Pre-service chemistry teachers' pedagogical content knowledge of the nature of science in the particle nature of matter

Oktay Bektas *a, Betul Ekiz b, Mustafa Tuysuz b, Elif Selcan Kutucu b, Aysegul Tarkin b and Esen Uzuntiryaki-Kondakci b
aErciyes University, Faculty of Education, Kayseri, Turkey. E-mail: obektas@erciyes.edu.tr
bMiddle East Technical University, Faculty of Education, Ankara, Turkey

Received 24th December 2012 , Accepted 4th February 2013

First published on 7th March 2013


Abstract

This study investigated pre-service chemistry teachers' pedagogical content knowledge of the nature of science (NOS) in the content of the particle nature of matter. Qualitative research design was utilized. Data were collected from seven pre-service chemistry teachers (PCTs) by using open-ended questions, interviews, observations, lesson plans, and reflection papers. The results indicated that while most of the PCTs showed improvement in terms of understanding of the target aspects of NOS, knowledge of learners and instructional strategies, the majority of PCTs did not make progress regarding knowledge of assessment during the study. Implications for science teacher education are also presented.


Introduction

Understanding the nature of science (NOS) has been one of the main goals of science education in recent years. Students should have an appropriate understanding of NOS in order to be scientifically literate members of a society (Lederman, 1999; Khishfe and Lederman, 2006). In other words, if students understand NOS, they appreciate scientific information, comprehend the relationship between science and society, interpret and make decisions on socio-scientific matters (Driver et al., 1996). Students' understanding of NOS is closely related to their teachers' instructions on NOS (Akerson et al., 2000). However, teaching NOS is a challenging process. It is clear that to teach NOS, teachers should have sufficient knowledge about it, which is not enough all by itself (Abd-El-Khalick and Lederman, 2000). Kim et al. (2005) claimed that even if teachers have appropriate NOS understanding, they do not tend to teach NOS explicitly or they use ineffective strategies for teaching NOS. Teachers should be able to transform their NOS knowledge into their teaching practice to equip their students with well-developed NOS understanding, which can be defined as pedagogical content knowledge (PCK) for NOS. PCK expresses teachers' knowledge which they use in their teaching process. Studying PCK will help science educators understand the ways of effective teaching (Abell, 2008; Kind, 2009). Therefore, teaching NOS should be investigated within a PCK framework. In other words, more research is needed regarding PCK of NOS.

Therefore, the present study aimed to fill the gap in the literature focusing on the pre-service teachers' PCK of NOS. In particular, studying PCK of NOS will enable science educators to identify what teachers do in their classes to teach NOS, how they integrate NOS aspects into the science content they teach, to what extent they are knowledgeable about their students' conceptions of NOS, and how they assess their students' understanding of NOS, all of which may lead to an improvement in the quality of teaching. The purpose of this study was to investigate the pre-service chemistry teachers' understanding of target NOS aspects and their teaching of these aspects in the particular nature of matter (PNM) context within the PCK framework. This study, as an example of pre-service teachers' PCK of NOS, will contribute to the research area related to developing pre-service teachers' PCK of NOS and understanding of NOS through the teacher education program. The following sections give information on NOS, PCK, and PCK of NOS, respectively.

The nature of science

The nature of science (NOS) includes philosophy, sociology, psychology, history, and epistemology of science (McComas, 2002). Lederman (1992) defined NOS as the values and assumptions inherent in the development of science and scientific knowledge. Different aspects of NOS give direction to researchers in the analysis of the understanding of NOS (Abd-El-Khalick, 1998, 2005; Abd-El-Khalick et al., 1998; Lederman et al., 2002; Niaz, 2001, 2009). Indeed, most of the researchers expanded the previous views on NOS. For instance, Abd-El-Khalick (1998) suggested five aspects of NOS which are empirical basis, tentativeness, theory-laden NOS, creativity and imagination, and socio-cultural embeddedness. In a later study, Abd-El-Khalick et al. (1998) added two more aspects: observation and inference, and theories/laws. In addition to their views, in a recent study, Lederman et al. (2002) argued that there is no universal step-by-step scientific method to do science.

In the present study, theories/laws and tentativeness aspects of NOS were examined since both students and teachers generally have difficulties in understanding these two aspects (Lederman et al., 2002; Abd-El-Khalick, 2005; Khishfe and Lederman, 2006). Moreover, in the literature, there have been many studies on pre-service teachers' conceptions of NOS (Akerson et al., 2000; Bell et al., 2000; Abd-El-Khalick, 2005; Abd-El-Khalick and Akerson, 2009; Akerson and Donnely, 2010). These studies revealed that pre-service teachers had many difficulties in understanding NOS aspects. Regarding the tentativeness aspect, pre-service teachers believe that scientific knowledge consists of absolute facts and science is not changeable. Yet, it is obvious that atom models have been developed in time. In terms of the theories/laws aspect, they think that there is a hierarchical relationship between laws and theories and laws have a higher position than theories, thus theories become laws (Lederman et al., 2002; Abd-El Khalick, 2005). However, the fact that Boyle's law was stated before the kinetic molecular theory would be evidence for the absence of hierarchy between theories and laws. It is important to reveal pre-service teachers' views on NOS and identify their learning difficulties so that their students in the future do not hold inappropriate NOS understanding. From this perspective, teaching NOS is another issue to be considered in pre-service teacher education. In the literature, there are two approaches for teaching NOS: content embedded or non-content embedded. In the content embedded approach, NOS is taught as embedded within the context of the science content. On the other hand, in the non-content embedded approach, NOS is taught as a separate topic within the domain of science (Khishfe and Lederman, 2006). In terms of effectiveness of these approaches on enhancing students' learning of NOS, Khishfe and Lederman (2006) compared these two approaches and found that neither of the approaches has superiority over the other although these two approaches improved students' understanding of NOS. Recently, teaching NOS in the science context has been seen as more valuable for promoting pre-service and in-service teachers' both learning and teaching of NOS (Schwartz, 2007; Buaraphan, 2012; Faikhamta, 2012). When teachers learn NOS as a separate topic, they have difficulties in embedding NOS into their science teaching. The integrated NOS instruction within all science contexts is suggested since a variety of contexts may provide more learning opportunities for students' understanding of NOS. In addition, teaching NOS within the context of the science content may help pre-service teachers see the connections between NOS and the science context and experience the pedagogy of teaching NOS within science contexts during the teacher education program (Schwartz, 2007). In our country, the curriculum does not include specifically the topic of NOS in the chemistry domain. Thus, teachers must teach NOS within the particular chemistry content. For this purpose, they need to transform their understanding of NOS into their chemistry teaching. Therefore, in this study, we focus on pre-service chemistry teachers' understanding of NOS and learning to teach NOS within the context of the chemistry content. For this study, PNM is the context in which NOS is taught.

