Social justice in the mathematics classroom London Review of Education DOI:�10.18546/LRE.14.2.07 Volume�14,�Number�2,�September�2016 Social justice in the mathematics classroom Pete�Wright* UCL Institute of Education, University College London Despite�increases�in�educational�attainment�in�London,�too�many�mathematics�lessons�remain� focused�on�factual�recall�and�procedural�understanding,�resulting�in�disaffection�among�learners.� This�study�reports�on�the�establishment�of�a�research�group,�comprising�five�teacher�researchers� and�myself,�which�aimed�to�challenge�this�situation�through�adopting�a�participatory�action� research�methodology.�By�planning,�teaching,�and�evaluating� innovative�classroom�activities,� the�group�demonstrated�how�making�mathematics�more�relevant�and�meaningful�can�enhance� students’�engagement�and�agency.�The�collaborative�and�mutually�supportive�nature�of�the� group�developed�teacher�researchers’�self-efficacy�in�addressing�issues�of�social�justice�in�their� mathematics�classrooms. Keywords:�social�justice;�mathematics;�participatory�action�research Introduction You� could� be� forgiven� a� degree� of� complacency� towards� the� current� state� of� mathematics� education�in�England�given�apparent�increases�in�attainment�over�the�past�20�years.�The�percentage� of�candidates�achieving� top�grades� (A*�to�C)� in�mathematics� in� the�General�Certificate�of� Secondary�Education�(GCSE)�examination,�taken�at�the�end�of�compulsory�schooling�at�age�16,� has�risen�steadily�from�45�per�cent�in�1995�to�63�per�cent�in�2015.�Children�in�London�schools� outperform�others�across�England.�The�above�measure�of�mathematics�performance�is�currently� 2�per�cent�higher�in�London,�which�has�also�seen�a�significantly�higher�rate�of�improvement�in� GCSE�performance�in�recent�years�than�elsewhere�(GLA,�2014). Yet�these�figures�contrast�with�growing�evidence,�some�of�which�is�presented�in�the�next� section,�suggesting�unacceptably�high�levels�of�alienation�and�disengagement�from�mathematics� among�a�large�proportion�of�learners.�They�also�hide�worrying�differences�in�achievement�between� different�groups�of�learners�that�highlight�persistent�inequities�in�mathematics�education. This�paper�argues�that�the�current�situation�that�predominates�in�mathematics�classrooms,� described�below,�should�not�be�taken�as�given,�and�that�alternative�approaches�towards�teaching� mathematics� should� be� adopted� that� address� issues� of� equity,� fairness,� and� social� justice.� It� reports�on�a�research�project�involving�a�group�of�secondary�mathematics�teachers�in�London� schools,�committed�to�the�principles�of�teaching�mathematics�for�social�justice,�who�set�out�to� put�some�of�these�ideas�into�practice.�It�recounts�the�experiences�of�the�teacher�researchers� and�discusses�how�the�development�of�their�thinking�and�classroom�practice�has�implications�for� others�involved�in�mathematics�education. *� Email:�pete.wright@ucl.ac.uk � ©Copyright�2016�Wright.�This�is�an�Open�Access�article�distributed�under�the�terms�of�the�Creative� Commons�Attribution�Licence,�which�permits�unrestricted�use,�distribution,�and�reproduction�in�any� medium,�provided�the�original�author�and�source�are�credited. London Review of Education� � 105 What’s wrong with mathematics education? By�the�age�of�16,�children�in�England�will�typically�have�spent�approximately�2,000�hours�learning� mathematics�in�school.�Yet�very�few�will�have�considered�questions�such�as�‘What�is�mathematics?’� and�‘Why�do�we�spend�so�much�time�learning�it?’,�suggesting�a�general�acceptance�of�its�position� in�our�society.�Mathematics�plays�an�important�role�as�a�‘critical�filter’,�providing�greater�access� to�further�education�and�higher-paid�employment�for�those�who�are�successful�(Black�et al.,�2009;� Wolf,�2002).�However,�not�everyone�agrees�that�this�status�is�fully�warranted�and�some�question� the�extent�to�which�mathematics�qualifications�provide�skills�that�are�useful�to�employers. Lerman�(2000:�21)�attributes�the�privileged�position�mathematics�occupies�in�the�curriculum� to�the�status�the�subject�has�been�afforded�‘as�an�exemplar�of�truth�and�rationality�since�ancient� times’.�Success�in�mathematics�is�often�used�as�a�measure�of�general�intelligence,�a�damaging� misperception�that�is�associated�with�a�view�of�mathematical�ability�as�fixed�rather�than�incremental� (D’Ambrosio,�2008).�Notions�of�fixed�mathematical�ability�underlie�the�predominance�of�setting� in�England,�where�students�considered�to�be�‘higher�ability’�are�taught�in�separate�groups�and� provided�with�a�more�demanding�curriculum�than�those�considered�to�be�‘lower�ability’�(Morgan,� 2009).�Despite�a�lack�of�evidence�that�setting�is�effective�(Winbourne,�2009),�the�vast�majority� of�students�in�England�aged�12�or�older�are�taught�mathematics�in�ability�groups,�with�many�in� lower�sets�receiving�a�largely�uninspiring�curriculum�and�considering�themselves�as�failures�from� an�early�age�(Hodgen�and�Marks,�2009;�Brown,�1999). Successive�UK�governments,�driven�by�international�comparisons�of�performance,�have�given� increasing�priority�to�raising�attainment�in�mathematics.�Mathematics�assessment�in�England�has� become�increasingly�high-stakes,�with�GCSE�mathematics�given�particular�importance�in�a�new� measure�of�performance�for�schools.�Together�with�accountability�measures�introduced�in�the� 1990s,�this�has�been�blamed�for�an�increasing�tendency�to�‘teach�to�the�tests’,�with�a�greater� focus�on�factual�recall�and�procedural�understanding.�This�is�at�the�expense�of�skills�that�are�more� difficult�to�assess�(i.e.�problem�solving,�reasoning,�and�communication),�which�are�precisely�those� demanded�by�higher�education�and�employers�(ACME,�2011). Nardi�and�Steward�(2003)�describe�the�‘quiet�disaffection’�of� large�numbers�of� learners� who�characterize�school�mathematics�as�being�boring,� irrelevant,�passive,� ignoring� individual� needs,�and�teaching�rules�without�any�rationale.�Even�successful�learners�become�alienated�from� mathematics�through�fear�of�identifying�themselves�as�passive�receivers�of�knowledge�(Boaler� and�Green,�2000).