A qualitative research of the conceptual learning process of the heat concept http://www.ied.edu.hk/apfslt/v17

Findings obtained from the interviews with the student (Ekin) were used to describe how the students understood the heat concept. However, the definition of heat, the relationship of heat within matter, and the relationship between heat and other concepts frequently changed within five weeks. Conflicting opinions were observed even in the same interview. In case of conflicting opinions, we considered which one Ekin repeated more and her persistence. This is defined as "balance of dominance" by researchers. The intersection of two conflicting ideas is given as "dominance" in charts. In these charts, other codes were proportioned according to the most frequently repeated code.

In this section, the change in Ekin's opinions over time was examined under four categories: (1) general opinions about heat, (2) opinions about the relationship between the heat concept and temperature concept, (3) opinions about the relationship between the heat concept and thermal energy concept, and (4) opinions about the quantitative aspect of heat. These were examined separately.

Analytical Assessment of Ekin's General Opinions about Heat

Ekin's general opinions about heat are examined under two sub-categories. The first one is the relationship between heat and matter and the second one is the definition of heat. The following codes can be used to demonstrate opinions asserted by Ekin regarding the relationship of heat with matters.

a. Matters does not store heat.

b. Matters stores heat or possesses heat.

c. There is a concept called heat change.

d. Matter only stores heat when it is not at thermal balance.

These four propositions asserted by Ekin show the relationship between heat and matter in her mind. The first two propositions (a and b) conflict with each other. The last proposition (d) can be accepted as an interim proposition which supports both propositions to a certain degree. The third proposition (c) is the proposition where the heat change concept was asserted. This new concept supports the proposition that heat is stored by matter. Figure 1 shows how the dominance of these propositions changed throughout five weeks.

Figure 1. Temporal change in Ekin's opinions about the relationship between heat and matter

Ekin's opinions about the relationship between heat and matter changed during the five- week process. As shown in Figure 1, all propositions were asserted in the first week. In other words, Ekin had all these opinions more or less in the first week. However, the most dominant was the idea that heat is stored in matters. It is followed by the idea that the heat change concept is a real concept. She mentioned the idea that matter does not store heat but she did not dwell on it. The idea that matter stores heat only when there is no thermal balance is at its peak in the first weak. It disappeared after the third week.

The ideas that matter does not store heat and idea that matter stores heat are inversely proportional naturally. The third week and the fourth week can be seen as the breaking point in this sense. Because the idea that matter does not store heat disappeared in the second week and while the same idea had not formed yet in the third week again, the conflicting idea, the idea that matter stores heat was considerably reduced in the fourth week.

Another important finding is the decrease and disappearance of the idea of heat change in parallel with the idea that matter stores heat. So, it can be said that the idea of heat change is based on the idea that matter stores heat. Ekin had the idea that matter possesses heat or store heat, thus the idea that the quantity of the stored heat changes in cases such as temperature change. These two propositions explain and support each other.

The proposition that matter stores heat only when it is not at thermal balance might be a proposition asserted as a result of the indecision between matters storing and not storing heat. It might also be a result of misinterpreting Q = m.c.DT, which is used to calculate the quantity of heat transfer. As expected, the idea that matter does not store heat became more dominant while the idea that matter stores heat lost its dominance and gradually disappeared. The following dialog can be shown as an example:

Interviewer: Q = m.c.ΔT. What do you understand from this equation? What does it mean? So, what value do you calculate using Q = m.c.ΔT?
Ekin: It is actually heated change. For example, ΔT is what we use to calculate the thermal energy between the initial state and the final state by the final temperature minus the initial temperature.
Interviewer: So, you think that it is heated change. Is that correct?
Ekin: Yes, heat change. Since we calculate it, for instance, ice must have heat at the beginning. Because we subtract the initial value from the final value.
(First Interview)

In the fourth week, the idea that matter does not store heat became dominant. The other three propositions disappeared. As a conclusion, we can say that the idea that matter stores heat creates a suitable environment for the idea of heat change and the idea of heat storage. When the idea that matter stores heat lost its dominance, these other related propositions disappeared as well.

Another aspect which we addressed is the definition of heat. Ekin asserted five propositions related to the definition of heat, which are as follows:

a. Heat is a type of energy.

b. Heat is the transferred energy due to the difference in temperature.

c. Heat is the energy, which comes out due to friction or collision.

d. Heat is the total kinetic energy of matter's particles.

e. Heat is the mean kinetic energy of matter's particles.

