Ongoing concern about poor learner performance in mathematics has led to wide-ranging research on the subject, globally and in South Africa. Among the remedies identified is the reformation of pre-service teacher (PST) education programmes in a way that supports the acquisition of professional skills for pre-service teachers. Developing PSTs’ reflective practice (RP) is a significant component of the desired reformation. Our research explored PSTs’ RP development in the context of video-based mathematics lesson analysis. The aim was to contribute knowledge towards strengthening mathematics PST education and to report on whether increased benefits accrued from working with PSTs in small groups, guided by an experienced facilitator, as compared to whole-class lecturing. We draw on this extended analytic framework to compare two sets of reflections written by four selected PSTs based on viewing video recordings of their own teaching. One set was written in August 2018 after the PSTs completed three lecture sessions on RP in a Mathematics Methods course. The other was written in September 2019 after the four selected PSTs participated in three small-group, facilitator-guided sessions. The findings indicate some shifts towards higher-level reflections in the latter set, although only two of the four PSTs reflected at the highest level (reflectivity) following the small-group sessions. Implications for pre-service mathematics teacher education and refinement of frameworks for delineating levels of reflection are discussed.

The research contributes to mathematics teaching through refining and extending existing models of reflective-based practice to better analyse the shifting nature of mathematics teachers’ reflections with a view to supporting improved teaching and learning.

There is growing evidence that, despite qualifications, many teachers of primary mathematics do not have sufficient mathematical and pedagogical knowledge for teaching mathematics (e.g. Venkat & Spaull,

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Developing PSTs’ reflective practice (RP) is increasingly being incorporated into pre-service teacher education (PTE) as one of the strategies supporting transformation (Cadiz,

Teaching mathematics is a complex task for many teachers (Ziegler & Loos,

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Developing RP, therefore, becomes a critical element in teacher education programmes. Darling-Hammond (

This article emerges from a broader research study that explored PSTs developing RP through participation in sessions focused on the development of RP through video-based lesson analysis (Chikiwa,

Reflective practice is widely noted as key to professional development across various professions (for example healthcare; see Norrie et al.,

The concept of RP can be traced back to 1933, when Dewey first introduced what he called reflective thinking. Dewey (

Schon (

The researchers found Dewey’s early definition of reflection meaningful and more explicit for teacher education. Dewey (

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The process of reflection is thus a systematic cycle that needs constant reiteration. Reflective practice assists teachers in making links between various teaching experiences, thereby fostering progressive learning. Schon (

Reflection-in-action takes place during an action, and reflection-on-action takes place after an event has occurred. … Reflection-for-action is thinking about future actions with the intention of improving or changing a practice. This type of reflection requires teachers to anticipate what will occur during a lesson, as well as reflect on their past experiences, before a lesson occurs (Farrell

Schon (

Because of the many benefits associated with developing teachers’ RP, PTE programmes have increasingly embraced it as a useful means of

Studies conducted with PSTs confirm some benefits of RP in PTE with the use of video-recorded lessons. For instance, Hewitt et al. (

Teacher education remains actively in search of strategies for developing PSTs’ RP. Karsenty et al. (

Our research was underpinned by Vygotsky’s (

the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers. (p. 86)

The work of Karsenty and colleagues coheres with this framework as it emphasises social learning and the importance of careful mediation in the use of video of teaching practice as an artefact for development. Karsenty et al. (

The lenses provide the PSTs with opportunities to consider concepts that can be developed under a given topic. Karsenty et al. (

While the framework may appear straightforward for experienced teachers, it should be remembered that PSTs have almost no teaching experience other than practicum and are still in the process of developing their MKfT.

The research paradigm adopted was interpretive guided by the assumption that reality is multiple and shaped by social experiences (Cohen et al. 2011). We used a qualitative case study research approach (Creswell,

These sessions with the four PSTs began at the end of 2018 following Phase 1 of our research.

