Linking pre-service teachers’ enacted topic specific pedagogical content knowledge to learner achievement in organic chemistry

Abstract

This paper reports on the relationship between the pre-service teachers’ enacted Topic Specific Pedagogical Content Knowledge (eTSPCK) observable in the classroom teaching of Organic Chemistry and learner achievement in the topic. The study employed a mixed-methods research design with a sample of 17 pre-service teachers (PSTs). The PSTs were drawn from a Chemistry methodology class exposed to an intervention which focused on the pedagogical transformation of content knowledge of Organic Chemistry at a South African University. A sub-set of 4 of the PSTs was followed during a teaching practicum where the PSTs conducted lessons on Organic Chemistry with 88 Grade 12 Secondary School physical sciences learners in South Africa. Data collected were the video-recordings of the 4 PSTs’ classroom teachings, lesson plans, pre-and post-lesson interviews, and learners’ content knowledge pre-and post-achievement tests on Organic Chemistry prior to and immediately after the PSTs’ teachings, respectively. The video recorded lessons were analysed using an in-depth qualitative method of identifying TSPCK episodes and the interviews were analysed using content analysis. The learners’ achievement tests were scored using a memorandum of correct responses. The Rasch Model Analysis, Analysis of Covariance and Correlation analysis were employed in determining the relationship between PSTs’ eTSPCK and learner achievement. The analysis revealed a statistically significant difference across the means of the learners’ pre/post-tests, as well as a significant positive correlation between pre-service teachers’ eTSPCK and learners’ post-test achievement following the teaching. The correlation was found to increase in positive strength with the displayed higher quality categories of TSPCK episodes. The implications and recommendations for science teacher education are discussed.

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Introduction

Improving the quality of classroom teaching and learners’ conceptual achievement is one fundamental focus of most Initial Teacher Education programmes in science education (Sickel and Witzig, 2017). The learners’ conceptual achievement is however, widely understood to be influenced by a myriad of factors such as the learners’ background, interest, attitudes as well as the availability of teaching resources, etc. (Blömeke et al., 2016). The performance of teachers is particularly reported as having a major influence on learner outcomes (Keller et al., 2017). For developing countries, such as those in Sub-Sahara Africa, where the teaching of science is reported to be prevalently poor, the link between teachers’ professional knowledge and learners’ conceptual achievement is of high interest.

Pedagogical Content Knowledge (PCK) is acceptably viewed as the central component of teachers’ professional knowledge for effective teaching (Gess-Newsome, 2015) and accordingly, Richardson et al. (2018) argued that teachers with highly developed PCK would produce superior teaching and learning experiences for learners. In science education, a number of PCK researchers have made efforts to investigate the impact of teachers’ PCK on learner outcomes (Lange et al., 2011; Alonzo et al., 2012; Cross and Lepareur, 2015; Keller et al., 2017; Gess-Newsome et al., 2019; Liepertz and Borowski, 2019). While some of these studies reported positive impacts of teachers’ PCK on learner outcomes (Lange et al., 2011; Alonzo et al., 2012; Keller et al., 2017), some other studies could not find any positive relationship between teachers’ PCK and learner outcomes (Cross and Lepareur, 2015; Gess-Newsome et al., 2019; Liepertz and Borowski, 2019). As much as establishing the impact of PCK on learner outcomes with empirical evidence is a shared desire in the PCK science education community, the contradictory findings are naturally sending a mixed signal thereby leaving the issue lingering with uncertainty and thus, highly unresolved.

The current paper emanated from a larger study which examined the process of developing Topic Specific PCK (TSPCK) in chemistry pre-service teachers (PSTs) progressively from planning through actual classroom teaching of Organic Chemistry and ultimately the relationship between their enacted TSPCK and learner outcomes in Organic Chemistry. This paper reports specifically on the relationship between the PSTs’ enacted TSPCK observable in the classroom teaching of Organic Chemistry and learner achievement in the topic. The PSTs involved in this study were about to become teachers in the South African social context. South Africa is a developing country where possible solutions to improving the quality of science education in public schools were being sought. Thus, establishing the nature of relationship between the professional knowledge for teaching developed by PSTs and learner achievement is important feedback for improving the agility of the local PCK-based teacher education programmes. In science education research, little is known about the understanding of the relationship between teachers’ PCK and learner outcomes from the perspective of PSTs who are learning to teach and with PCK explored in classrooms at the level of a topic specific grainsize (eTSPCK). Thus, the findings from this study would offer an additional contextual perspective which contributes towards enabling the building of a conclusive agreement in fully describing the integral impact of PCK theoretical construct on learning sciences.

Challenges in establishing the link between teachers’ PCK and learner outcomes

As alluded to above, establishing a convincing correlation, let alone a causal effect, between teachers’ PCK and learner outcomes remains an ongoing challenge in science education research as there have been mixed findings. The reasons for the mixed findings could be linked to a few noticeable observations. First, with the benefit of hindsight, and having the current Refined Consensus Model of PCK (RCM) in place (Carlson and Daehler, 2019), we note the use of different operational definitions of PCK and measurement strategies employed in examining the relationship across different studies. For example, Liepertz and Borowski (2019) conceptualized PCK operationally from Shulman's (1986) original conception as the amalgam of content knowledge (CK) and pedagogical knowledge (PK) for teaching the concept of force in physics. The authors investigated the relationships among teachers’ professional knowledge, interconnectedness of content structure and learner outcomes. It was found that teachers’ PCK showed a negative influence on learner outcomes (Liepertz and Borowski, 2019). In another study where PCK was operational as the teachers’ CK with interactions with learners from the perspective of foregrounding the topic's concepts, learners’ learning difficulties and use of representations, Alonzo et al. (2012) explored the influence of German teachers’ enacted PCK on learner achievement and interest in the topic of Optics. The authors reported that the observed teachers’ PCK positively enhanced learners’ motivation and achievement (Alonzo et al., 2012). With the benefit of the RCM, it is now understood that such studies used different grain sizes of PCK, discipline-PCK in the former and the selective components of topic specific PCK in the latter. We do not claim this observation as the reason for the conflicting findings, it is a note on how the different operationalization of PCK construct, which the RCM is beginning to address, prevents ease of comparison and any form of standardization across the studies, to enable research designs that asks big questions in the field such as the teachers’ PCK-learner outcome link.

The second observation is with respect to the different methods of measurements used across the studies. Liepertz and Borowski (2019) used quantitative paper-and-pencil tests to measure teachers’ PCK versus learner achievement. On the other hand, in the study by study by Alonzo et al. (2012), there was an effort to qualitatively capture teachers’ enacted PCK versus learner outcomes. In terms of the RCM, and the derived benefit of making reference to it, the measurement of PCK through pencil and paper tests (e.g.Liepertz and Borowski, 2019) could be interpreted as measuring planned-PCK rather than enacted-PCK as in the case of Alonzo et al. (2012). The RCM points to enacted PCK being the closet to learners, and the form of teachers’ PCK to which learners are exposed. The different operationalization and dimensions of PCK (PCK realms) being measured in each of these studies point to the dire need for a shared language, and operationalization of PCK as now offered by the RCM in order to enable reasonable uniform interpretations of findings on issues of common interest in the literature.

The third observation relates to the epistemological challenges in creating research designs that would meet the needed criteria for establishing a conclusive causal effect across teachers’ PCK and learner outcomes with certainty (Blömeke et al., 2016; Hill and Chin, 2018). To start with addressing these current challenges in the science education literature as the findings are inconclusive, it is important to first establish that there is a kind of relationship. Also, there is the need to ensure that the research design employed eliminates historical threats and rules out alternative explanations for the possible observed effect. The last assumption is particularly difficult to consider as it is epistemologically challenging to plan for zero PCK scenarios or PCK in only teaching control samples (Nilsson and Vikström, 2015) especially in the cases of pre-service teachers. We contend that the establishment of the causal effect link between teachers’ PCK and learner achievement would require creative planning of multiple large-scale studies drawn from different contexts but sharing standardized tools as potentially enabled by the RCM of PCK and the newly developed framework describing features of a grand rubric for PCK measurement (Chan et al., 2019). Such studies naturally require extensive findings and sufficient baseline evidence pointing to the existence of some correlations between teachers’ PCK and learner outcomes. Thus, this paper purposefully seeks to contribute towards building the aforementioned necessary baseline requirements to enable the next steps of establishing a causal-effect relationship by examining the existence or lack of the said correlation from the perspective of PSTs’ eTSPCK in the topic of Organic Chemistry. We also noted the importance of re-visiting with care, the operational conception of TSPCK that we provide in the next section. The research question guiding this study was – How does the pre-service teachers’ enacted TSPCK visible in the actual classroom teaching of Organic Chemistry relate to learner achievement in the topic, if at all?

