7 Results 2: Development of external representations of DC-circuit phenomena in a small group
7.3 Fragments of external representations of DC-circuit phenomena
7.3.3 Results: Small group’s external representations of the source voltage The modelling process of the external representation of the source voltage extended to the
whole teaching experiment. Although the first half of the teaching experiment focused on experiments on the electric circuit and the electric current, they also outlined the modelling process of the source voltage: the meaning of a battery to the electric circuit was discussed in the PI and batteries were used in the experiments during the first three lessons. However, the primary lessons for modelling the source voltage were lessons four and five. In addition the final interview also included special questions concerning the source voltage. During the second half of the teaching experiment experiments – adding batteries to an electric circuit, connecting batteries in opposite polarity, changing the place of battery in the electric circuit, constructing a dollhouse-electrification, and solving the problem of a broken pocket lamp – were done. The types of experiments used were PC, CC, RC, OPT, WEG, and P, see the horizontal axis of Figure 38.
148 Figure 38 The fragment map for the external representation of the source voltage.
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As discussed above the modelling process of the source voltage was divided into a spontaneous part during the first three lessons, and to a more guided part during the 4th and 5th lessons. Moreover there were interviews PI, II and FI, which also included the themes of source voltage and batteries. Due to the different phases of modelling the source voltage, the fragment map (Figure 38) includes four not simultaneous fragment paths, which overlap less than the paths portrayed earlier in figures Figure 35 and Figure 37.
The fragments, which emerged during the content analysis, have been classified into four categories: 1) causal relations, 2) meaning of the battery, 3) strength of the battery, and 4) source voltage of the battery. The first of the categories deals according to its name with the causal relations of the circuit. Therefore, categories 2-4 stand for comparative fragments of different levels.
Causal relations: fragment path 1 2 3
Understanding the main causal relations is a basic requirement in a modelling process. In the case of DC-circuit phenomena the relation between the source voltage, or at least the battery, and the electric current is a fundamental part of the external representation of the source voltage. The fragment path 1 2 3 pictures the small group’s external representation of the causal relations of the DC-circuit phenomena. According to the small group the battery is the source of the electric current (1, 2, 3). This fragment of external representation of the source voltage appears unchanging in the talk of the group, and it is used in explaining the following phenomena: 1) bulbs light because of electric current flowing to them from the battery (1 and 3) and 2) bulbs go out because of stopping the flow of electric current from the battery (2). Table 19 below gives an example similar to fragments 1, 2 and 3.
Table 19 Content analysis leading to fragment 3, Electric current from battery to bulbs, which light.
ORIGINAL TALK REDUCED EXPRESSION FRAGMENT
M: Because that battery and those wires no longer bring the electric current to the bulb, it goes out.
The electric current from the battery via wires to the bulb
Electric current from battery to bulbs, which light (3)
L: They go out in a nice way, so that the electricity goes, whoosh. It goes away.
The bulb goes out, when the electricity leaves from it.
R: Why does the bulb light?
M: Because the battery gives the electric current to it.
The battery gives electric current to the bulb.
Meaning of the battery: fragment path 4 5 6
The fragment path Meaning of the battery stands for the first phase of prequantitative knowledge in the process of external representing the source voltage. This fragment path
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formed during the first three lessons, when the source voltage was not yet at the focus of learning. Fragment 4 was expressed during the preliminary interview as an answer to a question concerning the meaning of the battery in the electric circuit. A typical part of the talk was the following:
Teacher: What do you think, Milja? Will the bulb light?
Milja: No.
Matti: Because there isn’t a battery.
Laura: Because there isn’t that source of electricity (in the circuit).
Small group From this and similar representations expressed it was concluded that at the beginning of the teaching experiment the small group understood the battery as a source of electricity, so the fragment was named as Battery has electricity or electric current. During the next three lessons the small group got lots of experiences of connecting bulbs in series. The batteries used in these experiments were 1.5 V and 4,5 V ones. These were particularly the first experiments that made the small group compare properties of different batteries.
Table 20 Fragment 5 of the external representation of the source voltage of the battery.
ORIGINAL TALK REDUCED EXPRESSION FRAGMENT
M: We learnt that when we have…
N: Where two bulbs are lighting.
L: That when there is the bigger battery, and then three bulbs are lighting. And by that smaller battery they don’t.
More bulbs are lit by a bigger battery.
A bigger battery has more electric current (5)
T: Do you remember why the bulbs were lit by that bigger battery?
L: It had more electric current, so it was enough for every (bulb).
A bigger battery is used for more bulbs.
A bigger battery has more electric current, which is enough for every bulb.