Ekin's first proposition (a) describes the dimension of heat. However, it does not only have a dimensional approach, it also asserts that heat is a type of energy. The second proposition (b) is the most compatible with scientific theories. The third proposition (c) describes heat as the energy which comes out as a result of a mechanical phenomenon. The fourth proposition and the fifth proposition (d and e) are very similar, yet there is a difference between the two in terms of the effect of mass. Figure 2 shows how the dominance of these propositions changed throughout five weeks.

Figure 2. Temporal change in Ekin's opinions about the definition of heat

From the first interview until the last one, Ekin kept her idea that heat is a type of energy. In the first interview, she asserted collisions and frictions, i.e. mechanical phenomenon, as the reason behind the heat. She stated during interviews that her knowledge of "energy lost due to friction turns into heat" led to this idea. Ekin presented an example by rubbing her hands. She thought that it is how heat occurred and stored by matters. Her idea may be supported by false information, false definitions, or indirect expressions in some resources that she reached. This idea continued growing until the fourth week. In the fifth week, the idea disappeared with the increased dominance of other definitions. Ekin changed her ideas when she gained more knowledge about the type of molecular collisions, which she had thought to be the cause of friction. Her idea that heat is released as a result of friction disappeared when she found out that these collisions are perfectly elastic collisions. Ekin's following statements can be given as an example:

Interviewer: What do you think heat is?
Ekin: Heat is a type of energy.
...
Ekin: For example, matter does not have a heat when it is stable (Q70) but energies turn into each other and heat loss occurs.
Interviewer: So, there is a heat which matter stores and it gets lost? Is that what you mean? Ekin: Yes. For example, an energy loss occurs due to friction.
Interviewer: For example, your notebook... Does it have heat?
Ekin: I think it does.
(First Interview)

Ekin: Molecules, atoms in an object constantly vibrate. They are in motion. Heat is released when they touch one another. They produce a kinetic energy. The sum of this kinetic energy is referred to as heat. However, all molecules, not just a single one. This shows that matter has heat.
(Second Interview)

Ekin: After all, there is friction. Through friction, particles transfer heat. For example, when we put two objects next to each other, their atoms vibrate and energy transfer occurs due to vibration.
Interviewer: So, do you say that it happens through friction?
Ekin: Yes. And they collide. There is vibration. (Rubs her hands) For example, my hands got warm. It's friction...
Interviewer: They rub against each other when they vibrate. Heat is released at this time. Is that true? Do they collide with each other?
Ekin: They do it when they vibrate.
(Third Interview)

Interviewer: Can you tell me what kind of collisions these are?
Ekin: Perfectly elastic collisions.
Interviewer: What about kinetic energy in perfectly elastic collisions?
Ekin: Conserves. Oh... So it is not about friction. Then friction must be not involved in the occurrence of heat. They collide and they transfer their energy to each other. I thought there was friction during vibration. But there is not.
(Fifth Interview)

In the second and third week, Ekin strongly asserted the idea that the total kinetic energy of the particles of matter causes heat in addition to the proposition of mechanical phenomenon. This idea disappeared after the third week, in which the dominance of the idea that heat is stored within matter weakened. At this point, there might have been a connection between the idea that heat is stored in matter and the idea that the total kinetic energy of the particles of a matter causes heat. Because Ekin might have felt the need to explain how heat is stored in matter, which she had advocated since the first week, she might have asserted the total kinetic energy of particles idea in the second week. However, when she gave up on the idea that heat is stored in matter and the idea that heat is a type of energy which is not stored in matter got stronger in the fourth week, the idea that heat is the total kinetic energy of particles disappeared as well. Ekin's following statements can be given as an example:

Ekin: Now at least I can explain to you what heat and temperature are as concepts and when you asked me the last time, when you said, "Does this notebook have heat?", I was not sure. But it does. Now, I am sure.
(Second Interview)

Ekin: Now, I still define heat as the total kinetic energy of a matter. I mean, we refer to the total kinetic energy of particles as heat.
(Third Interview)

In the third week, when the idea that heat is not stored in matter became dominant, Ekin started to define heat as a transferring energy. This idea became even stronger in the final week. However, the idea that heat is the mean kinetic energy of particles appeared strongly in the final week. The emergence of this proposition is surprising. Because it was asserted at a time when the idea that heat is not stored in the matter was dominant. The emergence of this idea might be related to the temperature concept. This is addressed in the section involving the analytical assessment of the relationship between heat and temperature. Ekin's following statements can be given as an example:

