The retention of topic specific pck: a longitudinal study with beginning chemistry teachers

Josephat M. Miheso*a and Elizabeth Mavhungab
aUniversity of the Witwatersrand, Johannesburg, Science Education, Wits School of Education, P O Wits, 2050, South Africa. E-mail: mihesojosephat@gmail.com; Tel: +254722686246
bDeputy Head of School – Research, University of the Witwatersrand, Johannesburg, Science Education, Wits School of Education, P O Wits, 2050, South Africa. E-mail: Elizabeth.Mavhunga@wits.ac.za

Received 7th January 2020 , Accepted 21st February 2020

First published on 23rd March 2020


What evidence counts as teacher quality is a debate of continued interest to the teacher education community. Many education scholars have argued for the importance of retention of knowledge as an indicator of the quality of education acquired. This study explored the retention of the quality of planned Topic Specific Pedagogical Content Knowledge (TSPCK) in a case study of seven chemistry pre-service teachers in their final year of study towards a BEd degree. They were exposed to a TSPCK based intervention in either Organic Chemistry or Stoichiometry as a topic and subsequently followed two years later into their practice as beginning teachers. The study employed a longitudinal qualitative research design with sets of data collected at three different points: pre-intervention, post-intervention and delayed post-intervention (two years later). Data collected included a combination of completed TSPCK tools and audio-recorded stimulated recall interviews. The analysis of completed TSPCK tools entailed the use of a criterion-based rubric for shifts in the quality of planned TSPCK and the recorded interviews were analysed through content analysis. Evidence of learning during the intervention and in-practice was analysed using the qualitative in-depth analysis for developing TSPCK and the Vygotskian sociocultural theoretical framework. Findings from the first and second sets of data confirmed a gain in the quality of planned TSPCK at the end of the intervention. The findings from the second and third sets revealed the beginning teachers’ successful retention and continued growth two years in practice. Implications for teacher preparation are discussed.


Introduction

More and more graduate beginning science teachers (GBTs) leave the Initial Teacher Education (ITE) preparation programme with some exposure to Pedagogical Content Knowledge (PCK) as the knowledge germane to teaching content in a specific discipline (Shulman, 1986). Often the rationale for the early exposure to PCK in an ITE programme is based on the need to fast-track the development of effective science teachers, particularly in developing countries such as South Africa where the shortage for effective science teachers is severe (Mogoshoa, 2015). However, to measure the full impact of such an early PCK exposure is very difficult because of the various factors that influence the teacher's classroom performance (Aydeniz and Kirbulut, 2014). Measuring the extent to which the acquired knowledge is retained long into the place of work, is but one of the useful ways of appraising the experienced impact. Van Merriënboer and Kirschner (2017) have referred to retention of acquired knowledge as the key driving force behind the essence of training and education. While research studies in PCK are voluminous, focus however has been on various aspects of teacher development other than the measurement of its retention over extended periods. Attention in these studies has been given largely to PCK developed in pre-service teachers in the context of planning to teach (Davidowitz and Potgieter, 2016), or in the context of a classroom teaching for short periods such as during a practicum (Chan and Yung, 2015), or the translation of acquired PCK into enacted PCK and vice versa (e.g. Alonzo et al., 2019). However, not the same wealth of studies exists on the retention of acquired PCK into the real world of teaching practice, especially, in the early years of beginning teachers. This points generally to the paucity of longitudinal PCK studies that examine the long-term value of PCK. We believe that understanding the extent of retention of the acquired PCK by the GBTs, would empirically demonstrate the long-term advantage derived from the early exposure of PSTs to PCK, as opposed to only relying on the protracted natural growth of PCK in practice (Hashweh, 2013). The outcome of the study would build towards the necessary evidence needed to advance (or not) the practice of pedagogical transformation of content knowledge as a core practice for developing science teachers (McDonald et al., 2013). The research question thus asked in this study is.

To what extent is PCK acquired in specific topics by Chemistry pre-service teachers retained into the early years of their teaching practice as graduate beginning teachers?

Literature review

Retention of acquired knowledge

The fundamental goal of teacher education programmes globally is to produce high quality teachers (Loughran and Hamilton, 2016). The underlying rationale for any kind of formal instruction, is therefore the assumption that knowledge, skills, and attitudes learned in school or training programmes will be recalled accurately, and transferred for use in daily life settings and in solving new problem situations (Van Merriënboer and Kirschner, 2017). Several scholars have contended that the value of education depends largely upon the quality of what has been learned, or what a teacher or any other professional can eventually recollect over the years that shapes their practice (Custers, 2010). According to Ausubel (2012), retention of knowledge into the future is linked to meaningful learning that involves the acquisition of new meanings from both the presented meaningful learner material and a meaningful presentation. Likewise, if PCK based science teacher education programmes are to aspire to the possible retention of the acquired PCK by graduate teachers as they enter their teaching practice, both the content and the manner of delivery of the PCK programmes to which pre-service teachers (PSTs) are exposed, do matter. It is hoped that the findings of this study will share a possible response to the question on retention of PCK, thereby bringing to view its long-term value as derived from its early implementation in ITE programmes.

Retention of PCK as teacher knowledge

There are a handful of studies that have explored and reported on the retention of PCK from in-service programmes. For example, in a study that examined the extent of retention of discipline PCK of three in-service teachers who were exposed to training in a two year long-term professional development program, Rozenszajn and Yarden (2014) found that the teachers were able to retain major parts of their expanded PCK a year after the termination of the programme. The observed retention was linked to the content of the programme, particularly the development of teaching materials. In a similar study that compared different kinds of induction programmes for beginning Secondary School science teachers, Luft et al. (2011) found that an induction programme with a special focus on a specific topic had more impact in supporting PCK development. In contrast, beginning Secondary School science teachers who lacked the focused exposure either persisted at their entry science teacher orientations or regressed to less reform-based orientations. The emerging understanding, as alluded to by Ausubel (2012), is that the nature of the training programme matters when the retention of teacher knowledge such as PCK is considered. It is however equally important to acknowledge the influence of the contextual environmental issues often experienced by GBTs when the retention of teacher knowledge is considered. It is widely accepted that newly qualified beginning teachers often struggle to shift from a student's perspective to that of a practicing teacher (Luft et al., 2011) amidst the complexity of the school environment. Their view of the profession and the role they play in it, is shaped by many factors that typically include: handling heavy workloads, maintaining discipline, the different school contexts, etc. (Helms-Lorenz et al., 2016). For instance, in a study with beginning teachers, Schmidt et al. (2017) found that their daily ‘hassles’ such as interactions with colleagues and the actual act of classroom teaching, were factors associated with emotional exhaustion. In another study, Schuck (2009) found that the culture of the school was a factor that beginning teachers had not been prepared for, as was the need to fit into the operational constraints of working within school protocols and practices.

Darling-Hammond (2006) identified three fundamental problems of learning to teach among beginning teachers. First, is the apprenticeship of observation. This is where new teachers have to understand teaching in ways that are quite different from their own experiences as students. Second, is the problem of enactment, where the new teachers are required to not only learn to ‘think like a teacher’ but also ‘act like a teacher’. Finally, “new teachers are faced with the problem of understanding and responding to the dense and multifaceted complex nature of the classrooms, which derives from the non-routine and constantly changing nature of teaching and learning” (Darling-Hammond, 2006, p. 35). Thus, in examining the extent of PCK retention by GBTs, it is important to also consider additionally, both the influence of the school environmental pressures, as well as the common learning difficulties that learners generally have in learning the Chemistry topics of Stoichiometry and Organic Chemistry.