�It�is�not�surprising�that�it�becomes�socially�acceptable�to�admit�to�disliking� or�being�bad�at�mathematics,�given�the�disengaging�way�the�subject�is�commonly�taught�and�the� perceived�failure�experienced�by�so�many�students�(NCETM,�2008). The�figures�for�GCSE�mathematics�attainment�also�hide�worryingly�high�levels�of�inequality� in� achievement� and� participation� among� students� from� different� groups.� Girls� continue� to� display�significantly�lower�participation�rates�in�post-compulsory�mathematics�education,�despite� their�GCSE�attainment�being�similar�to�boys,�and�there�remains�a�strong�correlation�between� achievement�in�school�mathematics�and�social�class�(Boaler�et al.,�2011;�Noyes,�2009).�Given� the� role� school� mathematics� plays� as� a�‘critical� filter’,� these� differences� in� achievement� and� participation�inevitably�lead�to�the�perpetuation�of�social�inequities. Evidence� suggests� that� teaching� mathematics� through� more� open-ended,� collaborative,� problem-solving� approaches,� with� students� in� mixed-attainment� groups,� leads� to� more� equitable�outcomes�and�promotes�greater�participation�among�both�boys�and�girls� in�post- compulsory� mathematics� education� (Boaler,� 2008).� So� why� do� conventional� approaches� to� teaching�mathematics�persist�despite�the�priority�afforded�by�governments�towards�mathematics� education�over�the�past�30�years?�Over�the�same�period,�consensus�has�grown�among�the� mathematics�education�community�that�a�more�relevant�and�engaging�mathematics�curriculum� 106� � Pete Wright is�needed,�with�greater�emphasis�on�conceptual�understanding�and�problem�solving�(Cockcroft,� 1982;�ACME,�2011;�Ofsted,�2012). Bourdieu�(1998)�argues�that�one�of�the�primary�functions�of�schooling�is�to�reproduce�the� current�social�order�and�to�maintain�unequal�power�relations�existing�in�society.�It�does�this� by�concealing�these�relations,�for�example,�by�falsely�attributing�academic�success�to�notions� of�giftedness�or�merit,�which�is�evident�in�the�prevalence�of�setting�in�mathematics�classrooms.� Schools�claim�that�they�offer�equality�of�opportunity�–�whereas,�in�reality,�some�students�possess� higher� levels�of� the�‘cultural�capital’� that� is�recognized�and�valued�by�schools� (Jorgensen� et al.,�2014).�Bourdieu�argues�that,�through�their�upbringing,�children�from�middle-class�families� acquire�higher�levels�of�cultural�capital�than�those�from�working-class�families,�placing�them�at�an� advantage�before�they�arrive�at�school�(Noyes,�2008). I�outline�in�a�previous�paper�(Wright,�2012)�how�successive�UK�governments�have�increasingly� intervened�in�the�development�of�the�school�curriculum.�This�has�led�to�a�greater�influence�on� school�mathematics�of�educational�ideologies�that�champion�the�abstract�and�rigorous�nature� of�the�subject,�and�promote�practices�common�in�business�and� industry,� including�selection� and�marketization.�This�helps�to�explain�why,�despite�government�rhetoric�calling� for�a�new� generation� of� creative� and� mathematically� proficient� problem-solvers� able� to� drive� forward� economic� growth,� most� students� continue� to� experience� mathematics� lessons� that� involve� completing�a�series�of�almost�identical,�closed�questions. Skovsmose�(2011:�9)�describes�this�as�the�‘exercise�paradigm’,�which�cultivates�a�‘prescription� readiness’� and�‘prepares� the� students� for� participating� in� work� processes� where� a� careful� following�of�step�by�step�instructions�without�any�question�is�essential’.�Gutstein�(2006:�10)� argues�that�such�a�disempowering�mathematics�education�for�the�majority�reflects�capitalist� economies’�need�for�‘an�ever-growing�army�of�low-skilled,�compliant,�docile,�pleasant,�obedient� service�workers’.�As�well�as�helping�to�understand�and�explain�the�current�situation�described� above,�such�critical�perspectives�offer�an�alternative�vision�of�what�mathematics�education�might� look�like�in�practice. Teaching mathematics for social justice This�study�develops�a�conceptualization�of�‘teaching�mathematics�for�social�justice’,�which�provides� a�challenge�to�the�status�quo,�described�above,�that�disengages�and�disempowers�mathematics� learners.�It�draws�on�Freire’s�notion�of�‘critical�education’,�which�advocates�the�emancipation�of� learners�and�the�development�of�critical�citizenship�(Skovsmose,�2011).�It�is�based�on�the�premise� that�mathematics�education�can�and�should�play�a�role�in�addressing�difficulties�faced�by�our� society,�including�growing�inequality,�human�rights�abuses,�and�unsustainable�economic�growth� (Cotton,�2013). Skovsmose�(2011)�argues�that�a�critical�mathematics�education�should�include�reflecting� ‘through’,�‘with’,�and�‘on’�mathematics.�Learners�should�reflect�‘through’�mathematics�by�engaging� in�meaningful�mathematical�inquiries�in�which�they�pose�their�own�questions�and�make�their� own� decisions,� while� interacting� and� communicating� with� others.�They� should� reflect�‘with’� mathematics�by�using�it�as�a�means�to�develop�their�understanding�of�a�range�of�social,�cultural,� economic,�and�political�issues.�They�should�reflect�‘on’�mathematics�by�considering�its�nature�and� privileged�position,�and�appreciating�how�it�can�be�used�to�make�and�justify�decisions�affecting� their�lives. Gutstein�(2006)�outlines�how�adopting�a�curriculum�which�emphasizes�reasoning,�problem� solving,�and�communication,� in�order�to�develop�‘mathematical�power’�or�the�confidence�to� engage�in�complex�mathematical�tasks,�is�a�necessary�–�but�not�sufficient�–�condition�for�the� London Review of Education� � 107 empowerment�of�learners.�He�goes�further,�drawing�on�Freire’s�notion�of�‘praxis’,�to�argue�that� students�should�use�mathematics�to�investigate�and�challenge�injustices�and�inequities�relating� to�their�own�lives�and�wider�society.