In 2018, 52 PSTs, in their third year of Bachelor of Education studies at a university in South Africa were taken through three sessions of analysing video-recorded mathematics lessons with the intention of developing both their MKfT and their RP. The lecturer participating in our study identified the need for drawing on support tools to aid PSTs’ reflection on video lessons. Having come across the SLF of Karsenty and colleagues she chose to draw on this tool as a device to support PSTs in focusing on a range of important aspects of video-recorded mathematics lessons as they reflected on them. Since the aim of the sessions was to develop the PSTs’ MKfT and RP, we took the opportunity to investigate how the PSTs fared with RP directed to mathematics education. In the whole-class RP sessions, the lecturer started by introducing the SLF, and asked the PSTs to reflect on video-recorded mathematics lessons she perceived to be relevant to the PSTs’ context. She asked different groups of PSTs to use different lenses from the SLF to discuss and report back reflections relevant to each lens. The PSTs were requested to write individual reflections before they could discuss as a group, then present to the whole class, leading to a class discussion. Thus, PSTs were given opportunities to co-create knowledge and learn from each other.

All 52 PSTs in the cohort were invited to participate in the research and all ethical protocols were followed. Nineteen PSTs volunteered and signed consent forms for Phase 1. The PSTs were provided anonymity and were informed they could withdraw their participation at any point. The ethics application was approved by our university Education Research Ethics Committee in 2017. Elsewhere (Chikiwa & Graven,

In Phase 2 we asked the four PSTs to write reflections on these videos of their own teaching using the SLF they had used in lectures during 2018. They submitted these written reflections to us in the last term of 2018. In the third term of 2019 we invited the same four PSTs to participate in three small-group, facilitator-led RP sessions focused on selected video episodes of other teachers’ lessons as a way of scaffolding their RP skills. The video lessons used during these sessions were chosen by the facilitators for their appropriateness to FP teaching as well as their experience of these lesson videos having rich material to stimulate reflective discussion. The facilitators, being experienced in reflecting on video of mathematics lessons according to the SLF, served as the mediating MKOs, modelling RP focused on important mathematical aspects of teaching and learning. Following these sessions (September 2019), the four PSTs were asked to use the SLF once again to provide written reflections on the video recording of their own lesson they used previously in 2018. They completed these towards the end of the fourth term in 2019. We analysed their reflections using content analysis (Stemler,

As mentioned above, in Phase 2 the four PSTs were taken through three reflection sessions led by experienced facilitators to support their RP development. In these sessions the facilitator probed for reflections as the PSTs analysed selected video recordings of other teachers’ mathematics lessons. In

Excerpt from a facilitator-guided reflective development session.

Time | Speaker | Quotation | Lens |
---|---|---|---|

13:09 | Facilitator | What does she want to do? | Goals |

13:43 | Facilitator | Do you remember a time when you had evidence from the video that this is what she wants? I think there is one moment where she actually says it, do you remember? | |

18:02 | Facilitator | So, does anyone have more mathematical ideas to add? You were concentrating really on your lens. Okay. You didn’t say though, Joy, where is she is heading, what will she do … [ |
MMI |

18:57 | Facilitator | What can you say about the task that the teacher chose to introduce in the lesson? Try to characterise the task in light of what you see in the clip. What can you tell us there? | Tasks and Activities |

21:25 | Facilitator | Did you notice that Joy also said that, and actually I think that this does not belong to the mathematical ideas and does not belong to the activity, it belongs |
Tasks and Activities |

28:08 | Facilitator | Next one is interactions, so Dumi got this question: try to characterise the interactions between the teacher and students in the part of the lesson shown in the clip because we only can refer to what we saw, state any type of interaction that you, Dumi, you identified? | Interactions |

49:48 | Facilitator | Before the lesson on what might happen. And try to, you know the Japanese say that there a good mathematics teacher is to make the unexpected expected. You try to think in advance what might happen, what answers I might get, what difficulties might I get and prepare in advance for that. That’s a very good point; I’m glad that’s what you’re taking. Anything else you wanted to say? You the last one? | Dilemmas and Decision-making |

MMI; meta-mathematical ideas.