Difficulties in teaching and learning stoichiometry and organic chemistry

Stoichiometry and Organic Chemistry are some of the topics that learners find difficult to learn. Stoichiometry is the study of the quantitative aspects of chemical reactions as they are expressed in balanced chemical equations (Aleksandrov, 1989). This is a topic learners consider to be abstract and complex (Huddle and Pillay, 1996). Common learning difficulties include learners’ struggle with common quantitative calculations, an understanding of the mole concept, constructing and balancing chemical equations, algebraic skills, and an interpretation of a word problem into procedural steps that lead to the correct answer (Okanlawon, 2010). A review of the various teaching strategies and common learner alternative conceptions indicates that learners tend to misunderstand the term ‘amount’ of substance and confuse it for the ‘mass’ of a substance (Dahsah and Coll, 2007). Furthermore, learners struggle to understand that reactants need to be present in the stoichiometric ratios represented by balanced chemical equations. Despite being given initial masses of reactants, Huddle and Pillay (1996) found that learners did not calculate the amount of substance in moles represented by the given masses. All these misconceptions impact on learners’ ability to solve stoichiometric problems. Organic Chemistry, on the other hand, is about the study of carbon, its structure, properties, composition, reactions, and the preparation of carbon-containing compounds. Organic chemistry has several interrelated concepts such as: ionization energy, electronegativity, chemical bonding, molecular structure, and stability that are central to much of chemistry as a discipline. However, students often find these concepts difficult to understand (Ealy, 2018). Furthermore, they find it difficult to establish the relationship between structural representations and the associated chemical and physical properties (Talanquer, 2018). The difficulty in determining structure–property relationships is ascribed to the nature of structural representation as the explicit part, and its respective implicit, conceptual counterpart (Graulich et al., 2019). Thus, it was of interest to this study to determine the retention of the acquired PCK in these topics by beginning teachers.

Theoretical framework

PCK as a theoretical framework applicable across changing teaching contexts

While there is consensus in the literature about the multidimensional nature of PCK, however, what has been lacking for a long time was a clear language to refer to and distinguish PCK as observed in the different contexts of teaching, by its different grainsizes and by who possesses the knowledge. The newly refined consensus model (RCM) of PCK (Carlson et al., 2019) has made an attempt at addressing this need. Fig. 1 presents a simplified version of the RCM showing the different dimensions of PCK.
image file: d0rp00008f-f1.tif
Fig. 1 A simplified illustration of the multidimensional nature of PCK as in the RCM.

The RCM, as a model, reflects the science education community's expanded understanding of the complexity of the multidimensional nature of PCK. Presented in Fig. 1 are the ways in which the RCM distinguishes between the different dimensions of PCK. First, the RCM distinguishes PCK by grainsize as first alluded to by Veal and MaKinster's (1999) through the PCK taxonomies. The grainsizes of PCK are considered to be discipline specific, topic specific and concept specific. However, unlike Veal and MaKinster's (1999) PCK taxonomies, the RCM defines the smallest grainsize of PCK as concept specific PCK (Carlson et al., 2019). The second way in which the RCM distinguishes PCK is by reference to its nature as collective vs. personal knowledge. To clarify this dimension, the RCM refers to this contextual location of PCK as PCK realms. The first realm is called collective PCK (cPCK). c-PCK is knowledge about PCK shared in the literature publicly. The second PCK realm is called Personal PCK (pPCK). This refers to the knowledge acquired by and in possession of an individual teacher. The extent of its acquisition will naturally differ from one teacher to another as each teacher's learning is enabled and filtered by various factors differently. pPCK refers to both planned-PCK (plPCK)) and enacted-PCK (ePCK). Thus, PCK may be explored in each of these realms at any of the given three grainsizes (discipline, topic or concept). What remains common across all the grainsizes of PCK, irrespective of the realms, is the fundamental benefit of PCK as the theoretical construct enabling pedagogical transformation of difficult content into versions accessible for learner understanding (Shulman 1987). The RCM is thus relevant in this study as it provides a projectile through which the teachers’ PCK development may be traced with differentiation. Accordingly, in this study we selectively focused on the grainsize of topic specific PCK (TSPCK), possessed by chemistry PSTs in their personal capacity (pPCK) in their trajectory of becoming professional chemistry teachers and situated in a setting of planning to teach (plTSPCK). In order to help us track and measure the extent to which plTSPCK was retained over time, we drew on the conceptual framework for TSPCK, which distinguishes it from other grainsizes of PCK by defining it as made-up of five knowledge components that are content specific. These are: (i) students’ prior knowledge, including common learner misconceptions, (ii) curricular saliency; (iii) what makes the topic easy or difficult to teach; (iv) representations, including analogies; and (v) conceptual teaching strategies (Geddis and Wood, 1997). Like discipline PCK, TSPCK is teacher knowledge that is tacit, reflected best through component interactions, rather than the understanding of the individual components or their sum (Park and Suh, 2019). Thus, in our aim to determine the extent to which the GBTs retained their plTSPCK acquired during their training as PSTs, evident interaction of the different TSPCK components was considered as a useful feature that was consistently sought across the changing contexts – the different PCK realms. Furthermore, it was important to keep in mind that despite the widely acknowledged challenges associated with beginning teachers, GBTs were nevertheless expected to naturally continue to learn and develop their pPCK by virtue of being situated in a school context. Thus, it was important to also make provision to recognise such growth when this becomes visible.

Vygotskian mediation and concept development. In acknowledgement that teacher knowledge is not static, but dynamic, and is influenced by daily classroom experiences and thus likely to grow, we further drew on the concepts of mediation and concept development, contained in the Vygotskian sociocultural theory (Vygotsky, 1986). We found the theory useful as it promotes a view that regards teacher knowledge as both dynamic and situated. Furthermore, the concept of mediation provides a rich theoretical framework for understanding the relationship between a teachers' developing knowledge, and the social contexts and interactions through which such knowledge develops. For Vygotsky (1986), mediation is the process through which a person encounters and draws on a variety of tools around and in the social plane, to influence his or her own thinking and activity. According to Vygotsky (1986), spontaneous concepts develop through our day to day experiences in the world. The structure of such concepts is therefore concrete and practical in nature. In this study, we associated this element of the Vygotsky theory to the new understanding that GBTs evidently learned in practice about the concepts they are teaching. On the other hand, in contrast, the Vygotskian scientific concepts are systematic, hierarchical, and logical, and are typically learned in formal instructional contexts such as in a formal course. Accordingly, we associated this element of the Vygotsky theory to the structured TSPCK that the GBTs learned from the formal intervention as PSTs. For Vygotsky (1986), the desired state of concept development then is for the outlined spontaneous and scientific concepts to seamlessly work together to enhance the acquisition of new concepts (teaching chemistry in this case). We then associated the Vygotskian desired state of concept development, as the moments where additional understandings developed by GBTs, from their practice in the real world, were evidently observed to have been used seamlessly with plTSPCK, as an indicator of their continued learning in practice.