�He�emphasizes�that�‘reading�and�writing�the�world�with� mathematics’�depends�upon�students�being�willing�to�rethink�their�views�of�mathematics,�teachers� appreciating�the�socio-political�nature�of�mathematics,�and�developing�meaningful�relationships� between�students�and�teachers. The�following�conceptualization�of�teaching�mathematics�for�social�justice�(Wright,�2015:� 27),�drawing�on�the�ideas�of�Skovsmose�and�Gutstein�described�above,�is�adopted�for�this�study: •� employ� collaborative,� discursive,� problem-solving,� and� problem-posing� pedagogies,� which�promote�the�engagement�of�learners�with�mathematics •� recognize�and�draw�upon� learners’�real-life�experiences� in�order�to�emphasize�the� cultural�relevance�of�mathematics •� promote�mathematical�inquiries�that�enable�learners�to�develop�greater�understanding� of�their�social,�cultural,�political,�and�economic�situations •� facilitate�mathematical�investigations�that�develop�learners’�agency,�enabling�them�to� take�part�in�social�action�and�realize�their�foregrounds •� develop�a�critical�understanding�of�the�nature�of�mathematics�and�its�position�and�status� within�education�and�society. The research project In�May�2013,�I�contacted�120�mathematics�teachers�who�were�nearing�the�end�of�their�first�year� as�qualified�teachers,�and�who�I�had�previously�worked�with�as�a�tutor�during�their�initial�teacher� education�programme.�I�invited�them�to�take�part�in�a�research�project,�which�aimed�to�develop� ideas�and�classroom�practice�that�challenged�the�status�quo,�and�which�addressed�issues�of�social� justice�in�the�mathematics�classroom.�The�invitation�included�details�of�the�conceptualization�of� teaching�mathematics�for�social�justice,�which�was�to�serve�as�a�useful�starting�point,�and�the� ‘critical�research�model’�(see�below),�which�was�to�be�adopted�for�the�project.�Participants�were� self-selected�on�the�basis�of�sharing�a�commitment�to�the�aims�of�the�project�and�a�willingness� to�make�the�necessary�time�commitments.�These�included�attending�seven�twilight�meetings,� carrying�out�at�least�three�classroom�interventions�over�one�academic�year,�participating�in�three� interviews�–�at�the�start,�midway�through,�and�at�the�end�of�the�project�–�maintaining�a�research� journal,�and�completing�a�short�report�at�the�end�of�the�project. The�Teaching�Mathematics�for�Social�Justice�Research�Group�was�established�in�June�2013.�It� comprised�five�teacher�researchers�and�me�(as�university-based�researcher).�The�research�group� was�collaborative�and�participatory�in�nature.�While�I�played�an�important�role�in�facilitating� the�meetings�of�the�group,�and�collecting�and�analysing�research�data,�the�teacher�researchers� took�much�of�the�initiative�for�developing�their�own�practice.�They�chose�which�teaching�ideas� to�develop,�led�the�evaluation�and�discussion�of�activities�they�tried�out�in�the�classroom,�and� decided�the�method�for�collecting�feedback�from�students�(through�a�written�survey�administered� immediately�after�the�activity). The�design�of�the�research�project�was�based�on�the�‘critical�research�model’�of�participatory� action�research�(Skovsmose�and�Borba,�2004).�This�model�assumes�that�the�‘current�situation’� –�in�this�case,�the�typical�experience�of�mathematics�learners�in�classrooms�–�should�not�be� taken�as�given.�It�stresses�the�importance�of�an�alternative�vision�or�‘imagined�situation’�–�in� this�instance,�the�initial�conceptualization�of�teaching�mathematics�for�social�justice�described� earlier.�It�proposes�the�use�of�an�‘arranged�situation’,�whereby�the�participants�in�the�research,� 108� � Pete Wright taking�into�account�the�constraints�of�the�current�situation,�put�into�practice�some�aspects�of� the�imagined�situation.�The�three�key�processes�of�the�critical�research�model�(i.e.�‘pedagogical� imagination’,�‘practical�organization’,�and�‘explorative�reasoning’)�were�integral�to�the�operation� of�the�research�group. Pedagogical imagination�involves�developing�a�critical�understanding�of�the�current�situation;� for�example,�by�gaining�insight�into�how�critical�perspectives�(Gutstein,�2006;�Skovsmose,�2011)� might� help� to� explain� this� situation.�Teacher� researchers� were� encouraged� to� engage� with� research�findings�and�discuss�how�these�related�to�their�own�experiences�and�represented�viable� alternatives�to�current�practice.�The�first�meeting�of�the�research�group�focused�on�theoretical� ideas�underlying�the�research�project;�for�example,�I�asked�the�teacher�researchers�to�read�and� discuss�a�short�introductory�chapter�from�a�book�focusing�on�rethinking�school�mathematics� from�a�social�justice�perspective�(Gutstein�and�Peterson,�2005). Practical organization� involves� cooperation� between� research� participants� in� organizing� an�arranged�situation.�The�second,�fourth,�and�sixth�meetings�of�the�research�group�focused� primarily�on�jointly�planning�activities�to�try�out�in�the�classroom.�Teacher�researchers�were� encouraged�to�present�ideas�taken�from�currently�existing�resources�(Wright,�2004;�Gutstein� and�Peterson,�2005),�discussing�how�they�might�incorporate�these�into�their�lessons,�bearing�in� mind�the�constraints�of�the�classroom. Explorative reasoning�involves�analysing�the�arranged�situation�in�order�to�better�understand� the�current�situation�and�the�feasibility�of�the�imagined�situation.�The�third,�fifth,�and�seventh� meetings�of�the�research�group�focused�primarily�on�evaluating�and�reflecting�on�the�activities� tried�out�in�the�classroom.�Teacher�researchers�took�it�in�turns�to�present�their�evaluations,� making�use�of�student�feedback,�examples�of�students’�work,�and�notes�from�their�research� journals�to�inform�their�presentations.�Presentations�were�followed�by�questions�from�other� teacher�researchers�and�a�general�discussion,�which�informed�subsequent�planning,�teaching,�and� evaluation�cycles. Data collection and analysis Semi-structured�interviews�were�conducted�by�me,�in�the�teacher�researchers’�own�schools,�using� an�‘empathetic’�approach,�in�which�a�relationship�of�trust�is�established�and�a�story�is�constructed� jointly�through�interaction�and�dialogue�between�interviewer�and�interviewee�(Fontana�and�Frey,� 2008;�Kvale�and�Brinkmann,�2009).�Initial�questions�focused�on�the�development�of�interviewees’� thinking�and�classroom�practice�relating�to�social�justice.�Individually�tailored�follow-up�questions� were� used� to� explore� responses� in� more� detail� and� to� stimulate� further� discussion.�Audio� recordings�of�all�research�group�meetings�and�individual�interviews�were�transcribed�using�a� literary�style�(i.e.�ignoring�pauses,�fillers,�and�voice�intonations). A�thematic�approach�was�used�to�analyse�the�transcripts�using�‘meaning�condensation’,�in� which�the�text�is�broken�down�into�units�of�meaning�and�summarized,�and�‘meaning�interpretation’,� involving�assigning�a�category�to�each�unit�of�meaning�(Kvale�and�Brinkmann,�2009).