Ekin: Now, I changed my mind about the heat a little bit. I used to define heat as the mean kinetic energy of particles. In a way, this is the definition of temperature. Also, this is why I told you that all matter has heat, but they do not. It must be understood as such: There must be a temperature difference. And there must be a transfer for heat to exist.
Interviewer: So?
Ekin: So, when you asked, "Does a notebook have heat?" and "Can you measure its heat?", I said, "Yes, I can." I meant that I could calculate it given its mass and specific heat. However, this matter does not actually have heat.
(Fourth Interview)

Ekin: Heat is actually a transfer. I mean, it is a transfer occurring between two or more bodies of matter with different temperatures.
(Fifth Interview)

The third week, important changes occurred in Ekin's conception of heat. Examining the transcription of the third week's session, it was seen that her study of basic concepts related to heat and heat transfer improved. Ekin's study in this week might have caused her to re-shape the heat concept in her mind, correctly or incorrectly.

Analytical Assessment of Ekin's Opinions about the Relationship Between Heat and Temperature Concepts

Ekin's opinions about the relationship between heat and temperature concepts were mainly examined in terms of the cause and effect relation between heat and temperature. Ekin essentially asserted four propositions related to the cause and effect relation between heat and temperature:

a. Heat and temperature are different quantities.

b. Temperature is why heat exists. / Heat increases because temperature increases.

c. Heat is why temperature exists. / Temperature increases because heat increases.

d. The temperature difference is why heat exists. / There is no heat if there is no temperature difference.

In terms of the first proposition (a), Ekin sometimes implied heat and temperature are the same and sometimes implied they are not. The dominance balance between the two ideas was considered in this study. Ekin sometimes asserted temperature as the reason behind heat's existence, sometimes asserted temperature difference as the reason behind heat's existence, and sometimes asserted heat as the reason behind temperature's existence. The last proposition (d) is the most compatible with scientific theories. Figure 3 shows how the dominance of these propositions changed throughout five weeks.

Figure 3. Temporal change in Ekin's opinions about the relationship between heat and temperature

While Ekin doubted that heat and temperature might be different concepts in the first week. Its reason might be wrong using these terms interchangeably. But she had a strong stance in the following weeks and was convinced these are separate concepts.

For the first two weeks, Ekin had the idea that heat exists due to temperature. It is important to remember that during this time Ekin also had the idea that heat is a type of energy which can be stored within matter and temperature is a quantity which is always seen in matter. In the first week, Ekin usually defined heat as energy arising from collisions and frictions. Also, Ekin thought that the average kinetic energy of particles is temperature and the total kinetic energy of particles is heat. Thus, we can say that she thought that the temperature of matter is its particles' motion energy and this energy is collected and stored as heat, thus heat is a quantity dependent on temperature. However, she seems to have given up these ideas after the third week. This can be observed in Ekin's following words:

Ekin: I think there is temperature as long as there is heat. Heat depends on the quantity of a body. For example, when you put your finger in a glass of water at 25 °C, it feels warm. If we add some more water at the same temperature, the temperature is the same, but the heat has increased because its mass has increased.
(Third Interview)

Ekin's idea that heat exists due to temperature changed constantly, but it was always there. At first glance, it is interesting that this proposition which conflicts with the second proposition (b), a quite dominant proposition for the first two weeks, always existed. Q = m.c.ΔT might be effective in this case. Because in this equation, heat and temperature seem related. The symbol "∆", which shows the difference, is interpreted as the absolute zero and sometimes as the freezing temperature of water at 1 atm pressure (0 ̊C) by Ekin. For this reason, the idea that if there is no temperature, there is no heat might be possible. Small fluctuations in the dominance of this idea might be a result of times of indecisiveness regarding the fitness between her idea and the equation.

Although Ekin mentioned the relationship between temperature difference and heat in the first week, she gave up this idea in following weeks. In the fourth week, the idea that heat cannot exist without temperature difference became dominant. It is important to note that the dominance of ideas that matter does not store heat, the energy transferred is referred to as heat, the temperature is not energy, yet a quantity related to the kinetic energy of particles increased after the fourth week. When the heat concept started to become clear in Ekin's mind, its relationship with temperature started to become clear as well. Although Ekin's ideas about the definition of the temperature concept followed a more complicated route, the determining factors might be her ideas about temperature's relationship with heat and whether the temperature is a type of energy or indicator. The main problem related to heat, the problem of whether it can be stored in matter or not, seems to have played a key role in the relationship between heat and temperature.

