Policy Enactmentin Primary Mathematics05 December 2017

Nicholas WollastonUCL Institute of Education

Interview #108: A teacher positions herself in relation to policy

Analysis of “Interview #108”Presentation Overview

• A bit about me: PhD Student/Research Officer• Theory: Policy Enactment and Maths Education• Methodology: How did I analyse?• Findings: The teacher draws on four areas of

discourse in accounting for her practice• Evaluation: What worked, and what didn’t?

A bit about Me

• Former Primary Teacher and School Leader• MRes Student at IoE (Full time)▫ Teaching of Subtraction in two Primary Schools

• PhD Student at IoE (Part time)▫ Teaching of Calculation in Primary Schools in

England since Liz Truss criticised the Grid Method• Research Officer at IoE (Part time)▫ KS2 Maths Test Preparation Project

KS2 Maths Test Preparation Project

• High stakes testing and its consequences• New National Curriculum in 2014• Changes to KS2 SATs in 2016• Interviews with 30 Y6 teachers (24 schools)▫ Spring/Summer 2015: before the new NC for Y6▫ Summer 2016: After the new tests in Y6

• How do teachers say their teaching has changed since changes in the tests were introduced?

PhD: Discourse Theoretic Analysis• Policy as Text

• Policy as Discourse (e.g. of ‘standards’)▫ seeks to deny us a language to challenge the

assumptions inherent within the discourse itself

“Social Constructionist line […] taking policy as discourse as it basis. It makes us think about the ways in which we have been positioned to think of education in certain ways. It notes the mechanisms by which policy performs certain functions.” (Adams, 2014, p34)

Policy as Text?

• Some texts are never read first hand▫ 7% of maths teachers had never read any National

Curriculum documents in a study of the Mathematics National Curriculum (Ball, 1993).

• Head teachers are often key mediators of policy▫ “Policies do not normally tell you what to do; they

create circumstances in which the range of options available in deciding what to do are narrowed or changed.” (Ball, 1993, p12)

Policy as Discourse?• In professional decision-making, action is

embedded in certain ways of seeing the world that stem from culture.

• We therefore need to examine▫ the uses of and effects of policy in relation to the

influences▫ ways in which policy is deployed professionally▫ social conditions which have created the language

used in the policy itself.(Adams, 2014, p34)

‘Policy Enactment’“An understanding that policies are interpreted and ‘translated’ by diverse policy actors in the school environment, rather than simply implemented.” (Braun et al., 2010, p549)

“Policy enactment involves creative processes of interpretation and recontextualisation – that is, the translation through reading, writing and talking of text into action and the abstractions of policy ideas into contextualised practice.” (Braun et al., 2010, p549)

Policy Enactment Roles

• Ball et al. (2011) suggest that teachers take up a variety of positions with regard to ‘enactment’▫ Narrators▫ Entrepreneurs▫ Transactors▫ Enthusiasts▫ Translators▫ Critics▫ Receivers

Research in Mathematics Education

• Teaching Orientations▫ transmission, discovery, connectionist (Askew,

Brown et al. 1997)

• Mathematical Knowledge and Understanding▫ Procedural, Conceptual (Hiebert & Lefevre, 1986)▫ Relational, Instrumental (Skemp, 1987)

Number Sense requires Conceptual Knowledge (e.g. magnitude) and Relational Understanding (e.g. comparisons)

Theoretical Coding: Policy Enactment

• Policy Implementation▫ Expressing disquiet, Satisfaction, School policy.

Government policy, Policy conflict, Reluctant compliance, Embracing change, Refusal

• Policy Implementation Roles▫ Narrator, Entrepreneur, Transactor, Enthusiast,

Translator, Critic, Receiver• Performativity▫ High stakes testing, pressure, results, good teacher

• Teacher Role▫ Curriculum implementation, Test preparation, Wider

teaching role, Interviewee

Theoretical Coding: Maths Education

• Teaching orientations▫ Transmission, Discovery, Connectionist

• Mathematical Understanding▫ Procedural, Conceptual, Relational, Instrumental

• Calculation Methods▫ Mental Strategies, Repeated Addition, Grid Method,

Extended Methods, Formal Written Algorithm, Progression in Calculation

• Resources▫ National Curriculum, NNS, Sample Papers, Old SATs

papers, Commercial tests, Textbooks, Revision books, Other guidance material, Concrete Apparatus, Pictorial representations

Findings

• Teacher draws on four main areas of discourse▫ National Curriculum▫ Other guidance e.g. NCETM website▫ Ensuring mathematical understanding▫ KS2 SATs

• This presentation will focus on coding for ▫ Teaching orientations▫ Mathematical knowledge and understanding

Findings: National Curriculum• Raised expectations• Cramming of new content• Teach ‘content’ far later in year• Delayed ‘revision’ programme

“We were still in a point though, this year, when we were still teaching content after the Easter break. Now that is usually unheard of, you know, usually it’s very much you teach a heavy, heavy, heavy, bulk of your number, calculation and things like that, and usually from the February half-term, or even just a few weeks after the Easter break is your revision. And we weren’t in that position this year, we just weren’t there.” (#108, p21)