Theoretical framework

This study was rooted in the Shulman's (1987) argument that, “comprehended ideas must be transformed in some manner if they are to be taught” (p. 16). It was also based on the argument that, the value of the ‘pedagogically transformed content understanding’ lies in its desired effect of enhancing learner performances (Rollnick and Mavhunga, 2015). In this line of thought, PCK is regarded as the teachers’ knowledge that enables the competence to pedagogically transform content knowledge (CK) with the purpose of facilitating learners’ learning. Following the Shulman's conceptualization of PCK, various models emerged from numerous studies (e.g.Grossman, 1990; Park and Oliver, 2008) where the Magnusson et al.'s (1999) model represent the most widely cited especially in science education research. The similarities and differences in the emerging PCK models conspicuously call for convergence in thoughts among PCK researchers. The most recent product of two PCK Summits held in 2012 and 2016 was the Refined Consensus Model (RCM) of PCK (Carlson and Daehler, 2019) which constitutes the essential foundation for this study.

The RCM of PCK recognizes the different dimensions or teaching realms in which PCK is visible namely: collective PCK (cPCK); personal PCK (pPCK); and enacted PCK (ePCK) with learner outcomes as a key downstream product. It identifies cPCK as the shared professional understanding about PCK that teachers may acquire from coursework, texts, and other sources and which is commonly agreed upon as teacher knowledge for effective teaching and learning (Carlson and Daehler, 2019). In the case of PSTs who take coursework that focuses on developing their PCK, they are being taught cPCK which they could individually personalize to generate personal PCK (pPCK) mediated by filters and amplifies such as personal beliefs, varying extent of understanding of cPCK and other affective factors (Carlson and Daehler, 2019). Teachers’ pPCK portrayed while thinking about and planning for teaching has been commonly referred to as planned PCK (plPCK) (Park and Oliver, 2008; Aydeniz and Kirbulut, 2014). Teachers’ ePCK has been described as PCK portrayed by teachers in the actual classroom teaching (Carlson and Daehler, 2019). Thus, cPCK, pPCK and ePCK represent the three distinct realms that must be explored for a detailed description of the nature of teachers’ PCK which plays an active role in the overall development of professional knowledge required for effective teaching.

In this paper, we had a specific focus on the topic specific grain size of PCK (TSPCK) in the realm of enactment as eTSPCK and the relationship between eTSPCK and learner achievement. We acknowledge that the value of PCK is widely agreed upon to be accessed most readily when teaching topics within a discipline (Gess-Newsome, 2015). We worked with the transformation of content knowledge of a given topic (Organic Chemistry) similar to the descriptions provided by Geddis et al. (1993) and Geddis and Wood (1997). Thus, pedagogical transformation of CK in a given topic emerges from the understanding and interactive usage of certain content specific knowledge components (Mavhunga, 2016). The knowledge components are: learner prior knowledge; curricular saliency; what is difficult to understand; representations; and conceptual teaching strategies (Mavhunga and Rollnick, 2013). The component ‘learner prior knowledge’ comprises learners’ common correct knowledge, alternative conceptions and misconceptions with respect to a given content. The component ‘curricular saliency’ encompasses the understanding of several topics in relation to the entire curriculum, core and subordinate concepts, logical sequencing of concepts and prior knowledge which is essential for understanding the current content. The component ‘what is difficult to teach or understand’ comprises the knowledge of gate-keeping concepts within a given topic which are difficult for learners to understand and hence, calling for the teachers’ consciousness and mediation. The component ‘representations’ comprises the analogies, models, simulations, and visual illustrations which are important in promoting learners’ conceptual understanding of a given content. The component ‘conceptual teaching strategies’ consists of teaching techniques which draw on learners’ misconceptions, what is important to emphasize about a content, aspects of difficulty relating to the content and use of representations to make the content understandable.

The five knowledge components constitute the content-specific components of TSPCK observable in the teachers’ lesson plans prior to classroom teaching and explanations provided by teachers during actual teaching of a given topic (Rollnick and Mavhunga, 2014). The engagement of these TSPCK components interactively places focus on the specific learner regarding the specific topic, and on what is also commonly known about the learning of the topic by other learners. Furthermore, such content specific perspectives deliberately pay attention to one topic at a time, where reference to other topics within or across the discipline is made in relation to the benefit of learning the topic at hand. It is this dedicated attention to pedagogical transformation of CK in a topic that distinguishes PCK at a topic level (Mavhunga, 2020). Hence, the quality of PCK at a topic level is associated with the extent to which a teacher demonstrates the knowledge of individual TSPCK component and interaction among the components in making a given content understandable to learners (Park and Chen, 2012; Mavhunga, 2020). We operationalized TSPCK by defining it through the interactions of the five content-specific components enlisted above. The focus of TSPCK is embedded in understanding how these content-specific knowledge components are interactively used in making the teachers’ CK of a given topic accessible to learners. In this study, the interaction among TSPCK components is the specific feature used for the analysis of teachers’ eTSPCK in relation to learner achievement in Organic Chemistry.

Methodology

The study employed a mixed methods design using a case study research approach as illustrated by Creswell and Clark (2017). The research design was chosen because it holistically provides perspectives of teachers’ PCK known to be tacit and complex in nature. Both the qualitative and quantitative methods were employed in the process of collecting and analysing data. The initial sample comprised 17 physical sciences (Chemistry and Physics) PSTs at a University in South Africa and 88 physical sciences learners drawn from Secondary Schools in the same geographical location as the University where this study was conducted. All the research activities were carried out in line with the guidelines for Human Research Ethics Clearance (non-medical), guarded by the institution's Ethics Clearance Committee, as well as the Head of School, so as to ensure the rights and protection of the participants. Participation was voluntary, and pseudonyms and codes were used throughout the study to preserve confidentiality. All the work in this study reports from a South African University, where the language of instruction is English.

Intervention

This study began with an intervention located in the chemistry methodology class of the participant 17 PSTs who were in their final year of study at a South African University. The class of PSTs was bound by the common purpose of obtaining a Bachelor of Education degree majoring in Physical Sciences (Chemistry and Physics) at the University. The focus of the intervention was on a module targeting the development of TSPCK in core chemistry topics contained in the South African's National Secondary School curriculum. We focused on the topic of Organic Chemistry which is one of the highly weighted topics in the Secondary School Curriculum in the country. The intervention consisted of explicit discussions of the five content-specific knowledge components of TSPCK, one at a time and their interactions, all needed for the pedagogical transformation of content knowledge of a given topic, Organic Chemistry in this study (see Table 1).

Table 1 Intervention activities

Week/Session	TSPCK component	Activities	Aspects of content knowledge
Week 1 Session 1	Administrating pre/post TSPCK and CK tests	Introducing research, TSPCK construct and ethics issues	Administrating pre/post TSPCK and CK tests
Week 1 Session 2	Learner Prior Knowledge	• Identification of widely researched learners’ misconceptions in organic chemistry according to the literature.	• Misconception relating to identifying longest continuous carbon chain in IUPAC naming of aliphatic hydrocarbons.
		• Dividing pre-service teachers to discuss the identified misconceptions and strategies for addressing.	• Misconceptions relating to the effects of type of bond on the reactivity of homologous series of organic compounds.
		• Combined discussions with the pre-service teachers on the conceptual teaching strategies drawing on TSPCK components.
Week 2 Session 1 and 2	Curricular saliency	• Discussions on the importance of identifying and emphasizing Big Ideas (core concepts) and subordinate concepts in organic chemistry.	Core concepts: carbon unique nature; functional groups; reactions of organic compounds. Subordinate concepts: Isomers and homologous series; Alkanes and its members.
		• Completion of Content Representations prompts on Learner Prior Knowledge and Curricular saliency.	Prior knowledge needed: chemical bonding; covalent bonding; chemistry of carbon as an element; intermolecular forces.
Week 3 Session 1 and 2	What is difficult to understand or teach	• Identifying difficult concepts and reasons for the difficulty.	Molecular and structural formulae; organic compounds with similar functional groups; IUPAC naming of organic compounds; and isomerism.
		• Potential learners’ difficulties in accurately understanding the full meaning of a big or subordinate idea.
		• Completion of prompts on Content Representations tool.
Week 4 Session 1 and 2	Representations	• Discussing three levels of representations: macroscopic; sub-microscopic; and symbolic.	Representing organic compounds (e.g. isomerism) at macroscopic, symbolic, and sub-microscopic levels.
		• Emphasizing concurrent use of three levels of representations in explaining each organic chemistry concept.
		• Completion of Content Representations tool prompts on representations.
Week 5 Session 1 and 2	Conceptual teaching strategies	• Discussions drawing placing organic chemistry concepts side-by-side in explaining the similarities and differences.	Alcohols and Thiols; Aldehydes and Ketones.
		• Addressing identifying a misconception by emphasizing key concepts that must be understood, identifying learning difficulties relating to the concepts and use of multi-levels of representations in making the concepts understandable.
		• Completion of Content Representations tool prompt.
Week 6 Session 1	Pulling it all together	CoRe discussed explicitly as a tool to organize one's thoughts when reasoning through a topic.
Week 6 Session 2	Administration of post-TSPCK and CK tests	Formal closure and sharing of the next steps of action by the researcher in the research study – This included logistics and seeking consent for participation in the next stage of the study in the upcoming teaching experience (practicum).