Method

The study employed a longitudinal qualitative research design with three data collection points over a period of two years. It was regarded as a case study of a specific cohort of beginning science teachers who experienced the same significant life event (as in being taught TSPCK) within a given period (Cohen et al., 2011). The study adopted case study as a research strategy, due to its benefits in enabling in-depth interactions with the participants, and consideration of the issues under investigation (Stake, 1994). 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 are used throughout the manuscript to preserve confidentiality. All the work in this paper reports from a university, where the language of instruction is English.

Participants

The participants in the study were a subset of seven chemistry GBTs. The subset was drawn from a chemistry methodology class of a cohort of thirty-four (34) GBTs who attended intervention studies based on cTSPCK during their final year (4th year) as PSTs. The topic of the intervention was a choice of either Organic Chemistry or Stoichiometry. The criteria for choosing the subset of seven participants was primarily that the GBTs were in fulltime employment for two years as chemistry teachers in the local Secondary Schools, for ease of access. In addition, the GBTs had not received any additional formal training in form of in service teacher development in PCK since graduation. They also shared a common element of willingness to participate in the study.

The intervention

The intervention, in either topic, followed a similar content structure, where each topic was discussed from the perspective of each of the five knowledge components of the TSPCK. The structure of the intervention is regarded as a signature intervention (Mavhunga and Rollnick, 2017) used in several studies that used the TSPCK construct (e.g. Mavhunga, 2016; Davidowitz and Potgieter, 2016). The intervention typically runs over a period of six weeks with three-hour contact sessions in each week. A chemistry topic, e.g. Organic Chemistry in the one stream and Stoichiometry in the second stream, was discussed from the perspective of the five content specific components of TSPCK. The participants attended a single intervention on one of the two topics, and not both. In each case, the discussions started in sequence, from Learner Prior Knowledge (LPK) which included: teachers’ identification and acknowledgement of correct learner prior knowledge; as well as common learner misconceptions, Curricular Saliency (CS), which included the identification of Big Ideas in a topic (Loughran et al., 2004), and the emphasis of core concepts in a topic; what is difficult to teach (WD), which comprises identifying gatekeeping concepts without which, learners’ understanding of the topic becomes difficult; representations (REP) explained at the three levels of understanding chemistry: the macroscopic, symbolic and sub-microscopic levels (Johnstone, 2000). Last to be discussed was the component of Conceptual Teaching Strategies (CTS), which refers to teaching strategies based on concepts rather than general pedagogical knowledge. Table 1 below presents the specific content concepts discussed against each TSPCK component in each topic of intervention.
Table 1 Specific concepts discussed against each TSPCK component
Knowledge component Intervention activities Concepts in Organic Chemistry Concepts in Stoichiometry
Introduction Formal introductions of TSPCK construct distinguishing from broader discipline PSK    
Learner prior knowledge Discussions are based on widely researched common learners’ misconceptions drawn from literature. IUPAC naming of organic compound; effects of type of bond on the reactivity of homologous series. Conception of the mole vs. mass of a substance.
Curricular saliency Establishing an understanding that each topic has core meanings to be understood, referred to as Big Ideas and peripheral concepts designated as ‘subordinate concepts’ that are important for the topic to be well understood. Also, emphasis was placed on sequencing of the Big Ideas, and the importance of the foregrounding concepts. Key concepts: Key concepts:
– Carbon unique nature The mole is the SI unit for amount of substance and allows us to connect the macroscopic scale of matter with the microscopic scale
– Functional groups – Concentration is a property of a solution and relates to the number of solute particles per unit volume.
– Reactions of organic compounds (e.g. substitution, addition, and elimination) – Limiting reagent is the reactant that is used up in a chemical reaction and determines the amount of product formed.
Subordinate concepts:
– Isomers and homologous series
– Alkanes and its members
Prior knowledge needed
– Chemical bonding; covalent bonding
What is difficult to teach Exploration of concepts considered difficult to learn, and identifying the actual issues that make understanding difficult. – Molecular and structural formulae – Relationship between moles and concentration and molar mass
Emphasis placed on the realisation that these concepts are different from misconceptions, they pose potential learners’ difficulties in accurately understanding the full meaning of a big or subordinate idea. – Functional groups – Appreciation that the Avogadro's number expresses the equivalent relationship between one mole of a substance and the number of entities it contains.
– IUPAC naming of organic compounds
– Homologous series
– Combustion
– Esterification.
Representations Introduction of different levels of representations. This includes: macroscopic, sub-microscopic and symbolic representations. The emphasis was placed on the concurrent use of these forms of representations when explaining a concept. Representing organic compounds at molecular, structural and microscopic levels using various models Representing the idea of a mole using different illustrations including analogies.
Conceptual teaching strategies Emphasis was placed on establishing an understanding that the component is informed largely by the generated knowledge from the other four knowledge components rather than on general pedagogical knowledge.    


While discussions that demanded reasoning through a topic from the perspective of each of these components were important, focus during the intervention was placed on making explicit how the components interacted with each other in the formulation of explanations and teacher responses. The last week of the intervention pulled all the discussions together into a coherent teaching programme for a specific topic using Content Representations (CoRes) (Loughran et al., 2004).

Data collection

In order to evaluate the extent to which the subset of seven GBTs retained the quality of their plTSPCK, which they first acquired during their final year of training as pre-service teachers, the same data was collected at three different points in a sequence. The first point, was at the beginning of the intervention, followed by a second point immediately after the six week-long intervention. The third point of data collection was conducted after two years in-practice, after the participants had graduated as qualified Chemistry teachers. Data was collected using specially designed TSPCK tools for capturing and measuring the quality of the GBTs’ plTSPCK in the topic of the intervention. The TSPCK tools were designed and first validated in a separate study on Organic Chemistry (Vokwana, 2013) and on Stoichiometry (Malcolm et al., 2019). The tools have also been widely used in several similar studies, particularly with PSTs in the same contextual setting as those in the study under similar conditions (e.g. Rollnick et al., 2017). The TSPCK tool is structured in a similar way for the respective topics. It comprises five sections that correspond to the five content-specific components of TSPCK, respectively. Each section has a few test-items that are presented as teacher tasks, formulated to allow both closed and open-ended responses. An example of one of the test-items in Organic Chemistry on the TSPCK component of Learner Prior Knowledge (LPK) is provided in Fig. 2.
image file: d0rp00008f-f2.tif
Fig. 2 An extract from a TSPCK tool in Organic Chemistry-LPK (Part 1).

The test item is comprised of two questions that bear learner prior knowledge, one in the form of a misconception as shown in part one (Fig. 2), and another reflecting a doubt that a learner may have in part two (Fig. 3). Both questions are in a classroom setting, and require the pre-service teachers to formulate a response.


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Fig. 3 An extract from a TSPCK tool in Organic Chemistry-LPK (Part 2).