Findings: National Curriculum• Move from preferred connectionist orientation to

transmission• Suggests more instrumental rather than relational

understanding

“Well we always go through at the very beginning, ensuring there was a solid written method for each of the four operations. Of course these have been more formalised methods this year, so we’ve bypassed, where in previous years we’d stay with chunking for example, we bypassed that and introduced long division, long multiplication, column addition and column subtraction are all pretty standard, coming up through the school, so that’s been a change.”(#108, p2)

Findings: Other Guidance• NCETM et al.• Role of Maths Coordinator• Dissemination to other staff

“I’m maths coordinator, so I’ve done a lot of research looking at actually how you can put that across using place value counters...” (#108, p2)

“OK. I mean I’ve read various aspects of that, you know, so I mean I mentioned the mastery documents from the NCETM, sort of introduced those as a guide for other members of staff to look at use of it, so I suppose we are aiming to take it as a school…” (#108, p5)

Findings: Ensuring Understanding

• Visualising and Conceptual Understanding

• Connections

• Multiplication

• Fractions

Findings: Ensuring Understanding• She expresses a preference for teaching which helps

children to visualise

“I think content wise yes, so there’s been, looking at using the bar method representations has been something that I’ve been trying to develop through the school […]. So that’s on-going and developing, it’s not a result of these tests, it’s a result of wanting children to actually have a depth of knowledge and understanding and for them to get it.” (#108, p18)

Findings: Ensuring Understanding• She values the connections between the various

areas mathematics

“It’s being able, not only to do something, you know, there’s being able to carry it procedurally, there’s being able to carry out very formulaic problems if you like, but there’s that ability then to make those connections, I think, if you’ve mastered it, and mastery itself means you, the child is making connections between the different things that they’ve learnt…” (#108, p5)

Findings: Ensuring Understanding“Where we teach something, we go back over it, we revisit it, we apply it to a problem, we do a gap analysis, right this group needs to come and work here, and it’s…we’ve worked in the same way in that essence, you know, so we’ve taught it, we’ve looked in books, how they achieve with the lesson, how do they feel about it, right, there are gaps here, let’s close it, there’s gaps there, we need to intervene, you’ll come out with me on that Monday afternoon, you’ll go out with Ann, our learning support assistant, after lunch, you clearly just need ten minutes to practice an extra two. ” (#108, p4)

• Is this procedural or conceptual knowledge?• Is this a transmission approach, rather than a connectionist

approach?

Findings: Ensuring Understanding

• She talks about a ‘knowledge package’ (Ma, 1999) for multiplication▫ place value▫ related multiplication facts

• She goes on to indicate that she values the use of equipment to support understanding, as children move from the more visual Grid Method to the more abstract formal algorithm.

Findings: Ensuring Understanding• An emphasis on the formal algorithm for multiplication

“The biggest changes, you know, in the actual delivery, is because we have to move on to column methods, that’s been the biggest drive, the biggest change […] And it’s been sped up a bit more hasn’t it, because children are expected to do these methods much sooner, and you know, where ordinarily this would not be something that we would be doing. So I wouldn’t say that we’ve necessarily changed the methods as such, but we are doing a lot more a lot sooner, and yes, in year six, in year five, new stuff for us is delivering as a teacher.” (#108, p15)

Findings: Ensuring Understanding

• She places a great deal of emphasis on this change to a focus on formal algorithms, repeatedly using the word ‘biggest’

• She indicates her desire that this is done through a progression of methods which promotes understanding.

• Is the use of the word ‘delivering’ indicative of a of a transmission approach to teaching?

Findings: Ensuring Understanding• Procedure for long multiplication▫ Children’s difficulties with procedural knowledge

“What I’ve found interesting this year is with the written calculations they’ve found long multiplication more tricky than long division, and I find that very…bizarre, and I think it’s probably the use of the place holder when you are multiplying it by your tens number, and things like that, but that’s been something, so quite a few of them have stumbled there.” (#108, p19)

Findings: Ensuring Understanding

• Fractions

“This year all things fractions, percentages and decimals, most certainly, most certainly, that was a big, big, big focus. Purely for the amount of depth and the amount of additional knowledge and understanding the children needed to have, so most certainly.” (#108, p20)

Findings: Ensuring Understanding• Fractions taught with a focus on procedural knowledge• Abandoned previously described ‘connectionist’ orientation• Deliberate choice to teach the methods in isolation from each other• This ‘transmission’ orientation, teaching of procedures separate from

each other, risks leading to ‘instrumental understanding’

“Um…well I mean the calculating with fractions, it’s an awful lot to have to add, subtract, multiply, divide, there are different rules for each of them, different ways of representing each of them, and having to teach them all one after the other, trying to separate it out a little bit, you know, much in the way that you would initially teach area and perimeter separately for example because they are often the, who can remember which one does which side of things, so that’s been a big sort of focus.”(#108, p21)