At the start of the session the facilitator Carol (who was highly experienced in the use of the SLF for supporting teacher reflection on videos) provided some orienting comments that included an explicit statement about the importance of noticing mathematical over general aspects of lessons, such as:

‘Our focus is on the mathematics, so we try to talk less about generic aspects such as the teacher’s voice or the teacher’s body language; these things are interesting [

Thereafter she assigned each of the PSTs a metaphorical lens to look through as they analysed the video-recorded mathematics lesson she had selected for the session. She played the video and allowed the PSTs to write reflections using the lenses they were assigned. She began the discussion by calling for more reflections through probing questions. In the process she assisted the PSTs by guiding them to comment on aspects of the lesson specific to each lens. In

As seen in the session excerpts in

After three such sessions focusing on different videos, we asked the four PSTs to provide written reflections again on the video recordings of their own teaching (which they had done a year earlier). We then analysed their written reflections using the four levels of reflection framework (FLRM) and compared their first reflections on their own practice (ROP1 in 2018) with their second (ROP2 in 2019). Below we give a brief account of how we developed our analytical framework.

The literature offers a wide range of useful analytical frameworks for analysing RP, but none of them quite met our needs in relation to coding and analysing written reflections of the 19 PSTs who participated in Phase 1 of the study. We therefore had to create our own, merging and adapting existing frameworks following a detailed and wide-ranging review of existing frameworks. We began by merging elements of Lee’s (

After using samples of data in these two combined frameworks we identified the need for an additional level in our framework as well as some refinement of a set of sub-indicators across the levels. We particularly noted that ‘suggestion’ (as evidenced by our data) did not cater for reflectivity or critical reflection in its full sense as described by Lee (

The four levels of reflection framework.

Level of reflection | Description of level | Indicators/phrases | Examples |
---|---|---|---|

Level 1 description | PSTs describe classroom incidents without explanation for them. | Description of classroom occurrences. | The teacher encouraged learners to respond in full sentences. |

Level 2 explanation | PSTs identify the classroom occurrences and provide explanations for them. | Explanations of events. |
This was to encourage children to answer questions in full in order to build their communication skills. |

Level 3 suggestion | PSTs go beyond identifying and providing explanations for classroom occurrences to analysing classroom experiences and suggesting alternatives. | Alternative suggestions. |
Other strategies such as using a spider diagram could have made her lesson more interesting and easier. |

Level 4 reflectivity | PSTs engage dialogically with the classroom event, analysing it from different perspectives. | PSTs engage dialogically with the classroom event, analysing it from different perspectives. |
I shouldn’t have put together addition and subtraction because learners were not really focused and couldn’t understand the subtraction part, they needed it to be done separately. These two [ |

We used the FLRM that we developed to analyse our data. Each statement written by the PST was broken into small chunks of single ideas to allow for coding. The chunked data was levelled against the levels of reflection in the FLRM. The PSTs’ reflections were either general or mathematical, which led us to code each idea as such. General reflections referred to reflections that were not specific to the teaching and learning of mathematics but generally applicable to the teaching and learning of any subject, for example ‘The teacher put learners in groups of four’. A reflection was deemed to be general when the PST did not make mention of mathematical concepts, terms, symbols, numbers, or mathematical ideas.

We referred to mathematical reflections as reflections that were specific to the teaching and learning of mathematics. These were evidenced by explicit mention of the mathematical concepts, terms, numbers, symbols or ideas, for example ‘The teacher wrote 39+9 on the board’, or when an implicit reference is made to mathematical terms, numbers, symbols or ideas, such as ‘The learners did this activity in groups’. If the activity that is described before this statement was mathematical, then the reflection also becomes mathematical because of the reference. Following a process of repeated refinement of codes we settled on the codes in

Summary of codes developed from the analytical tool and data.