The emphasis of the test-items in the tool is on knowledge for teaching the topic, where the accurate understanding of the content knowledge is taken as a given necessity. The completed TSPCK tools were labelled pre-intervention, post-intervention, and in-practice TSPCK tools following the three points of data collection respectively. Alongside both the intervention and the in-practice TSPCK tests were freshly audio recorded stimulated-recall interviews conducted face to face with all the seven GBTs in the subset while in practice (at the last point of data collection). During the face to face stimulated recall interviews, the GBTs were presented with extracts of their responses to test items from the intervention TSPCK tool to help them recall the event (Schön 1995). Questions asked during the stimulated recall interviews were more probing for the rationale behind the written responses. Examples of questions asked during the interview sessions included questions such as: Could you recall the reasons for responding to this test item as you did in this extract? Do you notice any difference in your responses written to the same test item across the different TSPCK tools? The interviews were conducted in a single session with each GBT, lasting about one hour. This allowed the participants enough time to reflect and think through their written responses. The interviews were video recorded and captured in a form of researcher written notes. Information from the interviews is presented throughout the findings to provide the added confirming or additional insight at points where appropriate.

Data analysis

All tests, the pre-/post-intervention, the in-practice TSPCK tests and the recorded interviews were analysed at the single point two years after the intervention. The analysis of all the TSPCK tests entailed scoring the GBTs responses, using a criterion-based rubric for plTSPCK. Similarly, with regard to the structure of the TSPCK tools, the scoring rubric caters for responses to the test items in the five components of TSPCK. Each TSPCK component was rated on a four-point quality scale. The quality scale ranged from the lowest category Limited denoted by a 1; followed by the Basic category denoted by a 2; a Developing category denoted by a 3; and the highest quality category called Exemplary denoted by a 4. See sample extract in Table 2 on the same component of learner prior knowledge as provided in Fig. 2 and 3.
Table 2 An extract of TSPCK rubric for scoring the TSPCK component of LPK (Mavhunga, 2012)
  Limited Basic Developing Exemplary
Learner prior knowledge • No identification/No acknowledgement/No consideration of student prior knowledge or misconceptions • Identifies misconception or prior knowledge • Identifies misconception or prior knowledge • Identifies misconception or prior knowledge
• No attempt to address the misconception • Provides standardised knowledge to counteract the misconception • Provides standardised knowledge as definition • Provides standardised knowledge as definition
• Repeats standard definition drawing on one other component of TSPCK • Expands and re-phrases explanation drawing on two other components of TSPCK interactively • Expands and re-phrases explanation correctly
• Confronts misconceptions/confirms accurate understanding drawing on three or more other components of TSPCK interactively


The categories across the TSPCK rubric increase in quality, as the complexity emerging from the increasing number of components found interacting in a given teacher response increases.

Therefore, as alluded in our literature review, it is the interactions of the TSPCK components, rather than the sum of individual components, that reflect the pedagogical transformation of content knowledge derived (Park and Suh, 2019). The nature of the interactions of the components is thus a key feature defining the increasing quality across the four quality categories in the rubric. Also, it is worth noting that while the structure of the rubric examines each TSPCK component at a time, the demand for evidence of interaction with other components is a feature referred to in each of the quality categories of the rubric. So, Table 2 presents the possible various extents to which TSPCK component interactions could be seen from the perspective of the LPK component. The GBTs’ responses to each of the test items under each TSPCK component were scored by matching them to the best fitting category in the rubric. Each participant would have a numerical score denoting the best fitting quality category for each of the five TSPCK component categories. In order to determine an overall score for each participant from each TSPCK test, the scores generated for each individual per TSPCK component were averaged to a single numerical value, considered as a proxy for reflecting the extent of overall component interactions. This value is referred to as Proxy Average Score. As mentioned before, it is important to note that the proxy average score does not represent a mechanical mixing or adding of the individual components, but is rather a symbolic reflection of all the inter-component interactions evident from the perspective of each TSPCK component, as determined by the criteria in the rubric. Furthermore, it is nevertheless important to note that the calculated proxy average scores naturally occurred in the form of mathematical fractions which were rounded up or down to a single digit, in order to locate the aggregated score in the appropriate categories in the scoring rubric.

Three independent raters, familiar with the theoretical construct of TSPCK and the rubric, scored the completed TSPCK tools. The extent of agreement across the raters was calculated across all tests as an inter-rater agreement Cohen Kappa value, calculated at 0.80 for each test and considered acceptable. The responses captured during the stimulated recall interviews were first transcribed verbatim into a textual format. The converted texts were then analysed using the postmodern representation method (Roulston, 2010), where the interviewer and interviewee co-construct meaning, a method that also improves trustworthiness.

Findings

The findings demonstrate three points, salient for science teacher education. Firstly, a continued confirmation of the positive impact of the signature intervention in developing PSTs’ TSPCK. Secondly, there is retention of the quality of the PSTs’ acquired plTSPCK into the early years of teaching practice. Lastly, there is continued growth of GBTs in several aspects of teacher knowledge including plTSPCK while in practice.

The impact of the cTSPCK based intervention on the then PSTs’ plTSPCK

The performance of GBTs in the pre- vs. post-intervention TSPCK tests, at the time of their training as PSTs, is presented in Table 3 below. This is the analysis of data collected at the first two points of data collection in the study.
Table 3 Pre-post-intervention-TSPCK tests scores (N = 7)
Participant Topic of intervention The five components of TSPCK Overall proxy score
LPK CS WD REP CTS Pre Post
Pre Post Pre Post Pre Post Pre Post Pre Post
Sharon Stoichiometry 1 3 2 3 2 4 1 3 1 3 1 3
Michael Organic Chemistry 1 3 1 2 1 3 1 3 1 2 1 3
Menjo Organic Chemistry 2 3 1 3 2 3 1 3 1 3 1 3
Tzepo Stoichiometry 1 3 2 3 1 3 1 3 2 3 1 3
Kgomotso Stoichiometry 1 2 1 3 2 3 1 3 2 2 1 3
Jaba Organic Chemistry 2 3 2 3 2 3 1 3 2 3 2 3
Ntombi Organic chemistry 1 3 2 3 1 2 1 2 1 2 1 2
Overall proxy score per component 1 3 2 3 2 3 1 3 1 2 1 3
Overall proxy score                     3 3


Table 3 shows two major observations about the knowledge gained by GBTs during their training on TSPCK in their final year as PSTs. Firstly, the pattern from the individual proxy scores indicates a positive shift across the pre-/post-intervention TSPCK scores by 2 quality category levels, moving from a score of 1 to 3 for most of the GBTs in the subset. Only two teachers were an exception to this pattern, as their shift across the pre-/post-intervention tests scores was by a single quality category jump, nonetheless signalling a gain in knowledge. At the end of the intervention, all the GBTs, except for one teacher (Ntombi), were located in the category denoted by a score of 3, which according to the rubric used in this study is the Developing level of TSPCK. A developing category reflects the ability of the participant to formulate teacher responses evident of three TSPCK components used in a complementary manner in interaction.

The second pattern is derived from a closer look at the proxy scores generated per TSPCK component. Table 2 shows that the GBTs as a subset, experienced an overall growth in each of the TSPCK components as a result of the intervention. The extent of the overall shift across pre-/post-intervention proxy TSPCK scores per component is at least by 1 category up across all the TSPCK components as presented. A much closer look indicates generally that the GBTs experienced growth in the different TSPCK components to different extents. Almost everyone, except for Kgomotso, experienced 2 category levels growth in some TSPCK components, and 1 category growth in others. Kgomotso, like the others, experienced growth across the different components at least by 1 quality jump, but as an exception, experienced no growth in the component of CTS. In a way, the CTS component appeared to have been challenging to most of the GBTs, as it registered the least overall proxy growth. Additionally, Table 2 reflects that the GBTs experienced most growth in understanding two of the five TSPCK components, namely, the REP and LPK. This is indicated by the high number of individual GBTs who experienced a shift of 2 quality categories in these respective components.