Pedagogical content knowledge

Shulman (1986) described pedagogical content knowledge (PCK) as one of the sub dimensions of teacher content knowledge which “…goes beyond knowledge of subject matter per se to the dimension of subject matter knowledge for teaching” (p. 9). He claimed that PCK helps teachers introduce content to their students in an understandable way. Accordingly, PCK is viewed as the central part of the knowledge base for teaching (Shulman, 1987). Along with PCK, this knowledge base includes content knowledge, curriculum knowledge, learners and their characteristics, educational contexts, and educational purposes.

Other researchers extended Shulman's model over time (e.g.Tamir, 1988; Magnusson et al.,1999; Hashweh, 2005). In this study, we adopted Magnusson et al. (1999)'s model which described PCK as a transformation process “of several types of knowledge for teaching” (p. 95). They claimed that PCK is composed of five components: (a) orientation toward science teaching, (b) knowledge of science curriculum, (c) knowledge of science assessment, (d) knowledge of students' understanding of science, and (e) knowledge of instructional strategies. Each of these components represents specific knowledge. In this study, we dealt with knowledge of science assessment, knowledge of students' understanding of science, and knowledge of instructional strategies. The knowledge of the science assessment component includes both teachers' knowledge of dimensions of science learning and teachers' knowledge of methods to assess students' learning within a specific topic. The knowledge of students' understanding of science includes requirements for learning science concepts which students find difficult to learn. The last component, knowledge of instructional strategies, refers to subject-specific (e.g. learning cycle) and topic-specific (e.g. laboratory activities) strategies.

Abell (2008) claimed that PCK is topic-specific; for instance, teaching the mole concept and teaching chemical equilibrium require different use of teacher’s knowledge. Considering this characteristic, research studies included PCK in the content of PNM (Kokkotas et al., 1998; De Jong et al., 2005; Boz and Boz, 2008), chemical equilibrium (Van Driel et al., 1998; Harrison and De Jong, 2005), macroscopic and microscopic properties of matter (Van Driel et al., 2002), gas laws (Sande, 2010), acids and bases (Dreschler and Van Driel, 2008), and methods of separation of mixtures (Aydın et al., 2010). In a similar vein, NOS can be viewed as a content to teach (Hanuscin and Hian, 2009; Hanuscin et al., 2011). In the present study, we examined pre-service teachers' PCK for teaching NOS in a specific chemistry content. PNM is one of the fundamental topics in chemistry because understanding chemistry topics like chemical equilibrium or rate of reactions depends on comprehending the nature of particles (i.e. ions, molecules and atoms). In addition, this topic is appropriate to emphasize tentativeness and theories/laws aspects of NOS. Therefore, in this study we examined how pre-service chemistry teachers teach the target aspects of NOS within the PNM content.

PCK of NOS

In line with the model proposed by Magnusson et al. (1999), PCK of NOS involves knowledge about NOS, science as a subject matter, and pedagogy (Schwartz and Lederman, 2002). To articulate, teachers' usage of a variety of examples, demonstrations, activities, and historical events to teach NOS, as well as their knowledge about NOS and science contents, constitutes their PCK (Abd-El-Khalick and Lederman, 2000). PCK of NOS also addresses knowledge about possible misconceptions of NOS and appropriate teaching approaches (Hanuscin and Hian, 2009).

The relationship between teachers' views on NOS and their PCK is not certain and it should be investigated (Lederman et al., 2001; Lederman, 2007; Hanuscin et al., 2011). However, in the literature, there have been a few studies investigating teachers' PCK of NOS (Kim et al., 2005; Hanuscin and Hian, 2009; Hanuscin et al., 2011; Faikhamta, 2012). For example, Hanuscin et al. (2011) examined the PCK of NOS of three elementary teachers who have been successful in improving their students' understanding of NOS. Researchers used interviews, questionnaires, classroom observations, and classroom artifacts to collect data over a 3-year period. The results indicated that while the participants had adequate knowledge of instructional strategies to teach NOS, they had inadequate knowledge about assessment. In another study, Hanuscin and Hian (2009) investigated changes in the development of PCK of NOS of a pre-service teacher and a science teacher educator by using a self-study. Narrative vignettes were used primarily to collect data from the pre-service teacher. The results indicated that the pre-service teacher encountered pedagogical dilemmas during her NOS instruction in traditional science teaching. In a more recent study, Faikhamta (2012) designed a nature of science course (NOSC) for developing Thai in-service science teachers' understanding of NOS and their orientations towards teaching it by using PCK as a framework. In this qualitative study, he used NOS questionnaires, field notes, and in-service teachers' weekly journal entries and assignments as data collection tools. As a result of the study he found that by participating in NOSC in-service teachers developed their understanding of NOS and orientations towards teaching NOS.

Although these studies shed light on PCK of NOS, it is insufficient to understand the nature of PCK of NOS in a specific topic like PNM. In the current study, we examined pre-service chemistry teachers' views on theories/laws and tentativeness aspects of NOS and their PCK of NOS in terms of the knowledge of learners, instructional methods/strategies, and assessment within the content of the particulate nature of matter (PNM) during the practice teaching course in a semester. Research questions of the study are presented below:

(1) How do pre-service chemistry teachers perceive the relationship between laws and theories, and tentativeness aspects of NOS before and after taking the practice teaching course?

(2) What is the knowledge of pre-service chemistry teachers in terms of students' understanding of and difficulties in understanding theories/laws and tentativeness before and after taking the practice teaching course?

(3) How do pre-service chemistry teachers teach PNM considering the knowledge of learners, instructional methods/strategies, and assessment of theories/laws and tentativeness before and after taking the practice teaching course?

