Naturally-occurring student discourse in Naturally-occurring student discourse in adult numeracy classroomsadult numeracy classrooms

Helen OughtonHelen OughtonUniversity of BoltonUniversity of BoltonALM-16 8ALM-16 8thth July 2009 July 2009

““We all play teacher”We all play teacher”

IntroductionIntroduction

Taking advantage of recent increase in Taking advantage of recent increase in collaborative groupwork in adult numeracy collaborative groupwork in adult numeracy classroomsclassrooms

Source of naturally-occurring discourse for Source of naturally-occurring discourse for audio recording and analysisaudio recording and analysis

Research questionsResearch questions How much do students draw on informal How much do students draw on informal

numeracy practices and ‘funds of knowledge’?numeracy practices and ‘funds of knowledge’? What else can classroom discourse tell us about What else can classroom discourse tell us about

experiences of adult numeracy learners?experiences of adult numeracy learners?

Theoretical perspectives: Theoretical perspectives: Numeracy as a Social PracticeNumeracy as a Social Practice Numeracy practiced differently in different Numeracy practiced differently in different

domainsdomains Some forms of numeracy more powerful Some forms of numeracy more powerful

than othersthan others Takes into account beliefs, attitudes, fears Takes into account beliefs, attitudes, fears

and aspirations of people carrying out and aspirations of people carrying out activities involving numbersactivities involving numbers

((Street 1984; Barton and Hamilton 1998; Baker Street 1984; Barton and Hamilton 1998; Baker 1998; Street, Baker and Tomlin 2005) 1998; Street, Baker and Tomlin 2005)

Theoretical perspectives:Theoretical perspectives:Funds of KnowledgeFunds of Knowledge Moll et al (1992) - Ethnographic research Moll et al (1992) - Ethnographic research

among Mexican families in Arizonaamong Mexican families in Arizona Extended by Baker (2005) to adult Extended by Baker (2005) to adult

numeracy learners numeracy learners knowledge, experiences, histories, identities and knowledge, experiences, histories, identities and

images of themselves images of themselves attitudes, dispositions, desires, values, beliefs, attitudes, dispositions, desires, values, beliefs,

and social and cultural relationsand social and cultural relations relationships with learning, teachers and relationships with learning, teachers and

mathematics itselfmathematics itself numeracy practices beyond the classroomnumeracy practices beyond the classroom

Collaborative groupwork as Collaborative groupwork as research opportunityresearch opportunity Breaks with IRE traditionBreaks with IRE tradition Based on work of Swan and Based on work of Swan and

colleagues colleagues (e.g. Swan 2006; Swain and Swan (e.g. Swan 2006; Swain and Swan

2007)2007) Legitimated as good practice by Legitimated as good practice by

Ofsted (2006)Ofsted (2006)

MethodologyMethodology

Classroom talk as dataClassroom talk as data

Many informal numeracy practices invisibleMany informal numeracy practices invisible ““The facts of greatest value for the study of The facts of greatest value for the study of

education are…most readily displayed in education are…most readily displayed in classroom talk.”classroom talk.” (Edwards and(Edwards and W Westgate 1994:55)estgate 1994:55)

Linguistic EthnographyLinguistic Ethnography Language and social world mutually shapingLanguage and social world mutually shaping Close analysis of naturally-Close analysis of naturally-

occurring talk givesoccurring talk givesinsights into social settings insights into social settings and wider structures and wider structures (Rampton et al 2004)(Rampton et al 2004)

Research SettingResearch Setting

Adult education centres in north of EnglandAdult education centres in north of England Classes chosen where discursive groupwork Classes chosen where discursive groupwork

encouragedencouraged 6-11 students in each class6-11 students in each class Working in groups of 3-5 Working in groups of 3-5

Participants largely female, white-BritishParticipants largely female, white-British Age range 20-60 years Age range 20-60 years Working towards Level 1 and Level 2 Adult Working towards Level 1 and Level 2 Adult

Numeracy qualificationsNumeracy qualifications

Method of data collectionMethod of data collection Audio recording Audio recording ofof student-student student-student

discussion during collaborative discussion during collaborative groupworkgroupwork Little intervention from teacherLittle intervention from teacher

Naturalistic data?Naturalistic data? Mobile phones unobtrusively on Mobile phones unobtrusively on

classroom tablesclassroom tables Labov Labov (1972) - speakers’ talk becomes (1972) - speakers’ talk becomes

more natural when intensely engaged in more natural when intensely engaged in subject under discussion subject under discussion