In order to demonstrate the nature of the reported growth across the pre-/post-intervention TSPCK scores, a sample of extracted qualitative responses from two GBTs is given. These GBTs represent the typical pattern seen in the responses of most of the subset, where there are GBTs who experienced a combination of 1 and 2 category level shifts in growth per TSPCK component.

Typical example 1 – an extract from Sharon

Sharon's responses in the TSPCK component of LPK are shown in Fig. 6. The test item in this component required the teachers to provide a response on how they would respond in writing, when giving feedback to learners who consistently demonstrate difficulties when working on how to prepare molar solutions. This item is also shown as an extract from the TSPCK tool in Fig. 4.
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Fig. 4 Extract of the test-item from the TSPCK tool on stoichiometry.

Sharon's responses captured from the pre-/post-tests are provided in Fig. 5 below.


image file: d0rp00008f-f5.tif
Fig. 5 Sharon's pre-/post responses in the component of learner prior knowledge.

In the pre-test, teacher Sharon suggested referring learners to the periodic table before applying a calculation to explain the theory behind molar concentrations. She does not however clarify how the periodic table as a representation links to the suggested calculation in building conceptual understanding for purposes of teaching. Here we see no evident links nor considerations of TSPCK component knowledge for integration of concepts in the explanation. She was therefore assigned an average score of 1, which denotes limited quality of TSPCK.

In the post-test, she points out that “the mass of the salts does not mean that the numbers of particles are the same”. This is a common learner misconception in Stoichiometry that she then explicitly considered in her explanation. She went on to state that; “the ions of different salts have different relative atomic masses and therefore the molar mass of each salt is different, which means the concentration of solutions will be different, and therefore, the amount of salt, measured in moles, will also be different”.

In the above statement, we see identification of specific gate keeping concepts (mass in relation to molar masses) that when not fully understood adds to the difficulty in understanding the reason behind salts of the same mass being of different amounts (moles). Furthermore, there is an emphasis on concepts, with clear links in terms of cause and effect. This is evidence of elements of curricular saliency working in an integrated manner with the key gate keeping concepts and the common learner misconceptions given in the earlier statement. Sharon further suggested referring to the periodic table, which is a form of representation, to confirm the molar masses of sodium chloride and sodium bromide, and to help explain the differences in the sizes of atoms of different salts, as linked to the calculation for moles.

She lastly emphasised that “If you add ten grams of the salt to the same volume of solvent you are not adding the same number of ions for the different salts”. The explicit emphasis of the meaning of same number of grams not to refer to the same number of ions for different salts, indicates an awareness of a common misconception about the topic, an aspect of the component of learner prior knowledge. When asked in a stimulated recall interview about the differences in her pre-/post responses, she referred to her understanding of the importance of creating a physical picture for learners to understand the concept of moles, by linking in some way, the natural sizes in which the different atoms occur, which influence their mass, to the idea of counting their quantity. She was assigned an average score of 3 in the post-test, based on her ability to interactively draw on the components of LPK, WD and REP in her explanations.

Typical example 2 – an extract from Jaba

Another example indicating improved quality of TSPCK in the topic of intervention is seen in the way the component of representations was used by teacher Jaba, whose intervention was on Organic Chemistry. The test item from the TSPCK tool required the teachers to first identify two representations they find most useful in teaching the topic, and then explain the differences in the boiling points of butane (−0.5 °C) and pentane (36 °C).

A comparison of responses lifted from teacher Jaba's pre-/post-intervention tests is shown in Fig. 6.


image file: d0rp00008f-f6.tif
Fig. 6 Teacher Jaba's pre-/post responses in the component of representation.

In the pre-test, teacher Jaba selected the three representations shown in Fig. 6. He did not however provide explanatory notes linking the selected representations to aspects of the concepts being explained. In the stimulated video recall interview, conducted retrospectively during the collection of data in practice, the teacher indicated that although he understood that the representations were useful in teaching, at the time he was not sure of how to conceptually explain his thoughts from a teaching perspective, as at that stage, he just understood the usefulness of the representations from a visual perspective. The teacher was assigned a limited category score. However, in the post-test, the teacher selected the same representations, but dropped the condensed formula option, and provided accompanying explanatory notes. For instance, we see him point out that “the line structural diagram representation provides good visual mode, useful for seeing bonds broken and new bonds formed as one compares the structural diagrams of products and reactants to identify what took place”. Here the teacher goes beyond the citation of visual effects and indicates the specific aspect of focus as argued by Klafki (1958), that the use of representations in teaching is to point out the actual element to be noted for learner consideration. This case reflects Jaba's ability to highlight the key gate keeping concepts that maybe difficult to understand (WD), about chemical change, which is not necessarily a misconception. He then identified the second representation as a 3D molecule. This kind of a representation is widely reported (e.g., Johnstone, 2000) to be desirable in helping learners to better understand the configuration of atoms within organic molecules and link them to their shapes (REP). He further referred to electronegativity, in the context of explaining the configuration of atoms that yield to the shape of the molecule. His statement indicated awareness of the foregrounding concepts that need to be pulled into formulating a response (CS) as well as the continued identification of gate keeping concepts needed to explain shapes of molecules (WD). So, taking the teacher's written responses as a whole, we see evidence of a total of three components: Representations (RP), used in a way that complements understanding what is difficult to understand (WD), while drawing on aspects of curricular saliency (CS). Accordingly, the teacher was assigned a score of 3, denoting the ‘developing’ category of TSPCK.

In summary, the findings above confirmed a gain in the quality of plTSPCK experienced by the subset of GBTs at the time of their training as PSTs, as a direct result of the cTSPCK based intervention. This finding is however not surprising, as it is consistent with other findings from earlier studies on the improvement in the quality of TSPCK in various science topics when the same intervention was conducted (Mavhunga, 2014; Davidowitz and Potgieter, 2016; Malcolm et al., 2019). However, it was important to repeat and conduct this analysis in this study, for the establishment of a trustworthy baseline from which the determination for retention of the acquired quality of TSPCK could be defined.