�The�analysis� drew�on�methods�from�grounded�theory,�which�I�considered�to�be�consistent�with�my�critical� research�methodology.�While�maintaining�that�current�practice�should�not�be�taken�as�given,�and� offering�an�initial�conceptualization�for�a�more�desirable�alternative,�there�was�no�pre-existing� hypothesis�on�how�this�conceptualization�should�be�translated�into�classroom�practice.�Thus� it�was�possible�for�theories�and�hypotheses�to�emerge�within�a�theoretical� framework�that� informed�and�guided�the�action�research�cycles. This�thematic�analysis�made�use�of�inductive�coding,�whereby�the�categories�assigned�to� each�unit�of�meaning�were�derived�from�initial�readings�of�the�data.�Categories�were�then�used� London Review of Education� � 109 to�facilitate�the�comparison�of�commonalities,�differences,�and�relationships�between�units�of� meaning,� enabling� new� themes� to� emerge� (Gibson� and� Brown,� 2009).� Such� comparisons,� in� contrast�to�simplistic�coding�that�is�more�easily�quantified,�take�into�account�the�context�of�the� text,�allowing�meaning�to�be�constructed�from�the�stories�of�the�research�participants.�Initial� findings�from�the�data�analysis�were�then�related�back�to�the�theories�underlying�the�project� in�order�to�generate�new�analytical�questions�giving�further�meaning�to�the�data�(Jackson�and� Mazzei,�2012). Careful� consideration� was� given� to� Lincoln� and� Guba’s� (2003)� framework� for� ensuring� the� trustworthiness� of� qualitative� research,� with� particular� attention� paid� to� the� credibility,� transferability,�dependability,�and�confirmability�of�the�research�findings. The�‘credibility’�and�‘confirmability’�of�the�findings�–�that�is,�confidence�that�the�phenomena� are� accurately� represented� and� derived� from� the� experiences� of� the� participants� –� were� promoted�through�adopting�various�procedures�focusing�on�reflexivity�and�triangulation.�These� included:�maintaining�my�own�research�journal�and�code�log;�‘prolonged�engagement’�with�teacher� researchers�over�a�period�of�one�year;�the�use�of�student�surveys�and�final�reports�to�triangulate� data;�‘iterative�questioning’�through�following�up�previous�responses�in�individual�interviews;�and� ‘member�checks’�through�presenting�my�analysis�back�to�teacher�researchers�for�their�comment� (Shenton,�2004).�A�second�thematic�analysis�was�carried�out�on�a�selection�of�the�data�in�order� to�assess�the�credibility�of�the�research�processes.�This�analysis�made�use�of�deductive�coding,� based�on�the�key�processes�of�the�critical�research�model,�and�previously�established�reliability� criteria�for�action�research�–�that�is,�the�extent�to�which�it�is�participatory,�collaborative,�relevant,� and�results�in�positive�social�change�(Brydon-Miller�et al.,�2003). The�‘transferability’�and�‘dependability’�of�the�research�(i.e.�enabling�the�reader�to�make�an� informed�judgement�about�the�relevance�of�the�findings�to�his�or�her�own�situation,�and�to�repeat� the�study�if�desired)�were�assured�by�providing�‘thick�descriptions’�of�the�context�of�the�research� and�its�design�(Shenton,�2004).�These�include�detailed�descriptions�of�the�research�model�and� framework�for�analysing�data,�my�own�background�and�the�development�of�my�interest�in�the� field,�and�a�detailed�case�study�of�the�research�group�and�the�teacher�researchers’�involvement� in�the�project.�These�descriptions,�while�too�lengthy�to�include�in�this�paper,�can�be�accessed� through�my�doctoral�thesis�(Wright,�2015). Research findings Four�themes�emerged�during�the�analysis�of�the�first�set�of�interviews�and�these�were�used�as� the�basis�for�the�thematic�analysis�of�data�from�subsequent�meetings�and�interviews.�The�four� themes�provided�a�useful�structure�for�reporting�the�findings�of�the�research�project,�using�a� case�study�approach�to�narrate�the�stories�of�the�teacher�researchers’�involvement�in�the�project� and�the�development�of�their�thinking�and�practice.�The�five�teacher�researchers�–�Anna,�Brian,� George,�Rebecca,�and�Sarah�(all�pseudonyms)�–�taught�in�multi-ethnic�comprehensive�schools�in� Inner�London�with�varying�records�of�attainment�in�GCSE�examinations.�Their�schools�all�shared� a�relatively�high�proportion�of�students�who�spoke�English�as�an�additional�language,�students� with�statements�of�special�educational�needs,�and�students�eligible�for�free�school�meals. Theme 1: Changing epistemologies of mathematics The�development�of�the�teacher�researchers’�classroom�practice�over�the�course�of�the�project� appeared� to� be� closely� related� to� their� changing� views� of� mathematics� and� their� students’� perceptions�of�the�subject.�While�they�all�considered�themselves�to�be�successful�learners�of� 110� � Pete Wright mathematics,�they�viewed�the�subject�as�entirely�content-focused�when�they�themselves�were� at�school,�only�later�beginning�to�appreciate�its�value-laden�and�socially�constructed�nature.�The� most�significant�changes�in�their�epistemologies�of�mathematics�took�place�during�their�initial� teacher�education�programme,�and�through�their�involvement�with�the�project: I�always�remember�this�session�we�did�where�they�were�saying�‘What�is�maths?’�And�I�was�like� ‘What�is�maths?�I’ve�just�joined�this�teacher�training�course�to�teach�maths�and�I�don’t�really� know�what�it�is’. (Anna,�Interview�2) Through�reflecting�on�the�nature�of�mathematics�during�research�group�meetings,�they�became� more�aware�of�their�own�perspectives�and�how�these�affected�their�approaches�to�teaching. By� engaging� with� research� theories� and� trying� out� ideas� in� the� classroom,� the� teacher� researchers�began�to�rethink�their�ideas�about�addressing�issues�of�social�justice.�There�was�a� distinct�move�away�from�viewing�these�ideas�merely�as�a�way�of�enriching�lessons�towards�seeing� them�as�a�legitimate�and�essential�aspect�of�teaching�mathematics,�which�promoted�mathematical� understanding�and�made�the�subject�more�relevant�and�meaningful�to�students: It’s�given�me�the�confidence�to�step�off�the�scheme�of�work�treadmill,�of�getting�through�different� topics�or�chapters,�and�actually�saying:�‘Well,�these�topics,�say�cumulative�frequency,�or�percentages,� I�can�fit�these�within�a�project�on�something�to�do�with�these�kids’�world,�or�to�do�with�our� world�as�a�whole.’ (Brian,�Interview�3) Over� the� course� of� the� project,� the� teacher� researchers� became� more� and� more� critical� of� conventional� mathematics� teaching,� increasingly� seeing� this� as� resulting� in� procedural� understanding�and�causing�students�to�view�mathematics�as�boring�and�pointless.�At�the�same� time,� they� strengthened� their� belief� in� student-led,� collaborative,� discursive,� problem-solving� approaches�to�learning: I�think�things�such�as�trying�to�give�them�a�bit�of�agency�and�choice�in�lessons,�things�like�encouraging� them�to�work�together�in�groups�…�have�been�things�that�I’ve�done�more�of�because,�as�part�of� the�project,�I’ve�found�them�to�be�helpful�and�useful. (Brian,�Interview�3) However,�they�continued�to�recognize�the�importance�of�learning�discrete�mathematical�skills,� which�they�believed�should�be�complemented�by,�rather�than�replaced�by,�tackling�issues�of�social� justice.�There�was�a�growing�appreciation�of�the�need�to�establish�stronger�links�between�social� justice�issues�and�mathematical�skills�at�an�appropriate�level�of�challenge�for�students.�While� incorporating�social�justice�issues�began�to�impact�on�students’�perceptions�of�mathematics,�the� teacher�researchers�reported�that�some�students,�particularly�where�they�found�the�mathematical� content�too�easy,�expressed�concern�that�they�were�not�studying�‘real’�or�‘proper’�mathematics. Theme 2: Developing student agency Three�of�the�teacher�researchers�cited�a�desire�to�change�society�for�the�better�as�a�reason� for�becoming�a�mathematics�teacher�in�the�first�place.�All�five�shared�a�strong�belief�in�tackling� inequity�through�raising�the�attainment�of�disadvantaged�students,�which�explains�their�choice�of� an�initial�teacher�education�programme�that�placed�them�in�schools�with�relatively�high�levels�of� socioeconomic�deprivation.�They�viewed�motivating�students�as�a�high�priority�and�convincing� students�of�the�utility�of�mathematical�procedures,�by�making�the�subject�more�realistic�and� meaningful,�was�seen�as�a�way�of�achieving�this. London Review of Education� � 111 The�maths�today�made�me�realize�how�the�simplest�maths�can�change�lives. (Year�10�student�in�Brian’s�class�in�response�to�activity�on�Fairtrade) The� teacher� researchers� initially� felt� most� comfortable� developing� activities� that� involved� using�mathematics�to�develop�a�better�understanding�of�social�justice�issues,�including�public� misperceptions�about�benefit�fraud�and�immigration,�the�sustainable�use�of�water�and�allocation� of�resources,�average�incomes�and�global�inequality,�voting�systems,�and�Fairtrade.�They�reported� a�genuine�interest�for�such�issues�among�students,�together�with�a�developing�appreciation�of� how�mathematics�might�be�used�to�solve�problems�in�real�life. Over�the�course�of�the�project,�there�was�growing�interest�among�the�teacher�researchers� in�developing�student�agency,�something�they�had�given�less�thought�to�previously. I�think�the�agency�thing�was�definitely�something�I�hadn’t�considered�at�the�start.�Like,�I�saw�it�more� as�applying�maths�to�different�situations,�rather�than�using�maths�to�actually�change�something. (Rebecca,�Interview�3) The�‘Making�a�Change’�project,�which� involved�students�using�mathematics�to�develop�their� understanding�of�an�issue�of�their�choice�and�present�an�argument�for�a�change�they�would� like�to�see�made,�became�the�focus�of�the�third�action�research�cycle.�While�fostering�students’� mathematical�engagement�and�agency�became�increasingly�important�to�the�teacher�researchers� in� the� development� of� their� practice,� there� was� a� growing� appreciation� that� the� notion� of� ‘student�agency’�needed�to�be�handled�carefully.�George�warned�that�agency,�on�its�own,�was� not�necessarily�desirable�as�students�also�needed�to�develop�open-mindedness�and�sensitivity� towards�issues�of�social� justice�in�order�to�become�positive�agents�of�change.�The�question� of� whether� teachers� should� encourage� students� to� explore� issues� and� arrive� at� their� own� conclusions,�or�guide�students�towards�developing�particular�beliefs�and�values,�was�highlighted� during�the�Fairtrade�activity�when�some�students�openly�questioned�the�validity�of�Fairtrade. I�think�maths�today�was�good�as�it’s�showing�actual�statistics�which�has�made�me�think�‘fair�trade’� isn’t�fair. (Year�9�student�in�Rebecca’s�class�in�response�to�Fairtrade�activity) The�teacher�researchers�reported�that�most�students�responded�positively�to�the�activities,� demonstrating�greater�levels�of�engagement�and�enjoyment�of�learning�through�their�behaviour� and�responses�to�the�feedback�survey.�This�was�particularly�noticeable�among�students�who�had� previously�been�poorly�motivated�and�badly�behaved�in�mathematics�lessons: I�tried�a�few�things�with�my�bottom�set�and�their�motivation�has�just�been�so�high�in�those� particular�lessons�that�I’ve�had�to�very�rarely,�like,�tell�them�to�get�on�with�things�or�to�do�things. (Anna,�Interview�3) Theme 3: Collaborative nature of research group The�teacher�researchers�described�how�the�opportunity�to�work�collaboratively�with�colleagues� from�different�schools�in�a�research�group�attracted�them�to�the�project.�The�invitation�came� towards�the�end�of�their�first�year�as�qualified�teachers,�after�which�they�would�no�longer�be� receiving�the�same�level�of�structured�support�and�professional�development�from�their�schools.� They�were�just�beginning�to�think�about�the�direction�they�would�like�their�practice�to�develop,� and�where�they�might�get�support�to�help�them�achieve�this. I�think�the�whole�project�is,�for�me,�about�developing�myself�as�a�practitioner,�and�in�a�way�that� I’d�like�to�develop. (Anna,�Interview�1) 112� � Pete Wright The�group�quickly�established�positive�working�relationships,�helped�by�the�fact�that�they�knew� each�other� from�their� initial� teacher�education�programme.�The�mutually�supportive�nature� of�the�group�encouraged�the�teacher�researchers�to�take�risks�and�overcome�many�of�the� challenges�and�constraints�they�encountered�in�developing�alternative�classroom�practices: And�it’s�also�provided�that�additional�incentive�to�do�it,�and�to�take�the�risk,�because�you�know� that�you’re�going�to�be�asked�to�talk�about�it.