Usual classroom activities – not Usual classroom activities – not specially planned for researchspecially planned for research Card matching (e.g. dominoes, jigsaws)Card matching (e.g. dominoes, jigsaws) Card sorting and categorisingCard sorting and categorising Traditional worksheets and assessment Traditional worksheets and assessment

paperspapers Data collectedData collected

3 centres3 centres 10 sessions10 sessions 18 participants18 participants 12 hours of recorded discussion12 hours of recorded discussion

Method of data collection Method of data collection (contd)(contd)

Examples of activities: Examples of activities: Thinking Thinking Through Mathematics Through Mathematics (DfES 2007)(DfES 2007)

Examples of activities: designed Examples of activities: designed by participating teacherby participating teacher

Emerging ThemesEmerging Themes

The adult numeracy classroom as The adult numeracy classroom as a site of social interactiona site of social interaction

Students join groupwork via legitimate Students join groupwork via legitimate peripheral participation (Lave and Wenger peripheral participation (Lave and Wenger 1991)1991)

Classroom has discourse of its ownClassroom has discourse of its own Regular practicesRegular practices Administration and accreditation proceduresAdministration and accreditation procedures

Laughter prevalentLaughter prevalent Humour as a “resource” in adult numeracy Humour as a “resource” in adult numeracy

classrooms (Baynham 1996) classrooms (Baynham 1996) Excluded from community of practiceExcluded from community of practice

ESOLESOL Disabilities or learning difficultyDisabilities or learning difficulty

The adult numeracy classroom as The adult numeracy classroom as a community of practicea community of practice

Uncertainty and Self-deprecationUncertainty and Self-deprecation

Lack of self-confidence amongst adult Lack of self-confidence amongst adult numeracy learners well-recognised numeracy learners well-recognised Generally regarded as Generally regarded as problematicproblematic

Expressions of uncertainty prevalent in my Expressions of uncertainty prevalent in my recordingsrecordings “…“…I think”I think” “…“…isn’t it?”isn’t it?” ““Would that be…?”Would that be…?” ““It was just a guess”It was just a guess” ““I’m getting myself muddled up“I’m getting myself muddled up“ ““Why can’t I do it?”Why can’t I do it?”

Uncertainty and Self-deprecationUncertainty and Self-deprecation

Expressions of uncertainty acknowledged Expressions of uncertainty acknowledged and accepted by groupand accepted by group By male as well as female studentsBy male as well as female students

Used by students to:Used by students to: Elicit encouragement and support from other Elicit encouragement and support from other

studentsstudents Invite other students to evaluate contributionsInvite other students to evaluate contributions Articulate difficulties and formulate questions for Articulate difficulties and formulate questions for

teacherteacher Elicit suggestions for metacognitive strategiesElicit suggestions for metacognitive strategies

E.g. “I draw pies” (to visualise fractions)E.g. “I draw pies” (to visualise fractions) Could almost be regarded as a resource?Could almost be regarded as a resource?

Uncertainty and Self-deprecationUncertainty and Self-deprecation

Donna That would be – that would be – 75mmJudith (…) cm is much more

Donna Is that right?

Judith I think it’s right – but I’m not

Not overconfident on these

Donna No, it’s just knowing which way to go round with them, isn’t it?

Judith Yes

Uncertainty and Self-deprecationUncertainty and Self-deprecation

Judith I think we need your help, ElizabethI’m confusing myselfWhich way round you do it?I’ve just really muddled myself up…

Elizabeth If you’re measuring in metres, and you want to change to centimetresAre you going to have more of them or are you going to have less of them?

Judith It’s – sorry? I’m going from metres to cmSo I’m going to have more, aren’t I?

Emerging themesEmerging themes

Context and RelevanceContext and Relevance

Students only occasionally drew on Students only occasionally drew on “funds of knowledge” “funds of knowledge” Most often in measure and data Most often in measure and data

handling discussion activitieshandling discussion activities Least often in traditional word problems, Least often in traditional word problems,

including practice assessment materialsincluding practice assessment materials

Relevance of classroom Relevance of classroom maths to adult learners lives?maths to adult learners lives?

Relevance of classroom Relevance of classroom maths to adult learners lives?maths to adult learners lives? ““Contexts” in traditional word problems Contexts” in traditional word problems

largely ignoredlargely ignored (Oughton 2009)(Oughton 2009)

Current assessment materials in England Current assessment materials in England consist entirely of word problemsconsist entirely of word problems Level 1 and Level 2 Adult NumeracyLevel 1 and Level 2 Adult Numeracy

Alternatives to word problemsAlternatives to word problems

allowed students to critique relevanceallowed students to critique relevance

DfES 2007DfES 2007

Alternatives to word problemsAlternatives to word problems

Judith: [reading from card] I would measure the weight of a mosquito in

Sally: I wouldn’t [laughter]

Seemed to encourage students to Seemed to encourage students to relate to out of classroom practicesrelate to out of classroom practices

Conditional tense?Conditional tense?