Code description | Code |
---|---|

General Description | GD |

General Description Followed by Explanation | GD^{→E} |

Mathematical Description | MD |

Mathematical Description Followed by Explanation | MD^{→E} |

(Simple) General Expalanation | GE |

Expanded General Expalanation | GE^{e} |

(Simple) Mathematical Expalanation | MD |

Expanded Mathematical Expalanation | MD^{e} |

General Suggestion | GS |

General Suggestion Followed by Explanation | GS^{→E} |

Mathematical Suggestion | MS |

Mathematical Suggestion Followed by Explanation | MS^{→E} |

General Reflectivity | GR |

Mathematical Reflectivity | MR |

GD, General Description; GD^{→E}, General Description followed by explanation; MD, Mathematical Description; MD^{→E}, Mathematical Description followed by explanation; GE, Simple General Explanation; GE^{e}, Expanded General Explanation; ME, Simple Mathematical Explanation; ME^{e}, Expanded Mathematical Explanation; GS, General Suggestion; MS, Mathematical Suggestion; MS^{→E}, Mathematical Suggestion followed by explanation; GR, General Reflectivity; MR, Mathematical Reflectivity.

We identified the codes that have an arrow with ‘E’ as indicative that the reflection was followed by an explanation. For example:

‘[^{→}E, to help the child that did not understand ME.’ (Lutho, ROP1, DDM, ref 44–45)

‘A simple explanation is when the rationale given was a statement with only one idea (like the one above). The expanded explanation was a rationale with more than one idea. For example:

‘I shouldn’t have put together addition and subtraction MS^{→E}, because learners were not really focused and couldn’t understand the subtraction part, they needed it to be done separately ME^{e}.’ (Bonga ROP2, ref 80–81)

As in the establishment of the levels of RP and the indicators thereof, these codes were similarly developed after several rounds of coding by the authors of the article along with a third researcher who was brought in to assist in establishing whether our coding and indicators were sufficiently recognisable to others to enable consistent coding across researchers. Some initial differences in coding resulted in further refining and clarification of the codes until there was general agreement between the researchers’ coding. Thereafter the first author of this article coded each of the four PSTs’ reflections. The second author served to check agreement with the coding and small discrepancies were resolved through discussion and through reverting to the indicators and providing further clarification where necessary. Below we present the comparisons we made for each of the four PSTs (in alphabetical order of their pseudonyms).

In this section we share both quantitative and qualitative data from our coding of two sets of reflections written by PSTs a year apart. The tables in each figure capture the quantitative descriptive statistics following the coding of all the written reflections, according to levels of reflection and according to mathematical versus general reflections. The pie charts following the tables compare the PSTs’ general versus mathematical reflections on each set of data.

Following the figures that summarise each of the four PSTs data we provide selected qualitative data that exemplifies and illuminates shifts from the first (ROP1) to the second (ROP2) written reflections.

Comparing Bonga’s 2018 and 2019 reflections on his own practice.

While we see a small decrease in the total number of ideas that were coded in Bonga’s ROP1 (100) to the number of ideas in ROP2 (92),

In ROP2 across the lenses, Bonga supported a few more of his mathematical descriptions with explanations. Excerpt 1 below provides an example of his reflections on MMI in ROP1 and ROP2 to illuminate the modest shift towards increased explanation. No suggestions were provided in either ROP1 or ROP2 for the lens of MMI. We have highlighted the explanations in both:

‘In this lesson I planned to teach learners bonds of 15 (MD). I wanted learners to come up with two numbers that can be added to make up the number 15 (MD). Each learner would raise a hand (GD) and give the two numbers (MD), explain to the class how they calculated it (MD). Learners had to justify their answers by explaining to the class (MD^{→E}) This was for helping them to have number sense, to help them with addition (ME^{e}) Aims of this lesson was to equip my learners with ‘adding on’ instead of starting from 1 when adding (MD). As learners were explaining how they arrived at making 15 with two digits (MD), I helped them to start with the larger number instead of small number to do so (MD).’ (Bonga ROP1, MMI, ref 1–10)