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Data collection

The sets of data for the larger study were collected at six distinct stages as summarized in the Fig. 1. The stages followed are sequentially described as follows.

Fig. 1 Stages of data collection.

Establishing a credible baseline from which to interpret enacted TSPCK: stage 1–3

At the first stage, planned TSPCK (plTSPCK) and CK data were collected at the beginning of the intervention with the entire class of 4th year PSTs comprising a total sample of 17. For this purpose, the plTSPCK and CK tools in Organic Chemistry developed by Davidowitz and Vokwana (2014) were administered to the PSTs as pre-tests. The plTSPCK tool is structured into five sections which correspond to the five content-specific knowledge components of TSPCK. Each section comprises a few questions which are described as teachers’ tasks and formulated to allow for open-ended responses from the participants. An example of one of the questions on the TSPCK component ‘Learner Prior Knowledge’ is provided in the Fig. 2. The question centres on addressing the learners' misconception relating to how the hydroxyl functional group (R-OH) in Alcohols differentiates them from other organic compounds which have hydroxyl functional group and inorganic compounds with an OH group which when dissolved in aqueous solution, releases OH⁻. The question is situated in the classroom setting and it requires the PSTs to formulate a response with emphasis on the knowledge for teaching rather than content knowledge. Also, the CK tool consists of test items which measure the PSTs’ conceptual understanding of Organic Chemistry as later explained under the 4th data collection stage. Both the plTSPCK and CK data were purposely used to establish a credible baseline for describing the observed enacted TSPCK demonstrated by the PSTs.

Fig. 2 A sample question items on Learner Prior Knowledge (TSPCK tool).

The second stage of data collection was during the intervention where Content Representations (CoRe) were being developed systematically by the PSTs as part of tutorials where each new prompt corresponded to the sequential discussion of the components of the TSPCK construct. Tutorials comprised activities which were designed to give the PSTs a space to engage more actively with the content of the intervention and provide them with a much better opportunity to get to know their fellow students by working in collaboration. The PSTs submitted the completed CoRe as a major assessment task on the last day of the intervention. The qualitative data generated from the completed CoRe tool assisted in gaining insights into how the PSTs’ understanding of the interactive use of content-specific knowledge developed throughout the intervention, revealing their areas of strengths and weaknesses.

The third stage of data collection was immediately at the end of the intervention where both the TSPCK and CK tools were re-administered as post-tests to the entire sample of 17 PSTs. At this stage, the stimulated recall interviews were also conducted with the PSTs to understand the factors that contributed to the quality of their plTSPCK following the intervention. As already indicated, the collection of completed pre-and post-TSPCK tools were useful in establishing the shifts in the quality of PSTs’ planned TSPCK as a credible base from which later observations of enacted TSPCK could be interpreted.

Capturing enacted TSPCK and learner achievement

The fourth, fifth and sixth stages of data collection were with a sub-set of 4 PSTs and 88 high school physical sciences learners. The focus of this paper is on the data collected at these last three stages. These stages happened three weeks after the intervention and during a teaching practicum where the PSTs were allocated to Secondary Schools for teaching experience. The decision to focus on a sub-set of 4 PSTs was based on two reasons. First, only 4 PSTs were found in the schools that were willing to grant permission to video-record classroom teaching as the current local regulations do not encourage the video recording of learners. Second, the accessibility to the schools and willingness of these 4 PSTs to participate in this component of the study were taken into consideration in alignment with the ethics protocol of the University's Human Research Ethics Committee (non-medical). The practicum took place at Secondary Schools which are categorized as township schools in the country. Historically, township schools are known to be poorly resourced with respect to teaching science, with teachers trained from poorly conceived teacher training programmes delivered by the then Teacher Education Colleges, thus, most of the schools produce poor academic results (Jawahar and Dempster, 2013). While all the 4 PSTs originated from different parts of the country, they were from previously disadvantaged communities and they had attended similar kinds of schools – township schools.

At the fourth stage, just before the delivery of lessons by the PSTs, the CK tool in Organic Chemistry developed by Davidowitz and Vokwana (2014) were administered to the participating Secondary School learners as a pre-achievement test (see Appendix I). The design of the CK tool was informed by the syllabus for Grade 12 physical sciences and also by the textbooks endorsed by the Department of Basic Education in South Africa (Davidowitz and Vokwana, 2014). The test included tasks on molecular structures, generating and naming isomers, functional groups, types of reactions, and the relationship between molecular structures, intermolecular forces, and physical properties. There were sixteen items in the achievement test and each item requires a single correct answer. A sample item in the CK tool is provided in the Fig. 3.

Fig. 3 A sample of the content knowledge test (Davidowitz and Vokwana, 2014).

The items in the CK test are classified according to the knowledge dimensions proposed by Jüttner et al. (2013). The dimensions are: declarative knowledge – knowing facts and other information appearing in texts; procedural knowledge – knowing how to execute a skill or apply concepts and principles to specific questions in organic chemistry; and conditional knowledge – knowing when and why to use declarative or procedural knowledge (Jüttner et al., 2013), for example to generate the formulae of isomers or to explain the trends in boiling points of alcohols. During the fourth stage of data collection, the pre-lesson semi-structured interviews were also conducted with the PSTs to understanding their intentions about their teaching.

At the fifth stage of data collection, each of the 4 PSTs (pseudonyms: Ruth, Hope, Rose, and Mark) delivered two lessons which lasted for a total lesson duration of 140 minutes. The lessons were video recorded. The classes taught by the PSTs comprised 14 to 30 Grade 12 learners who were within the age range of 15 to 17 years.

At the sixth stage of data collection, immediately after the delivery of the lessons by the PSTs, the same learners’ achievements test was re-administered with the respective learners as a post-test after the PSTs’ teaching. The learners took between 30–40 minutes to write each of the pre-test and post-test. Also, the post-lesson semi-structured interviews were conducted with the PSTs following the classroom teaching to gain insights into the reasoning behind their instructional decisions. The interviews were in the format of stimulated recall sessions, where the video-recorded lessons were replayed in the presence of each PST in a non-threatening environment. The lesson plans prepared by the PSTs were also collected as additional sources of data.

Data analysis

All the data collected were analysed. Of most relevance to the focus of this paper is the analysis of data collected in stage four, five and six (Fig. 1). This involves the data focusing on the classroom teaching of the 4 participant PSTs and learner achievement test, which were administered prior to and following the PSTs’ teaching. The analyses are sequentially presented as follows.

Analysis of lessons for enacted TSPCK

The video recorded lessons of the participant PSTs were examined for eTSPCK. Similar to how PCK has been qualitatively analysed in other previous studies (e.g.Park and Chen, 2012; Aydin and Boz, 2013; Park and Suh, 2019), an in-depth qualitative analysis was employed in this study to examine the PSTs’ lessons for TSPCK enacted during classroom teaching. The analysis focused on identifying teaching segments which demonstrated interactive use of two or more TSPCK components that we have termed ‘TSPCK episodes’ (Mavhunga, 2020). Based on the number of TSPCK components interacting in a given teaching segment, the identified TSPCK episodes were categorized either as a ‘simple TSPCK episode’ coded as 1, ‘proficient TSPCK episode’ coded as 2 or ‘sophisticated TSPCK episode’ coded as 3 using a validated TSPCK rubric (Miheso, 2018). A sample of the rubric is attached as Appendix II for illustrative purposes. The criteria for categorizing the emerging TSPCK episodes according to the rubric and excerpts of sample teaching segments are provided in the Table 2.