Alternatives to word problemsAlternatives to word problems

Alternatives to word problemsAlternatives to word problemsDonna I tell you what I always struggle with

You know, like litresHow many millilitres are there (…) Is it a thousand?

Abigail Mmm

Donna I get confused, because you think like ‘mil’ is a million

Abigail [showing her water bottle which is on the desk]

Yeah, well, if you think, one of them is five hundred millilitres

So two of them is a litre

Donna A litre

Abigail So, like, obviously if you do it in CL it’s like, um

Donna Centilitres… A hundred? No

Is it a cent – centilitre. A hundred, isn’t it?

Contd

Alternatives to word problemsAlternatives to word problemscontd

Judith Forgotten

[laughter]

Abigail Some of them do have ‘CL’ on them, most of them have millilitres on

Donna Wine bottle have centilitre on them, don’t they?

(…) centilitres (…)

Judith A hundred centilitres is a litre, so it’s right

Donna Oh, right. So a thousand millilitres is one litre

Abigail With water, sometimes you can buy it and it says five hundred mil

Sometimes you buy it and it says centilitres

I think it depends if it’s foreign water, or different places measure it in different ways, don’t they, like -

Donna Oh yeah. So, half a litre is fifty centilitres.

Alternatives to word problemsAlternatives to word problems Salaries in a small company used to Salaries in a small company used to

illustrate how outlying values (e.g. illustrate how outlying values (e.g. director’s salary) distort meandirector’s salary) distort mean Example often used in numeracy classrooms Example often used in numeracy classrooms

Given extra impact by randomly distributing Given extra impact by randomly distributing cards to each student showing a salarycards to each student showing a salary

Students spontaneously seized on chance Students spontaneously seized on chance to role playto role play

Alternatives to word problemsAlternatives to word problems

Donna: [receiving her card] Oh yeah. I’m the cleaner.

[laughter]

Teacher: I’m going to calculate what a typical wage (…)…So what have you got there? Donna?

Donna: 10,000 [pounds]

Sally: 12,000

Judith: Miss Moneybags here[laughter]

Abigail: [in ‘posh’ voice] I have 100, 000Donna: The director. You’re the director

Students’ interests not always in line Students’ interests not always in line with government focus on skills for with government focus on skills for employment!employment! Body image often seemed to be Body image often seemed to be

considered importantconsidered important Social practice a more useful framework Social practice a more useful framework

here than funds of knowledgehere than funds of knowledge

The relevance of learning to The relevance of learning to students’ livesstudents’ lives

The relevance of learning to The relevance of learning to students’ livesstudents’ lives

Sally Did you put your waist measure in?Donna I put 24 inchesAbigail In your dreams [laughs]Donna [‘prim’ voice] Actually, I’m thinner than Posh*

The waist measurement of a boy, an eight-year-old boy

Judith Probably our leg measurementAbigail Wouldn’t want to be like her anywayJudith She’s going to be ill

*Victoria Beckham

Emerging themesEmerging themes

Implications for PedagogyImplications for Pedagogy

(LSIS/Tribal 2008)

Implications for PedagogyImplications for PedagogyRarity of formal mathematical discourseRarity of formal mathematical discourse

Gemma The numbers are – wrong

Charlotte Yeah

Gemma They go up in 2s, and then 1s

Jackie Why, where you looking?

Gemma Look [pointing]

Jackie Oh, right

Gemma When it goes to there, it goes up

Melissa [reading from multiple choice options] “The vertical scale is incorrect”

Implications for PedagogyImplications for PedagogyRarity of formal mathematical discourseRarity of formal mathematical discourse

Implications for PedagogyImplications for PedagogyMultimodal representation and card Multimodal representation and card activities - scaffoldingactivities - scaffolding

Implications for PedagogyImplications for PedagogyMultimodal representation and card Multimodal representation and card activities – referencing abstract ideasactivities – referencing abstract ideas

Makes ‘invisible’ practices audibleMakes ‘invisible’ practices audible Multiplication by repeated additionMultiplication by repeated addition Addition by counting on Addition by counting on

Informal Calculation StrategiesInformal Calculation StrategiesImplications for PedagogyImplications for Pedagogy

Roz Yeah, so it’s 20 sixesSo its (…)

Dan YeahPete That’s one-forty isn’t itRoz No, it’s a hundred isn’t it?