‘In this lesson I taught learners bonds of 15 (MD^{→E}). This was to help learners know different numbers that make up the number 15 (ME) so that they can add or subtract faster without counters (ME^{e}). Learners had to come up with 2 digit that would make 15 (MD). This was first done as whole class (GD), learners giving the teacher numbers (MD) and showing how they arrived to their answer (MD). Justifying their answer (MD) and showing their calculations (MD^{→E}) helped learners understand their procedures (ME). Then we did it using a grid (MD). The grid had addition on it (MD^{→E}). We used it [

Through the MMI lens, which is focused on mathematical and meta-mathematical ideas, as expected, the reflections for both ROP1 and ROP2 are predominantly mathematical. Across other lenses we see a shift towards more mathematical than general reflection ideas. The tables and pie charts in

Of particular interest is that all Bonga’s suggestions (L3) are mathematical rather than general. While no suggestions appear in ROP1, several emerge in ROP2. For example, in the Task lens of ROP2 Bonga follows his description of learners using other learners’ fingers to count with: ‘I should have provided counters for my struggling learners’. In addition, following his reflections on each of the six lenses in ROP2, Bonga took the initiative to add a section, namely ‘What would I change?’. Of interest is that all ideas included here are mathematical:

‘I shouldn’t have put together addition and subtraction (MS^{→E}), because learners were not really focused (ME) and couldn’t understand the subtraction part (ME), they needed it to be done separately (MS^{→E}). These two [^{→E}) because I ended up spending more time on addition and very less time on subtraction (ME). Many learners seemed to get confused when I wanted them to subtract (MD). That was not good for the learners (MD). They didn’t learn much from it (MD). I should have stuck with only one (MS).’ (Bonga, ROP2, Beliefs, Ref, 80-87)

In the above paragraph we see that Bonga brings several L1 (descriptions), L2 (explanations), and L3 (suggestions) into dialogue with each other. When these were considered as a whole, we decided that the paragraph constituted an example of L4 reflectivity. Recall that our definition of reflectivity requires that PSTs engage dialogically with the classroom event; it incorporates suggestions that are considered from different perspectives. We noted here that Bonga brings observations, descriptions, explanations, suggestions, and justifications for these into dialogue, constituting L4 reflectivity. Thus, while no single idea is coded as reflectivity, the paragraph as a whole constitutes reflectivity. For this reason, we have placed L4 as separate from the total L1, L2, and L3 ideas coded and we have put NA in the table under the percentage for reflectivity.

As this instance (and two cases in Joy’s reflections) were the only reflections across the data sets that met the indicators for reflectivity, we did not have sufficient data to expand the sensitivity of our coding system for this level of reflection. The idea that multiple ideas together display reflectivity, rather than a single utterance or idea, suggests further consideration is needed in terms of how this L4 of the reflection framework subsumes (is constituted by) L1, L2, and L3 utterances, rather than having its own distinct utterances.

The above shifts suggest that the facilitator-guided reflection sessions may have influenced Bonga’s attention to focus on mathematical learning and teaching aspects of the lesson, and to extend his response to include engaging with some reflectivity, particularly in relation to engaging with suggestions and explanations (or justifications) for these suggestions. This was not however the case across PSTs, as we see in Dumi’s reflections in

Comparing Dumi’s 2018 and 2019 reflections on his own practice.

As seen in

‘First of all, I was walking around the classroom (GD), helping learners who had questions (GD) and those who were stuck (GD). I was addressing them as a group since I grouped them (GD), but I noticed that some of them were confused (GD), I decided to sit with them one on one (GD). The time was a problem (GD^{→E}) because, I ended up spending lot of time with some students (GE) while others were struggling (GD) and I couldn’t finish all of them to see whether they were following the activity (GD). The questions that I was asking to students, some of them were questions like: if you have 12 dominos and added 7 dominos, how many of them in total (MD). I also told them that addition means putting together (MD 68) and subtraction means taking away (MD). Some of the students had questions revolving around how to use the counters (MD). Some they were not familiar on how to use them [^{→E}) so that I can give, there is order in class (GE). Even though the class was a little bit chaotic (GD) when I was busy with a group of students (GD) some would make noise (GD).’ (Dumi, ROP1, Interactions, ref 56–76)