Methodology

Research design and the context of the study

Qualitative research design was utilized in order to explore the research questions of the study (Patton, 2002). The unit of analysis was pre-service chemistry teachers (PCTs) enrolled in the practice teaching course at the Department of Secondary Science and Mathematics Education in a university in Turkey. The study lasted for a semester (14 weeks). Seven PCTs (five females and two males) voluntarily participated in the study. Their age ranged from 22 to 24. The chemistry teacher education program in our country is a five-year integrated program. Pre-service teachers complete chemistry courses such as general chemistry, analytical chemistry, organic chemistry, and other similar courses in the first seven semesters and then, teaching profession courses on curriculum development, measurement and evaluation, teaching methods, school experience, classroom management, guidance, practice teaching, and other pedagogic oriented courses in the last three semesters. On completion of these courses, they are expected to become qualified for teaching chemistry to high school students using innovative methods, assessing their understanding with appropriate techniques, and guiding their students to enhance their understanding of chemistry. In addition, they learn the “nature of science” topic in the methods of science teaching courses in the ninth semester of the program before taking the practice teaching course. Three weeks of this course (12 classroom hours) were devoted to teaching NOS. During this period, students conduct activities related to the aspects of NOS which are derived from the literature such as “New Society” (Cavallo, 2008) and “The Cube Activity” (Lederman and Abd-El Khalick, 1998). Students take part in a discussion after these activities.

In the practice teaching course given in the last semester, pre-service chemistry teachers (PCTs) are given the opportunity to apply their theoretical knowledge of teaching methods/strategies, chemistry, and pedagogy in classroom settings. PCTs spend two class hours per week in their university and six class hours per week at the placement school. In the university setting, PCTs conduct microteaching sessions. Each PCT is supposed to teach two assigned chemistry topics to the class. Each instruction lasts for approximately 30 minutes. The chemistry topic is chosen from the national high school chemistry curriculum of our country. A checklist is used to evaluate the instruction. After the instruction, the instructor and teaching assistants, who were also the researchers of the study, discuss the strengths and weaknesses of the instruction with pre-service teachers. Each instruction is videotaped and pre-service teachers watch their instructions after the class to evaluate themselves.

The other component of the course takes place in the placement school. PCTs are supposed to take part in instruction, administration, and other school-related tasks in this setting. Similar to their instruction in their university, they teach two chemistry topics to high school students. Each class hour lasts for 45 minutes approximately. The mentor and the course instructor evaluate the instruction using the same checklist as in the university. After each instruction, PCTs are given feedback by their mentor and teaching assistants. The participants also observe their mentor's instruction at their placement school. Pre-service teachers prepare lesson plans for their instruction both the university and at the high school.

During this study, the participants taught several chemistry topics both in the university and at the high school. Topics related to PNM were considered for this study. These topics were atom models, chemical bonding, gases, basic laws of chemistry, chemical equilibrium considering PNM, and acids–bases considering PNM. Each participant instructed at least one of these topics. The participants were supposed to use instructional methods/strategies and assessment techniques appropriately, to be aware of students' common misconceptions and learning difficulties related to the topic that they instructed, and to teach aspects of NOS and integrate them into their instructions.

Data collection instruments

Open-ended questions, interviews, observations, lesson plans, and reflection papers were used to collect data in the study. These sources allowed for triangulation to ensure the validity of the data (Marshall and Rossman, 2006; Bogdan and Biklen, 2007).

An open ended question involving several parts was developed by the researchers in order to determine pre-service teachers' understanding of NOS and their PCK of NOS within the content of PNM. For content validity, six experts in chemistry education examined the question and provided suggestions. The question was revised in the light of these suggestions in order to obtain the final form. The question was administered to all PCTs both at the beginning and at the end of the practice teaching course. The question was as follows:

“Assume that your students have the following ideas:

Idea-1: scientists firstly develop their theories, and then these theories become laws.

Idea-2: science is not a process that develops and changes; there are absolute facts in science.

(a) Do you agree with these ideas? Why?

(b) How do you think your students have/develop these ideas? Please explain.

(c) In order to defend your ideas, which examples do you give on the topic of PNM? Why?

(d) Which instructional/teaching methods would you use while teaching NOS within the content of PNM considering the aspects presented in Idea-1 and Idea-2? Why?

(e) Which evaluation techniques would you use to assess whether your students understand the aspects of NOS within the content of PNM presented in Idea-1 and Idea-2? Why?”

After the administration of the open-ended question, interviews were conducted with three PCTs in order to validate their written responses to the question and to get more detailed information related to their PCK of NOS. During the interviews, the participants were asked for clarification or elaboration of their written responses. For example, in written responses, one of the participants stated that she disagreed with Idea-1 since theories and laws are completely different concepts. However, she did not give detailed information. Therefore, in the interview, she was asked to explain what theories and laws were. Another participant wrote that she would use discussion and demonstration in her NOS instruction without explaining the discussion questions and activities for demonstration in detail. During the interview, she was asked what kinds of questions she would ask, what kinds of activities she would use for the demonstration, and how she would use those activities. Each interview lasted for approximately 50 minutes. All interviews were audio-recorded after obtaining permission from the participants and transcribed verbatim for the analysis.

Researchers observed pre-service teachers' instruction both in the university and at the placement school using an observation checklist and taking observation notes. In addition, pre-service teachers' instructions in the university were video-taped. The observation checklist included 27 items related to classroom management, the nature of science, instructional strategies, assessment techniques, chemistry knowledge, etc. Based on this checklist and observation notes, PCTs were given feedback on the strong and weak parts of their instruction after each teaching practice. This checklist was also used to monitor how their instruction developed over time.

Lesson plans were used to gain information about whether pre-service teachers' teaching practices were compatible with what they planned for their instruction. The lesson plans included teaching objectives, materials, and strategies, pre and post assignments, evaluation and assessment techniques of student learning, historical background of the related topics, as well as detailed explanations of how to teach the topic, how to implement the teaching strategy, how to use the teaching materials, and how to reach each learning objective.

Pre-service teachers wrote four reflection papers regarding their experiences in practice teaching both in the university and at the high school, their observations at the placement school, and their thoughts about chemistry teaching in general.

