5. Anna: the ‘young whippersnapper’
5.3 Orchestrating pedagogical discourses about mathematics
discourses about mathematics
Anna is ‘selfishly’ focused on achieving test results and views interruptions to this as an inconvenience. For example, she reluctantly complies with whole-school initiatives such as at the start of the year when the Headteacher asked for Assessment for Learning (AfL) approaches to be introduced:
(A) Well we brought it in probably – oh when were we observed? – third week back after the summer holidays. The first thing David said was, “I want you to put AfL in the classroom.” So I was like, “Oh bugger, how can I do something quickly to keep him happy?” So we did the bronze, silver, gold [trays]. (A-int1)
She claims to have introduced something ‘quickly’ which will ‘keep him happy’, suggesting that she did enough to meet the word if not the spirit of David’s request. She also describes recruiting the children in her attempt to please the Headteacher and Governors. In one lesson, Anna told the class what to do ‘if someone with a snooping eye comes in’ (A-obs7)21 and asks them about their targets, reminding them that these are now stuck in their mathematics books.
It seems that Anna is worked by authoritative discourses to such an extent that she does not have time to do anything other than ‘quickly’ so as to interrupt her teaching as little as possible.
5.3.1
‘I’m guilty of just using skills-base.’
As part of her self-authoring as a competent Year 6 teacher, Anna describes having made the appropriate or necessary pedagogical decisions; for example as a good Year 6 teacher, she adopts a ‘skills-base’ (A-int2) pedagogy which she perceives will guarantee results. Anna articulates that her choice of ‘skills-base’ was not made freely and that it was what she felt she had to do; it was a ‘selfish’ choice to maximise results and something that she
feels ‘guilty’ about. For Year 6 teachers, ‘skills-base’ is the authoritative pedagogical discourse.
As well as being driven to meet an accountability agenda, Anna also authors as working to a secondary-readiness agenda. She says that in Year 6, ‘we’ve got to expect more because we’ve got to take them further’ (A-int1) citing the ways in which pupils will be expected to ‘apply fractions in a numerical sense as opposed to a visual sense’ (A-int1) as another justification for the way in which she teaches. ‘Skills-base’ focuses very much on building pupils’ ‘numerical sense’ of fractions and Anna positions herself as teaching as secondary school teachers do, focusing on what she sees as more challenging. The testing and secondary-readiness agendas are cited by Anna as reasons for adopting ‘skills-base’ in Year 6 and also as reasons to not adopt alternative approaches.
5.3.2
‘It sort of puts a cast of doubt in your mind
… “Oh, Brian never taught it like that!”’
Although I do not know and have never met Brian – I only know of him what Anna has chosen to tell me – Anna regularly refers to him in our discussions and he is an important figure for her. Despite Anna being in post for a year before this research project began, the ghost of Brian remains ever present through the voice and gaze of Zoe, the Year 6 TA, who worked with Brian previously. Anna appears to tell me that she feels constantly judged by Zoe who she describes as comparing her with Brian:
(A) Zoe is fantastic. She is a very experienced Year 6 TA and the teacher who sort of was in here before me oeveryone sings his praiseso and it sort of puts a cast of doubt in your mind. And it was sort of a conversation we’d had, “Oh, Brian never taught it like that!” And sometimes when you see something so clearly it’s really difficult to see how someone can’t see it that way. And that’s where I found myself thinking, I found myself thinking, “Well I get it. Have I made it really hard so they don’t get it?” And yeh, I completely panicked! (A-int1)
Zoe appears in this story as a constant witness to Anna’s teaching and Anna seems to worry that Zoe judges her to be not as good as Brian. Anna opens this story with a confirmation that Zoe is ‘fantastic’ and ‘very experienced’: she is a suitable judge of character and worth listening to. In this extract, having seen herself through the eyes of Zoe, Anna reveals a rare doubt in her own ability to do the job. Whilst she consistently authors as being good at mathematics – she sees the mathematics ‘so clearly’ – the implication here is that she is less good at explaining the mathematics to those who
‘don’t get it’. Brian on the other hand, is positioned as teaching in a different way which did not confuse the pupils, a way which Zoe knows and which provides the yardstick for her judgments of Anna.
Anna aligns herself with James Kennedy and Mr. Jones, positions them as good pedagogues and adopts their approaches. While Brian features in Anna’s narrative about pedagogy, she appears to not know how to align herself with him. This story reveals that Anna is aware that there are better ways of explaining mathematical concepts and that she is worried about a comparison with Brian. Nowhere in our interactions does Anna articulate the pedagogical approach adopted by Brian – or incidentally how her results compare with his – however through the voice and gaze of Zoe, the ghost of Brian lives on.
5.3.3
‘Give them the resources … but that won’t
get us through our SATs will it?’
As part of a lengthy interchange about the use of concrete materials and pictures in the teaching of fractions, Anna authored as able to force such pedagogy upon colleagues teaching lower down the school in order to give children a ‘solid knowledge’ of the topic and prepare pupils for later ‘skills-base’ teaching:
(A) … children should come into upper KS2 with a secure understanding of fractions – and that is putting a lot of pressure on three four [Year 3 and Year 4] and one two [Year 1 and Year 2] – that they introduce them and children have that solid knowledge. (A-int1)
Anna understands that achieving this ‘secure understanding’ of fractions across Year 1 to Year 4 is a tough task for her colleagues – who after all have weaker subject knowledge than her – but it is an important platform upon which Year 6 teachers can build.