‘Firstly the teacher is explaining the lesson to the whole class (GD^{→E}), reason [^{e3}). He grouped them into three groups (GD) and gave each group different task (GD) and material to do (GD) and use (GD^{→E}). Reason is that he was developing different strategies for each group (GE). Teacher is moving to each group (GD^{→E}) to ensure that everyone understand the instructions and they are doing what they supposed to be doing (GE^{e2}). The teacher is asking learners during the lesson in each group questions such as: show me how did you do it? Double check is the answer is right, how did you calculate it? (GD^{→E}) Reason is that he wants them to make sure that they know how they got the answer. He also wants them to self-correct themselves (GE^{e}). He kept on saying yes as his response (GD^{→E}) to show that he is listening to the learners and he wants them to carry on (GE^{e2}). He encourages learners to do different sums (MD^{→E}) to develop different strategies of calculating and understanding the operations (GE^{e2}). Teacher also instructing learners to help each other (MD^{→E}). Reason for this is some learners understand it better when they get help from peers and some are developing confidence in mathematics (ME^{e3}). He encourages them by saying good to learners who are doing well (GD^{→E}) reason for this he wants them to give their best and even if they fail, they cannot be afraid to try hard (GE^{e2}). He also instructs learners to recount when they have forgotten a number (MD^{→E}) so that they remember which number follows what (ME).’ (Dumi, ROP2, Interactions, ref 1–20)

In terms of the mathematical and general foci, there was an unexpected shift away from reflecting on mathematical events towards more general events. The mathematical reflections decreased from 59% in 2018 to 41% in 2019. This could be a result of the keen interest he displayed in the lens of interaction with students, which generally motivates reflections that are more general than mathematical (see Chikiwa & Graven,

Comparing Joy’s 2018 and 2019 reflections on her own practice.

Unlike Bonga and Dumi, there was an increase in the quantity of Joy’s coded ideas from 58 in ROP1 to 97 in ROP2. Thus, Joy wrote more ideas about her teaching after the facilitator-guided sessions. Joy’s reflections shifted steadily to higher levels after the series of facilitator-guided sessions. As seen in

‘Rote counting in 10s (MD). Mental maths activity – number plus 2 (MD), Measuring desks using pencils (MD). Writing down their measurement observation in their workbooks (MD). I asked the learners leading questions (GD^{→E})so as to scaffold them (GE). Sometimes the learners would not understand what answer I was looking for (GD). In rote counting, as mentioned before some of the learners were not counting correctly (MD) or even counting at all (MD). But that was difficult for me to pick up (MD). By doing the mental maths activity (MD^{→E}) they got to revise on their addition skills (ME). They did the measuring activity (MD^{→E}) so that they got to see how many pencils can fit into the length of their desk (ME) They should have written their observation in their workbooks (GS^{→E}). The benefits of this are they get to connect what they observe with writing it down, a form of report (GE).’ (Joy, ROP1, Tasks, ref 29–43)

‘I introduced the task by asking questions (MD^{→E}) so that I could see how much they knew about measurement (ME). The responses were accurate (GD) but only came through once I started asking leading questions (GD). This showed me that they had an idea of what measurement was (MD) but did not connect the concept to their prior knowledge (MD). I then demonstrated what I wanted them to do by using the board (GD) instead of using a desk and a pencil which they were also using for measuring (MD). Using the board may have confused some of the learners (MD^{→E})because I just started to [^{e}).’ (Joy, ROP2, Tasks, ref 37–63)

