Enhancing pedagogical content knowledge in a collaborative school-based professional development program for inquiry-based science teaching

Case One: School A (Grade 3)

Topic: Expansion and contraction of air Teachers involved (all teachers in both schools are given pseudonyms): Nancy (the panel head), Helen, George, and Tim

Planning of the Lessons.

In the planning meeting, the teachers were passive and expected input from the teacher educator. Nancy referred to a reference book with an interesting science experiment to illustrate the expansion and contraction of air: a glass bottle is covered with a deflated balloon and immersed into either hot or cold water. This initiated a discussion on inquiry activities and the scientific concepts they sought to develop.

Nancy: I used to think that the skin of the balloon expands, but not the air. The results of the experiment do not convince me that I am wrong.

Helen: I guess students might have the same idea as you.

George: So, how are we going to convince students that it is the air that expands?

This episode shows that some of the teachers confused the expansion of air with the expansion of solids and assumed their students would have the same misconception. This was followed by another exchange.

Teacher educator (TE): Do you know about the trick of dropping an egg into a bottle with a narrow neck using hot and cold water?

Nancy: Yes, but I am not sure how it works exactly.

The TE then explained the principles of this experiment.

George: Yes, that sounds interesting, but I don’t think Grade 3 students have any clue about air pressure, because even we are not familiar with it. Please could you explain to us what exactly air pressure is about.

As can be seen from this exchange, the SMK of these teachers was quite varied. Their own unfamiliarity with air pressure appeared to influence their prediction that the concept was beyond the reach of their students. They were then asked to discuss the students’ conceptions of the topic of air, as follows.

Nancy: They should not have done anything about air in lower grades, because we plan according to our textbook. The unit on air and its properties is for Primary Four.

TE: But do you have any clue why the topic of the expansion and contraction of air precedes more basic topics about air?

George: It is probably because this topic is not restricted to air. It also introduces the expansion of solids and liquids, whose properties have already been covered.

Helen: Yes, the curriculum seems to be problematic. The topic of air should precede the topic of expansion and contraction, because if students have no idea about air, they will not be able to make sense of its expansion and contraction.

In this episode, the teachers are reflecting on and integrating different types of knowledge, including their knowledge of the learners’ abilities and the topic sequences deemed to be conducive to the progressive development of relevant concepts, and transforming them into their PCK for this air expansion and contraction unit. All teachers agreed that it was instructive to check the children’s understanding before designing the lessons. With input from the teachers, the TE helped them to design a pre-test to check students’ understanding of the relevant concepts of air, such as air occupies space, air is capable of contraction and expansion, and air exerts pressure. Two selected pre-test items are provided in Appendix 1A.

The results were then discussed in the second LPM, during which the teachers began to analyze students’ understandings of the topic. This led to the generation of some reasonable hypotheses about students’ understanding of air, which can be seen in the following transcript.

George: Quite a lot of students (42%) said that water would fill up an inverted cup as it was lowered into water. This seems to show that not many of them knew that air occupies space.

Nancy: The results show that although many students were able to predict that a balloon will expand when it is placed in hot water and contract in cold water, many of them did not realize that air will leave the bottle when it is immersed in hot water.

TE: What does that tell you about students’ understanding of the expansion of air?

Nancy: It may show that students do not really understand that it was the air in the balloon that expanded. They might interpret it as the skin of the balloon expanding, but not the air inside.

Tim: Quite a number of students (39%) have the idea that a balloon bursts when it is pricked with a needle because of the high air pressure inside. Based on this analysis, the teachers discussed the activities to be included in the lessons, thus connecting their knowledge of students with their instructional strategies.

Nancy: I think it is very important to consolidate students’ conception about the existence of air and that air occupies space before leading them to inquire into its expansion and contraction.

George: We could ask the students to invert a cup with tissue paper inside it and then force the cup into the water. The tissue paper will not get wet because of the air inside. These episodes show the teachers becoming increasingly aware of the necessity of sequencing the topics in a progressive manner, so that the teaching of fundamental concepts preceded that of the more advanced ones. Recognizing that the teachers were ready to progress further, the teacher educator continues to lead the teachers through the planning process.

TE: How could you develop students’ conception of expansion and contraction? The teachers began to blend the content to be learnt by students with the pedagogy of inquiry-based learning by drawing on the activity they just learnt from the teacher educator.