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As it is described in Table 20 fragment 5 was expressed in a discussion with the teacher at the beginning of the third lesson when the teacher asked what kinds of things the small group had learnt the last time. The small group seemed to be in agreement with the property of the battery: a bigger battery has more electric current. This fragment of the external representation of the source voltage appeared also in the intermediate interview, when the small group used an expression A Poor battery cannot light bulbs (6) in differentiating batteries from each other. So, the small group had actually formed independently the prequantitative relation between different batteries.
Strength of the battery, fragment 7
The fourth lesson included experiments of adding several batteries in series. Batteries were added in series both by connection cards at the beginning of the lesson, and later by real connections. Also picture cards (see Figure 39 below) were used to help the small group to think of a new situation with a different number of batteries in series.
Figure 39 Picture cards used to chart the small group’s external representation of adding more batteries in series. What happens if another battery is connected to circuit 1? What if a third battery is added? The batteries are identical. What happens if there is only one battery in the circuit as shown in number 4?
Fragment 7 is a hypothesis, which the small group expressed before the real connections of adding more batteries in series. The result Adding batteries brightens bulb
bulb has more electricity is a logical continuation to the fragment path 4 5 6 described earlier. Thus, it appears that for the small group the strength of the battery is a natural way of perceiving the DC-circuit phenomena. Though fragment 7 again includes the incorrect theoretical explanation of the battery as a source of electricity (or electric current), the fragment shows quite a well-developed empirical based external representation of the strength property of the battery. The same kind of picture of
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understanding the strength of the battery also appeared during the last lesson when the small group worked with open problem tasks. For more discussion in context of fragment 7 see Appendix 8: Adding batteries brightens the bulb.
Table 21 Fragment 7 of the external representation of the source voltage of the battery.
ORIGINAL TALK REDUCED EXPRESSION FRAGMENT
T: Could it be possible to add more batteries to this kind of circuit?
Small group: [everybody nods]
It is possible to add batteries to a circuit.
Adding batteries brightens the bulb
the bulb has more electricity (7)
T: What would happen in this circuit? There are two batteries now.
N: Well, I don’t know, but I think that the bulb will brighten more. It has more electricity now.
M: That number two and three, I have thought that the bulb will light brightly.
Adding batteries brightens the bulb. The bulb has now more electricity.
L: I am thinking about this number four, I suppose that the bulb would light as brightly by this as by two of these little poorer.
T: Yes. What do you think, in which circuit would the bulb be as bright as with this battery (number 4)? If there would be one of this of battery (number 4), so how many of these kinds would be needed (number 1) to get as bright a bulb?
L: [shows number 2]
M: Three.
N: Two.
Mi: Two.
Batteries can be added: two or three poorer batteries equals one better battery.
Fragment 8: Voltage?
Fragment 8 is separated into its own fragment, because it represents an interesting detail of the small group’s knowledge structure of the source voltage of the battery. The small group had no conception of the voltage of a battery (8). The role of the battery was just to act as a store of the electric current, so there was no need for a special property of the battery. The size of the battery seemed to be related to its capability to storage the electric current.
153 Source voltage of the battery, fragment 9
Fragment 9 stands for the small group’s final external representation of the source voltage.
To the external representation has been collected all the main aspects of the source voltage, which the small group expressed during the final interview. If started from the top (see fragment 9, Figure 38), the first part of the external representation is the following:
source voltage relates to battery, strength of electricity. This kind of representation appears from the following discussion:
Table 22 Source voltage relates to battery.
ORIGINAL TALK REDUCED EXPRESSION FRAGMENT
T: What does the voltage mean, do you remember?
Mi: It is that current.
L: But no it that … voltage affair…
T: What is the voltage relate to?
T: Milja?
Mi: Nothing.
Teacher: To what part of the circuit does the voltage
voltage is related to the battery
how strong the electricity is voltage is the battery’s current
Source voltage relates to the battery, strength of electricity (9)
As the discussion reveals, it was still quite difficult in the end of the teaching experiment for the small group to distinguish the source voltage from the electric current.
Moreover, it seemed to be difficult to precisely localise the source voltage. However the language used in the small group reveals that to the external representation contains a mental picture of the source voltage, which is related to the battery, and according to this image, the source voltage measures the strength of electricity.
The next part of the external representation (9) discusses the idea of strengthening the property of the battery. Firstly, the source voltage is produced by connecting the batteries in series. Secondly, the property can be strengthened either by adding more batteries or using bigger batteries. Here the small group has achieved the empirical law between the number of batteries in series and the brightness of the bulb.
The last part of the external representation (9) includes the small group’s conception of the causal relations of the electric circuit. Although the external representation is incorrect,
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when it describes the role of a battery as a source of the electric current instead of a property of a battery to cause the electric-current phenomenon, the external representation however includes the picture of the direction of the causal relations. According to the small group the battery is the starting point and the lighting of the bulb is an effect-phenomenon.