‘I used the board (GD^{→}E) because I wanted the entire class to see what I was demonstrating (GE), but in the process, I took it for granted that I was starting in the middle of the entire board (GD). A clearer demonstration could have avoided this (GS) paired up with a clearer instruction (GS). Using this practical way of teaching could be beneficial to the learners (GS^{→}E) because they can see and do what I am explaining in the abstract (GE^{e}). Demonstrating how to measure would have been ideal (MS^{→}E) because they would ideally be able to link it to daily activities of measurement (ME).’ (Joy, ROP2, Tasks, ref 37–63)

‘The potential shortfall is the form in which I communicated the instruction (GS^{1}^{→E}) was to create a link between measuring and recording (ME). However, next time I would combine the recording with the measuring (MS^{→E}) so as to improve this part of the lesson (ME). I will ask one learner to measure (MS) and the other to record (MS^{→E}). This is because the time between them measuring and me handing out their books may be too long for others to remember what they had measured (ME^{e}).’ (Joy, ROP2, Tasks, ref 37–63)

Elaborating in ROP2, Joy followed most of her described classroom events with a rationale or explanation. She further made several mathematical and general suggestions for improving future instruction whereas in ROP1 she had only provided a single general suggestion. In ROP2 she reflected with intention to improve instruction, which we see as probably a result of participation in the facilitator-guided sessions. We also found that in ROP2 Joy wrote two reflections at L4: GR (highlighted in the excerpt above) and MR. As mentioned in Bonga’s section, L4 reflectivity constitutes a collection of reflections (description, explanation, and suggestion) that together are in dialogue with each other and at the level of paragraph.

The second and third paragraphs in ROP2 above point to possible instances of reflectivity. In the first instance of reflectivity, Joy is having a dialogue with herself about how she used the board in a manner that hindered the learners’ conceptual understanding of measurement. She ends the dialogue with a proposal that carrying out a demonstration accurately would have helped learners to link measurement with daily activities. In the second instance of reflectivity, Joy again enters self-dialogue, reflecting on the ‘less than ideal’ way she taught the learners. She provides her reason for her judgement and suggests a way forward also backed by reason. The excerpts provide some examples of the qualitative shifts in Joy’s reflection between the two years. The proportion of mathematical (versus general) reflections remained relatively consistent across ROP1 and ROP2 at 63% to 59%.

Comparing Lutho’s 2018 and 2019 reflections on her own practice.

There was a small increase in the quantity of Lutho’s reflections between 2018 and 2019, from 61 to 63. In ROP2 more attention was paid to some lenses while attention was removed from others. For example, Lutho’s MMI reflections increased from 8 in 2018 to 14 in 2019, while her reflections on interaction halved from 12 in 2018 to 6 in 2019. As in Joy’s case, we noticed steady shifts from the lower levels to higher levels of reflection. As seen in

‘The teacher brought forward the money concept (MD). The aim was to teach about the currency used in SA [^{→E}) to acquire concrete understanding (GE). In her teaching she incorporated addition (MD) when asking children how much money is needed to produce a certain amount (MD).’ (Lutho, ROP1, MMI, ref 1–8)

‘[^{→E}) for the children to see (GE). Using the chart (MD^{→E}) allows them to link the pictures that are in the chart and the manipulatives that are in front of them (ME). Nonetheless, she could have allowed the children to explore the manipulatives themselves before she showed them the chart (MS^{→E}) to check how much understanding of money do they already have (ME). She allows the children to find the correct currency by themselves (MD) after seeing the picture of that currency (MD^{→E}). This helps the children to acquire concrete understanding of what the different currencies look like (ME). On the other hand all children with different intelligences are catered for (GD).’ (Lutho, ROP2, MMI, ref 1–14)

The overview of the four PSTs’ reflections shows that for all PSTs there was an increase in the proportional percentage of ideas that went beyond L1 descriptive reflections. Thus, there was a greater proportion of explanations (L2) and suggestions (L3) from ROP1 to ROP2 for all four of the PSTs, other than Dumi, whose percentage of suggestions remained relatively constant (6% in ROP1 and 5% in ROP2). Two of the PSTs, Bonga and Lutho, had not provided any suggestions in ROP1 and provided several in ROP2. Furthermore, while no examples of L4 reflectivity reflections were found in ROP1, in ROP2 three examples are found in which Bonga and Joy each engaged with descriptions, explanations and suggestions in a dialogic way that met our definition of reflectivity.