Tim: I would include the egg-in-a-bottle activity to make the inquiry more fascinating. It is very interesting and can be treated as a problem-solving task to test students’ application of what has been learnt. Again, the issue of content sequencing was brought up by George.

George: We need one more activity in between to give students some basic idea of the expansion and contraction of air.

Helen: Could we use the balloon-in-the-bottle activity? The teacher educator stepped in again to remind the teachers of what have been discussed earlier, that is, students may confuse the expansion of air with that of solids.

TE: Aren’t we a bit wary that students may confuse the expansion of air with the expansion of the balloon?

The TE suggested an alternative activity to replace the balloon-in-the-bottle activity: placing soap film over the mouth of a plastic mineral water bottle. This film then becomes a soap bubble when the bottle is placed in hot water, with the bubble reverting to flat film and continuing to move down the neck of the bottle when it is placed in ice-cold water. The teachers were very excited about this activity and considered it a better alternative. Through this process of deliberation, the teachers generated some feasible teaching strategies.

Teachers’ Reflections on Implementation

The teachers were asked specifically to reflect on their SMK in the TJs and TEMs, as well as their perceived knowledge of the learners and their instructional strategies

Subject Matter Knowledge (SMK)

The teachers were particularly positive about the improvement in their SMK, as illustrated by this entry in Nancy’s journal:

The planning sessions helped me a lot in clarifying my conceptions about the topic. I used to think that the reason the egg dropped into the bottle is that the egg contracted when cooled. I now have more confidence in teaching this topic.

However, not all of the teachers were as confident. George was particularly explicit in this regard in his TJ:

George: I also know more about the concept of air pressure after the planning meetings, but I think air pressure is too difficult for the students probably because I don’t have enough confidence to explain it to them. That is why I explained the results of the last two activities solely in terms of the expansion and contraction of air instead of air pressure.

This shows that teachers’ SMK is still very much an issue. They tended to avoid concepts that they did not understand well and considered to be too difficult for the students, for example, air pressure, even after some students had shown some understanding in the pre-test.

Pedagogical Content Knowledge (PCK)

Knowledge of learners’ conceptions and reasoning. In the second part of their reflection, the teachers shared their insights and understanding of the conceptions and abilities of their students after the lesson. For instance, Nancy was surprised that the students’ ability to conduct inquiries was far better than she had expected.

Nancy (in her TJ): Students could design their own methods to solve the egg-in-the-bottle problem, which was beyond my expectation.

However, there were times when the teachers’ perceptions contradicted the evidence, as can be seen in the following excerpt from a TEM.

Helen: After the experiments to demonstrate the presence of air, students could tell that the air inside the inverted bottle prevented water from entering, but I don’t think that they had any clue about the existence of air pressure.

At this point, the TE shared from his field notes the results of a discussion with a group of students from Helen’s class immediately after they had completed the inverted bottle experiment.

TE: Why can’t the water move into the bottle?

Student1 (S1): Because of air.

S2: Because the air presses on the water; therefore it cannot enter.

S3: Because the air resists the water.

S4: Because there is pressure (critical episode 1). [From the TE’s FN.]

When the teachers were asked what this episode said about the students’ understanding of air, Helen made the following response.

Helen: I didn’t realize that some students had the idea of pressure in their minds. I should have explored their ideas further.

This episode created cognitive dissonance among the teachers, which not only stimulated them to reflect critically on the way they assessed their students’ level of understanding, but also forced them to reexamine their approach to guiding students toward reasonable explanations. It vividly demonstrated to the teachers that student ideas are worthy of further exploration and that underestimating them may actually restrict their learning. The exchange between the students and teacher also enables students to learn from each other, and encourage others to raise their own questions for further exploration of the phenomenon concerned.

Teachers’ instructional strategies. During the TEM, the teachers discussed the student instructions and explanations that they had found to be particularly effective.

Nancy: I had tried to use analogy to make the concept of the existence of air appear to be less abstract. I had some sweet-smelling candies in a cup. I also let go of an inflated balloon so that they could feel the air coming out of it.

George: When students were working on the inverted bottle, I noticed that some had difficulty in observing the water level inside because the bottle was too tall. So, I asked them to take out the bottle, screw on the cap, and push it into the water again. If the water level stayed the same, we knew that water had not entered the bottle.