Data analysis

The researchers analyzed pre-service teachers' written responses to the pre and post open-ended question under five sections: understanding of NOS, knowledge of the learner, integrating the aspects of NOS into PNM, knowledge of instructional strategies, and knowledge of assessment. The researchers constructed categories to assess the understanding of NOS and knowledge of the learner sections. In this process, they analyzed PCTs' responses to the open-ended question independently constructing coding categories suggested in the literature (Patton, 2002; Bogdan and Biklen, 2007). Then, they all came together and discussed the answers. The discussion process continued until the researchers reached a consensus on the answers. To assess the understanding of NOS, the researchers followed similar procedures as reported in the related literature (Abd-El-Khalick, 2005; Khishfe and Lederman, 2006; Abd-El-Khalick and Akerson, 2009). In this study, the views of participants on the aspects of NOS were categorized as naïve, transitional, and informed. The descriptions of these categories are given in Table 1.
Table 1 Description of the categories on understanding of NOS aspects
Categories Description of the category
Naïve Having misconceptions
Failing to explain the reason for disagreement with Idea-1 or Idea-2
Transitional Deficient explanation of the aspects of NOS
Lack of an appropriate example of the aspects of NOS
Informed Giving an appropriate example of the aspects of NOS
Sufficient explanation of the aspects of NOS


For knowledge of the learner, the researchers constructed three categories regarding sources of students' misconceptions and learning difficulties in NOS aspects: prior experience, teachers, and textbooks. For other sections (integrating the aspects of NOS into PNM, knowledge of instructional strategies, and knowledge of assessment), the researchers analyzed pre-service teachers' pre and post responses considering whether they provided an appropriate explanation of NOS within the content of PNM, gave relevant examples to defend their views about NOS aspects, how they used teaching methods/strategies to address target NOS aspects while teaching PNM, and whether they can propose questions regarding linkage of NOS aspects to the PNM content to evaluate students' learning.

Results

The results are presented in five sections: the understanding of NOS, knowledge of learners, integration of the aspects of NOS into PNM, knowledge of instructional strategies, and knowledge of assessment. Except for the knowledge of the learner section, each section was examined in terms of PCTs' views on Idea-1 and Idea-2 separately. PCTs' pre and post responses to the question were compared considering coding categories related to NOS views. The results of interviews, lesson plans, reflection papers, and observations were used to support data obtained from the pre and post question. Throughout the study, the names of pre-service chemistry teachers were coded as from PCT-1 to PCT-7.

Understanding of NOS

Results for Idea-1. Table 2 presents views of PCTs on the pre and post question for Idea-1:
Table 2 Coding categories of PCTs' pre and post views on the theories/laws aspect of NOS
Participants Pre view Post view
PCT-1 Transitional Informed
PCT-2 Informed Informed
PCT-3 Transitional Transitional
PCT-4 Naïve Transitional
PCT-5 Transitional Transitional
PCT-6 Naïve Informed
PCT-7 Naïve Naïve



Results of the pre question and first interview. In the pre question, PCT-7 agreed with Idea-1 while PCT-4 and PCT-6 could not assert any reason why they disagreed with Idea-1; thus, they were coded as naïve. PCT-1, PCT-3, and PCT-5 had transitional views on NOS in Idea-1. These PCTs only considered the definitions of laws and theories without discussing any hierarchy between them. For instance, PCT-5 wrote that “Theories are the explanations of scientific phenomena, whereas laws are just rules or formulations that help us to compute scientific data.” PCT-2 was coded as informed since she disagreed with Idea-1 and explained her reasons properly. For example, she wrote: “There is not a hierarchical order between theories and laws. Laws provide a mathematical expression. For example: ideal gas law PV = nRT. However, theories provide a working mechanism how these phenomena occur. For example: kinetic theory of gases.”
Results of the post question and the second interview. PCT-4, developed her idea from a naïve to a transitional view; however, she still could not state why there is no hierarchy between theories and laws in her post response. PCT-6 showed huge development of Idea-1 and stated correct responses to whether there is a hierarchical relationship between theories and laws and explained her ideas by indicating the relationship between the law of definite proportions and Dalton's atom model; therefore, she was coded as having an informed view. On the other hand, PCT-7 had a misconception about hierarchy between theories and laws and was coded as the naïve view on Idea-1. For instance, he wrote that “There is no absolute facts because scientists develop their theories then it becomes law.” However, PCT-1 developed her view from transitional to informed and explained her ideas correctly as follows:

I do not agree with Idea-1 as there is no hierarchical order between theories and laws. In other words, laws are not obtained as a result of the development of theories. For example, law of definite proportions was stated by Proust first and then Dalton proposed his atomic model by using result of this law.

Moreover, PCT-3 and PCT-5 had continued their transitional views. They only defined theories and laws, but they did not state why there is no hierarchy between theories and laws. Furthermore, PCT-2 gave correct explanations and was again coded as holding an informed view. Both PCT-2 and PCT-3 confirmed their views during the interview.

Results for Idea-2. All PCTs disagreed with Idea-2 both on the pre and post questions. However, considering the depth of their explanations, their ideas were categorized as naïve, transitional or informed as shown in Table 3.
Table 3 Coding categories of PCTs' pre and post views on the tentativeness aspect of NOS
Participants Pre view Post view
PCT-1 Transitional Informed
PCT-2 Informed Informed
PCT-3 Transitional Informed
PCT-4 Transitional Informed
PCT-5 Transitional Informed
PCT-6 Transitional Transitional
PCT-7 Naïve Transitional



Results of the pre question and the first interview. Although PCT-7 disagreed with Idea-2, he was coded as naïve due to his unclear response. Participants coded as transitional could not explain why they disagreed with Idea 2, sufficiently. However, during the interview, PCT-1 and PCT-3 explained the reasons why they disagreed with Idea-2 and considering their explanation they could be accepted as possessing informed views. For example, PCT-1 stated

If this statement was true, in the history, Dalton's atomic model would be accepted and any study about atomic models hadn't been conducted, but it didn't happen like that and today atomic models have been developed until modern atomic theory.

Lastly, PCT-2 explained her ideas appropriately. For example, she wrote “If scientific knowledge is insufficient to explain some points, it can be changed and developed. There are no absolute facts in science, only there are explanations which are most appropriate for the reality”. In the interview, she confirmed the view she had given in the pre question.


Results of the post question and the second interview. Although PCT-7 disagreed with Idea-2, his explanation about why there are no absolute facts in science was inadequate; thus he was coded as transitional. While only PCT-6 continued having a transitional view, PCT-1, PCT-3, PCT-4, and PCT-5 were considered as having an informed view in terms of the tentativeness aspect. They explained their views, using atom models as an example. For instance, PCT-1 wrote:

I do not agree with Idea-2 as science is changeable and developing. There are no absolute facts in science. For example: as we know, there are many atomic models proposed in science in history. After Dalton proposed his atom model, other scientists continue to work on issue and proposed different models. If there were absolute facts, scientists would accept Dalton's truth as absolute and they didn't work and propose any model.