�But�also�you�know�you’re�going�to�be�allowed�to� talk�about�it�in�a�way�that�says�that�messing�up�doesn’t�matter. (Brian,�Interview�3) This�was�exemplified�by�the�way�in�which�the�rest�of�the�group�encouraged�and�reassured� Rebecca�after�she�presented�the�evaluation�of�her�initial�attempt�at�the�Making�a�Change�project.� Having�been�the�first�in�the�group�to�try�the�activity,�she�was�clearly�disheartened�by�the�logistical� problems�she�encountered.�However,�the�rest�of�the�group�recognized�the�potential�of�her�ideas� and�went�on�to�develop�them�into�a�successful�activity. It�is�quite�useful�having�that�kind�of,�I�don’t�know,�support�almost,�and�being�able�to�just�tell� someone�exactly�what�happened�and�have�their,�kind�of,�outside�view�on�it. (Rebecca,�Interview�2) The�teacher�researchers�were�keen�to�engage�with�the�research�theories�underlying�the�project,� and�reported�how�these�challenged�their�preconceptions,�enabling�them�to�develop�a�broader� and�deeper�understanding.�They�acknowledged�the�role�I�played,�as�university-based�researcher,� in�raising�their�awareness�of�these�theories�and�providing�a�structure�for�developing�ideas.�They� concurred�that�engaging�with�theories,�discussing� ideas,�and�comparing�experiences�–�along� with�the�collaborative�planning,�teaching,�and�evaluation�of�classroom�activities�over�a�sustained� period�–�had�a�considerable�impact�on�their�thinking�and�practice: It’s�been�the�most�impactful�CPD,�in�my�opinion,�that�I’ve�had�this�year,�because�it’s�sustained�…� I’ve�actually�seen�the�impact�of�this�project�on�the�children�and�the�lessons�that�I�teach,�whereas� very�often�with�CPD,�it’s�one�afternoon,�you�go�away�and�come�back,�and�it�goes�out�of�your� head�like�that. (Anna,�Interview�3) The�teacher�researchers’�growing�confidence�in�translating�research�theories�into�classroom� practice�was�evident�in�the�way�they�began�to�encourage�other�teachers�in�their�school�to�take� on�board�the�ideas�from�the�project.�Anna,�Brian,�and�Rebecca�ran�related�training�sessions�for� their�departments,�and�three�of�the�schools�used�activities�from�the�project�with�an�entire�year� group.�It�became�apparent�that�news�of�the�positive�impact�the�activities�had�on�students�spread� quickly�and�generated�interest�in�the�project�across�departments. Success�has�bred�more�success,�because�if�they’ve�seen�a�lesson�go�well,�then�they�want�to�teach� it,�and�then�their�lesson�goes�well,�and�then�it�sort�of�spreads. (Rebecca,�Interview�3) Theme 4: Dominant discourses on ability and attainment The�teacher�researchers�became�increasingly�aware�of�constraints�that�they�felt�might�discourage� teachers�from�promoting�social�justice�in�the�mathematics�classrooms�–�in�particular,�the�exam- focused�culture�in�schools,�excessive�workload,�and�high�levels�of�scrutiny�of�teachers.�There�was� growing�appreciation�that�a�narrow�focus�on�raising�the�attainment�of�disadvantaged�students,� while�ignoring�structural�inequities,�resulted�in�low-risk�teaching�and�procedural�understanding: London Review of Education� � 113 I�think�it�makes�you�less�likely�to�take�risks�with�your�classes.�If�you�know�that�there’s�a�chance� that�someone�pops�in,�you’re�more�likely�to�do�lots�of�very�average�lessons,�than�one�lesson�that� could�blow�up�in�your�face�or�it�could�go�amazingly,�because�you�know�that�you’d�be�judged�on� that�one�lesson. (Brian,�Interview�1) The�teacher�researchers�concurred�that�the�mutual�support�provided�by�the�research�group� helped�them�to�overcome�many�of�these�constraints.�Developing�a�greater�understanding�of�the� links�between�social�justice�issues�and�mathematical�skills�enabled�them�to�resolve�the�conflict� between�tackling�these�issues�and�getting�through�the�scheme�of�work.�Sharing�ideas�and�resources� within�the�group�compensated�for�the�additional�time�required�to�plan�meaningful�activities.� The�positive�impact�of�the�project,�on�students’�engagement�and�mathematical�understanding,� reassured�the�teacher�researchers�that�the�project’s�aims�were�not�in�conflict�with�the�desire�to� raise�mathematical�attainment: I�do�think�I�feel�under�more�pressure�to�get�through�all�the�material.�I�am�struggling�a�bit�on�that� front,�which�means�that�any�social�justice�activity�has�to�be�very�specifically�linked�to�something,� a�mathematical�skill�that�is�not�going�to�be�taught�in�any�other�way. (Rebecca,�Interview�2) The�teacher�researchers�reported�an�initial�tendency�to�try�out�new�ideas�with�higher-attaining� students,�who�were�generally�better�behaved�and�more�positively�disposed�towards�learning.� However,�over�the�course�of�the�project,�they�began�to�realize�that�the�benefits�were�most� apparent�for�lower-attaining�students,�who�demonstrated�greater�improvements�in�their�levels� of�engagement�and�achievement.�It�became�noticeable�that�the�highest�attaining�students�showed� the�least�enthusiasm�towards�alternative�teaching�approaches�advocated�by�the�project,�perhaps� because�they�associated�their�own�relative�success�with�conventional�teaching�approaches: I�think,�if�you�are�at�the�top�end�of�the�top�set,�you’ve�put�your�hat�on�the�fact�that�you�get�things� right,�and�as�soon�as�in�maths�it’s�no�longer�about�you�getting�the�right�numerical�answer,�you� suddenly�feel�like�things�are�not�under�your�control�any�more,�and�you’re�not�top�dog�any�more. (Brian,�Interview�2) Over�the�course�of�the�project,� the�teacher�researchers�began�to�question�previously�held� assumptions�about�mathematics�teaching,�particularly�the�notion�of�mathematical�ability�being� fixed.�Initially,�there�was�little�criticism�of�the�rigid�setting�prevalent�in�their�departments.�However,� they�began�to�question�its�benefits,�expressing�increasing�concern�that�concentrating�together� students�with�lower�confidence�and�less�positive�dispositions�towards�learning�might�contribute� towards�widening�differences�in�attainment. Implications of the research project The�research�project,�with�its�methodology�based�upon�the�critical�research�model�and�the�initial� conceptualization�of�teaching�mathematics�for�social�justice,�was�focused�as�much�on�the�process� for�bringing�about�change�as�on�what�that�change�might�look�like.