert, S., Pettersson, S., Aasa, S., Johansson, O. & Larkin, J. H., McDermott, J., Simon, D. P. & Simon, H. A.

Norman, R. (2005). Gruppdiskussioner runt kontextrika (1980). Expert and novice performance in solving

problem i fysik – Hur ska problemen utformas? [Group physics problems. Science, 208, 1335–1342.

discussions around context-rich problems in physics – Leach, J. & Scott, P. (2003). Individual and Sociocultural

How is the problemsbest formulated?] NorDina nr 2, Views of Learning in Science Education. Science &

36-50. (In Swedish) Education, 12, 91-113.

Booth, K.M. & James, B.W. (2001). Interactive learning in a Lemke, J. L. (1990). Talking Sience: Language, Learning and

higher education Level 1 mechanics module. International Values. Norwood, New Jersey: Ablex Publishing

Journal of Science Education 23(9), 955-967. Corporation.

Leonard, W. J., Dufresne, R. J. & Mestre, J. P. (1996). Using

qualitative problem-solving strategies to highlight the

© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 133

group where the group several times had made a correct Cohen, E.G. (1994). Restructuring the classroom: Conditions

description but when the teacher came to the group for productive small groups. Review of Educational

they still had to ask if it is the frequency or the wave- Research, 64(1), 1-35.

length that will be constant when the sound travels DiSessa, A.A. (1993). Towards an epistemology of physics.

Cognition and Instruction, 10, 105-225.

across an interface. To listen to the questions of the

Driver, R., Asoko, H., Leach, J., Mortimer, E. & Scott, P.

students can be an important occasion for the teacher to (1994) Constructing scientific knowledge in the

learn about students‟ difficulties with physics. It is classroom. Educational Researcher, 23(7), 5-12.

important for the teacher to listen to the discussions to Enghag, M., Gustafsson, P. & Jonsson, G. (2007) From

be able to treat important questions raised in the group everyday life experiences to physics understanding

discussions in a following lecture. occurring in small group work with context-rich

Maloney (1994) says that if we expect students to problems during introductory physics work at

learn concepts and principles we may need to alter the university. Research in Science Education. Published online

form of the assigned problems. He mentions context- 11 January 2007.

rich problems introduced by Heller and Hollabaugh Gautreau, R. & Novembsky, L. (1997). Concepts first – A

small group approach to physics learning. American

(1992) as one possibility. Context-rich problems,

Journal of Physics, 65 (5), 418-428.

however, can differ in content and form. The problem Hake, R. R. (1998). Interactive-engagement versus traditional

in special relativity was very engaging and the problem methods: A six-thousand-student survey of mechanics

in mechanics less so. It is essential to put energy in test data for introductory physics courses. American

designing good problems. The qualitative helium Journal of Physics, 66 (1), 64-74.

problem gave rise to lively discussions, even though our Halloun, I. A. & Hestenes, D. (1985). Common-sense

experience was that qualitative questions in general give concepts about motion. American Journal of Physics, 53,

rise to rather shallow discussions. The conclusion is that 1056–1065.

qualitative questions as other context-rich problems Hammer, D. (1996). Misconceptions or P-Prims: How may

should be formulated so that they result in some alternative perspectives of cognitive structure influence

instructional perceptions and intentions? The Journal of

puzzling experience for the students.

The Learning Sciences 5(2), 97-127.

We find that group discussions around physics Heller P., Keith R. & Anderson S. (1992). Teaching problem

problems can lead to stimulating and learning solving through cooperative grouping. Part 1: Group

discussions of physics. The students discussed physics versus individual problem solving. American Journal of

concepts and principles and evolved their knowledge Physics, 60 (7), 627-636.

gradually. Misunderstandings known from the literature Heller P. & Hollabaugh M (1992) Teaching problem solving

came up in the discussions but the students also through cooperative grouping. Part 2: Designing

detected new „problems‟. In the discussions most problems and structuring groups. American Journal of

misunderstandings and problems were treated and Physics, 60 (7), 637-644.

solved either by the students themselves or by the Hestenes, D., Wells, M. & Swackhamer, G. (1992). Force

Concept Inventory. The Physics Teacher, 30, 141–158.

students together with the teacher. Factors that

Hewson, P. (1982). A case study of conceptual change in

stimulate a good discussion are engaging problems and a special relativity: The influence of prior knowledge in

teacher at hand to answer questions and to discuss with learning. European Journal of Science Education, 4, 61-76.

the students. A taught problem-solving strategy can also Huffman, D. (1997). Effect of explicit problem solving

in some occasions be valuable. Factors that can prevent instruction on high school students‟ problem-solving

a fruitful discussion are too little knowledge of the performance and conceptual understanding of physics.

actual physics among the students and bad functioning Journal of Research in Science Teaching, 34 (6), 551-570.

of the groups. Johnson, D. W., Johnson, R. T. & Smith, K. A. (1998).

Cooperative learning returns to college. Change, 30 (4),

REFERENCES 26 – 35.

Johnson, M. (2001). Facilitating high quality student practice

Barnes, D. & Todd, F. (1995). Communication and Learning in introductory physics. Phys. Educ. Res. American Journal

Revisited. Portsmouth: Boynton/Cook Publishers. of Physics Suppl. 69 (7), S2-S11.

Benckert, S., Pettersson, S., Aasa, S., Johansson, O. & Larkin, J. H., McDermott, J., Simon, D. P. & Simon, H. A.

Norman, R. (2005). Gruppdiskussioner runt kontextrika (1980). Expert and novice performance in solving

problem i fysik – Hur ska problemen utformas? [Group physics problems. Science, 208, 1335–1342.

discussions around context-rich problems in physics – Leach, J. & Scott, P. (2003). Individual and Sociocultural

How is the problemsbest formulated?] NorDina nr 2, Views of Learning in Science Education. Science &

36-50. (In Swedish) Education, 12, 91-113.

Booth, K.M. & James, B.W. (2001). Interactive learning in a Lemke, J. L. (1990). Talking Sience: Language, Learning and

higher education Level 1 mechanics module. International Values. Norwood, New Jersey: Ablex Publishing

Journal of Science Education 23(9), 955-967. Corporation.

Leonard, W. J., Dufresne, R. J. & Mestre, J. P. (1996). Using

qualitative problem-solving strategies to highlight the

© 2008 Moment, Eurasia J. Math. Sci. & Tech. Ed., 4(2), 121-134 133

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S. Benckert & S. Pettersson

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