Furthermore, PCT-2 explained her views, giving an example, acid–base definitions, and stated that people discover new situations that cannot be explained with the existing scientific knowledge. She also mentioned that scientists might work on some issues, but arrive at different conclusions. In the interview, PCT-1, PCT-2 and PCT-3 confirmed their views on Idea-2 and considered that there are no absolute facts in science.

In summary, many students had inadequate views on theories/laws and tentativeness aspects of NOS at the beginning of the study. They generally could not explain why there is no hierarchy between theories and laws, and why science is tentative. However, at the end of the study, most of the students showed an improvement in their understanding of NOS, especially in the understanding of the tentativeness aspect.

Knowledge of learners. Table 4 lists PCTs' views about possible sources of students' misconceptions or learning difficulties related to theories/laws and tentativeness aspects of NOS.
Table 4 PCTs' views about sources of misconceptions of NOS aspects
Participants Pre question Post question
PCT-1 Teachers, textbooks Teachers, textbooks
PCT-2 Prior experience, teachers Prior experience, textbooks, teachers
PCT-3 Textbooks, teachers Textbooks, teachers
PCT-4 Textbooks, teachers Textbooks, teachers
PCT-5 Prior experience Prior experience
PCT-6 Teachers, textbooks Teachers, textbooks
PCT-7 Trivia Prior experience


As it can be seen, PCTs thought prior experiences, chemistry teachers, and textbooks as sources of students' misconceptions of NOS on both the pre and post questions. Although they seemed to be aware of the sources of students' misconceptions before and after the practice teaching course, they gave more detailed explanations at the end of the course. Examples from participants' responses for each source of students' misconceptions and learning difficulties are given in Table 5.

Table 5 Examples of each source of students' misconceptions and learning difficulties
Sources Examples from participants' responses
Prior experience “During experiments, students propose a theory and check whether their theory is correct or not but any example testing the truth of a law is not given. Therefore, students think that laws are superior on theories”
Teachers “Students might have misconceptions due to their teachers' insufficient NOS instructions”
Textbooks “In textbooks, usually, scientific method is described in the following manner: if theory is tested to be true, it turns to law”


All interviewees confirmed their views about the sources of students' misconceptions and learning difficulties related to the target aspects of NOS in the interviews. In their reflection papers, PCT-2, PCT-3, and PCT-4 considered “teachers” as a source of students' misconceptions due to their own experiences with their mentors at the placement school. They observed their mentors who did not emphasize the aspects of NOS; thereby, the students had misconceptions about NOS. For instance, PCT-2 wrote:

During one of the lessons I realized that 9th grade students had misconceptions such as theories become law if enough time passes over it and laws cannot be changed. Unfortunately, students will carry their misconceptions to next year because the teacher did not do anything to eliminate those thoughts.

Integrating NOS into PNM

Results for Idea-1.
Results of the pre question and the first interview. PCT-4, PCT-6 and PCT-7, who had naïve NOS views, chose to use atomic models to defend their views on Idea-1. However, they failed to explain how atomic models are related to the theories/laws aspect of NOS. For example, PCT-6 wrote: “I give some examples from atom theories. I explain that different atom theories are formed but they didn't become a law”. PCT-3, who had a transitional view on Idea-1, gave atomic models as an example of PNM to defend her views. However, she gave a scientifically incorrect explanation as “We can say that there is a relationship between theories and laws. For example; law of definite proportions is formulated with the help of the Bohr atomic model”. In the interview, she still had scientifically incorrect knowledge and was confused about the law that John Dalton used to propose his atomic model. On the other hand, PCT-1, who holds a transitional view on NOS, explained her example correctly in the pre question: “I will give them an example that the law (i.e. law of constant proportions) used to state a theory (i.e. Dalton's atom model for theory)”. However, she failed to explain how she would integrate this example into NOS to defend her views on Idea-1. On the other hand, in the interview, she gave a correct explanation for her example to integrate the theories/laws aspect of NOS into atomic models. For instance, she stated that “…I think there is no hierarchical relationship between theory and law because, as in my example, laws could be used to propose a theory”. PCT-5, who had also a transitional view, could not give any example from the PNM content to defend his views. PCT-2, who only had an informed view, failed to explain PNM in terms of NOS. We concluded that her explanation included scientifically incorrect statements as “In order to explain law of definite proportions, Dalton's atomic theory is used.” In the interview, she corrected her wrong explanation: “Dalton used law of definite proportions to explain his atomic theory.”
Results of the post question and the second interview. PCT-6, who improved from naïve to an informed view at the end of the teaching practice course, could not give a relevant example to defend her views on Idea-1 in the post question. Moreover, PCT-7 who had a naïve view in both the pre and post questions could not give any example to defend his views. On the other hand, PCT-4, whose views on NOS change from naïve to transitional, chose atomic models and gave an example: “Several atomic models were presented like: Dalton's atomic model, Thomson's, Rutherford's etc. As we can see these theories did not change to law.” It was observed that she did not emphasize why there was no hierarchical relationship between theories and laws.

PCT-5 continued his transitional view and did not give any example in the post question. On the other hand, PCT-1 having an informed post view and PCT-3 having a transitional post view gave an appropriate answer. For instance, PCT-3 stated “For this subject, I will choose the atomic theories and the relationship of Dalton's atomic theory with the law of constant proportions. By this example, students will understand that laws may help the development of theories”. In the post question, PCT-2 possessing an informed view gave a correct example to defend her views by using gas laws and kinetic theory. In the interview, all interviewees confirmed their explanations by giving the same example.