Table 2 Criteria for categorising the pre-service teachers' TSPCK episodes and excerpts of related teaching segments

Type 1: Simple TSPCK episode (Coded 1)	Type 2: Proficient TSPCK episode (Coded 2)	Type 3: Sophisticated TSPCK episode (Code 3)
• Evidence of two different TSPCK components interacting evidently and distinguishably in a specific teacher task segment. Both components work together to support an explanation of a single concept or a pair of concepts that are related.	• Evidence of three different TSPCK components (OR two different TSPCK components where one of the components is repeating and bringing a different level of explanation that complements the initial emergence) interacting evidently and distinguishably in a specific teacher task segment.	• Evidence of four different TSPCK components (OR three different TSPCK components where one of the components is repeating and bringing a different level of explanation that complements the initial emergence) interacting evidently and distinguishably in a specific teacher task segment.
• An example	• An example	• An example
For example, in her teaching, Hope probed learners’ prior knowledge and realized that while learners described organic compounds as carbon-containing compounds, some of them thought all inorganic compounds that contain carbon are organic compounds. In an attempt to address this misconception, Hope stated that:	In Rose's lessons, some learners incorrectly indicated to her that, propanol has weak intermolecular forces and hence, it would have higher boiling point compared to propane with strong intermolecular forces. The excerpt of Rose's interactions with learners is provided as follows:	Ruth had a teaching segment on an alcohol functional group during which a sophisticated TSPCK episode emerged. She started by writing ‘R-OH’ on the chalkboard and probing the learners’ knowledge about what the symbolic expression represents. Through their responses, the learners recognized the symbol as a hydroxyl group for representing the functional group of alcohols. She further explained as follows:
[An excerpt from Hope's Lesson 1, 6–7 minutes]	[Excerpts from Rose's teaching, Lesson 2, 20–22 minutes]	[Excerpts of Ruth's teaching, Lesson 1, 16–18 minutes]
“… as we can see here [she referred to the molecular formula of sodium hydrogen carbon, NaHCO3], our Sodium cation Na^+ is only bonded to our bicarbonate anion right HCO3^−. So, our NaHCO3 is an inorganic compound but as you can see it contains carbon, it is a carbon-containing compound. Here is a different but similar example. Here again we’ve got chloromethane [she referred to CH4Cl], carbon is covalently bonded to 4 atoms of Hydrogen and 1 atom of chlorine so what is important for you here is carbon is bonded covalently to hydrogen, this type of covalent bond is essential for a molecule to be regarded as an organic compound, the understanding helps you to recognize organic compounds when you come across them, hope you all got that.	Rose: … okay guys, let's start from here. In Grade 11, you learnt about the different types of intermolecular forces like dipole–dipole interactions which other ones can you remember?	Ruth: … yeah, that's very right, it's called a hydroxyl group, OH it's for the alcohols so here we’re talking about our oxygen which is covalently bonded to hydrogen, that's fine then I wouldn’t expect anyone of you to think, it's the same as the hydroxide group which we normally represent as OH^− right, please take note of that guys (LP), in different compounds you see hydroxyl group and hydroxide ion symbolic represented as OH as that's where the problem lies if you forget the kind of compounds you are dealing with, is it organic, is it inorganic, you must be able to say to avoid unnecessary difficulty (WD), here this is what we’re saying, hydroxide ion as in this example [she wrote KOH on the chalk board], it's OH^− right, that's potassium hydroxide, potassium ion and hydroxide ion and you’ve got an ionic bond but here [she wrote C2H5OH], (RP) carbon covalently bonded to hydrogen and hydroxyl group, OH, that's organic, with this understanding you can easily distinguish organic molecules from inorganic molecules now?
Ss: yes	S1: London dispersion forces	Ss: yes
Qualitative in-depth analysis	S2: hydrogen bonds	S9: very well ma’am, one is OH– and the other one is OH, hydroxyl group
Based on the Hope's good content knowledge of how inorganic compounds differ from and similar to organic compounds, Hope used the molecular formulae to explain the place of carbon bonding covalently to hydrogen for a compound to be classified as an organic compound. This was emphasized by her as an important aspect for learners to understand in studying this aspect of organic compounds. This is an element of TSPCK component ‘Curricular saliency’ (CS). Her explanation also revealed her knowledge of the use of symbolic representations (RP).	S3: metallic bonds	Ruth: Yeah, hydroxide is found in inorganic compounds, hydroxyl group is found in organic compounds, good. Most importantly, we use hydroxyl group to identify all alcohols as one homologous series in organic compounds such as ethanol here [she pointed at C2H5OH], that's the functional group, it's like a common identify, it determines their IUPAC naming and also the type of reactions they commonly undergo, please note of that (CS) so in R-OH, alkyl R, is bonded to OH group so we do represent all alcohols by R-OH it means all members in the alcohol homologous series have got same OH. Because they’ve all got OH, they all undergo reactions like oxidation, esterification and so on, one important thing for you note, you see when alcohols are oxidized, they produce other organic compounds like ketones, carboxylic acids, that's not the focus for today ……
The above Hope's teaching segment is coded as ‘1’ because it demonstrates an understanding of the interactive use of two TSPCK components (CS/RP) at a simple level of TSPCK episode as shown in the TSPCK map below.	Rose: Yes, they are all correct, those are good examples of intermolecular forces as you’ve previously learnt you must always remember them, (LP) now I’m saying whenever you need to compare the boiling points of two different compounds which belong to different homologous series, ask yourself what type of intermolecular forces are in here, also here is another big issue, what is the strength of the intermolecular forces? You see even if you know that type of forces but you can’t remember the strength then it's gonna be difficult, so you don’t stop at being able to say what category of intermolecular forces you have got in a compound, you must also understand and be able to indicate its strength and that's makes it easier when dealing with difference molecules (WD) yeah so looking at propane [she referred to the molecular structure on the chalk board], it's an alkane right, Propane [she pointed at the structure of propane shown on the chalk board] is non-polar, it has got van der Waals dispersion. In propanol here [she pointed at the structure of propanol], (RP) it has got an hydroxyl group OH so hydrogen bond is present and you see, by nature hydrogen bonds are much stronger than van der Waals forces, you got that? So, we gonna need much energy to break propanol since it's got stronger intermolecular forces this makes it's boiling point to be higher but propane not gonna need much energy making it's boiling point to be lower than propanol.	Qualitative in-depth analysis
	Qualitative in-depth analysis	In the excerpt above, Ruth did not only confirm the learners’ prior knowledge of hydroxyl functional group but she also moved on to calling their attention to a possible misconception that could emerge from the symbolic representation of OH in two different types of compounds. This is an element of TSPCK component ‘Learner Prior Knowledge’ (LP). Her knowledge of TSPCK component, what is difficult to understand, (WD) was demonstrated when calling learners’ attention to the similarity and difference between hydroxide ion (OH^−) in potassium hydroxide which is an inorganic compound and hydroxyl group (OH) in ethanol which is an organic compound in order to avoid any related conceptual difficulties. In this course of explaining, she used symbolic representations (RP) in making the concepts understandable to her learners. She further emphasized and referred to as most important, the hydroxyl functional group as the basis for IUPAC naming and organic reactions of all alcohols with examples. She also referred to the different types of organic reactions, the aspects learners would be learning in the next class (post-concepts). This is an element of TSPCK components ‘Curricular saliency’ (CS).
	Rose started by reminding learners of the intermolecular forces which they had previously learnt in Grade 11, asking them to give additional examples of intermolecular forces and confirming their correct responses. This describes Rose's understanding of TSPCK component ‘Learner Prior Knowledge’ (LP). She further called the learners’ attention to the importance of going beyond identifying intermolecular forces to understanding the strength of intermolecular forces, a way of preventing the related conceptual difficulties. This is an element of the TSPCK component ‘what is difficult to understand’ (WD). In her demonstration of good content knowledge of how the strength of intermolecular forces influences the boiling point of compounds, she supported her explanations with the use of molecular structures. This describes her knowledge of the use of representations (RP) at a symbolic level.	The above Ruth's teaching segment is coded as ‘3’ because it demonstrates an understanding of the interactive use of four TSPCK components (LP/WD/RP/CS) at a sophisticated TSPCK episode level as shown in the TSPCK map below.
	The above Rose's teaching segment is coded as ‘2’ because it demonstrates an understanding of the interactive use of three TSPCK components (LP/WD/RP) at a proficient TSPCK episode level as shown in the TSPCK map below.

