Looking at engagement with representations for the topic of transfer

The rank order difficulty of engagement with TSPCK components for various topics should not be expected to be similar, in that generating TSPCK related to a particular component is unique, as the concept is unique, which requires unique pedagogical considerations. The TSPCK component of representations was experienced by the sample of pre-service teachers as easiest in the topic of transfer. This may be due to the uniqueness of the specific topic of Organic Chemistry. The high scores generated for the TSPCK component of representations, making it the easiest in the rank order as observed, mean that pre-service teachers can select a preferred representation that is specific to the topic of Organic Chemistry and justify their selection from a

teaching perspective. This is different from the general teaching methodology that representations per se are useful in teaching.

In this case of pre-service teachers engaging with representations for transformation of CK in the topic of Organic Chemistry, representations chosen are specific with good conceptual and pedagogical justification. As a result of this finding, the responses in the TSPCK tool for the topic of transfer were re-examined looking for evidence that would support the calculated rank order of difficulty for the component of representations. A particularly interesting finding was that pre-service teachers used representations when engaging with other TSPCK components. Table 6.3 shows cases where representations were used other than in the discussion for the representation component.

Table 6.3: Representations used in other TSPCK components

What can be seen in Table 6.3 is that twelve out of sixteen, or 75% of the sample of pre-service teachers used representations when engaging with other test items related

Pre- service teachers Learner Prior Knowledge Teacher Strategies Curricular Saliency KV X QM X X MMJ X KS X X SA X X LVM X X ANM X NCR X X TS X XS X X TLG X JN X MBN BG IM DG

to learner prior knowledge, curricular saliency and teacher strategies components. Figures 6.1 and 6.2 show extracts of completed TSPCK tools for the topic of transfer for pre-service teachers KS and TLG respectively. These extracts show examples of how most of the pre-service teachers from the sample engaged with the component of representations while engaging with learner prior knowledge and teacher strategies in the topic of transfer.

Figure 6.1: An extract showing the use of representations when engaging with learner

misconceptions

The extract shown in Figure 6.1 shows KS confronting a learner misconception related to learner prior knowledge and used a representation to support the explanation. This extract supports the argument made earlier that the thinking about representations demonstrated by the pre-service teachers is very specific to the CK of the topic, as argued by Ball, Thames and Phelps (2008), rather than being general. In Figure 6.2 an extract from the written response of pre-service teacher TLG shows utilisation of multiple sub-micro representations as part of a conceptual teacher strategy to explain isomers. The component of teacher strategies was the most difficult to engage with in both topics of intervention and transfer. It is possible that TLG made recourse to representations when engaging with teacher strategies, because it was easier to think of representations.

Figure 6.2: An extract showing the use of representations in engaging with teacher

strategies

TLG used representations to come up with a teacher strategy. From the extract shown in Figure 6.3, pre-service teacher QM justifies the sequence of Big Ideas for a test item related to curricular saliency by referring to sub-micro representations.

Figure 6.3: An extract showing the use of representations when engaging with the

The discussion above point to use of the TSPCK component of representations as recourse to express thoughts generated as pre-service teachers in this study engaged with a new topic. Further analysis of representations used in the written responses revealed different levels of representation, specifically symbolic and sub-microscopic shown in Table 6.4. Treagust, Chittleborough and Mamiala (2003) argue that novices do not have the ability to transfer between different levels of representation. One way to assist such novice students is to make different levels of representation explicit. It is interesting that only three pre-service teachers recommended that both symbolic and sub-microscopic representations be used in order to confront a misconception when they were engaging with teacher strategies. These pre-service teachers namely ANM, TS and JN achieved high scores in the TSPCK tool for the topic of transfer.

Table 6.4: Use of different levels of representations when engaging with teacher

strategies Modelling clay Sub-micro representa tion Paper model Computer simulation Ball and stick model QM X IM X SA X LVM X BG X ANM X X X MBN X NCR X TS X X XS X TLG X JN X X KS DG MMJ KV

It therefore seems that pre-service teachers found representations helpful in order to engage with other TSPCK components. This conclusion is drawn from the written responses that showed that the sample found representations to have been the easiest component to engage with for the topic of transfer. The occurrence of representations in other TSPCK components support this conclusion. The discussion above points to the use of representations as a possible tool that enabled engagement in the new topic towards pedagogical transformation.