Results of analysis of lesson plans and observations. In the lesson plan for the first instruction at the faculty, it was observed that PCT-1 and PCT-2 planned to use the theories/laws aspect of NOS in chemical bonding and basic laws of chemistry topics, respectively. In their lesson plans for the second instruction at the faculty and the instruction at the placement school, it was observed that PCT-2 intended to use the theories/laws aspect of NOS on the structure of atoms and acids–bases, respectively. Moreover, when observation checklists and video records were analyzed, it was observed that they used this aspect of NOS as they mentioned in their lesson plans correctly.
Results for Idea-2.
Results of the pre question and the first interview. PCT-7 who had a naïve NOS view on the pre question failed to give a correct example to explain his views. All pre-service teachers with a transitional NOS view on the pre question (PCT-1, PCT-3, PCT-4, PCT-5 and PCT-6) gave atomic models as an example to explain their views. For instance, PCT-4 explained her example on the pre question as: “Atomic model has been changed starting from the Ancient Greek times to the modern atomic model. From this we derive that science doesn't have the absolute truth”. Moreover, PCT-2 defended her view on Idea-2 as “Many scientists proposed different atom models. Some of these models have some postulates and they were changed or developed by other scientists.” In the interview, she also confirmed the view she had given in the pre question.
Results of the post question and the second interview. PCT-7 improved his NOS understanding from a naïve to a transitional view and he gave atomic models as an example to explain his view. Nevertheless, he could not integrate the tentativeness aspect of NOS into this topic. PCT-6, who continued her transitional view on NOS, gave a correct example to integrate NOS into PNM to defend her views as in the pre question. Four other PCTs (PCT-1, PCT-3, PCT-4, and PCT-5), who developed their views as informed, gave correct examples to integrate NOS into PNM to defend their views. For instance, PCT-3 wrote:

I will emphasize the differences of Aristotle and Democritus way of thinking with Dalton's. Then I will go on with Thompson's, Rutherford's and Bohr's atomic theories … After these examples they will also understand that there is no absolute fact in science, because Dalton's theory that was thought to be true has changed.

In the interview PCT-3 used the same example to defend her views by saying “The best example could be the atomic theories to teach the development of science”.

PCT-2, who continued her informed view on NOS, used acid–base definitions as an example to defend her views:

Since definitions of acids and bases explain what kind of particles (ions, H+, OH) are formed in acid–base reactions, this topic is also related to PNM. From Arrhenius to Bronsted–Lowry, and from Bronsted–Lowry to Lewis definition some changes and developments had occurred in ideas. Therefore, science is a continuous process developing and changing.


Results of analysis of lesson plans and observations. In the first lesson plan for the first instruction at the faculty, it was observed that PCT-1 and PCT-2 intended to use the tentativeness aspect of NOS on chemical bonding and basic laws of chemistry topics, respectively. In the second lesson plan, PCT-2 and PCT-4 planned to use the tentativeness aspect of NOS on the structure of atom and chemical bonding, respectively. In the lesson plan for their instruction at the placement school, PCTs intended to use this aspect on chemical bonding (PCT-3), the periodic table (PCT-5 and PCT-7), acids–bases (PCT-1, PCT-2, and PCT-6), and chemical equilibrium (PCT-4). Furthermore, when we examined the observation checklists and video records of their instructions, we observed that they properly used this aspect of NOS in their instructions as they stated in their lesson plans.

In summary, although some of the participants had an adequate view on the theories/laws aspect of NOS at the beginning of the study, none of the participants, except for PCT-1, could give a proper example of the topic of PNM to defend their views. Regarding the tentativeness aspect of NOS, all participants, except for PCT-7, could integrate this aspect into the PNM content at the beginning of the study. At the end of the study, some of the participants improved their knowledge on how they could integrate the target aspects of NOS into the PNM content and explained their examples more clearly.

Knowledge of instructional strategies

Results for Idea-1. The analysis of responses to the pre question indicated that seven participants failed to explain how to use teaching methods/strategies while teaching NOS within PNM. On the other hand, responses to the post question revealed that three PCTs (PCT-1, PCT-2, and PCT-3) explained and PCT-4 partially explained how to teach NOS within PNM.
Results of the pre question and the first interview. All participants, except for PCT-4, proposed only the names of instructional strategies (e.g. lecturing, discussion and cooperative learning) to teach the theories/laws aspect of NOS within PNM; however, they could not explain how they would use these teaching methods in their instructions. In the interviews, they were not able to teach NOS within the chemistry content by using instructional strategies they proposed.
Results of the post question and the second interview. PCT-4 stated that she would use lecturing to teach the theories/laws aspect of NOS within atom models. However, she could not give a detailed description. For instance, she wrote “…In order to make students see that theories are different from laws, I would give the example of Law of definite proportion”. PCT-5 also stated that he would use the discussion method, but he could not give any explanation concerning his instruction on the theories/laws aspect of NOS. The other two PCTs (PCT-6 and PCT-7) could not propose any teaching methods/strategies. Although PCT-6 had improved her idea from a naïve to an informed view on NOS, she could not develop her PCK of NOS in terms of knowledge of instructional strategies. On the other hand, three of the PCTs (PCT-1, PCT-2, and PCT-3) were able to explain how to use teaching strategies in their instruction in a rather detailed way in the post question. They also confirmed their explanations in the interview. For instance, PCT-2 stated that she would use discussions, demonstrations, and lecturing supported by animations in her instructions and explained the use of these teaching strategies successfully. It was observed that they developed their PCK of NOS concerning knowledge of instructional strategies throughout the course.
Results for Idea-2. From the analysis of the responses to pre questions, it was observed that seven PCTs failed to explain how to use teaching methods/strategies while teaching NOS within PNM. On the other hand, responses to the post question revealed that four PCTs (PCT-1, PCT-2, PCT-3, and PCT-4) explained how they could use methods/strategies while teaching NOS within PNM in an extensive way. PCT-7 partially explained how to use teaching methods/strategies while teaching NOS within PNM.
Results of the pre question and the first interview. All PCTs, except for PCT-7, proposed many different kinds of instructional strategies (e.g. inquiry, lecturing enriched with videos and visuals, discussions) to teach the tentativeness aspect of NOS within the PNM content; however, they failed to explain how they would use these teaching methods during their instruction. PCT-5 did not give any response to the question regarding instructional strategies. In the interview, one of them, PCT-2, articulated that she would use the discussion method in order to reveal students' misconceptions related to the topic she selected namely atomic models but her explanations related to her instruction were still superficial.
Results of the post question and the second interview. PCT-7 mentioned that he would use lecturing and he explained how to use this method, but not clearly. For instance, he stated

I would ask students to draw an atom. Then I would collect their drawings and explain that everyone in class have different models for atom. Atom theories developed like this and every scientist stated their theories about atom. In science, we cannot talk about absolute truths.

