Let's talk about maths: using classroom data for collaborative ... 3) language support: withdrawal, generally capped at 2 years, one fund in second level for all ...
Let’s talk about maths: using classroom data for collaborative professional development
JOANNA BAUMGART
Presentation overview 1) Project
2) Context 3) Frameworks 4) Data and participants 5) Results 6) Conclusions and future directions
Project
Interviews: Teacher Educators
Classroom recordings
Reflective
meetings
Interviews: Teachers
Context: Irish education and changing classrooms 1) 12% speak languages other than Irish and English at home 2) 182 different language spoken across Ireland 3) language support: withdrawal, generally capped at 2 years, one fund in second level for all support needs
Context: language in non-linguistic mainstream subjects 1) In multilingual contexts: BICS and CALP (Cummins 1979)
2) In L1 contexts: subject specific cognitive academic language (Vollmer 2009, Beacco 2016) 3) The case of mathematics: lexis: technical vocabulary, lexical words with meanings similar to everyday language, everyday words (Pimm 1987, Shuard and Rother 1984, Raiker 2002, Schleppegrell 2007) grammar: grammatical metaphor, long NP, conjunction for logical relations (O’Halloran 2000, Barwell 2005, Schleppegrell 2007)
Frameworks: learning in the classroom Sociocultural view of learning (Vygotsky 1978, 1986; Roberts 2016) learning is social, collaborative and dynamic in nature: from interpersonal to intrapersonal key role of language as a mediating tool
Frameworks: reflective practice Key aspects of dialogic reflective practice
articulation facilitates the move from tacit and unconscious to conscious knowing (Ghaye and Ghaye 1998) articulation facilitates understanding of the important factors in play (Tarrant 2013) collaboration (see also: Farrell 2008, Ghaye 2011, Farrell 2012, Mann and Walsh 2013, Mann and Walsh 2017)
Frameworks: action research 1) Practitioner-based research: powerful tool for change and improvement at the local level (McNiff 2002) 2) Benefits for teachers (Ferrance 2000): allows teachers work on problem they identified themselves encourages collaboration facilitates professional learning and development
Review and evaluate
Identify problem
Reflection
Implement intervention (Adapted from: Tripp 2003)
Plan intervention
Data and participants 1. Who: a) 18 students b) 2nd year secondary school c) ordinary level maths d) Project Maths 2. Where: A large town in County Limerick, west of Ireland. 3. When: 5 lessons from October to December 2011
Data and participants 4 students from the Traveller community 1 students with considerable learning difficulties 2 students with serious medical conditions 1 student in care of guide counsellor 1 student with ADHD 2 EAL students discipline problems: bullying overall reading age below chronological age
Corpus of lessons Lesson
Topic
Stages
Number of words
Lesson 1
Distance formula
opening, presentation, main, closing
3801
Lesson 2
Equation of a line
opening, presentation, main, closing
4293
Lesson 3
Revision
opening, main, closing
5028
Lesson 4
Compound interest
opening, presentation, main, closing
4100
Lesson 5
Simultaneous equations
opening, presentation, main , closing
5156 TOTAL: 22378
Reflection on action 1. Lesson 1: starts a sequence of lessons on distance formula
2. Procedure: teacher did up an example on BB SS practise with other examples and 2 are done up on BB 3. Reflective meeting: “I’m doing all the work (…) it’s all my energy.” “(…) the class is 37 minutes long. 32 or 33 minutes are teacher turn in it.” “They need to be doing more work.”
Reflection for action INTERACTIONS
• "steps" • posters • competition
• pair and group work • peer teaching
LANGUAGE IN MATHS (Reflection for action: Killion and Todnem 1991)
Lesson 2: peer teaching and steps L6: How is that a plus? (to peer) L4: What’s wrong with you like? (correcting something in the copy)
Lesson 3: revision with posters
Right so you'd say amm the next person /say/
/Me!/
this is the slope and this is the point we're using and you've to put M over the slope
and X one Y one over the point.
/And then Rita/
/Then Rita you would say/
No I'd say this! No you're not!
Lesson 4: pair work and competition
You're done? Oh Mona is first in! No answer and me coming over
Oh Kaitlin add in!
What is it? 48?
Four eight four zero
Four eight four zero divided by a hundred /divided by /
Lesson 5 What do I do now?
Yeah you put brackets around here
Lesson 4: setting up competition Is it in pairs?
Amm it's not going to be in pairs /you're going to be individually/
/LL/ /Oh! Ah Miss can we go in pairs? Please!/
Do you want to go in pairs?
/Yeah!/
Analysis: discursive features
Questions Low-order, closed, procedural
Moving beyond monosyllabic
Interaction patterns IRF (Sinclair and Coulthard 1975) Interactive/ authoritative (Mortimer and Scott 2003)
Discourses Right/wrong (Lyons et al 2003) Quickly providing answers
Analysis: word ratio 16
14
12 Opening 10 Presentation 8 Main
6
Closing
4
2
0 Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Let’s talk about maths… But who is talking? Mathematical metadiscourse plus minus equals multiply* formula*
bracket point* sign* equation
Let’s talk about maths… But who is talking? Student talk changes 3
2.5
2
Lesson 1
1.5
Lessons 2-5 1
0.5
0 plus
minus
equals
multiply*
formula
bracket
point*
sign*
equation
Let’s talk about maths… But who is talking? Teacher talk changes 5 4.5 4 3.5 3 Lesson 1
2.5
Lessons 2-5
2 1.5 1 0.5 0 plus
minus
equals
multiply*
formula
bracket
point*
sign*
equation
Conclusions
Dialogic reflection and CPD
CL in mainstream classrooms
Teacher’s reflection “Maths is such an individual thing but they were not afraid to talk. And these words are not only new for the international students but also the Irish.”
Joanna Baumgart wishes to acknowledge the support of Irish Research Council for the Humanities and Social Sciences which awarded funding for this research.
Joanna Baumgart wishes to acknowledge the support of the Faculty of Arts, Humanities and Social Sciences, UL and the School of Modern Languages and Applied Linguistics, UL which awarded funding for this conference.
