Ann-Marie Pendrill1 and Åke Ingerman2
1) Department of Physics, Göteborg University, Sweden, Ann-Marie.Pendrill@physics.gu.se
2) Department of Education, Göteborg university, Sweden, Ake.Ingerman@ped.gu.seABSTRACT
An encounter with a phenomenon in a science center exhibit can provoke many questions and discussions among the visitors. Interaction with a guide can enhance the experience and help the visitors develop a deeper understanding and see more connections to other phenomena. The outcome of the discussions depend on the visitors, but also on the guide's strategy. This paper builds on empirical material in more formal learning situations, but with relevance for interactions e.g. in a science center. We first consider formal learning outcomes based on informal learning experiences in an amusement park. We then consider tutor preparation and tutor choices, with respect to entering in the dialogue, engaging with the students and finally, ending the teaching interaction. We find that an alliance between formal and informal learning situations can be mutually beneficial.
In this work, we are particularly interested in quasi-informal learning situations where e.g. a science center exhibit is visited and interacted with as a part of a formal course. How can a teacher prepare such visits? Understanding common ways of thinking about concepts related to the exhibit is essential for the design of the exhibit itself, but also for the approach of the guides and for possible assignments by a teacher. In informal learning situations, the interaction is often limited in time and the goals are open. The guide would like to understand the aim of the visit and also to know the visitor's thoughts and previous knowledge, to be able to build on that knowledge. Strategies for eliciting visitor preconceptions are thus important. Thoughts on the strategy for the interaction can be part of the design, and, ideally, also developed in collaboration with the designer and the guides during the testing of the exhibit.
In order to develop a model for analysing the interactions, we draw on material from more formal learning situations. In section 2 we consider a question with possible learning goals in connection with a playground or amusement park visit. The physics content concerns acceleration as a swing passes the lowest point and the question arose from a group dialogue among first year engineering students at Chalmers during their second week of term. The group dialogue was paraphrased as a problem on a written test given to a large group of students, as a way to find the different ways students would describe this situation. The results demonstrate that many students hold incompatible views without noting the conflict between the everyday and physics use of the term acceleration. The results of this analysis can be used to create tasks for group discussions in preparation for future amusement park visits for physics learning. This type of conflict can often lead to interesting group discussions, where teacher interaction may be essential to bring out more clearly the challenge inherent in the contradiction.
In section 3 we consider the situation where a teacher supervises small- group discussions as part of a larger class. As in the case for science center dialogues, the interaction time with the group is often a small part of the total time the group may be involved with the exhibit, challenge or problem at hand. In both cases the teacher or guide would like to know the thoughts, questions and difficulties of the group concerning the topic in order to optimize the interaction. The limited time available for the total interaction emphasizes the need for a strategy to elicit the thoughts of the group. Our consideration is based on video-recordings of group tutorials with limited teacher interaction. The students are studying physics during the first year of their engineering programmes at Chalmers. The video recording provides a window to analyse what happens to the discussion in the group before, during and after the teacher intervention. The results presented aim to be of direct relevance both to physics teachers and science center guides, through the focus on restricted interaction with groups around a given physical situation.
Figure 1: A spiral rabbit and a "slinky" mounted in a swing to demonstrate forces on the rider during various parts of the ride |
Light, heavy, light, heavy. During the pendulum motion in a swing, the body feels a periodic change in the forces acting on the body. In everyday life we experience the force required for acceleration in all its vector character. However, the experience of the body is rarely utilized in the teaching of mechanics. The study of the laws of motion often starts in non-motion or in uniform rectilinear motion, where the absense of net forces is counterintuitive.
What is the acceleration at the lowest point of a swing? Newton's second law relates acceleration to force, as a=F/m, so the acceleration is experienced throughout the accelerated body. A visual measure of the forces on the body can be obtained e.g. using a spiral toy as in Figure 1 (Pendrill and Williams, 2005). At the lowest point the swing has maximum speed. The everyday conception of acceleration as increase of speed, contrasts with the mathematical definition of acceleration as the time derivative of the velocity vector. Although the acceleration along the line of motion is zero, the maximum speed leads to a maximum in the centripetal acceleration due to the motion along the circle. However, since this acceleration is orthogonal to the motion, it involves changes only the direction of the velocity, but not the magnitude.
In a small-group discussion, one student (A) argues that, since the potential energy is lowest at the lowest point, the velocity has a maximum, and the derivative must then be zero. Another student (B) thinks that there must be something wrong with this argument, since you feel heavier than usual at the bottom. When the teacher asks if they could try to discuss the situation to resolve the contradiction, they asked if they should repeat their arguments. This dialogue was later used for an end of term quiz for first-year students, who were asked how they would help the students sort out the physics. From the replies we can identify different ways of thinking about force and acceleration in circular motion. The main categories found an analysis of the student replies are
Acceleration is zero
Some of the students' replies in the first category are undisturbed by the
experience of forces
at the bottom, and just express support for student A, or rephrases his claims.
Other replies seem to treat force and acceleration as unrelated concepts, e.g.