In his instruction on the post question, he did not give detailed information about the content of atom models and gave a general explanation for the steps of his instruction. The other two PCTs (PCT-5 and PCT-6) did not give any response to the question regarding instructional strategies. Thus, it was observed that they did not possess adequate knowledge of instructional strategies to teach the tentativeness aspect of NOS within the PNM content. On the other hand, the other four PCTs not only proposed instructional strategies to teach the tentativeness aspect of NOS within the PNM content, but also explained how to use these instructional strategies during their instruction in a detailed way. For instance, PCT-1 used the discussion method along with the lecturing method and she wrote that she would create a discussion environment with a question “why did Thomson continue to study on issue and propose another theory different from Dalton's theory?” in her instruction. Another participant, PCT-2, mentioned that she would use the discussion method supported by animations and by using this she intended to create an interactive learning environment for students. Both of them also confirmed their explanations in the interview. It can be concluded that four of the PCTs (PCT-1, PCT-2, PCT-3 and PCT-4) developed their PCK concerning knowledge of instructional strategies for teaching the tentativeness aspect of NOS within the PNM content.

In summary, at the beginning of the study, even if all the participants proposed only the name of the instructional strategies to teach target aspects of NOS, they could not explain how to enact these strategies in their classes. At the end of the study, most of the participants improved their knowledge in terms of instructional strategies and how to enact them in their instructions while teaching target aspects of NOS.

Knowledge of assessment

Results for Idea-1.
Results of the pre question and the first interview. Regarding PCTs' responses to the pre question, the participants stated to use open-ended questions (PCT-1, PCT-2, PCT-6 and PCT-7), project work (PCT-7), homework (PCT-1 and PCT-5), concept maps (PCT-4), and activity papers (PCT-3) in order to assess their students' opinions about the theories/laws aspect of NOS after their instructions on PNM. However, they could not give examples of their evaluation techniques integrating the theories/laws aspect of NOS into PNM.

During the interview, PCT-1 and PCT-3 gave examples for their evaluation techniques related to the theories/laws aspect of NOS after their instructions on atom models. However, they asked questions related to only NOS or only PNM. For example, regarding NOS, PCT-3 asked that “What is the theory and law? Is there a relationship between theory and law?” Regarding PNM, PCT-1 wrote “How do you explain Dalton's atom model by using law of definite proportions?”


Results of the post question and the second interview. When we investigated PCTs' responses to the post question, we found that all PCTs had still some difficulties in evaluating students' views on the theories/laws aspect of NOS within the PNM content. PCT-6 did not answer the question related to evaluation techniques. Six PCTs stated to use open-ended questions. Only PCT-2 asked a question integrating NOS into PNM. However, her question was not related to the topic she selected for her instruction (gas concept) and the hierarchical relationship between theories and laws. She asked: “Try to explain how law of definite proportions was used to propose Dalton's atomic theory by using your 9th grade knowledge. What can be inferred about the difference between law and theory?” It was observed that her question emphasized the difference between definitions of theories and laws. However, during the interview, she changed her question: “Considering the ideal gas law and kinetic theory of gases can you identify the purposes of laws and theories? Are laws superior to theories?” Hence, she could make a correct evaluation of Idea-1 by considering the PNM content. Other participants gave examples of their evaluation techniques, but their examples were related to either NOS or PNM. Thus, they could not integrate the NOS aspect into PNM. For example, PCT-3 asked “What are the differences between theories and laws, Can theories turned into laws? Explain.” PCT-7 asked that “How modern atom model developed explain shortly?”

When we examined their lesson plans, we found that PCT-1 and PCT-2 did not evaluate what their students have learned about the theories/laws aspect of NOS on PNM after their instruction.

Results for Idea-2.
Results of the pre question and the first interview. PCTs used the same evaluation techniques as they stated in Idea-1. However, they were not successful in assessing their students' views of the tentativeness aspect of NOS within the PNM content. For example, PCT-4 claimed that “I could apply a concept map to see whether the students have understood atomic theory and its changes. The empty parts of the map will be filled by the students.” All interviewees had difficulties in evaluating the tentativeness aspect of NOS within the PNM content in the interview.
Results of the post question and the second interview. Five PCTs asked open-ended questions. PCT-4 and PCT-6 did not answer the question related to evaluation techniques. Most PCTs still had some difficulties in assessing Idea-2. Whilst PCT-1 and PCT-2 improved their knowledge in terms of evaluation techniques and integration of NOS into PNM in a question, other PCTs were still not successful in evaluating their students' understanding of the tentativeness aspect of NOS within the PNM content. For example, PCT-2 stated: “Why scientists need many theories for acids–bases in the past?” She also supported her response during the interview. Moreover, PCT-1 stated “I will ask whether science is developing or not? Give explanation from your learning regarding atom models in this class”. During the interview, she also gave the same response. Other PCTs asked questions related to only NOS or only PNM in the evaluation part of their instruction or they could not evaluate their students' opinions about Idea-2. For example, PCT-7 asked a question related to only PNM: “How modern atom model developed explain shortly.”
Results of analysis of lesson plans. The analysis of lesson plans indicated that although all PCTs stated the tentativeness aspect of NOS in their instruction, only PCT-2 and PCT-3 presented appropriate questions integrating this aspect of NOS into PNM. For instance, PCT-2 asked: “Can atom models change in time? Do atom models represent the truth?”

In summary, at the beginning of the study, all participants had difficulties in assessing students' understanding of theories/laws and tentativeness aspects of NOS within the PNM content. At the end of the study, although most of the participants' understanding of these aspects of NOS was adequate, many participants still had difficulties in assessing the target aspects of NOS within the PNM content.

Discussion

This study aimed to investigate pre-service chemistry teachers' views on theories/laws and tentativeness aspects of NOS. In addition, we examined their PCK in terms of the knowledge of learners, instructional methods/strategies and assessment of NOS on the PNM during a practice teaching course in a semester.

This research study contributes to the development of pre-service teachers' understanding of NOS. In science education, the understanding of NOS has a crucial role; however, the result of previous studies indicated that learners had inadequate views on NOS (Abd-El-Khalick, 2005; Afonso and Gilbert, 2010). Likewise, in this study, we found that some of the participants possessed inadequate views on the theories/laws and tentativeness aspects of NOS at the beginning of the study. At the end of the study, most of the PCTs showed improvement in the target aspects of NOS and realized that there is no hierarchical relationship between theories and laws, and scientific knowledge is subject to change and is not absolute. Instruction based on NOS and preparing lesson plans for teaching related NOS aspects might be the reason for this progress as also stated by Abd-El-Khalick and Akerson (2009). Akerson et al. (2000) also highlighted that classroom discussions and writing reflections have an important role in improving NOS understanding. In line with their study, in the present study, other reasons for improvement in PCTs' views on the target aspects of NOS might be classroom discussions on the NOS aspects in terms of their meaning and how they were used in PCTs' instructions, and writing reflection papers during the practice teaching course. The results indicated that PCTs broadened their understanding of NOS throughout the course.