Findings on retention of acquired plTSPCK

Table 4 below shows a comparison of shifts in the quality of the intervention GBTs’ post-test at the end of the intervention vs. in-practice-tests as beginning teachers, two years after their final year as PSTs.
Table 4 GBTs’ post-intervention vs. in-practice TSPCK scores in the topics of intervention
Participant Topic of intervention The five components of TSPCK Overall proxy score
LPK CS WD REP CTS Post In-prac.
Post In-prac. Post In-prac. Post In-prac. Post In-prac. Post In-prac.
Kgomotso Stoichiometry 2 2 3 3 3 3 3 3 2 2 3 3
Sharon Stoichiometry 3 3 3 3 4 4 3 4 3 3 3 3
Michael Organic Chemistry 3 3 2 3 3 4 3 2 2 2 3 3
Menjo Organic Chemistry 3 3 3 3 3 3 3 3 3 3 3 3
Jaba Organic Chemistry 3 3 3 3 3 3 3 4 3 3 3 3
Tzepo Stoichiometry 3 3 3 3 3 3 3 3 3 2 3 3
Ntombi Organic Chemistry 3 2 3 1 2 1 2 1 2 2 2 1
Overall proxy score per component 3 3 3 3 3 3 3 3 2 2 3 3
Overall proxy score as a group                     3 3


Two major patterns are observed from Table 4. The first pattern is derived from the comparison across the individual GBTs’ overall proxy person scores. The pattern signals an overall retention of a person score of 3, between the post-intervention and in-practice tests in almost all but one GBT in the subset. As alluded to earlier, the score of 3 reflects the ability of the GBTs to formulate teacher responses and explanations that draw on three TSPCK components in an interactive manner. The observed retention is over a period of two years since the intervention and into the early years of the GBTs’ teaching practice. A noticeable exemption to the overall pattern that indicates retention of the proxy person scores, was one GBT teacher (Ntombi), who experienced a visible overall drop by 1 quality category down into the lower Limited category in almost every TSPCK component. Ntombi's growth at the time of the intervention was denoted positive by a single category jump across her pre-/post-tests. The score in the post-test, however remained in the lower quality categories of the TSPCK rubric, the Basic category, while the rest of her colleagues in the subset experienced a shift into the next higher category, the Developing category, as reported earlier.

The second pattern is derived from looking at the individual scores per TSPCK component. The emerging overall major pattern similarly suggests that the GBTs as a group, had largely retained the same average proxy score for each of the five TSPCK components two years after the post-intervention test. However, a much closer analysis of the pattern in Table 4, indicates a few cases where GBTs experienced a slight gain or drop in personal scores across individual components. For example, GBT Michael experienced a positive gain by 1 quality category level, up in three TSPCK components (CS, WD and CTS). GBTs Sharon and Jaba, likewise, experienced growth in the single component of REP. On the other hand, teacher Ntombi notably consistently experienced a drop in performance in almost all the TSPCK components (LPK, CS, REP and WD) with CS reflecting a huge drop of 2 categories.

Both Michael and Ntombi, registered a drop in their use of representations. In a stimulated interview with Ntombi, she ascribed her depreciation in her overall TSPCK score to the culture of the school where she is constantly advised and expected by the head of the department to teach in a particular way, contrary to the ideas promoted in the TSPCK intervention. When pointed out to her, that her overall proxy gain of TSPCK as a result of the TSPCK intervention during her ITE programme was noted to have remained in the lower quality sections of the scale of the TSPCK rubric, she still felt that she learnt a lot from the intervention. Michael, on the other hand, identified his own personal determination and the desire to excel, as encouraging him to reflect regularly on his practice, and on the advice shared by the experienced teachers around him. Michael however seemed undisturbed by the slight drop in the use of the representations, and assigned no specific reason to it, even when asked directly, but instead visibly focussed on his positive motivation.

We provide sample extracts showing the nature of qualitative evidence that reflect the overall pattern pointing to retention in the GBTs quality of TSPCK per component, as well as the slight growth in certain TSPCK components, as identified in the close-up analysis. For purposes of consistency and tracked progress, we have used the same GBTs, (Sharon and Jaba) whose responses were used earlier to confirm improvement in the quality of TSPCK in the pre-/post-intervention tests. We have also added extracts from teacher Michael who uniquely showed continued growth in multiple TSPCK components.

A typical example for retention in-practice – an extract from Sharon. Teacher Sharon's post- vs. in-practice responses on the topic of stoichiometry, with respect to the component of LPK, are presented in Fig. 7. As mentioned earlier, the GBTs were asked how they would respond in writing, when giving feedback to learners who consistently demonstrate difficulties when working on how to prepare molar solutions.
image file: d0rp00008f-f7.tif
Fig. 7 Sharon's post (in-practice) responses in the component of learner prior knowledge (LPK).

In the extracts above, teacher Sharon first acknowledges the common learner misconceptions about mass, relative to molar concentration, by pointing out that “the same mass of the different salts does not mean that their respective number of particles is the same”, in both the post- and in-practice tests. She then, in the post-test, identified the specific concepts to be emphasised (different molar masses), stating that; “the ions of different salts have different relative atomic masses, which mean the concentration of solutions will be different, and therefore, the amount of salt, measured in moles, will also be different”. In this statement, the teacher links the concepts of concentration, molar mass and moles more explicitly. The relationship between these concepts is often found to be difficult for learners to understand. She then suggests referring learners to the periodic table to confirm the molecular masses of sodium chloride and sodium bromide (NaCl and NaBr), while in the in-practice test, she introduces a formula that reflects the relationship between moles and molar mass to work out the number of moles, which both indicate drawing on the component of representations at the symbolic level. The teacher lastly emphasises that adding ten grams of the different salts to the same volume of solvent does not mean adding the same number of ions for the respective salts. The explicit emphasis of the meaning of grams (mass) not to mean the same as the number of individual ions for different salts in both the post- and in-practice tests, indicates understanding of a common learner misconception about the topic, an element of LPK. The teacher retained a score of 3 between the pre- and post-tests.

Findings on signals of teacher knowledge improvement while in practice including plTSPCK

The extracts in Fig. 8 below, present qualitative evidence of retention, as demonstrated by teacher Jaba in the post vs. in-practice tests. In the post-test, teacher Jaba selected the line diagram structural molecule and a 3D molecule as the most useful representations for teaching in the post-test. For the line diagram molecule, the teacher explained that: “in teaching organic reactions, the representation provides good visual mode, useful for comparing products and reactants to identify what took place.” This aspect, as stated earlier, reflects the teacher's ability to draw attention to the exact feature to be observed in a representation, thereby making explicit an aspect that is not easy for learners’ understanding. The second representation identified by the teacher, (3D molecule) is widely reported, as pointed out by Johnstone (2000) to be desirable in helping learners to better understand the configuration of atoms in organic molecules. He then refers to electronegativity, in the context of explaining how the configuration of atoms yield to the different shapes of molecules. This demonstrates an awareness of the foregrounding concepts, needed prior to teaching a particular concept. So, taking the teacher's written responses together, we see evidence of the component of representations used in a way that complements the components of what is difficult to understand and curricular saliency. The teacher was assigned a score of 3, which falls in the developing category of TSPCK in the post-test.
image file: d0rp00008f-f8.tif
Fig. 8 Teacher Jaba's post (in-practice) TSPCK responses in the component of representations (REP).