Centripetal force
In the second category, most students' replies give expressions for the
centripetal force
and its dependence on velocity, but do no address student A's concerns, as e.g.:
Change of direction
In category III, students' replies more
explicity discuss the
change of direction
of motion.
Change of angle
The change in angle between the direction of the centripetal acceleration and
the
acceleration of gravity certainly accounts for the change in normal
force from the swing acting on the rider, as referred to in replies in
category IV, and would not happen in the absence of a circular motion.
In the case of uniform circular motion in
a vertical plane, which had been discussed in detail in class, this is the only
contributing effect, whereas in a swing, the angular velocity is changing
periodically
and is largest at the bottom, leading to a maximum also of the centripetal
acceleration,
itself.
Orthogonal components
Finally, some students clearly express in their replies (category V) that
Group discussions can be one way to invite students to challenge contradicting, but coexisting points of view. However, teacher intervention can often be essential to expose or resolve the contradiction. Additional excerpts from supervised small-group discussions about acceleration can be found in Pendrill (2008). The replies from the student tests presented here give input to revise the task for student group discussions on acceleration, and also emphasized common incomplete understanding worth addressing. The next section focuses more directly on the interaction between the teacher and a group.
A common feature of physics courses is that students work on various problems, often in small groups tutored by teachers. At our physics department the forms of the group work are relatively free. Students are free to form and reform groups, work in the presence of other groups or separately. The content is set by a list of problems, and no particular form for the group interaction is imposed on the students, and the students receive no particular training in how to work in groups. From a small informal survey among some of the teachers at the department it is clear that typical preparation mainly consists of different kinds of consideration of the conceptual and mathematical difficulties of the problems set for the students – sometimes restricted to ‘solving’ the problems. From our personal experience of teaching at various physics departments, this situation is not uncommon.
Ideas for interaction are mainly drawn from personal experience, partially from discussions from colleagues and sometimes from literature such as Jacques (2000). However, it is scarce to find less generic literature which gives opportunities for reflection in relation to the teachers’ practice and which is suitable to draw on with respect to how to facilitate students’ learning of the physics content and to spot and address conceptual difficulties in the groups you encounter – in short literature supportive in developing good practice. Most literature is concerned with investigating cooperative learning, more stable groups, favourable mixing, size and physical arrangements, and looking for achievement differences (see e.g. Springer et al, 1999, and Bennet et al, 2004, for overviews). In connection with informal learning, the dialogues within family groups have been investigated e.g. by Ash (2003). These issues are discussed also in connection with the presentation of Context- Rich problems in physics. (for example, see Heller and Hollabaugh, 1992, Heller et al 1992, and Waltner et al 2007)
The empirical data consists of video and audio recordings of groups of three or four, while they were working with two mechanics problems. During the hour they had at their disposal, a teacher visited them two times each, on average for five minutes. The students were first year university students in a MSc program on biotechnology at Chalmers University of Technology, taking a service course in mechanics (almost identical to the course given to students majoring in physics). The students were volunteers from the full class of 35 students, and for the duration of the hour they were in separate rooms, while the students not participating in the study worked in groups in their normal classroom with the same problems, also tutored on the same level. At the time, lecturing on non-accelerated mechanics had just come to a close, and these problems were the last of this kind ‘officially’ considered in class with tutoring. The first of these problems presented the students with the situation of an ox dragging a box. They were asked what forces acted in the situation. Then, they were asked how the forces would be affected if the mass of the box doubled and if the mass of the ox was doubled. The second problem concerned the best choice of angle for a string used to drag a board over rough ground.
Having transcripts of the students’ conversation readily available, we closely followed the supervisory episodes, as well as a few minutes running up to and following the episode where the teacher was present. Initial discussions resulted in a simple model of the episodes, which was used to systematically structure observations in the whole of the material.
The model we use to structure our analysis of the tutoring episodes can be described by four questions:
Here we will limit ourselves to consider one episode in part to show some basics of our analysis. In the extract below the students H, I, J, K have been working with the first problem about five minutes, and the teacher (T) enters. The minute before the students have been discussing whether friction (unclear what friction) is the 'driving' force that makes the whole thing move. They are certain there must be a force directed forward, which is larger than the friction on the box when moving at constant velocity.
We can observe several conceptual problems such as where force balance is requested (in the rope, on the ox etc), whether the forces should be equal for constant velocity or there should be a driving force, and what system is considered (the ox and box together, separately, or something else). When the teacher does not confirm the student question (end of line 10), the hint is taken (line 11). The teacher then makes a decision on how to proceed, and on line 15 starts thematising the force balance in the rope on a quite detailed level, similar to a short interactive lecture. She unconsciously chooses to ignore the other possibilities of addressing conceptual problems that was displayed in the student conversation. Further down the line, when the teacher no longer is present, the students initially fail to see the connection between force balance in the rope and force balance in the whole system of ox, box and rope. Only after considerable discussion (approximately 10 minutes), the group starts to recognise what force balance requires in the present problem (that the sum of all forces external to the system should equal zero for constant velocity).