Pete 20, 40, 60 , 80, 100 and 20

‘‘Gestalt’ moments audibleGestalt’ moments audible Students’ (over-)reliance on Students’ (over-)reliance on

algorithmsalgorithms Groupwork flounders if students Groupwork flounders if students

tackle work outside ZPDtackle work outside ZPD Potential of this method as a CPD Potential of this method as a CPD

tool for teacherstool for teachers

Other implications for Other implications for PedagogyPedagogy

Emerging implications for Emerging implications for practice and further researchpractice and further research Simplicity / effectiveness of research Simplicity / effectiveness of research

methodmethod Irrelevance of ‘contexts’ in word-problem Irrelevance of ‘contexts’ in word-problem

genregenre Numeracy ‘funds of knowledge’ not often used Numeracy ‘funds of knowledge’ not often used Alternative activities encouraged more links to Alternative activities encouraged more links to

out-of-classroom numeraciesout-of-classroom numeracies Has implications for roll-out of ‘Functional Has implications for roll-out of ‘Functional

Skills’ in EnglandSkills’ in England Expressions of uncertainty not so much a Expressions of uncertainty not so much a

‘problem’ as a ‘resource’?‘problem’ as a ‘resource’? Exclusion of some students from Exclusion of some students from

participation in collaborative groupworkparticipation in collaborative groupwork

Limitations and opportunities Limitations and opportunities for further studyfor further study Reflects only adults who have Reflects only adults who have chosenchosen to to

return to studyreturn to study Data seems ‘naturalistic’, but hard to prove Data seems ‘naturalistic’, but hard to prove Audio data only one aspect of classroom Audio data only one aspect of classroom

interactioninteraction Future directionsFuture directions

How to make collaborative How to make collaborative groupwork more inclusivegroupwork more inclusive

Potential for teacher CPDPotential for teacher CPD Application to functional Application to functional

skills agenda (in England)skills agenda (in England)

References Baker, D. (1998) ‘Numeracy as Social Practice; an adult education context in

South Africa’ Journal of Literacy and Numeracy Studies 8(1) pp. 37-50Baker, D. (2005) ‘Numeracy and “funds of knowledge” ’ Reflect 3 pp. 16-19Barton, D. and Hamilton, M. (1998) Local Literacies: Reading and writing in one

community London: Routledge Baynham, M. (1996) ‘Humour as an Interpersonal Resource in Adult Numeracy

Classes’ Language And Education 10 (2&3) pp.187-200DfES (2007) Thinking Through Mathematics: Strategies for Teaching and Learning

London: Department for Education and Skills (Maths4Life)Edwards, A. and Westgate, D. (1994) Investigating Classroom Talk London:

FalmerLabov, W. (1972) Sociolinguistic Patterns Philadelphia, PA: University of

Pennsylvania PressLave, J., and E. Wenger (1991). Situated Learning: Legitimate peripheral

participation. Cambridge: Cambridge University Press LSIS/Tribal (2008) Key skills application of number/ Adult numeracy Level 2 Test

Paper L [Available on-line at www.move-on.org.uk/downloadsFile/ downloads1576/Num_Level2_TestL_Jan08.pdf accessed 27.6.09]

Moll, L., Amanti, C., Neff, D., & González, N. (1992). Funds of knowledge for teaching: using a qualitative approach to connect homes and classrooms. Theory into Practice, 31, pp.132-141.

Oughton, H. (2007) ‘Constructing the “Ideal Learner”: A Critical Discourse Analysis of the Adult Numeracy Core Curriculum’ Research in Post-Compulsory Education 12 (2) pp.259-275.

References Ofsted (2006) Evaluating mathematics provision for 14–19-year-olds. London:

HMSO Oughton, H (2008) ‘Mapping the Adult Numeracy Curriculum: Cultural capital

and Conscientization’, Literacy and Numeracy Studies 16 (1) pp 39-61Oughton, H. (2009) ‘A willing suspension of disbelief? “Contexts” and

recontextualisation in adult numeracy classrooms’, Adults Learning Mathematics: An International Journal 4(1) pp16-31

Rampton, B., Tusting, K., Maybin, J., Barwell, R., Creese, A. and Lytra, V. (2004) UK Linguistic Ethnography: A discussion paper. Available on line at www.ling-ethnog.org.uk/documents/discussion_paper_jan_05.pdf [accessed 22/07/07]

Skillsworkshop (2007) Percentages – Level 2. Available on-line at www.skillsworkshop.org/l2num/l2percentageprobs.pdf [accessed 29/11/08]

Street, B. (1984). Literacy in Theory and Practice. Cambridge: Cambridge University Press.

Street, B., Baker, D and Tomlin, A. (2005) Navigating Numeracies: Home/School Numeracy Practices Dordrecht: Kluwer

Swain, J. and Swan, M. (2007) Thinking Through Mathematics Research Report London: NRDC.

Swan, M. (2006) Collaborative Learning in Mathematics: A Challenge to our Beliefs and Practices. London: National Institute for Adult and Continuing Education (NIACE); National Research and Development Centre for adult literacy and numeracy (NRDC).