The analysis of the students‘ answers to the two problems previously presented includes two parts: 1) a deep analysis of the students‘ answers to each problem and 2) an analysis of comparison and relationships between the various aspects of the answers to both problems.
The problem to problem analysis begins with a qualitative analysis to the interviews we have done to some students and to the individual written answers. We try to establish some categories and subcategories, some of which may be mutually excluding while others may be produced at the same time. We collect this categorization structure using the Systemic Network technique (Bliss, Ogborn & Monk, 1983). After this qualitative data analysis, we perform a quantitative data analysis of both problems and its comparisons based on categories and subcategories of Systemic Networks.
1. Analysis of answers to problem 1 and problem 2
Because both problems are very similar from the Physics point of view, we will present the analysis of both problems together. At first, we interviewed two students immediately after they had answered the problems. Interviews have been of help to build the network from the written answers. We include and comment below some of the parts of these systemic networks that correspond to the big categories found in both problems.
The first big category is Drawing. Here we classified the students according to the making or not making of a drawing criterion, and according to the type of drawing. We don‘t present the network here.
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The second category is type of Answer (problem 1 and problem 2), in which we classify the students according to the chosen answer. In problem 2 we also have the big category of type of Answer to question b). We represent here the systemic network of problem 2, which includes the network of problem 1 because the categories of the Answer to problem 1 are exactly the same of the Answer to problem 2a).
Answer (Aa)
Fig. 1: Network of Answers to problem 1 and problem 2.
In our Teachers sample, the biggest percentage corresponds to the correct answer, but the percentages of incorrect answers (vertical and backwards) are also high. Students with higher scientific level answer better than non-scientific students. This problem is similar to the problems students usually solve at Physics classroom, so these results are not surprising.
In problem 2 a) the biggest percentage of students answer Aa2 (vertically), an incorrect answer. But by levels, the biggest percentage of correct answers is at Science 3rd level, as in problem 1. Students with less or none scientific background answer Aa2 (vertically), an answer that coincides with the ancient ideas we commented in the HC –these are pre-Galilean students. Most of the students answer question b) in problem 2 incorrectly at all levels. That means the scientific background students have is not useful to answer correctly this question.
The third big category is velocity of the object/ball. We include below the network of this big category. It would seem logical that, if students say that the object/ball will go forward, they must bear in mind that it should be at exactly the same velocity of the train/lorry, but it is not true in all the cases. Thus, we introduce a sub-categorization in order to count students that have a good understanding of this problem. (See fig. 2).
Velocity of
Fig. 2: Network of Velocity of the object / ball in problem 1 and problem 2.
The fourth category is the Type of Justification students give when answering the problems. According to the general Physics‘ concept they use to justify their choice, we classify the students‘ justifications in five big categories that also have some subcategories (See fig. 3).
Justifications
By using Dynamics Concepts (J4) Forces and Impetus (J41) Gravity as a force (J42) By using Trajectory (J5)
Fig. 3: Network of Types of Justifications answering problem 1 and problem 2.
3. Comparison between problem 1 and problem 2a)
After the analysis of each problem we will compare the students‘ answers to the two problems. We‘ll do this comparative study from the categories of the systemic networks.
The first category we compare is Type of answer (We won‘t count here Not clear answers).
Table 1: Comparison of types of answers.
Answer to problems
1 and 2a) Forward Vertically Backwards Not answered Total problem 1
The results collected in the table indicate that students interpret differently these problems, which are very similar from the Physics point of view.
We also compare the categories of the velocity of the object/ball when it leaves its carrier in motion. This comparison says that, mainly, students don‘t attribute velocity in the direction of the carrier‘s motion to the object that separates from it, and this category is significantly higher in problem 2 than in problem 1.
To compare the students justifications, we don‘t consider justification of Trajectory because most of these justifications can be considered as a Kinematics justification, thus we have a new table of Reduction of justifications with only five excluding categories. There are differences in the percentages related to the categories in the two problems. From the differences found in the results of the two problems, we can infer that students interpret each problem in a different way, and they find problem 2 more difficult than problem 1, but in both cases non-scientific students answer both problems worse than scientific ones.
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The performed research with these specific problems proposed to students has been very useful to evidence that nowadays students participate of many ideas and conceptions identified in pre-Galilean history of science. In particular, many students have a non-relative conception of motion trajectory and velocity; many of them have an absolute conception of these scientific entities.
Students mainly answer problem 1 better than problem 2. This result may be interpreted by the fact that this first problem is more similar to problems that students use to solve in Physics classroom. A very relevant characteristic of these problems is that, while through the question proposed in problem 1 students have to use a FR at rest, in problem 2, that has two questions, students have to use a FR in motion (relative to the observation point) and also a FR at rest.
An interesting comment we can do from these results is that only with question b) in problem 2 have we been able to really know about the students comprehension of the physical situation in which an object drops or is thrown away from a moving system. This interpretation brings us to the importance and relevance of some particular characteristics of problems or questions proposed to students.
Implied from research and comparison with HC, is that the HC would have to be included in the Teacher Training curriculum. Researches done tell us that the topic of Galilean Relativity is not easy, students have to change their own way to see the world in a new way that is against their common way of thinking. This can never be easy, and is more a persuasion issue than a discovering. Thus, teachers will have an essential role in convincing students, and the HC is an important source of new approaches and also of specific ideas for the design of appropriate activities, and also new multimedia resources can be useful; but without an adequate orientation and scaffolding by the teacher, convincing of these new ideas will be quite impossible.
Acknowledgements:
We would like to acknowledge the support of the DIUE (Generalitat de Catalunya) by project 2008ARIE00071 and the support of the ARCE2009 of the Universitat de Barcelona.
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