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The rubric, through the nominal scale, enables the capturing and portraying of different levels of sophistication of TSPCK episodes that were visible in a classroom lesson thereby allowing the construction of pictorial profiles of the PSTs’ eTSPCK. The eTSPCK profiles depict the identified TSPCK episodes, particularly its quality category, in the sequence in which they emerged from the lessons. For example, based on the rubric, a sample TSPCK lesson profile could be a combination of different TSPCK episodes as seen in the Ruth's lesson 1 (Fig. 4).

Fig. 4 Ruth's enacted TSPCK profile for lesson 1.

Using the rubric, the generated teacher TSPCK episode profile (as shown in the Fig. 4 for example) is coded into a set of numerical scores and this was done for each lesson taught by each of the 4 PSTs. Three experienced PCK researchers including the authors of this paper were involved as independent raters. Each of us independently identified TSPCK episodes in the video recorded lessons and thereafter, the three of us engaged in thorough discussions to resolve any disagreements. Then, we calculated the Cohen Kappa inter-rater reliability which gave a value of 0.92, a highly acceptable level of consensus (Landis and Koch, 1977). The numerical scores obtained from the coding of PSTs’ TSPCK episodes were converted into probability measures normalized using the Rasch Analysis Model (Bond and Fox, 2015). The inductive analysis of lesson plans and lesson-interviews was conducted as complementary data and content supporting the identified TSPCK episodes and pedagogical strategies employed by the PSTs.

Analysis of learners’ pre-and post-tests

The learners’ pre-and post-achievement tests were marked by the same three raters using appropriate marking memorandum of correct answers where the mark of 1 was awarded for the correct answer and the mark of 0 for the incorrect answer. The estimate of Cohen Kappa inter-rater reliability calculated among the raters of achievement tests gave a value of 0.86 which signalled a good strength of agreement among the raters (Landis and Koch, 1977). For each class of learners taught by the PSTs, the pre-test and post-test scores were analysed separately by applying the Rasch Model Analysis (RMA) Winsteps 3.75.0 software version (Linacre, 2014). The achievement test scores were translated into person probability measures using the RMA, Winsteps 3.75.0 software version (Linacre, 2014). The RMA performs statistical analysis that describes connective likelihood in which both the person ability and item difficulty are placed along a single continuum with a similar measuring scale (Bond and Fox, 2015). Also, the RMA enables the anchoring of tests for a clearer measurement of the shift from one experience of the test items, such as before the teaching, to another experience after the teaching. In this study, to analyse for a significant difference between the pre-test Rasch person measures and post-test Rasch person measures, the Rasch person measures were anchored (Wright, 2003). Then, the anchored pre-test Rasch person measures were analysed with the anchored post-test Rasch person measures using Wilcoxon paired signed rank test for non-parametric data, appropriate for small sample data (Whitley and Ball, 2002) (n = 30, 30, 14 and 14) in the cases of classes taught by the PSTs in this study. This generated a more convincing quantitative result to determine whether there was or not a significant difference between the learners’ pre-and post-tests. The calculation of validity in RMA is based on the understanding, that the test performances are reflections of a single, underlying construct, which is made explicit by the relationship between test items and human ability in the sample measured (Bond and Fox, 2015). Item difficulty and person ability measures that fall within the fit statistic range of −2 to +2 are considered a good match, coherent and measuring a single construct, which therefore constitutes a valid measure. This served as the statistical framework for interpreting the validity of the measures presented in this study.

Analysis of the link between the pre-service teachers’ eTSPCK and learner achievement

The generated Rasch person measures from the analysis of PSTs’ TSPCK episodes were used as an indicator of the quality of eTSPCK in the analysis for the link between PSTs’ eTSPCK and learner achievement in Organic Chemistry. We further considered that in addition to eTSPCK, the level of PSTs’ content knowledge (CK) is an important factor previously reported to influence learner achievement. As a result, the Analysis of Covariance (ANCOVA) was chosen and performed using the SPSS IBM version 27 on the entire statistical measures generated from the learners’ achievement tests and PSTs’ TSCK and CK tests. In ANCOVA, both the PSTs’ post CK-test (post-Rasch person measures) written after the intervention and eTSPCK episodes Rasch measures were taken as the fixed factors (independent variables). We entered the learners’ post-test Rasch person measures as the dependent variable, and the learners’ pre-test Rasch person measures as the covariate. The ANCOVA particularly helps to control the effect of pre-test (a covariate) which may have a relationship with the post-test (a dependent) but has no relationship with independent variables (PSTs’ eTSPCK and CK) (Jamieson, 2004; Aldrich, 2018). Secondly, to understand the strength and direction of the relationship between PSTs’ eTSPCK and post-test learner achievements, the Pearson's product-moment correlation coefficient (r) was further calculated using the same SPSS IBM software. For this analysis, the focus was on the PSTs’ eTSPCK (TSPCK Rasch Person Measures) and learners’ post-test Rasch person measures as the independent variable and dependent variable, respectively. As highlighted by Hinkle et al. (2003), the strength of r between two variables could be negligible (r = 0.00 to 0.30), low (r = 0.30 to 0.50), moderate (r = 0.50 to 0.70), high (r = 0.70 to 0.90) or very high (r = 0.90 to 1.0) and either negative or positive in terms of direction.

Results

The investigation of the PSTs’ eTSPCK-learner achievement relationship in this study revealed two main findings. First, the pre-service teachers demonstrated different quality of eTSPCK measured by the varying extents of interactive use of content-specific knowledge components at the simple, proficient, and sophisticated levels of TSPCK episodes in teaching Organic Chemistry. Second, there was a statistically significant difference across the means of the learners’ pre/post-tests, as well as a positive correlation between the pre-service teachers’ eTSPCK and learners’ post-test achievement. Finally, the correlation was found to increase in positive strength with the displayed higher quality categories of TSPCK episodes. These findings are sequentially presented below.

Pre-service teachers demonstrated eTSPCK in the classroom teaching of organic chemistry

The analysis of lessons delivered by the PSTs revealed a demonstration of eTSPCK as the teacher knowledge visible in the classroom teaching. The insights into this demonstration of eTSPCK are illustrated by the eTSPCK profiles as provided in the Table 3.

Table 3 Pre-service teachers' enacted TSPCK profiles

Pre-service teacher	TSPCK profile showing sequence of emergence of TSPCK episodes
Ruth (Lesson 1)
	Coding: 2 3 1 2 3 2 3 2 3 3 3 3 2 2 2
Ruth (Lesson 2)
	Coding: 1 2 2 2 3 3 3 2 2 2 2
Overall	Simple (1) = 2; Proficient (2) = 14; Sophisticated (3) = 10
Hope (Lesson 1)
	Coding: 1 2 2 2 3 3 3 2 2 2 2
Hope (Lesson 2)
	Coding: 1 2 1 2 2 3 1 3 2 2 1 1 1
Overall	Simple (1) = 10; Proficient (2) = 12; Sophisticated (3) = 3
Rose (Lesson 1)
Rose (Lesson 2)
	Coding: 2 2 2 2 3 3 2 3 3 2
Overall	Simple (1) = 2; Proficient (2) = 13; Sophisticated (3) = 6
Mark (Lesson 1)
Mark (Lesson 2)
	Coding: 1 2 2 2 2 2 2 2 2 2
Overall	Simple (1) = 3; Proficient (2) = 16; Sophisticated (3) = 1

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The salient observation about the eTSPCK profiles is that, almost all the 4 PSTs’ eTSPCK profiles portray a combination of episodes that are in the simple, proficient, and sophisticated categories of TSPCK episodes. However, higher quantities of desirable proficient and even sophisticated TSPCK episodes are seen in Ruth's and Rose's lessons and to a lesser extent in Hope's and Mark's lessons. The category of TSPCK episode emerging from a given teaching segment is associated with the depth of explanations provided by the PST in making a concept understandable to learners. For example, Mark and Rose had a similar teaching segment during which different depths of explanations were provided leading to the emergence of different categories of TSPCK episodes (see Table 4).