Findings: Ensuring Understanding• Expresses her dissatisfaction at▫ overlooking the relationships▫ teaching procedures in a more fragmented way

• in the run up to KS2 SATs

“And actually closing the gap between understanding fractions has been, in particular the link between fractions, percentages, decimal numbers, just having that interplay of being able to convert, find equivalents, mixed numbers, to improper fractions, a lot of groundwork had to go into looking, finding the gaps, and packing those in right up towards the test, it was right, you times that by that, and that goes there and that goes there, and that’s how you get the answer. So it’s been not the best way to teach in that very last lead up to the tests.” (#108, p2)

Findings: KS2 SATs

• Changes in the tests lead to changes in practice

“The big change I suppose was a lot more regular arithmetic tests given rather than practising the mental maths, so one’s been switched for the other if you like.” (#108, p2)

Findings: KS2 SATs• Teaching to the Test

“I’m very stubborn and taught year six the past nine years or so, been very adamant that I wouldn’t teach to a test and want to teach using visual, pictorial, representations. We sort of got to a certain point in the year where unfortunately yes we had to learn a few roles shall we say, in order to make sure we could meet the requirements with the arithmetic papers and things like that, so yes, there has been a difference there in that sense…” (#108, p1)

Findings: KS2 SATs• Impact on Teaching

“And then actually they’ve probably struggled a little bit more with areas where you would expect them to ordinarily have used mental calculation strategies because coldly speaking there were more marks available on the arithmetic paper, so we’ve made sure that they can do all of those column methods, not at the cost of mental strategies but the limelight has been less so on them...” (#108, p19)

Findings: KS2 SATs• Cramming

“And actually closing the gap between understanding fractions… […] a lot of groundwork had to go into looking, finding the gaps, and packing those in right up towards the test, it was right, you times that by that, and that goes there and that goes there, and that’s how you get the answer. So it’s been not the best way to teach in that very last lead up to the tests.” (#108, p2)

Findings: KS2 SATs• Gaming Strategies

“Playing the game of knowing where the majority of marks will come from is where things have heavily gone in, but I think you could easily say that’s done in every year, but just the standards are ridiculously high.” (#108, p4)

“Well yeah, most certainly, you can play the odds as well sometimes, if you know what’s come up in previous years, you might sort of feel there hasn’t been a real hone in or focus on use of a pie chart, there’s always been that, that’s more like bookies making their bets isn’t it, nothing more than that.”(#108, p17)

Findings: KS2 SATs• Impact on Understanding…

▫ Reduces longer term learning gains▫ For example , calculate the area of a rectangle 3.3m by 4.2m, procedure for multiplying decimals seemingly with a transmission orientation

▫ Questions whether the children will remember it a few weeks later▫ Reluctant compliance with this type of teaching

“I have been teaching them this year to actually multiply these out, so…they don’t look very nice as decimal numbers but because we could actually multiply those both by making both ten times bigger we could effectively do thirty three multiplied by forty two… […] They could do that. And then they could divide it back down, that would be a strategy taught this year. Whether they do it or not is a whole other matter, that’s been a few weeks, and we’ve been in the Isle of Wight and we haven’t taught maths because all we’ve done is writing this last week. We’ve been playing the game all year.”(108, p12)

Evaluation: Teaching

• Codes for transmission, discovery, and connectionist were useful in identifying different approaches to the teaching of calculation▫ Discovery orientation was not found in this

interview▫ Contrast between the transmission and

connectionist orientations was illuminating.

Evaluation: Understanding

• Codes for Procedural and Conceptual Knowledge, Relational and Instrumental Understanding▫ It was possible to distinguish between these four

categories▫ Some extracts were ambiguous or difficult to code

Evaluation: Teaching & Understanding

• Evidence of some association between the codes for understanding and the codes for teaching orientation▫ e.g. between the transmission orientation and

procedural understanding.• Occasions when responses focussed solely on

teaching or solely in learning▫ seems sensible to retain the use of both of these

sets of codes

References• Adams, P. (2014). Policy and education, Routledge.• Askew, M., et al. (1997). Effective teachers of numeracy, London: Kings College.• Ball, S. J. (1993). "What is policy? Texts, trajectories and toolboxes." The Australian

Journal of Education Studies 13(2): 10-17.• Ball, S. J., et al. (2011). "Policy actors: Doing policy work in schools." Discourse: Studies in

the Cultural Politics of Education 32(4): 625-639.• Braun, A., et al. (2010). "Policy enactments in the UK secondary school: Examining policy,

practice and school positioning." Journal of education policy 25(4): 547-560.• Hiebert, J. and P. Lefevre (1986). Conceptual and Procedural Knowledge in Mathematics:

An Introductory Analysis. Conceptual and Procedural Knowledge: The case of Mathematics. J. Hiebert. Hillside, NJ, Lawrence Erlbaum Associates.

• Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States, Lawrence Erlbaum Associates Mahwah, NJ.

• Skemp, R. R. (1987). The psychology of learning mathematics. Hillsdale, N.J. ; Hove, Lawrence Erlbaum.