Policy Enactment in Primary Mathematics 05 December 2017 Nicholas - - PowerPoint PPT Presentation

Policy Enactment in Primary Mathematics

05 December 2017

Nicholas Wollaston UCL Institute of Education

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

Analysis of “ Interview #108”

Present at ion 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

KS 2 Maths Test Preparation Proj ect

• 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

▫ transm ission, discovery, connectionist (Askew, Brown et al. 1997)

• Mathematical Knowledge and Understanding

▫ Procedural, Conceptual (Hiebert & Lefevre, 1986) ▫ Relational, Instrum ental (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 w ere still in a point though, this year, w hen w e w ere still teaching content after the Easter break. Now that is usually unheard of, you know , usually it’s very m uch you teach a heavy, heavy, heavy, bulk of your num ber, calculation and things like that, and usually from the February half-term , or even just a few w eeks after the Easter break is your revision. And w e w eren’t in that position this year, w e just w eren’t there.”(#108, p21)

Findings: National Curriculum

• Move from preferred connectionist orientation to

transmission

• Suggests more instrumental rather than relational

understanding “ Well w e alw ays go through at the very beginning, ensuring there w as a solid w ritten m ethod for each of the four operations. Of course these have been m ore form alised m ethods this year, so w e’ve bypassed, w here in previous years w e’d stay w ith chunking for exam ple, w e bypassed that and introduced long division, long m ultiplication, colum n addition and colum n subtraction are all pretty standard, com ing 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 m aths 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 m ean I’ve read various aspects of that, you know ,

so I m ean I m entioned the m astery docum ents from the NCETM, sort of introduced those as a guide for other m em bers of staff to look at use of it, so I suppose w e are aim ing 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 w ise yes, so there’s been, looking at using the bar m ethod representations has been som ething 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 w anting children to actually have a depth of know ledge 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 som ething, you know , there’s being able to carry it procedurally, there’s being able to carry out very form ulaic problem s if you like, but there’s that ability then to m ake those connections, I think, if you’ve m astered it, and m astery itself m eans you, the child is m aking connections betw een the different things that they’ve learnt…”(#108, p5)

Findings: Ensuring Understanding

“ Where w e teach som ething, w e go back over it, w e revisit it, w e apply it to a problem , w e do a gap analysis, right this group needs to com e and w ork here, and it’s…w e’ve w orked in the sam e w ay in that essence, you know , so w e’ve taught it, w e’ve looked in books, how they achieve w ith the lesson, how do they feel about it, right, there are gaps here, let’s close it, there’s gaps there, w e need to intervene, you’ll com e out w ith m e on that Monday afternoon, you’ll go out w ith Ann, our learning support assistant, after lunch, you clearly just need ten m inutes to practice an extra tw o. ” (#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 w e have to m ove on to colum n m ethods, that’s been the biggest drive, the biggest change […] And it’s been sped up a bit m ore hasn’t it, because children are expected to do these m ethods m uch sooner, and you know , w here ordinarily this w ould not be som ething that w e w ould be doing. So I w ouldn’t say that w e’ve necessarily changed the m ethods as such, but w e are doing a lot m ore 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
• f 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 w ith the w ritten calculations they’ve found long m ultiplication m ore tricky than long division, and I find that very…bizarre, and I think it’s probably the use of the place holder w hen you are m ultiplying it by your tens num ber, and things like that, but that’s been som ething, so quite a few of them have stum bled there.”(#108, p19)

Findings: Ensuring Understanding

• Fractions

“ This year all things fractions, percentages and decim als, m ost certainly, m ost certainly, that w as a big, big, big focus. Purely for the am ount

• f depth and the am ount of additional know ledge

and understanding the children needed to have, so m ost 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 …w ell I m ean the calculating w ith fractions, it’s an aw ful lot to have to add, subtract, m ultiply, divide, there are different rules for each of them , different w ays 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 , m uch in the w ay that you w ould initially teach area and perim eter separately for exam ple because they are often the, w ho can rem em ber w hich one does w hich 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 betw een understanding fractions has been, in particular the link betw een fractions, percentages, decim al num bers, just having that interplay of being able to convert, find equivalents, m ixed num bers, to im proper fractions, a lot of groundw ork had to go into looking, finding the gaps, and packing those in right up tow ards the test, it w as right, you tim es that by that, and that goes there and that goes there, and that’s how you get the answ er. So it’s been not the best w ay to teach in that very last lead up to the tests.”(#108, p2)

Findings: KS 2 S ATs

• Changes in the tests lead to changes in practice

“ The big change I suppose w as a lot m ore regular arithm etic tests given rather than practising the m ental m aths, so one’s been sw itched for the

• ther if you like.”

(#108, p2)

Findings: KS 2 S ATs

• Teaching to the Test

“ I’m very stubborn and taught year six the past nine years or so, been very adam ant that I w ouldn’t teach to a test and w ant to teach using visual, pictorial,

• representations. We sort of got to a certain point in

the year w here unfortunately yes w e had to learn a few roles shall w e say, in order to m ake sure w e could m eet the requirem ents w ith the arithm etic papers and things like that, so yes, there has been a difference there in that sense…”(#108, p1)

Findings: KS 2 S ATs

• Impact on Teaching

“ And then actually they’ve probably struggled a little bit m ore w ith areas w here you w ould expect them to

• rdinarily have used m ental calculation strategies

because coldly speaking there w ere m ore m arks available on the arithm etic paper, so w e’ve m ade sure that they can do all of those colum n m ethods, not at the cost of m ental strategies but the lim elight has been less so on them ...”(#108, p19)

Findings: KS 2 S ATs

• Cramming

“ And actually closing the gap betw een understanding fractions… […] a lot of groundw ork had to go into looking, finding the gaps, and packing those in right up tow ards the test, it w as right, you tim es that by that, and that goes there and that goes there, and that’s how you get the answ er. So it’s been not the best w ay to teach in that very last lead up to the tests.”(#108, p2)

Findings: KS 2 S ATs

• Gaming Strategies

“ Playing the gam e of know ing w here the m ajority of m arks w ill com e from is w here 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, m ost certainly, you can play the odds as w ell som etim es, if you know w hat’s com e up in previous years, you m ight sort of feel there hasn’t been a real hone in or focus on use of a pie chart, there’s alw ays been that, that’s m ore like bookies m aking their bets isn’t it, nothing m ore than that.” (#108, p17)

Findings: KS 2 S ATs

• 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 m ultiply these out, so…they don’t look very nice as decim al num bers but because w e could actually m ultiply those both by m aking both ten tim es bigger w e could effectively do thirty three m ultiplied by forty tw o… […] They could do that. And then they could divide it back dow n, that w ould be a strategy taught this year. Whether they do it or not is a w hole other m atter, that’s been a few w eeks, and w e’ve been in the Isle of Wight and w e haven’t taught m aths because all w e’ve done is w riting this last w eek. We’ve been playing the gam e all year.” (108, p12)

Evaluation: Teaching

• Codes for transm ission, 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

Know ledge, Relational and Instrum ental 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

• rientation

▫ 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.