In the in-practice test, the teacher selected the same representations, noting similarly to the post-test, that he would use the line structural diagram representation to simplify the identification of functional groups and the types of organic reactions, while the 3D representation would be used in showing the nature that is responsible for the shape of molecules. Different to the post-test however, he succinctly described how he would apply the 3D representation to explain the boiling points of butane and pentane, by identifying the effect of the net dipole moments (intermolecular forces) on the electronegativity of the molecules. He then acknowledges the usefulness of the representation in depicting the butane molecule as having a shorter structure and thus less surface area, which results in a lesser effect of the van der Waals forces of interaction than the pentane molecule. He goes on to link the lower boiling point of butane to the effect of weak van der Waals forces of attraction, which would require less energy to overcome the intermolecular forces (IMF). In his explanation, we see an explicit link between the selected representations and the grounding pre-concepts operationalising Shulman's (1986, p. 16) posit that choosing suitable representations involves ‘thinking through the main ideas in the lesson and identifying alternative ways of representing them to students’. When asked in the stimulated interview about his in-practice response being expanded to include a reference to how boiling points are linked to intrinsic properties of the molecule, he referred to his realisation of the emphasis placed on boiling points in the curriculum for the grade he was teaching. His written response in the in-practice tool was considered to reflect a retained extent of TSPCK, however, with a noticeable increased depth in his teacher response. The increased depth in his response emerged from the expanded connections across multiple content concepts. The observed improvement did not qualify for a higher TSPCK score in terms of the criteria of the rubric, as the observed improvement was related to an increase in content connectivity of the concepts considered to be foregrounding prior learner knowledge, concepts that fall within the same kind of TSPCK component (LPK). Nonetheless, this was considered to be a desirable development.

A second example demonstrating signals of improvement in teacher knowledge while in-practice – an extract from Michael. Another example demonstrating growth of teacher knowledge TSPCK, in this case while in practice, is that of Michael. Fig. 9 below presents an extract from Michael's responses taken from his post-test vs. in-practice test, responding to a test item linked to the TSPCK component-curricular saliency. The test item required the GBTs to first identify three Big Ideas (which are the most important understandings to be achieved) in teaching the topic of Organic Chemistry at Grade 12. The second part required the GBTs to suggest pre-concepts that must be covered prior to teaching the topic, and further identify reasons why the teaching of the topic is important for learners. The extract from the post-test indicates Michael struggling to identify three Big Ideas that are most important when teaching Organic Chemistry. His response included concepts that could be regarded as subordinate ideas. For example, the reference to IUPAC could be seen as a subordinate concept for a core idea that acknowledges that there are different ways of naming substances (e.g. IUPAC is a system for writing structural formulae and their names, homologous series, etc.). The reasons provided for the importance of the topic were shallow, with no evidence of consideration of the topic from the perspective of the TSPCK components. Michael was assigned a score of 2, which falls in the Basic category of TSPCK. Noticeably different, however, in the in-practice test, Michael provided three Big Ideas that identified core meaning to be established when teaching Organic Chemistry. The reasons given for importance of the topic included making links to conceptual understanding of other concepts in the subject such as bond energy, electronegativity etc. He further linked the importance of understanding the topic to learners’ everyday experiences, such as the synthesis of plastics, and how glue works as examples. In his stimulated recall interview, he refers to the importance of covering (referring to the curriculum) important main concepts in a topic and creating a logical teaching sequence. Here we see Michael demonstrating an improved plTSPCK.
image file: d0rp00008f-f9.tif
Fig. 9 Teacher Michael's post (in-practice) TSPCK responses in the component of curricular saliency.

In summary, the findings above, first confirmed the acquisition of TSPCK by the GBTs in the respective topics of intervention as a result of the structured intervention on TSPCK in their final year of training as PSTs. Secondly, that the GBTs largely retained the extent of quality of their acquired plTSPCK, and in some selective cases, demonstrated signals of teacher knowledge improvement, which appeared to have been influenced by the School curriculum in different ways. We discuss these findings in detail below.

Discussion

In this study we argued for the need to explore the long-term value of an early exposure of PSTs to cTSPCK. We set out to determine the retention of the acquired TSPCK into the early practice of GBTs amidst the myriad of factors that influence their practice. We acknowledge the limitation of exploring a complex construct, like TSPCK, from the one aspect of teaching, and planning for teaching, as not sufficient (Aydeniz and Kirbulut, 2014), and the small sample size used in this study, is reflective of the challenges of maintaining a sample in longitudinal studies (White and Arzi, 2005). We therefore attempted to focus on retention as determined from the shifts in plTSPCK that were measurable across the different sampling points. Despite these limitations, the findings from this study moves our understanding of the long-term value of PCK, a little further. According to Ausubel (2012), retention of acquired knowledge is an acceptable indicator of meaningful learning having taken place, and further reflects on the quality of the provided teaching. Two important, but not generalised conclusions are drawn from the findings of the study as a case-study: (i) An early exposure to cTSPCK appears to yield a retained quality of the acquired plTSPCK into the early years of teaching practice; and (ii) GBTs, exposed to cTSPCK, appear to experience further growth in different types of teacher knowledge including TSPCK.

(i) The value of an early exposure to cTSPCK in retaining the quality of plTSPCK

The analysis for retention of GBTs’ plTSPCK in practice, was based on a baseline that confirmed the acquisition of their plTSPCK from the intervention (cTSPCK). The confirmation was based on the observed improvement in the then PSTs’ plTSPCK scores across the pre-/post-intervention tests. In addition, the qualitative extracts and the information from the stimulated interviews provided evidence indicative of learning having taken place from the intervention, as described by Vygotsky's mediation process (Vygotsky, 1986). For example, in the post-test, Jaba showed an improved ability to expand on the rationale for his pedagogical choices for the use of specific representations in teaching Organic Chemistry. In the stimulated recall interview, he pointed to his lack of language and pedagogical insight at the beginning of the intervention, as having prevented him from providing sound reasons for his choices that were technically accurate, however lacking the pedagogical competency to express them. In Vygotsky's terms, mediation that leads in learning, comes in the form of symbolic tools, most notably language, as well as social interactions with others. Individuals are then enabled to internalise these tools of language and reflectively use them to direct and regulate their own thinking, as seen in Jaba's case (Fig. 6). Similar experiences were observed across the GBTs, with positive shifts across the pre-/post-intervention scores, thus forming a trustworthy baseline, and confirming the acquisition of plTSPCK from the intervention, and accordingly proving reliable for exploring the retention of the acquired teacher knowledge. The findings on retention of the quality of the GBTs plTSPCK in Table 3 could thus be interpreted from a reliable baseline. All the GBTs, except for one discussed later below, reflected the retained quality of plTSPCK in practice as well as in the post-test. Sharon's in-practice response is a typical case, which is discussed in detail. Fig. 7 indicates the similarity in the manner in which Sharon drew on multiple TSPCK components to formulate a teacher explanation that would help learners develop an understanding of the mole concept in Stoichiometry. She provided a response that brought to view the relationship between related but confusing concepts of mass vs the meaning of moles as a number quantity, and concentration vs moles. Her bringing of the mathematical formula expressing moles as mass in relation to molar mass at the specific time, was pedagogically strategic, aiding her effort to point out the difference across related concepts. In her stimulated recall interview, she emphasised the need to create a physical picture for learners to recognise the causal effect brought about by the different sized atoms that would naturally have a higher mass even when the same quantity number was counted. Sharon's case demonstrated evidence of the retention of plTSPCK, to the same extent as in the post-test, a pattern observed in most of the GBTs in the sample.