�This�focus�is�reflected�in�the� research�findings,�which�have�implications�in�three�areas:�mathematics�teaching,�the�professional� development�of�mathematics�teachers,�and�mathematics�education�research. Implications for mathematics teaching The�project�demonstrated�how�mathematics�can�serve�as�a�powerful�means�for�developing� students’�understanding�of�issues�of�social�justice,�and�that�students�are�likely�to�develop�an� 114� � Pete Wright understanding�of�both�social�justice�issues�and�mathematical�concepts�when�there�is�a�meaningful� link�between�the�two.�It�showed�how�student�agency�can�be�developed�by�adopting�collaborative,� problem-solving�approaches�to�teaching,�and�encouraging�students�to�choose�which�issues�to� explore�and�which�mathematical�procedures�to�apply.�Developing�and�presenting�their�own� arguments�enables�students�to�gain�an�appreciation�of�how�mathematics�can�be�used�to�better� understand�a�situation�and�to�argue�for�a�change. The�project�highlighted�how�making�mathematics�more�meaningful�and�relevant�to�students’� real-life�experiences�can�raise�their�levels�of�engagement�with�the�subject�as�they�develop�an� appreciation�of�its�purpose�and�possible�future�application.�This�is�particularly�noticeable�among� lower-attaining�and�previously�disaffected�students,�suggesting�that�such�an�approach�has�the� potential�for�closing�the�attainment�gap�among�students�–�although�the�duration�of�the�project� was�too�short�to�provide�any�evidence�of�this�happening.�However,�care�needs�to�be�exercised� when� relating� mathematics� to� students’� real-life� experiences.� Educational� opportunities� for� disadvantaged�students�can�be�restricted�if�connections�are�made�only�with�their�backgrounds.�For� this�reason,�Skovsmose�(2011)�argues�that�mathematics�should�relate�to�students’�‘foregrounds’�–� that�is,�real-life�experiences�that�move�beyond�their�current�situations.�While�there�may�be�some� resistance�to�these�teaching�approaches�among�higher-attaining�students,� it�should�be�noted� that�many�such�students�choose�not�to�study�the�subject�beyond�the�compulsory�level.�Initial� resistance�might�therefore�be�outweighed�by�the�potential�of�these�approaches�to�encourage� more�students�to�study�mathematics�at�higher�levels. The�project�also�demonstrated�how�engaging�with�research�findings�enables�teachers�to� develop� insight� into� structural� inequities� in� mathematics� education.�Through� developing� an� appreciation�of�the�processes�that�lead�some�students�to�become�alienated�from�mathematics,� teachers�may�become�more�willing�to�use�a�range�of�alternative�pedagogies�with�students�who� are�less�predisposed�towards,�but�have�the�most�to�gain�from,�discursive,�open-ended�approaches� to�learning. Another�issue�highlighted�by�the�project�was�how�uncommon�it�is�for�students,�even�those� studying�mathematics�at�degree�level,�to�be�asked�to�reflect�on�the�nature�of�the�subject�despite� the�privileged�position� it�occupies� in�the�school�curriculum.�Encouraging�students�to�do�so� appears�to�be�an�effective�way�of�challenging�myths,�such�as�the�belief�that�mathematics�is�value- free�or�that�mathematical�success�is�pre-determined�by�innate�ability,�perhaps�preventing�these� myths�from�being�perpetuated�from�one�generation�to�the�next.�Enabling�students�to�better� understand�their�own�situation�can�help�those�who�are�disadvantaged�in�learning�mathematics� to�overcome�barriers�to�achieving�success.�Furthermore,�the�project�emphasized�the�importance� of�establishing�relationships�based�on�trust�and�mutual�respect�between�teacher�and�students�if� such�discussions�are�to�have�any�effect. Implications for the professional development of mathematics teachers The�project�demonstrated�how�the�critical�research�model,�with�its�focus�on�relating�theory�to� practice�and�ensuring�that�the�current�situation�is�not�taken�as�given,�can�have�a�considerable� impact�on�the�thinking�and�classroom�practice�of�mathematics�teachers�with�a�concern�for� social�justice.�The�role�of�the�external�partner�–�in�facilitating�the�engagement�of�such�teachers� with�research�findings,�and�encouraging�them�to�critically�appraise�their�own�practice�in�relation� to�theory�–�was�shown�to�be�a�crucial�aspect�of�the�model.�This�process�allows�teachers�to� develop�a�more�profound�and�critical�understanding�of�their�own�practice�and�how�this�relates� to�existing�practice�across�different�schools.�It�can�lead�to�greater�awareness�of�structural�causes� of�inequity�and�injustice�in�mathematics�education,�including�the�use�of�setting�to�group�students� by�attainment�and�ignoring�the�effect�of�social�class�on�students’�achievement. London Review of Education� � 115 Addressing�issues�of�equity�and�social�justice�was�shown�to�be�an�important�factor�for�some� mathematics�teachers�in�deciding�to�become�a�teacher�in�the�first�place.�The�project�suggested� that� such� teachers� are� favourably� disposed� towards� reflecting� on� their� epistemologies� and� experiences�as�learners.�In�so�doing,�they�are�likely�to�strengthen�their�belief�in�the�effectiveness� of�student-led,�collaborative,�problem-solving�approaches�to�learning.�The�critical�research�model� allows�these�teachers�to�re-engage�with�ideas,�which�they�may�have�lost�sight�of�as�a�result�of� pressures�they�face�in�the�classroom,�enabling�them�to�become�more�comfortable�in�their�roles�as� mathematics�teachers.�The�high�level�of�interest�in�the�project�shown�by�the�teacher�researchers’� colleagues�indicated�that�there�might�be�significant�numbers�of�mathematics�teachers�in�schools� sharing�a�concern�for�social�justice�issues. The� project� highlighted� the� effectiveness� of� a� collaborative,� participatory,� and�sustained� approach�to�professional�development.�Collaborative�relationships�that�develop�over�a�prolonged� period�of�time�enable�teachers�to�provide�the�mutual�support�necessary�to�overcome�constraints� and�to�take�risks�in�the�classroom.�Through�the�joint�planning�of�lessons�and�the�sharing�of� experiences�among�colleagues�from�a�range�of�different�schools,�teachers�are�able�to�engage�with� new�ideas�and�develop�their�thinking�appreciably.