Table 4 Mark's and Rose's teaching segments

Mark's Lesson 2 (4–5 minutes)	Rose Lesson 1 (12–14 minutes)
Mark: … let's say between propanone here [Mark drew the molecular structure of propanone on the board], it's got a carbonyl functional group and then, here is another, our propanoic acid [Mark drew the molecular structure of propanoic acid], (RP) are they gonna have same or different boiling points?	Rose: So now in here [Rose pointed at the structure of methanol], (RP) you would see that we’ve got one hydrogen bond, but take note guys, right it's as a result of our hydroxyl group right, that's our functional group for identifying members of alcohol homologous series don’t forget (CS), they’ve all got that in common in their homologous series, always remember so now no one should tell us that, ma’am since we’ve got hydrogen bond in methanol, it gonna dissociate to form H^+
S4: same boiling point	S2: So, methanol is not gonna dissociate to form H^+ even if it dissolves in water?
Mark: Why?	Rose: That's what we are saying, our hydrogen bond consists of one hydrogen bonded to oxygen, right it does not refer to a hydrogen ion commonly represented by H^+, (LP) there is no ionic bond here, the key to understanding the behavior of a molecule is you being able to identify what intermolecular forces it's got, we can only refer to hydrogen bond in alcohols, there is no ionic bond, does not make sense?
S5: I think ‘prop’ means they’ve both got the same number of carbon atoms yeah.	S3: It's hydrogen bond not ionic bond
Mark: Really?	S5: Exactly
Ss: [Learners laugh] …	Rose: You got it! So our methanoic acid is gonna have higher boiling point than methanol the reason being that, in the case of carboxylic acids, hydrogen bonding can occur between two molecules right, so when that happens, it forms a dimer, that's also significant guys don’t forget (CS) it's like similar molecules linked together, so it's the presence of dimers that normally increases the strength of the dispersion forces in carboxylic acids which then raises their boiling point making it to be higher than that of alcohols, hope my explanation is clear to someone?
S6: the boiling point for propanone is gonna be higher	S6: Ma’am it means all carboxylic acids would have higher boiling points than alcohols of the same number of carbon atoms since they form dimmers which cause the strength of their intermolecular forces to increase, now I understand, thanks ma’am.
Ss: No …. Yes… No…. [Chorus answer]	Ss: yes
Mark: See guys, it's worth noting here that the stronger the intermolecular forces, the more energy it will take to overcome these forces that's the central idea here (CS), as a result, the boiling point for propanoic acid is gonna be higher than that of propanone which has got weaker dipole–dipole forces is that understood?	TSPCK map
Ss: yes
TSPCK map

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The extract of Mark's teaching segment as provided in the reveals an instance of a learners’ misconception that was worth addressing by Mark to promote the learners’ conceptual understanding. Learner S5 had the misconception that since propanoic acid and propanone has the same main number of carbon atoms, they would have the same boiling point. The learner seemed not to understand, that these are two different organic molecules with different functional groups. The Mark's reference to the symbolic structures and difference in the strength of intermolecular forces as an important aspect of the concept demonstrated his knowledge of the use of a symbolic representation (RP) and curricular saliency (CS) respectively. This explanation demonstrates an interactive use of only two TSPCK components (RP/CS) falling into the simple level of TSPCK episodes. There was no reference made to the learner's misconception in the Mark's explanation and the explanation also lacked the depth needed to address the misconception. The emergence of this simple TSPCK episode could have been at a higher level if Mark had provided explicit explanations that took the learner's misconception into consideration.

Using the structure of methanol (see Table 3), Rose emphasized the presence of only one hydroxyl functional group in the molecule which is also used to identify all the members of alcohols. This emphasis on hydroxyl functional group as an important component for identifying alcohols is an element of Rose's knowledge of ‘Curricular saliency’ (CS) coupled with her knowledge of the use of molecular structures, a form of symbolic representations (RP). Then, she cautioned learners about a misconception that could emerge from the assumption that hydrogen ion H⁺ is produced by methanol when it reacts with water since it has got the hydrogen bond. This suggests the awareness of a possible learners’ misconception, an element of the TSPCK component ‘Learner Prior Knowledge’ (LP). She also explained the formation of dimers and referred to it as significant in understanding why methanoic acid would have a higher boiling point than methanol. This is another key aspect which was important for learners to know, an element of Rose's knowledge of curricular saliency (CS) that gives additional depth to the explanation she provided. In this teaching segment, Rose seems to have demonstrated the interactive use of TSPCK components at a sophisticated level of TSPCK episodes (CS/RP/LP/CS) accompanied by learners’ responses which suggest evidence of understanding the explanations provided.

Another example of teaching segment focusing on the same concept (Aldehyde functional group) was observed in the analysis of Ruth's and Hope's teaching as provided in the Table 5.

Table 5 Ruth's and Hope's teaching segments on Aldehyde functional group

Ruth's Lesson 1 – (28–30 minutes)	Hope's Lesson 1 – (22–23 minutes)
Ruth: … what do you know about aldehydes and their functional group?	Hope: Yeah guys having talked about alcohols functional group, we’ve also got another group, we call them aldehydes, any idea please?
There was no response from learners	S2: propanal
Ruth: Can you think of a molecule, one member in the aldehyde series guys?	S4: butanone
L1: They are like ketones in a way	Hope: buta what?
Ruth: In what way?	Ss: [Learners laugh]
L2: They’ve got carbonyl group	Hope: I think I heard butanone, I’m interested
L3: Yeah	S4: yes, it's got 4 carbon atoms
Ruth: I see what you mean. Indeed, Aldehydes and Ketones have both got a carbonyl as you rightly said group, that's correct but they do not belong to the same homologous series as you thought, so they are different organic compounds, (LP) are you listening to me? …. For us to understand it well, here we’ve got our aldehyde [Ruth she drew the molecular structure for the functional group on the board], (RP) so now what is important here? Carbonyl group is here bonded to hydrogen on one side, and we can see this carbon, it's bonded to an alkyl group, R on the other side, take note of this bonding arrangement. Also, here in ketones [Ruth faced the board and drew the molecular structure for ketone functional group], (RP) let's take a look at the two very carefully [Rose pointed at aldehyde functional group and ketone functional group] yeah, in ketones where carbonyl group is bonded to one alkyl group on one side and another alkyl group on the other side, so we can see the difference in how the carbonyl group is bonded in each case, that's very important (CS), you must not forget otherwise it becomes difficult to distinguish between the two functional groups of the two and then you keep thinking they are both the same, if you forget what is bonded to the central carbon atom on these two sides so don’t forget (WD) please guys….	Hope: Aldehydes in their functional groups [she drew the structure on the board], (RP) it's carbon with oxygen up here right?
	Ss: … yes….
	Hope: That's a double bond covalent bond between a carbon and oxygen atom, see guys, it's a double covalent bond, you don’t confuse it with single covalent bond (CS) between the same atoms right, so now we write it as [she wrote C = O], it's called carbonyl group right?
	Ls: …. yes ……

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As illustrated in the Table, both Ruth and Hope had an opportunity to address the learners’ misconception around the similarity between aldehydes and ketones in terms of their functional groups. In her explanation, Ruth drew on her knowledge of the use of symbolic representations (RP), confirmation of learner's prior knowledge (LP), and emphasis on the bonding arrangement as an important aspect for learners to understand (CS) linked to a possible conceptual difficulty (WD). Her explanation generated an interactive use of TSPCK components at a sophisticated level (LP-RP/CS/WD). With the same instance of a learner's misconception as observed in the Hope's lesson, she only drew on her knowledge of the use of a symbolic representation and curricular saliency (CS), and emphasis on what was considered important for learners to understand. Her explanation generated the interactive use of two TSPCK components (RP/CS) at a simple level of TSPCK episode.

Overall, Ruth and Rose had the most-high proficient, and the desirable sophisticated TSPCK episodes, rather than simple TSPCK episodes. Accordingly, Hope and Mark had the most-high simple, and proficient TSPCK episodes rather than sophisticated TSPCK episodes. Having higher categories of TSPCK episodes, such as those in the proficient and sophisticated categories, emerging from a teacher's lesson, indicates a deeper extent of explanations, which in turn influences the quality of the teacher's lesson. It also demonstrates the interactive use of more TSPCK components thereby providing additional depths to the explanations provided, while presenting the content to the learners.