As far as the mathematical versus general balance of reflections is concerned, despite the explicit orientation in facilitator-mediated sessions towards a focus on mathematical rather than generic observations of lesson events, only Bonga’s and Lutho’s mathematical reflections shifted upwards. Bonga’s mathematical reflections increased significantly, from 55% to 84%, while Lutho had a shift from 57% to 63%. The other two PSTs’ proportional focus on mathematical ideas decreased slightly from ROP1 to ROP2, although only for Dumi did this result in his focusing more on general than mathematical ideas in ROP2 (59% general vs 41% mathematical). For all others, mathematical reflections continued to dominate over general reflections (59%, 63% and 84% for Joy, Lutho and Bonga).

The above suggests that the facilitator-guided reflections (and perhaps the increased experience in both practicum and studies) supported shifts towards increased explanation and suggestion for the PSTs in ROP2. This said, descriptive (L1) reflections still dominated at between 63% and 77% of PSTs’ coded reflection ideas in ROP2.

Thus, across the four PSTs, reflections were still predominantly at the lowest level of reflection (description) with only modest shifts for some towards a greater proportion of higher-level reflections. This suggests that while small-group, facilitator-guided reflection sessions may be helpful in supporting some PSTs to provide occasional suggestions and instances of reflectivity, more work is needed if we wish to shift PSTs’ RP towards the deeper reflectivity needed for strengthening MKfT and allowing for transformation of practice. Therefore, while our findings provide some support for the finding of Johns (

A limitation of this research, especially in terms of the empirical contribution, is the small number of students in the sample, and the fact that the videos to which they responded in their reflections were of their own practice, while the facilitator-guided sessions featured the practice of other teachers. If the students had reflected on other teachers’ practice after facilitator-guided sessions, the results may have been different, although we do not expect this to be the case. We did not at the time deem it feasible to ask PSTs to do additional written tasks as they were busy with other assignments and courses. Alternatively, had the facilitator-mediated sessions focused on videos of their own teaching, shifts towards increasing proportions of higher levels of reflections may have appeared. An additional limitation is that as time passed between the gathering of the data on the two sets of reflections one cannot claim that the shifts are a result of the facilitator-led session and not general experiences in their studies that might have supported strengthened RP. Furthermore, we did not qualitatively code differences in various reflections within the levels of description, explanation and suggestion other than to distinguish between those that were relatively simple and those that were expanded on and connected to further explanation (as shown in

A contribution of the broader study is our adapting and developing a coding system for reflections in a way that might usefully reflect South African PST shifts in reflection. In our study the lecturer used Karsenty et al.’s (

Considering the limitations noted above, we have only tentative recommendations that build on the insights emerging from the study. The first is that, recognising the complexity and difficulty of developing RP, PTE needs to find ways to provide opportunities to model high levels of RP across multiple PST course offerings and opportunities for facilitator-led mediation of PSTs’ observations and reflections. Tools such as the SLF (Karsenty et al.,

This work is based on research supported by South African Research Chairs (SARCH) initiative of the department of Science and Technology and the National Research Foundations (Grant Number, 74658).

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

M.G. and S.C. collaborated on the published work. Both made a substantial contribution to conceptualisation and design, acquisition of data, analysis and interpretation of data, and drafting of the manuscript. M.G. further critically revised it for important intellectual content and approved the final version to be published.

Ethical clearance to conduct this study was obtained from the Rhodes University Faculty of Education Higher Degrees’ Committee (no. 2017.12.08.06.)

The data that support the findings of this study are available on request from the corresponding author, S.C.

The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of any affiliated agency of the authors.

In identifying the event as a shortfall, she is implicitly suggesting she needs to improve the way she instructs learners.