I go on to ask Anna whether there is a place for the use of concrete resources such as fraction pieces in Year 6:
(A) I need to stop being so rigid and you know, give them the resources and say, “Get on with it and try and work it out that way!” And let them explore. In a perfect world they’d be able to play with them for a bit and make Pack Man out of them. “OK so there’s Pack Man, lay him on a whole. What does he make up? What does he look like?” ((laughs)) That would be great! But that won’t get us through our SATs will it? … That would be wonderful but there’s always that thought on your shoulder of, ↑“Three weeks ‘til SATs.”↑ (A-int2)
Anna’s self-deprecation that she is ‘so rigid’ in relation to the use of concrete materials suggests that she recognises that her approach is out of step with what might happen ‘in a perfect world’, away from the pressures she experiences daily as Year 6 teacher. It ‘would be wonderful’ for pupils to ‘play with them for a bit’, and in doing so reveals that in her view, resources are merely for play, not building mathematical understanding. Her suggestion that the pupils could ‘explore’ and try to work things out for themselves suggests that Anna sees resources as something that pupils work with independently prior to her teaching fractions in a ‘numerical sense’, as opposed to an approach that could be integrated into her teaching as an essential part of pupils’ development of understanding.
Understanding that Anna views the use of resources as an additional stage to incorporate into her already packed schedule, serves to explain her comments about having little time for this approach. She also returns to her narrative of being forced to teach a certain way which will ‘get us through our SATs’, and as concrete materials cannot be used in tests, these are a pedagogic luxury which she cannot afford to accommodate. Here Anna also draws on irony in her rhetoric – ‘But that won’t get us through our SATs will it?’ – and in her use of ‘us’ and ‘our’ reminds me that the tests are something that both she and the pupils must endure and be successful in. Again, Anna authors as compromised.
I also try to encourage Anna to reflect on when or how images might be helpful in Year 6 teaching:
(A) I’m trying to think of a nice context when they’d be helpful, I was just talking to Julie over a cup of tea and we were just talking about this question on their homework and she was saying how she’s used images to represent the final question with her children. (A-int1)
In responding in this way, Anna says that she was unable to think of a ‘nice context’ of her own. Her use of ‘nice’ is akin to her earlier use of ‘wonderful’ in relation to using concrete materials and again suggests a lack of understanding of this pedagogy which has also been dismissed as unsuitable for Year 6. By describing Julie as using images, Anna positions her as more aligned with teachers from lower down the school who would be expected to do this than with her in Year 6. And in self-authoring as unable to think of an example herself, she positions herself as someone more focused on SATs and results, as more of a Year 6 teacher than Julie.
As in many of her other stories, Anna includes a personal flourish: in this case, her discussion with Julie happens ‘over a cup of tea’. She describes herself as someone collegiate and kind, and as engaging in cosy chats about pedagogy with her colleagues.
5.3.4
‘[It] sounds like a wonderful morning … but
in the build up to SATs is not my priority.’
In our second interview which took place a month before the tests, I notice that Anna is wearing a lanyard with lots of cards attached to it which she informs me are associated with Webb’s Depth of Knowledge (DOK, illustrated in Figure 19), a programme bought in by David. Webb’s DOK is designed to be used in all classrooms across all subjects as it incorporates four levels of generic task-types or questioning techniques (Figure 19). Anna tells me that DOK1 is being used in mathematics lessons across the school as it mirrors the nature of NC2014, an authoritative discourse for all teachers. It also fits easily with her ‘skills-base’ teaching, and she similarly suggests that DOK2 is useful to her.However, when thinking of how to integrate DOK3 Anna says, ‘I mean personally it stumps me’ (A-int2) which is a surprising admission for someone who authors themselves as good at mathematics, and DOK4 ‘sounds like a wonderful morning of maths but in the build up to SATs is not my priority’ (A-int2). As with the use of resources and pictures, it appears that Anna views these pedagogies as an irrelevance as opposed to an opportunity to enhance her teaching and improve pupils’ learning.
Anna suggests that she will have capacity to engage with DOK4 once SATs are over, and also suggests – in response to a discussion about incorporating ‘awe and wonder’ into lessons – that ‘[the pupils] can ‘awe and wonder’ all they like in summer two22!’ (A-int2). As elsewhere, she guiltily prioritises what she must because of the tests, viewing DOK4 as another ‘wonderful’, fun, unnecessary pedagogy that – along with ‘awe and wonder’ – can wait until after the tests when she has more time.
22
Summer two refers to the second half of the summer term. It is the final half term of the year and falls entirely after SATs tests. I did not observe any lessons post-SATs.
Figure 19: Webb's DOK taken from
https://courses.lumenlearning.com/educationx92x1/chapter/webbs-depth-of-knowledge/
Anna’s Headteacher and Governors monitor the adoption of Webb’s DOK shortly before the test date and Anna adapts her practices accordingly:
(A) We’ve got link Governors all walking round on Monday and Tuesday. You’ve got to perform to the camera so there will be problem solving galore going on! But I mean, in terms of [test] preparation and getting them [ready], in my eyes and in my head and in my LSA23’s head, that’s two lessons we could spend hammering multiplication and division for those who apparently don’t have it at the moment. And
getting our level sixes more exposure to the [level] six problems. It just feels like you’re trying to hold sand in a sand timer really, it’s just not happening. It’s very frustrating, very frustrating. (A-int2)
Anna is frustrated by needing to put on a special performance – ‘problem solving galore’ – for Governors so close to the test date. She says that she is too busy to incorporate problem solving into her lessons and would prefer to spend the time ‘hammering multiplication and division’ so that pupils can be successful at this in tests. Zoe, as the embodiment of Brian’s beliefs and ways of working, is positioned as having been in agreement with Anna and this serves to reinforce Anna’s stance. If Zoe (and by association, Brian) agrees with her then she must be right.