Learners’ significant improvement in the pre-and post-achievement tests

The percentage scores obtained from the marking of learners’ pre-and post-achievement tests are presented in the Fig. 5.

Fig. 5 Learners' pre-and post-test scores.

Overall, the learners’ score increased from 30.2% in the pre-test to 72.0% in the post-test by 41.8% following the PSTs’ teaching. This increase in the test scores was observed across the class of learners taught by the PSTs. This is good news because the learners were taught Organic Chemistry for the first time in this study and it shows that they learnt the concepts covered by the PSTs. Following the teaching, the achievement gains were 55.4%, 46.9%, 33.0% and 32.1% for Ruth's learners, Rose's learners, Mark's learners, and Hope's learners, respectively. This reveals that, the learners’ achievements improved to varying extents after the PSTs’ teaching.

The results of a more rigorous analysis of the learners’ achievement and the extent of difference between the pre-test and post-test using Rasch Model Analysis and Wilcoxon Signed Rank Test respectively are summarized in the Table 6. The table provides the Rasch Person Measures (M) with Standard deviation (SD) for each of the analysed pre-and post-test, person reliability and item reliability generated for each class of learners taught by the PSTs. The fit statistics are also provided for the determination of validity of measures obtained. The alpha value (p) calculated at a significant level of 0.05 based on the anchored pre-and post-test Rasch Person Measures is also recorded for each class of learners.

Table 6 Rasch analysis results of learners' pre-and post-tests (anchored)

		Class of learners
		Ruth's class	Rose's class	Mark's class	Hope's class
		(n = 30)	(n = 14)	(n = 14)	(n = 30)
Note: the mean for test items was set to zero and units per Logit = 1 for pre-and post-tests (UNIMEAN = 0 and SCALE = 1). Number of Items = 16.
Rasch person measure (standard deviation-Std)	Pre-test (Std)	−0.79 (0.56)	−0.86 (0.72)	−1.10 (0.23)	−0.55 (0.41)
	Post-test (Std)	2.88 (1.75)	2.58 (1.64)	1.70 (1.51)	1.61 (1.22)
	Gain	3.67	3.44	2.80	2.15
Wilcoxon signed test	Alpha, p	0.0001	0.0001	0.0010	0.0020
Person reliability (Rasch analysis)	Pre-test	0.54	0.52	0.50	0.51
	Post-test	0.89	0.82	0.76	0.78
Item reliability (Rasch analysis)	Pre-test	0.71	0.70	0.74	0.73
	Post-test	0.91	0.93	0.87	0.85
IN.ZSTD and OUT.ZSTD		Values fell within the acceptable range of −2/+2

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There are two noticeable observations about the learners’ conceptual performances as presented in the analysis results (Table 6). First, there was a significant difference (p < 0.05) between the learners’ pre-test Rasch person measures and post-test Rasch person measures in each case of the four PSTs. For example, the Rasch person measure for Ruth's learners increased significantly (p = 0.0001) from M = −0.79 (SD = 0.56) in the pre-test to M = 2.88 (SD = 1.75) in the post-test. Second, the four classes of learners differed in the extent of performances following the teaching. Ruth's and Rose's learners had a gain measure of 3.67 and 3.44 respectively following the teaching. Also, Hope's and Mark's learners had a gain measure of 2.15 and 2.80 respectively following the teaching.

The Rasch score measures generated for both the persons and items in each test fell within the conventional fit statistical range of −2 and +2 for each test, indicating that the conceptual knowledge of Organic Chemistry was being measured as desired and hence, both the pre-and post-tests measures were valid. For the pre-test, the Rasch Analysis Model generated a reliability index which is approximately 0.5 for persons (i.e. the learners) and 0.7 for the test items. The person reliability was a little lower than the desired value (i.e. values >0.5) as it was just on the border line which is still nevertheless considered acceptable. For the post-test, the reliability indices for the test items and persons were noticed to fall within the acceptable range of approximately 0.9 and 0.8, respectively. Across the four classes, there was a significant difference (p < 0.05) between the learners’ performances in the pre-test and post-test.

Positive relationship between pre-service teachers’ enacted TSPCK and learner achievement

In determining the relationship between the PSTs’ eTSPCK which was visible in the classroom of Organic Chemistry and learners’ conceptual achievement in the topic, the analysis of covariance was first performed and followed by the analysis for correlation. The results provided in the Table 7 present the analysis of covariance where the learners’ post-test Rasch Person measures were entered as the dependent variable. The first column presents the ‘fixed factors’ (independent variables) which are the PSTs’ TSPCK episodes Rasch measures (eTSPCK) and PSTs’ post-CK test (Rasch person measures) written after the intervention. It also involves the learners’ pre-test Rasch person measures regarded as the covariate. The second and third column contain the values for the sum of squares and degree of freedom (df) respectively which have been adjusted for the effect of covariate (pre-test). The column with the heading F (test statistic) is the ratio of the adjusted between groups mean square to the adjusted within groups mean square. The heading with ‘Sig. (p)’ provides the alpha value at a significant level of 0.05. The heading with the ‘partial Eta Squared’ provides values which indicates the effect size and should be compared with Cohen's guidelines (0.2 – small effect, 0.5 – moderate effect, 0.8 – large effect).

Table 7 Results of the analysis of covariance (dependent variable: learners’ post-test person Rasch measures)

Source	Type III sum of squares	df	Mean square	F	Sig. (p)	Partial eta squared (η^2)
a R squared = 0.823 (adjusted R squared = 0.801).Note: CK = pre-service teachers’ post-test content knowledge Rasch person measures. eTSPCK = pre-service teachers’ TSPCK episodes Rasch measures.
Corrected model	20.370^a	3	10.123	88.026	0.000	0.823
Intercept	17.204	1	17.204	150.156	0.000	0.658
Pre-test	1.179	1	1.1179	10.252	0.105	0.017
CK	5.234	1	5.234	45.513	0.021	0.222
eTSPCK	12.683	1	12.683	110.698	0.001	0.756
Error	8.937	78	0.115
Total	49.553	88
Corrected total	29.307	87

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For the pre-test (Table 7), the result F (1, 78) = 10.252; p = 0.105 suggests that there was no significant difference in the conceptual achievements between the classes of learners taught by the PSTs prior to the teaching. This means that there were no differences in the learners’ knowledge of Organic Chemistry before they were exposed to the PSTs’ eTSPCK through the teaching.

For the CK (Table 7), the result F (1, 78) = 45.513; p = 0.021 implies that the four classes of learners differed significantly in their post-test conceptual achievements in relation to the content knowledge possessed by the PSTs. The value Partial Eta Squared, η² = 0.222 shows a small effect size and suggests that the PSTs’ CK accounts for 22.2% of the variance observed in the post-test learners’ achievements across the four classes taught by the PSTs following the teaching.

For the eTSPCK (Table 7), the result F (1, 78) = 110.698; p = 0.001 implies a significant difference in the post-test conceptual achievements across the four classes of learners who were exposed to different combinations of quality of TSPCK episodes enacted by the PSTs. The Partial Eta Squared, η² = 0.756 shows a large effect size and suggests that the PSTs’ eTSPCK accounts for 75.6% of the variance observed in the post-test learners’ achievements across the four classes taught by the PSTs following the teaching. This particularly suggests further investigations into how the quality of TSPCK episodes captured in each PST's teaching relates to the post-test learners’ achievement in each case.

The scatter plot for the PSTs’ TSPCK episodes Rasch measures as an independent variable versus post-test learners’ achievement Rasch person measures as a dependent variable reveals an overall positive relationship (Fig. 6).

Fig. 6 Scatter plot for the PSTs’ eTSPCK and post-test learners’ achievement.

The scatter plot further reveals a closer interaction between Ruth's and Rose's eTSPCK and learner achievements. Also, there appears to be a closer relationship between Hope's and Mark's eTSPCK and learner achievements. For the strength and direction of these relationships, the analysis of correlation provides a useful insight as summarized in the Table 8.