(ii) Growth in the different types of teacher knowledge while in practice

Interestingly, teachers Michael, Sharon, and Jaba, in addition to retaining the quality of their plTSPCK, appeared to have experienced further growth in their teacher knowledge while in practice. Their growth seemed to have been influenced by the School Curriculum in different ways. In the one case, there is evidence of the School Curriculum promoting growth in ways that GBTs are enabled to connect different concepts of their content knowledge (CK) as foregrounding pre-concepts. While in another, the School Curriculum appeared to have enabled growth in plTSPCK, by promoting understanding of the topic structure from the perspective of the topic's Big Ideas and their logical sequencing. These cases are discussed separately below:
Growth in a special teacher's CK. Jaba (Fig. 8) demonstrated further growth in understanding complex links across foregrounding concepts while discussing his choice of a representation. He explicitly pointed to the connections between electronegativity, the link between shapes of organic molecules to the surface area of the bonding atoms, and ultimately to their boiling points (Talanquer, 2018). His response in the post-test to the same test item did not include reference to a link to boiling points. In his stimulated recall interview, he referred to his recognition that the School Curriculum required learners to explain the idea of different boiling points from a microscopic perspective. The point to note here, is that his inclusion of the new concept of boiling points was done in a manner that demonstrated the tying of several related foregrounding concepts, that he already knew (post-test), into more explicit links. In doing so, Jaba displayed a move beyond curriculum compliance into the dimension of deep content knowledge-connectivity. The addition of the link to boiling point in his response, increased the strength of the connections of related concepts, but not necessarily the quality of his plTSPCK. The reason lies in our operational definition of TSPCK, calling for evidence of the interaction of the different five knowledge components of TSPCK mentioned earlier. In this case, the added concept is categorised to fall into the knowledge component of Learner Prior Knowledge (LPK) that is already part of the evidence counted to make-up his demonstrated quality of TSPCK. According to Geddis and Wood (1997), LPK refers to the understanding of those concepts that serve as pre-concepts, foregrounding, and preparing for the understanding of the new concepts discussed. Thus, a demonstration of ‘more of the same’, that is, several LPK concepts and their connectivity, would not in our current definition of TSPCK, mean an increase in the quality of TSPCK. However, there is something desirable in the observed ‘connectivity of related concepts’ that in our view, is important, and rather points to another type of teachers’ content knowledge (CK) (Arzi and White, 2008). This is a kind of CK that fosters a teacher's understanding of the connectivity of concepts in a science topic. As with the idea of School Related Content Knowledge (SRCK) in mathematics education (Dreher et al., 2018), we posit ‘concept connectivity’ to be a feature of teachers’ SRCK in science education.

On another note, Sharon on the other hand, demonstrated the influence of the School Curriculum on her choice of use of scientific terms. Fig. 7, among other things, further reflected how Sharon in her in-practice responses was making multiple effort to use the term ‘molecular weight’, a term used commonly in the School Curriculum alongside the term ‘molar mass’, prevalent in the post-test. She demonstrated what Arzi and White (2008) called “the gradual distancing from academically acquired details”, on the one hand, and the assimilation into the school curriculum on the other. Both these experiences demonstrated the GBTs’ organic learning in practice, as influenced by their day to day experience of the School Curriculum, deepening their CK-connectivity and assimilation into the language preference for certain scientific terms. They demonstrated Vygotsky's (1986) desired state, where growth is brought about by the understanding of concepts learnt in the day to day environment (spontaneous) merging seamlessly with their existing TSPCK (scientific concepts).

Growth in teacher's plTSPCK. Michael's case pointed to direct growth experienced in several TSPCK components while in practice. These were the components of curricular saliency, and what is difficult to teach. The growth in the component of curricular saliency is noted in Fig. 9, where he demonstrated improved understanding of structuring the topic into meaningful Big Ideas and in some sequences that he pointed out were to be aligned with the School Curriculum. The observed growth was however insufficient to influence his overall proxy average score for TSPCK, because of his slight drop in the score of representations. In his stimulated recall interview, the teacher appeared unperturbed by the slight drop of his score in the use of representations, and rather enthusiastically expressed gratitude for the nature of the mentor support he was receiving from experienced teachers in his school. He expressed his continued self-motivation and personal determination as factors that are sustaining him and influencing his growth of teacher knowledge. It was of interest to the study to note, similar to the findings by Rozenszajn and Yarden (2014) with biology teachers, the influence of these affective factors which in his case were enablers for further growth.

Lastly, the findings indicated an uneven growth across the TSPCK components, a trend noticed not only across the pre-/post intervention (Table 3) but also across the post-/in-practice (Table 4) scores per TSPCK component. Teacher Michael's growth of TSPCK in-practice demonstrated this trend more visibly. The observed trend confirmed the process of learning, according to Vygotsky (1986), to be an uneven one, as we saw with all the three GBTs who experienced growth in-practice. Nonetheless, their overall growth in-practice demonstrated an ongoing process of “coming to understand the meaning and functional significance of the language one has been using all along” (Wertsch, 2007).

The case of a drop in TSPCK. In contrast to the majority trend, GBT Ntombi who registered a drop in the quality of acquired TSPCK, pointed to a non-supportive school environment as a major contributing factor to her lack of retention of TSPCK. However, based on her pre- and post-intervention TSPCK scores, we further noted that her acquisition of TSPCK in the topic of intervention, while it was a positive gain, however remained in the lower quality categories of the TSPCK rubric used in the study. It was interesting to note that despite her experienced drop, she spoke positively on the intervention during her PST years and felt she had learnt a lot from it. Ntombi's experience confirmed the observation by Roehrig and Luft (2004) that a GBT who exits an intervention on TSPCK during their pre-service teacher years with basic levels of growth in their teacher knowledge, is at risk of degenerating even further in this aspect. Ntombi's experience highlights the plight of many other GBTs, who struggle to develop their teacher knowledge both during their development as PSTs, and later in their early years of practice. This points to a need for pre-service teacher programmes to pay closer attention to such cases, and a dire need for PCK/TSPCK based in-service professional teacher development for GBTs.

Conclusion

The findings in this study indicate the retention of the quality of acquired TSPCK as the major long-term value derived from an early exposure to PCK/TSPCK from ITE programmes. Furthermore, it demonstrates that the retained TSPCK serve as Vygotskian scientific concepts in which the day to day requirements of the School Curriculum (spontaneous concepts) are merged to expand and grow various kinds of teacher knowledge seamlessly. Focusing on the retention of plTSPCK into the early years of practice of GBTs, exposed the kind of CK, working side by side with TSPCK, that teachers use, and thus should be noted and taught to prospective teachers. This is School Related Content Knowledge which among other things, includes a focus on teaching CK to reveal ‘concept-connectivity’ across related concepts. This means going beyond the teaching of content concepts as stand-alone concepts e.g. shapes of organic molecules to be taught in relation to electronegativity, surface area, van der Waals forces and the culminating influence on boiling points. Lastly, factors such as self-motivation and self-encouragement are often not included in formal science education programmes, as they are considered affective in nature, and not necessarily scientific. The findings in this study point to their importance, and the need for the design of PCK/ITC based ITE programmes with such specificity. We therefore recommend the recognition of the findings in this study as convincing ‘green-shoots’ that are encouraging for large scale studies on the long-term value of PCK/TSPCK and the exploration of a SRCK for science education.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support from the National Research Foundation (NRF) of South Africa (Grant CSUR114426) is gratefully acknowledged.

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