Another way to understand teachers’ PCK is by analyzing their use of questioning and the way they respond to students’ answers. Such analysis was also used to stimulate reflection in the TEMs. The TE introduced two teacher-student dialogues from the VRL and FN.

Nancy: Why did the soap bubble expand when the bottle was put into hot water and contract in cold water?

S1: The water vapor made the soap bubble larger.

S2: The hot water caused the soap bubble to expand; the ice cold water made it contract.

Nancy: You’ve got it almost correct. The fact is that the air inside the bottle expands when heated and contracts when cooled.

George: Which thing expands and contracts in the two experiments?

S1: Air George: What happened to the air inside the bottle with hot water outside?

S2: It expanded.

George: Yes, we could easily observe it with the aid of the soap bubble. And what about the ice cold water? What does this tell you about the air inside the bottle?

S3: It contracted.

The teachers were able to tell the difference between the questions used in the two cases. Nancy seemed to ignore the possible gap in students’ understanding, that is, they may not know that it is the expansion of air that causes the soap bubble to expand. George’s questions were more specific and led students to explain the results in terms of the air inside the bottle. In contrast to Nancy, George facilitated the students’ deduction of the correct answer from the results.

With regard to the development of their own PCK to improve inquiry-based instruction, teachers came up with different suggestions for future applications based on their own reflection.

Nancy: I think computer simulation may help to explain the concepts of air and its expansion and contraction to students.

Tim: Students should be led to think more about the results of one experiment before going on to the next. We may need additional experiments in between to consolidate students’ understanding.

Helen: I think students should be led to apply the knowledge learnt from the inquiry to their daily lives. That’s what we have not considered in this trial.

Case Two: School B (Grade 5)

Teachers: Greg (grade panel head), Judith, Clara, Mandy, Tom, Jane

Topic: Electricity

Planning of the Lesson

The teachers decided that they would like to teach the topic of electrical conductivity through scientific inquiry. The discussion was initially based on the textbook. As the meeting progressed, the teachers became very enthusiastic about clarifying their own doubts and misconceptions, and the TE was bombarded by an array of questions: Can water conduct electricity? Why are we told not to touch a switch with wet fingers if water is only a very weak conductor of electricity? The meeting then moved on to a discussion of what might be included in the pre-lesson test to elicit students’ ideas about electrical conductivity, and the teachers were asked to consider substances other than those suggested by the textbook, such as different liquids and graphite (in a lead pencil). They thought this was a good idea, but had never done anything like it before.

It was clear that the teachers’ SMK was not particularly strong and that their knowledge was derived mainly from everyday experience and the textbook. After the teachers tried out a number of activities themselves, pre-lesson items designed to elicit the students’ preconceptions about conductors and insulators were formulated (see Appendix 1B). The following transcript from the second LPM illustrates how the teachers tried to make sense of the students’ preconceptions as portrayed in the pre-test results.

Clara: I don’t understand why nearly 60% of the students did not know that coins can conduct electricity.

Greg: They probably do not know that coins are made of metal.

Tom: Ah! A lot of them know that tap water can conduct electricity. They probably got this from their parents.

Clara: I cannot imagine why some students (9%) considered that the colour of a substance may determine whether it can conduct electricity.

In the second LPM, the teachers focused on the planning and sequencing of activities, and it was agreed that students should learn about closed circuits before moving on to conductors and insulators. This was so they would be able to test the conductivity of materials. Although there were arguments over how open-ended the activity on closed circuits should be, due to different student abilities, the teachers eventually agreed to allow students to connect circuits by themselves and then determine which would work and which would not. Because some of the necessary materials such as ammeters were not available in the school, and the teachers apparently lacked the confidence to instruct the students in setting up the circuits, they suggested that the experiment be presented in the form of a videotaped demonstration.

Teachers’ Reflection on the Teaching Process

The teachers were asked to reflect on their SMK and PCK after the teaching process.

Subject Matter Knowledge

The following examples of teacher reflections about SMK were extracted from the TJs.

Judith: I have gained confidence, but there are still many everyday terms about electricity that I cannot completely understand, for example, watts and electric potential. Hence, I do not have enough confidence to teach this topic.

Clara: Although I have some knowledge about electrical conductivity, I don’t have enough confidence to deal with students’ questions.

Mandy: I was able to grasp the concept after reading some references.