Table 8 Results of the correlation analysis of pre-service teachers' eTSPCK and learners' post-test achievement

Variables		Ruth's eTSPCK (TSPCK episodes Rasch measures)	Learners’ post-test (Rasch person measures)
Note: ** correlation is significant at the 0.01 level (2-tailed).
Ruth's eTSPCK (TSPCK episodes Rasch measures)	Pearson correlation	1.000	0.854**
	Sig. (2-tailed)	Not applicable	0.000
		Rose's eTSPCK (TSPCK episodes Rasch measures)	Learners’ post-test (Rasch person measures)
Rose's eTSPCK (TSPCK episodes Rasch measures)	Pearson correlation	1.000	0.742**
	Sig. (2-tailed)	Not applicable	0.000
		Hope's eTSPCK (TSPCK episodes Rasch measures)	Learners’ post-test (Rasch person measures)
Hope's eTSPCK (TSPCK episodes Rasch measures)	Pearson correlation	1.000	0.647**
	Sig. (2-tailed)	Not applicable	0.002
		Mark's eTSPCK (TSPCK episodes Rasch measures)	Learners’ post-test (Rasch person measures)
Mark's TSPCK (TSPCK episodes Rasch measures)	Pearson correlation	1.000	0.605**
	Sig. (2-tailed)	Not applicable	0.004

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In the cases of the four PSTs, the Pearson correlation coefficient (r) reveals that there was a statistically significant positive relationship between the PSTs’ eTSPCK and post-test learner achievements. Particularly, this significant relationship appeared to be strong in the cases of Ruth (r = 0.854, p = 0.000) and Rose (r = 0.742, p = 0.000). Also, the significant relationship seemed to be moderate in the cases of Hope (r = 0.647, p = 0.002) and Mark (r = 0.605, p = 0.004). It is important to highlight that the analysis of PSTs’ eTSPCK had earlier showed, that both Ruth and Rose had the desirable most-high proficient and sophisticated TSPCK episodes rather than simple TSPCK episodes. Accordingly, Hope and Mark had the most-high simple and proficient TSPCK episodes rather than sophisticated TSPCK episodes.

In summary, following the PSTs’ teachings, the post-test learner achievement was positively associated with the PSTs’ eTSPCK and the correlation increased in positive strength with higher quality categories of TSPCK episodes.

Discussions and conclusions

The argument in this study built on the understanding that the overall purpose of developing teacher knowledge for teaching, is to improve the quality of classroom instruction, and ultimately, learner achievement. The PCK-learner outcomes relationship is an informed extrapolated proposition (Keller et al., 2017), needed as the foundational assumption for pursuing the establishment of a causal effect, which so far had produced findings with mixed signals within the PCK science education community (Alonzo et al., 2012; Liepertz and Borowski, 2019). It is acknowledged in this study, that learner achievement is directly influenced by various factors including teachers’ ePCK, all of which are associated with the complexity of classroom teaching and learning. With a particular attention on eTSPCK as the understanding for transforming the CK of a given topic in the classroom, this study revealed that the variance observed in the post-test learners’ conceptual achievement was influenced by the PSTs’ eTSPCK and CK. While eTSPCK was observed to have a large effect size (η² = 0.756, p = 0.001), CK was noticed to have a small effect size (η² = 0.222, p = 0.021). This finding points to the understanding that the teachers’ CK is not sufficient for improving learners’ conceptual understandings as reported in the previous PCK studies (Davidowitz and Vokwana, 2014; Kind and Chan, 2019).

Furthermore, the finding from this study revealed that there was a significant, linear positive correlation between the PSTs’ eTSPCK and post-test learner achievement in Organic Chemistry. The correlation was particularly found to increase in positive strength with the displayed higher quality categories of proficient and sophisticated TSPCK episodes rather than simple TSPCK episodes. In the cases of pre-service teacher Ruth and Rose, who had most high proficient and sophisticated TSPCK episodes rather than simple TSPCK episodes, there was a positive high correlation. Accordingly, in the cases of pre-service teacher Hope and Mark, who had most high simple and proficient TSPCK episodes rather than sophisticated TSPCK episodes, there was a positive moderate correlation. These two categories (high and moderate) of correlation reflect the pattern of the gradient correlation in cognizance of the respective different quality-kinds of TSPCK episodes. According to the eTSPCK rubric (Miheso, 2018) used in this study, the combination of a higher quantity of proficient and sophisticated TSPCK episodes indicates a more developed TSPCK, than a combination of higher simple and proficient TSPCK episodes. This finding in a way supports Richardson et al.'s (2018) opinion that teachers with highly developed PCK would produce superior instructional experiences for learners and hence, increase learning.

While the established correlation found in this study does not prove causal effect, it however contributes a convincing piece of evidence to the pool of studies pointing to a positive relationship which is one of the criteria for the subsequent advance research for the causal effect. Furthermore, what makes the contribution important is the systematic operationalization of TSPCK from its conceptualization consistently retained from the intervention through capturing and analysis of the enacted TSPCK demonstrated in the classroom teaching. This finding is equally significant for the full realization of the whole essence of developing the PSTs’ professional knowledge with achieving the ultimate goal of education, improving learners’ conceptual achievement. It brings the value of exposing PSTs to PCK early, rather than allowing them to gain this unique knowledge over long periods in practice. The eTSPCK observed as demonstrated by the PSTs was informed by their understanding of the interactive engagement of the TSPCK components acquired significantly from the intervention as established in the larger study and reported elsewhere (Akinyemi, 2020). The finding expands the existing understanding in the literature on the coherent interactions among TSPCK components, how they continue from the planning realm into the enactment realm. These interactions are considered more crucial to the quality and development of PCK in a given topic, than the strength of an individual knowledge component (Park and Chen, 2012; Akın and Uzuntiryaki-Kondakci, 2018).

The finding also contributes to the lingering confusing issue of the PCK-learner outcomes relationship by providing a carefully defined conceptualization of the grainsize of PCK (i.e. Topic Specific PCK), where all the components have been used in the operationalization. Similarly, the measurement issue is improved by measuring eTSPCK, using both qualitative and quantitative means – a better holistic measurement. This study contributes toward the issue of PCK-learner outcomes relationship with a clearer methodological structure as derived from the benefit of having the Refined Consensus Model of PCK (Carlson and Daehler, 2019) and the previous Consensus model of teacher professional knowledge and skill including PCK (Gess-Newsome, 2015).

The findings in this study are of the implication, that efforts should be made in teacher education programmes to enhance the quality of teachers’ TSPCK. This could be a promising channel for improving science classroom instructions, and ultimately, learner achievement in developing countries, particularly in Sub-Sahara Africa with its record of poor learners’ performances in the sciences. While the major findings from this study are interesting and potentially of a great contribution, the study had limitations in the sense that it employed a small sample of pre-service teachers, and it was within the specified dimension of PCK, which is at the grain size of topic specific PCK enacted in the classroom setting. Therefore, large scale studies are recommended in empirically establishing PCK-learner outcomes relationship and considering other dimensions of PCK.

Conflicts of interest

There are no conflicts to declare.

Appendices

Appendix I – organic chemistry content knowledge tool

Appendix II – enacted TSPCK rubric

Type 1: Simple TSPCK episode	Type 2: Proficient TSPCK episode	Type 3: Sophisticated TSPCK episode
• Evidence of two different TSPCK components interacting evidently and distinguishably in a specific teacher task segment	• Evidence of three different TSPCK components interacting evidently and distinguishably in a specific teacher task segment	• Evidence of four different TSPCK components interacting evidently and distinguishably in a specific teacher task segment
• The TSPCK component interactions maybe interwoven or have a linear sequence structural formation.	Or	Or
• Both components work together to support an explanation of a single or a pair of concepts that are related	• Evidence of three different TSPCK components interacting, evidently, and distinguishably in a specific teacher task segment, but one component repeating and bringing a different level of explanation that complements the initial emergence.	• Evidence of four different TSPCK components interacting evidently and distinguishably in a specific teacher task segment, with one of the components repeated more than once or one of the components bringing different levels of sophistication (e.g. representations used at macro, symbolic and submicroscopic levels).
	• The TSPCK component interactions maybe interwoven or have a linear sequence structural formation or both	• TSPCK component interactions maybe interwoven or have a linear sequence structural formation or both.
	• The three components work together to support an explanation of a single or a pair of concepts that are related	• All the TSPCK components work together to support an explanation of a single or a pair of concepts that are related

Acknowledgements

This work is based on the research financially supported by the Collaborative Postgraduate Training (CRT) grant from the National Research Foundation (NRF) of South Africa (Grant 105227). This support is highly appreciated.

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