It seems that Ekin did some of her own study about heat transfer in the third week. The fact that she researched what happens during heat transfer might have influenced Ekin's thoughts about the relationship between heat and temperature because the fact that heat transfer occurs in cases where there is a temperature difference is emphasized in sources which she cited. While Ekin had difficulties making the connection between heat and temperature, her study might have helped her achieve this task.

Analytical Assessment of Ekin's Opinions about the Relationship Between Heat and Thermal Energy Concepts

Ekin's opinions about the relationship between the heat and thermal energy concepts are essentially based on describing thermal energy through heat. Ekin essentially asserted three propositions about the relationship between heat and thermal energy:

a. Heat and thermal energy are different concepts.

b. Heat and thermal energy are directly proportional.

c. Thermal energy is about water's heat and a building's getting warmer.

In terms of the first proposition (a), Ekin sometimes implied that heat and thermal energy are similar and sometimes implied that they are separate concepts. The dominance balance between the two ideas is considered. The second proposition (b) and the third proposition (c) show the relationship between these concepts. Figure 4 shows how the dominance of these propositions changed throughout five weeks.

Figure 4. Temporal change in Ekin's opinions about the relationship between heat and thermal energy

Initially, Ekin thought that thermal energy is a sub-type of heat. She described thermal energy as a type of heat which can be applied in real life. She thought that it's related to water. It seems that the use of the term "thermal energy" for the energy of hot springs and geysers in everyday life can be effective. This is confirmed by Ekin's following words:

Interviewer: How is thermal energy is different from heat?
Ekin: I can say that thermal energy is a type of heat which we can apply to real life. For example, hot springs... as far as I know hot springs allow your muscles to relax. Thermal energy is a type of heat which we can use to apply to real life. It occurs with water's heat.
Interviewer: Can we not mention thermal energy without water?
Ekin: I mean... For example, there are varieties of thermal energy. Geothermal, hydrothermal... I know those. For example, hydrothermal is about water.
(First Interview)

In the next interview, Ekin's ideas about the relationship between heat and thermal energy did not change much. Ekin expressed her ideas in the first two weeks. Then she did not assert any new ideas and repeated the same ideas in the following weeks. However, the dominance of all three propositions is high. The fact that Ekin's definition of thermal energy was not clear until the final week might have had an impact on this. She thought that the concepts of heat and thermal energy had to be different, yet did not have a certain idea about what thermal energy is. Thus, she had difficulties with understanding the relationship between the two concepts. In the final week, Ekin asserted a thermal energy definition which is very different from her heat definition and independent from the water.

Analytic Assessment of Ekin's Opinions about Heat's Quantitative Aspect

Ekin's opinions about heat's quantitative aspect can be examined under three aspects: The measurement of heat, calculability of heat's value, and how to calculate heat's value.

Ekin's ideas about the measurement of heat can be briefly summarized as follows:

a. The unit of heat is the calorie.

b. The unit of heat is degree centigrade.

c. Heat is measured by a calorimeter.

Among these three propositions asserted by Ekin, the first two (a and b) are about heat's unit of measurement and the third (c) is about the device used to measure heat. In the first week, Ekin confused the unit of heat due to incorrect uses in everyday life. However, she later corrected her mistakes. She asserted that "degree centigrade" is unit of heat due to expression "body heat" that is a common misconception in everyday life. But, she later decided that heat's unit is "calorie". Ekin said that heat could be measured by calorimeter in the first week and did not change her opinion in the following weeks.

For the second aspect, Ekin's ideas about heat's calculability can be briefly summarized as follows:

a. Heat can be calculated.

b. Heat can only be calculated during heat transfer.

c. Heat can only be calculated during the change of state.

d. Heat can only be calculated for certain matter / pure matter.

The first proposition (a) asserted by Ekin can be seen that "Heat cannot be calculated" sometimes. The dominance was determined considering positive and negative statements. The second proposition (b) asserted heat could only be calculated during heat transfer and the third (c) asserted heat could only be calculated during the change of state. The last proposition (d) asserted heat could only be calculated certain matter which stores. Ekin thought these bodies of matter had to be pure. While Ekin's first proposition (a) is not wrong, the second and third propositions (b, and c) are the most coherent to scientific theories. Figure 5 shows how the dominance of these propositions changed throughout five weeks.