These comments provide further evidence that teachers’ SMK has a direct impact on their level of confidence in teaching a particular topic. Underlying this lack of confidence appears to be the common perception that the teacher’s major role is to impart scientific knowledge.

Pedagogical Content Knowledge

Knowledge of students’ conceptions and reasoning ability. In the eyes of the teachers, the students, regardless of their ability, were very interested in the inquiry activities. They were greatly impressed by their students’ ability to connect circuits, test their ideas, and then conclude that only a closed circuit would work. In the TEM, Judith vividly related her experiences and feelings in this regard, as follows.

Judith: Some groups tried to test as many contact points as possible on the light bulb. They were so observant, and they made very good drawings as well. However, I didn’t know how to explain to them why only some circuits worked, as I do not know how a light bulb is wired inside. I need to study that bit later.

The teachers were also struck by the students’ creativity in formulating and making logical explanations/hypotheses, although some of them were based on misconceptions. This can be seen by Greg’s comments in the TEM.

Greg: When I asked the students to figure out why a lead pencil could conduct electricity, they explained that it contains lead, which is a metal (the students thought that a lead pencil actually contained lead not graphite), but said that the light bulb is probably dimmer in this case because the amount of lead is not that high or because lead cannot conduct electricity as well as iron or copper.

Another example of students formulating hypotheses was cited by Jane. She wrote about an episode in her TJ to show how her students made sense of the results by their own reasoning based on their knowledge about the different types of liquids.

Jane [to the entire class after showing the videotape demonstration]: Can you explain why the four liquids differ in their ability to conduct electricity?

S1: Because there is nothing inside the distilled water.

S2: Mineral water and tap water contain impurities.

S3: Orange juice also contains impurities.

S4 [to the teacher]: What are these impurities?

S5: [to the teacher]: How is distilled water made?

This episode shows that students actually went beyond explaining the results to a more in-depth enquiry about the nature of those “impurities” that enables mineral water, tap water and orange juice to conduct electricity, and how these impurities could be removed.

Teachers’ instructional strategies. The teachers were also asked to reflect on how they had made use of questioning to further students reasoning ability and to identify problems for further investigation. An episode from one of Greg’s lessons was discussed for illustration. Some of Greg’s students discovered that the “copper” wire was able to conduct electricity only when its ends, but not its other parts, were connected to the circuit. In fact, this wire was coated with polyester, which is an insulator. Before the activity, the polyester coating on the two ends of the wire was removed with sand paper. As the students were obviously puzzled by this seemingly anomalous result, the TE intervened in the lesson with Greg’s consent, and the results from the VRL were shared with the teachers.

TE [to the entire class]: Can you figure out why this is the case?

S1: Electricity can flow through only when the ends of the wire are connected.

TE: Can you think of a reason for this? S2: I guess electricity can only flow from one end of the copper wire to the other end. It cannot flow out from the middle.

TE: Can you put your idea to the test? [Silence.]

TE: Can you test your idea using another type of metal wire, say, iron wire?

S3: Yes, we can test whether the iron wire lets electricity out at the middle. [The bulb lights up no matter which part of the iron wire is connected to the battery.]

S4: There must be something special about this copper wire. TE: That sounds reasonable. Any further idea as to what makes this wire so special?

S4: Ah! There might be something on the outside of that part of the copper wire that blocks the flow of electricity.

TE: How can you prove that your idea is correct? [The students could have been allowed to come up with more ideas for further inquiry, but as the lesson had already overrun, they were given the answer.]

The teachers were encouraged to share similar instances that could prompt further student investigations as an important part of PCK for inquiry. One idea was that students could be encouraged to further explore why some metallic objects conduct electricity better than others, thus leading to inquiry into the factors that influence electrical conductivity.

Questionnaire Findings

The questionnaire findings are presented in Appendix 2. Despite the small sample size, the average ratings provide some indication of teachers’ overall perceptions of the outcomes of this collaborative project. With regard to SMK, they generally agreed that they had become more familiar with the concepts relevant to the topic, although they did not rate their perceived competence in handling students’ questions as highly. They agreed that their knowledge of learners and their ability to design and implement inquiry-based instruction had also been enhanced. However, not all were confident enough to adopt such instruction independently. This is no doubt because of the limited opportunity they have had to practice this type of teaching. Particularly noteworthy is the near consensual view that collaboration with the TE had enhanced their professional skills in conducting inquiry-based instruction.