Most of the PCTs were aware of the sources of learners' misconceptions of theories/laws and tentativeness aspects of NOS, and difficulties in learning these aspects both before and after taking the practice teaching course. Participants in this study emphasized teachers, textbooks and prior experience as sources of misconceptions of NOS. This finding is consistent with the sources proposed by Sahin and Koksal (2010). Although PCTs were aware of students' learning difficulties in NOS, their explanations changed from general to specific and they gave more in depth information at the end of the study. The results indicated that pre-service teachers' knowledge about students' learning difficulties and misconceptions of the target aspects of NOS might develop with the teaching experience gained during their practice teaching, while observing their mentors, and utilizing chemistry textbooks while preparing their instructions. This result is parallel to the findings of De Jong et al. (2005) and Van Driel et al. (2002).

This study also helps science teacher educators understand the way for helping the development of pre-service teachers' PCK of NOS within specific chemistry content during a practice teaching course. The results of the study indicated that participants, who had a naive view on theories/laws and tentativeness aspects of NOS, could not give a proper example on the topic of PNM and could not explain how to teach the target aspects of NOS within the PNM content. As Schwartz and Lederman (2002) proposed, teachers must have sufficient knowledge on understanding of NOS to be able to teach NOS. In this study, some participants, who had sufficient knowledge on the target aspects of NOS, integrated these aspects into the PNM content by giving an appropriate example. However, some of these participants failed to integrate the target aspects of NOS into the PNM content in spite of their adequate knowledge on NOS. The reason why they could not use the aspects of NOS in their instruction might be their insufficient knowledge of PNM. In addition, PCTs learn NOS and specific chemistry contents (e.g. PNM) as separate subjects; thus, they might have difficulty in integrating NOS into their chemistry teaching. On the other hand, the results of the study indicated that more participants could integrate NOS aspects into PNM at the end of the study. This improvement might be due to the fact that PCTs had teaching experience and observed other participants' instructions integrating NOS aspects into chemistry topics. In the light of these results, it can be concluded that the practice teaching course including practice on content embedded NOS instruction helped pre-service teachers make connections between NOS and specific chemistry content, and improve their teaching of NOS within the chemistry context. However, some participants, who integrated the target aspects of NOS into PNM, could not explain how to teach NOS within the PNM content. The reason might be their insufficient knowledge of instructional methods/strategies.

The results indicated that some participants could not integrate theories/laws and tentativeness aspects of NOS into PNM and could not elaborate how to teach these aspects on the pre and post question. Thus, it can be stated that integrating NOS into PNM is necessary in order to develop their PCK for teaching NOS within the PNM content. On the other hand, four participants could integrate the theories/laws aspect of NOS into PNM and explain how to teach these aspects on the post question. It can be concluded that these participants might improve their subject matter knowledge of NOS and PNM during the course. As Abell (2008) and Kind (2009) pointed out, having adequate subject matter knowledge has an important role in the development of PCK. In addition, they might develop their ability to integrate NOS into PNM. Also, they might develop their PCK in terms of knowledge of instructional strategies to teach the target aspects of NOS within the PNM content through their teaching experiences during the semester. Moreover, while four participants could integrate the tentativeness aspect of NOS into PNM on both pre and post questions, these participants could explain how to teach NOS within the PNM content only on the post question. It can be concluded that they developed their PCK in terms of knowledge of instructional strategies to teach the target aspects of NOS within the PNM content through their teaching experiences during the semester as stated in the studies of De Jong et al. (2005) and Van Driel et al. (2002). This conclusion supports the dynamic nature of PCK (Abell, 2008).

Although many participants improved their PCK in terms of instructional strategies, the majority of the participants possessed some difficulties in assessing the target aspects of NOS within the PNM content at the end of the course. As Magnusson et al. (1999) and Hanuscin et al. (2011) stated, the changes in knowledge of one component may be independent of the changes in other components. We observed that PCTs assessed either NOS or PNM, without combining them with each other. Only one participant (PCT-2), who integrated NOS into PNM and stated how to teach NOS within the PNM content, could ask questions integrating NOS into PNM in the post question. This result indicated that PCT-2 improved her knowledge of assessment in the post question. Three participants, who integrated NOS into PNM and explained how to teach NOS within the PNM content, could not ask questions integrating NOS into PNM in the post question. Thus, it can be concluded that these PCTs had insufficient knowledge of assessment techniques of the target aspects of NOS regarding the PNM content. This result is consistent with the ones from previous research studies (Abd-El-Khalick et al., 1998; Hanuscin et al., 2011).

The findings of this study are limited to the pre-service chemistry teachers. Replication studies on PCK of NOS can be conducted with pre-service or in-service teachers in different chemistry contents and other science disciplines. Although this study is an example for developing PCTs' PCK of NOS during a practice teaching course, further research is needed to explore the ways to help teachers develop their PCK of NOS. Moreover, reflections of pre-service teachers on a practice teaching course based on content-embedded NOS instruction could be taken into consideration to improve the quality of the course. Furthermore, the current study did not consider all the components of PCK in Magnusson et al. (1999)'s model. Further studies focusing on all PCK components are warranted. Especially, considering the complexity of orientation toward science teaching, the relationships between orientations and other PCK components should be examined in further studies as also suggested by Friedrichsen et al. (2011).

Implications

The current study has several implications for teacher education: Teacher education programs should consider developing NOS views of pre-service teachers. The courses in these programs should include specific science content embedded NOS instruction to support pre-service teachers addressing NOS aspects in their teaching. In this integration, using appropriate instructional strategies is crucial. Therefore, science teacher education programs should emphasize these instructional strategies in order to improve pre-service teachers' PCK of NOS within specific science topics. Science teacher education programs should create awareness regarding misconceptions of NOS and sources of these misconceptions so that pre-service teachers may design their instruction considering students' possible misconceptions and learning difficulties in NOS in the future. Pre-service teachers should be given opportunities to integrate NOS into their teaching and assess their students' understanding of NOS in specific science contexts in practice. Moreover, science textbooks and curricula should be redesigned taking NOS aspects into account.

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