Figure 5. Temporal change in Ekin's opinions about heat's calculability

When directed questions about the calculability of heat in the first week, Ekin thought about examples, suggesting that heat could be calculated for matter changing state or exchanging heat and also only for pure matter. Because she thought that the specific heat of impure matter cannot be known. It can be said that Ekin probably thought based on Q = m.c.∆T for heat transfer and Q = m.L for the change of state. This can be observed in Ekin's following words:

Ekin: Maybe we cannot calculate it because we do not know the matter's specific heat or because the matter is not pure.
(First Interview)

Ekin: I mean, when you ask me to calculate its heat, I need to know its mass, specific heat, and temperature to do that.
(Second Interview)

Ekin thought matter can store heat in the first few weeks. However, she had difficulties with calculating the value of heat stored in matter. For this reason, she asserted that we cannot calculate the heat stored by the matter. It is interesting that while Ekin advocated that matter can store heat in the first week, but when she was asked to calculate this heat, she tried to do so firstly and then asserted it could not be calculated, and then could only be calculated for pure matter. However, she once again thought about calculability of heat stored in a matter without heat transfer and change of state. This is most likely because of the idea that matter can store heat. Ekin did not assert a different idea in the following interviews. However, she changed her definition of heat in the following interviews and replaced her idea of heat stored in matter with the idea that heat can be calculated during heat transfer. This is explained in the aspect about how to calculate heat's value.
The third aspect is about how to calculate heat's value. Ekin thought the aspect firstly as heat stored in matter and then only as heat. Ideas asserted by Ekin on this aspect can be summarized as follows:

a.      Heat's value has no limit.

b.      Heat's value cannot be negative.

c.      Q = m.c.ΔT gives heat that enters or leaves.

d.      Q = m.c.ΔT gives heat change.

e.      Q = m.c.∆T gives heat stored by matters (reference point is 0 °C).

f.       Mass and type of matter are indicative factors when calculating the heat that is stored by matter.

The first proposition (a) asserted by Ekin is that the heat stored in the matter has no limit. The second one (b) asserts that this heat cannot have a negative value. The last proposition (f) asserts that the heat stored in the matter is related to its mass and type of matter. Also, there are three different statements regarding what Q = m.c.∆T gives. Figure 6 shows how the dominance of these propositions changed throughout five weeks.

Figure 6. Temporal change in Ekin's opinions about how to calculate heat

In the first week, ideas supporting "heat is stored in the matter" such as that heat's value has no limit, heat's value cannot be negative, the equation (Q = m.c.DT) is used to calculate the heat stored in the matter, and heat is related to the matter's mass and type was dominant in Ekin's mind. We can also add the idea of "heat change" concept to this list. Because the idea of heat change is found to be related to the idea of heat storage. The idea which is the most compatible with scientific theories is that the equation gives the heat enters or leaves. It's less dominant compared to others in the first week. Ekin thought that the equation gives the heat change mostly. We can see this in the following dialog:

Interviewer: How do we calculate heat?
Ekin: For example, ice interacts with the water. Using Q = m.c.ΔT, the heat entered is equal to the heat left and that's how we calculate it.
Interviewer: What does Q = m.c.ΔT mean? What value do you calculate using Q = m.c.ΔT? Ekin: It is actually the heat change. For example, ΔT is final temperature minus initial temperature. We calculate the heat change that is the value between the final value and initial value of heat.
Interviewer: So, why do you think we use Q instead of ΔQ?
Ekin: ΔQ shows a change... But we use Q. Ice must have an initial energy. Because we subtract its initial energy from its final energy.
(First Interview)

Ekin: Heat increases when the temperature increases. So, they are directly proportional.
Interviewer: When you say directly proportional, what I can think that if I double one, another one is doubled too. Correct?
Ekin: No. Because heat depends on both mass and specific heat, that is matter type.
Interviewer: Let me ask this: If I increase the temperature of the same matter from 20 °C to 40 °C, do I also double the heat that it stores?
Ekin: In fact, yes. It doubles when we add as much energy as it initially has.
Interviewer: So, if the temperature is -10 °C, is the heat stored negative?
Ekin: Its energy cannot be negative. Heat cannot be negative as far as I know.
(First Interview)

Although there was a decrease in the dominance of these ideas in the second week, the ideas did not change. Ekin did not assert any new ideas in the following weeks. However, considering that Ekin's definition of heat changed in the last few weeks, her ideas about how to calculate heat's value should have changed as well entirely. But, no dramatic change was seen.