�The�critical�research�model�demonstrates�how� teachers�are�able�to�develop�their�agency�and�self-efficacy�in�deciding�the�direction�and�extent� of�changes�in�their�classroom�practice. Implications for mathematics education research The� project� demonstrated� how� the� critical� research� model� can� enable� teachers,� through� reflecting�on�classroom�practice�and�its�underlying�theories,�to�generate�relevant�knowledge� that�is�transferable�to�other�classroom�situations.�The�project�showed�how�research�undertaken� collaboratively�with�teachers�working�in�‘typical’�classroom�situations�(i.e.�those�where�common� issues�and�constraints�relating�to�developing�practice�are�present)�is�likely�to�be�perceived�as� relevant�and�authentic�by�other�teachers.�Such�research�therefore�has�the�potential�to�increase� teachers’�engagement�with�research�findings. The�critical�aspect�of�the�research�design�enables�new�knowledge�to�be�generated�that� challenges�existing�discourses�in�schools,�and�has�the�potential�to�address�inequities�and�injustices� existing� within� mathematics� classrooms,� schools,� and� wider� society.� The� project� outlined� processes�that�enable�transformations�in�classroom�practice�to�take�place,�and�highlighted�how� university-based�researchers�and�teacher�researchers�can�act�collaboratively�as�agents�of�change. Research� based� on� collaborative� and� participatory� methodologies� is� generally� under- represented�in�academic�journals,�reflecting�a�lack�of�confidence�in�its�reliability.�Through�the� attention�paid�to�issues�of�trustworthiness,�only�some�of�which�is�presented�in�this�paper,�the� project� demonstrated� how� participatory� action� research� from� a� critical� perspective� can� be� systematic�and�rigorous,�as�well�as�generating�relevant�knowledge�with�the�potential�to�bring� about�positive�social�change. Conclusion The� research� project� reported� in� this� paper� provides� some� insight� into� what� teaching� mathematics�for�social�justice�might�look�like�in�practice,�and�how�it�can�be�promoted�through�an� effective�model�of�professional�development.�It�also�demonstrates�how�teachers�and�researchers� can�work�collaboratively,�through�systematic�inquiry,�which�generates�reliable�and�trustworthy� findings,�to�challenge�the�current�situation�in�which�mathematics�teaching�perpetuates�inequities� and�injustices�within�society.�It�is�unlikely�that�those�in�positions�of�power�will�embrace�the� findings�of�this�research,�since�their�interests�might�be�better�served�by�maintaining�the�status� 116� � Pete Wright quo.�However,�it�is�hoped�that�those�committed�to�education�as�a�means�of�changing�the�world� for�the�better�might�gain�some�insight�from�the�project’s�findings�into�how�to�go�about�bringing� about�positive�change�in�the�mathematics�classroom. Notes on the contributor Before�joining�the�UCL�Institute�of�Education�as�a�Lecturer�in�Mathematics�Education�in�2011,�Pete�taught� for�15�years�in�comprehensive�schools� in�London,�Newcastle-upon-Tyne,�and�Brighton,� including�three� years�as�Head�of�Mathematics,�and�in�a�rural�school�in�Kenya.�Other�posts�in�education�include�five�years�in� curriculum�development�and�two�years�as�a�local�authority�mathematics�consultant.�His�current�research� interests�include�equity�and�social�justice�in�mathematics�teaching�and�participatory�action�research. References Advisory�Committee�on�Mathematics�Education�(ACME)�(2011)�Mathematical Needs: Summary. London:� ACME. Black,�L.,�Mendick,�H.,�and�Solomon,�Y.�(2009)�Mathematical Relationships in Education: Identities and participation. New�York:�Routledge. Boaler,�J.�(2008)�‘Promoting�“relational�equity”�and�high�mathematics�achievement�through�an�innovative� mixed-ability�approach’.�British Educational Research Journal, 34�(2),�167–94. 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University� of�Sussex�(Sussex�Research�Online). � Related articles published in the London Review of Education In this issue This�paper�was�published�in�a�special�feature�on�education�in�London,�edited�by�Tamjid�Mujtaba.� The�other�articles�in�the�feature�are�as�follows�(links�unavailable�at�time�of�publication): Brown,�C.,�Taylor,�C.,�and�Ponambalum,�L.�(2016)�‘Using�design-based�research�to�improve�the�lesson�study� approach�to�professional�development�in�Camden�(London)’.�London Review of Education,�14�(2),�4–24. 118� � Pete Wright Cajic-Seigneur,�M.,�and�Hodgson,�A.�(2016)�‘Alternative�educational�provision�in�an�area�of�deprivation�in� London’.�London Review of Education,�14�(2),�25–37. Jerrim,�J.,�and�Wyness,�G.�(2106)�‘Benchmarking�London�in�the�PISA�rankings’.�London Review of Education,� 14�(2),�38–65. Mujtaba,�T.�(2016)�Editorial:�‘Education�in�London:�Challenges�and�opportunities�for�young�people’.�London Review of Education,�14�(2),�1–3.� Mujtaba,�T.,�and�Reiss,�M.� (2016)�‘Girls� in�the�UK�have�similar�reasons�to�boys� for� intending�to�study� mathematics� post-16� thanks� to� the� support� and� encouragement� they� receive’.� London Review of Education,�14�(2),�66–82. Standish,�A.,�Hawley,�D.,�and�Willy,�T.�(2016)�‘The�London�Geography�Alliance:�Re-connecting�the�school� subject�with�the�university�discipline’.�London Review of Education,�14�(2),�83–103. Elsewhere in the journal Duffy,�G.,�and�Elwood,�J.�(2013)�‘The�perspectives�of�‘disengaged’�students�in�the�14–19�phase�on�motivations� and�barriers�to�learning�within�the�contexts�of�institutions�and�classrooms’.�London Review of Education,� 11�(2),�112–26. Golding,� J.� (2015)�‘What� has� the� Coalition� Government� done� for� the� development� of� initial� teacher� education?’.�London Review of Education,�13�(2),�113–24. Lupton,�R.,�and�Thomson,�S.�(2015)�‘Socio-economic�inequalities�in�English�schooling�under�the�Coalition� Government�2010–15’.�London Review of Education,�13�(2),�4–20. Mujtaba,�T.,�Reiss,�M.,�and�Hodgson,�A.�(2014)�‘Motivating�and�supporting�young�people�to�study�mathematics:� A�London�perspective’.�London Review of Education,�12�(1),�121–41. Ngware,�M.W.,�Ciera,�J.,�Abuya,�B.A.,�Oketch,�M.,�and�Mutisya,�M.�(2012)�‘What�explains�gender�gaps�in�maths� achievement�in�primary�schools�in�Kenya?’.�London Review of Education,�10�(1),�55–73. Parameshwaran,�M.,�and�Thomson,�D.�(2015)�‘The�impact�of�accountability�reforms�on�the�Key�Stage�4� curriculum:�How�have�changes�to�school�and�college�Performance�Tables�affected�pupil�access�to� qualifications�and�subjects�in�secondary�schools�in�England?’.�London Review of Education,�13�(2),�157–73.