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Sounding ways into teaching mathematics: an approach in Teachers’ Professional Development
or “the integration of music and mathematics”
KEY COMPETENCES FOR LIFELONG LEARNING
European Reference Framework, Luxembourg: Office for Official Publications of the European Communities, 2007
http://ec.europa.eu/education/policy/school/competences_en.htm
Mathematical skills can be learned and pupils' learning motivation can be fostered through cross-curricular activities based on music.
Rationale of and background to the EMP MATHS project
European added value
(1) Students will better master basic life skills (numeracy and transversal key competences), thus
(2) reduce the number of low achievers in basic skills,
(3) prevent early school leaving and increase tertiary education attainment.
Increasing key competences contributes to preparing young people for higher skilled jobs(millions of low-skilled job disappearing) for lifelong learning during longer working lives, thus addresses youth unemployment and the social integration of disadvantaged groups.
Global stakeholder networks
• European Association for Music in Schools www.eas-music.org/
• The abcmaths consortium working to improve instructional quality in mathematics classrooms, encouraging teachers’ reflection of both contents and instructional practice (503215-LLP-1-2009-1-DE-COMENIUS-CMP www.abcmaths.net
• The Fibonacci project (Inquiry-Based Science and Mathematics Education) http://fibonacci.uni-bayreuth.de/project/overview.html
• The ISME focus group PRIME (Practice and Research in Integrated Music Education), a network of about 70 researchers and practitioners around the World http://campus.ph.fhnw.ch/Music/PrimePage
Specific needs addressed:
• Teaching practices.
• Single-subject music education is disappearing.
• Lack of experience and confidence in collaborative working with other colleagues teaching the same and other subjects.
• Doubts and misperceptions about the relevance, transferability and multiple impacts of the methodology in different local, national and cross-border settings.
• Educational materials on verbal, visual, tactile and abstract mathematical approaches are limited and not readily available.
• Curriculum changes.
What about teachers?
The Logic of Professional Development in EMP MATHS
State and district policy: Model depicting theoretical relationship between professional development
and student achievement
The role of Semiotic function circle as a theoretical frame in EMP MATHS
General psychological model of the person–world relationship.
Semiotic function circle (according to Lang, 1993)
Teaching practice in Maths and Music
Teaching practice in Maths and Music
TEACHER TRAINING IN THE FRAMEWORK OF THE EMP-M
Albert Casals & Laia Viladot
On behalf of the Catalan EMP-M team:Cristina González-Martín, Jèssica Pérez-Moreno
& Carmen Carrillo
Framework
Music education can play an active role in innovations based on integratedcurriculum, in national and european level (Casals et al., 2014)
Integration is a creative activity that can be taught and learnt (Viladot & Cslovjecsek, 2014)
There is a lack of research, educational materials and school experiences related to integrate maths and music at school (EMP-M project)
Key ideas for designing CPD courses
• Working with an integrated educational approach (M&M)
• Promoting the relationships between the participants as a key to success
• Fostering teachers to think out of the box in their teaching approachesand develop own activities
• Taking advantage of shared activities between teachers and trainers fromEU as community of learners
(Viladot & Cslovjecsek, 2014)
5 different types of sessions :
•Relationship and informal contact between participants
•Basic disciplinary knowledge & skills and subject-specific teaching approaches & methods
•Practice and theory of integrated music and maths teaching
•Invite to be creative and develop your own examples of integrated activities
•Encourage to further collaborate within your schools and regions
What have we done?
EMP-M CPD Courses• EMP-M project developed different modalities of PD training:
• Up to 4h (intensive,1-day workshop)
• 15h 2-day course (intensive)
Along the academic period (extensive)
• 30h 5-day course (intensive)
Along the academic period (extensive)
EMP-M CPD Courses• EMP-M project developed different modalities of PD training:
• Up to 4h (intensive,1-day workshop)
• 15h 2-day course (intensive)
Along the academic period (extensive)
• 30h 5-day course (intensive)
Along the academic period (extensive)
EMP-M in Cat: Musicomàtics
I thought that Àfrica didn’t understand multiplication,but now I see that she does (2nd year classroom teacher)
Experiential and creative teaching & learning in CPD is fostered by:
• exploring, sharing and reflecting on activities that can be used inmaths and music education
• learning about the theoretical background and philosophy ofintegrated maths and music teaching and learning
• developing, enriching and empowering the participants’ music andmaths teaching skills and personal competences
• instruction in the use of the EMP webpage (activities, teacher’s handbook, exchange functions…)
• sharing ideas for teacher-initiated courses at the participants’schools and national CPD courses
• providing the opportunity for teachers from different countries to learn about other European cultures
CPD provides a space for active and collaborative learning
among professionals bringing into play entrepreneurship skills
Educational entrepreneur (Bresler, 2011)
Count the beat? Get inspiredTransforming professional development of Greek educators
teaching Music and Maths
Dr Maria Argyriouon behalf of the research team,
Greek Association of Primary Music Educatorswww.primarymusic.gr
Interdisciplinary education in Greek education system
• Open mindedness: the Greek educational community was ready to espouse a radical change.
• Modern teaching material, which meets the learning needs of its target group.
• The classes were supplied with technological equipment (CD players, computers, interactive whiteboards, music instruments etc.)
• Young teachers coming from the University into the “school market” were bringing innovative ideas.
Key features of the curricula for mathematics and music in the Greek National Curriculum (age 5-14 years)
Aims of the Mathematics curriculum:
• Develop basic mathematical skills
• Cultivate their mathematical thinking
• Develop special mathematical processes
• Create and solve problems
• Understand the language of mathematics as a means of communication
• Develop their personal and collective thought
• Develop critical thinking skills
• Use mathematics to analyse and interpret the social environment
• Build a dialectical relationship between the formal and informal knowledge of mathematics
• Apply the basic characteristics of mathematical knowledge: generalisation, certainty, precision and brevity
• Express themselves using multiple presentations
• Communicate and verbalize thoughts and arguments.
Aims of the Music curriculum:1. Develop:• Their musicality and musical skills through listening, playing and creating music • Their innate ability for artistic and creative expression• The ability for aesthetic pleasure during listening, playing and creating music• Their critical and creative thinking• Their personality• A lifelong relationship with the Art of Music
2. Link their musical experience to everyday life
3. Utilise new technologies for music creation and acquiring music knowledge.
The Survey
• Method and sample
• Outcome and Predictor Variables
• Analytic Strategy
Edu Didactics 2015 in Athens http://primarymusic.gr/conference2015/index.php
Results
Our main interest in this survey was the relationship between professional development and the reformers' vision of teaching practice in Maths and Music. The findings indicate that:
• Teachers before EMP MATHS CPD had more traditional practices.
• The quantity of professional development in which teachers participate is strongly linked with both inquiry-based teaching practice and investigative classroom culture.
• Each additional activity they created during CPD was associated with a more investigative classroom culture, after adjusting for differences both between teachers and their schools.
• Teachers with more sympathetic attitudes towards reform of teaching Math & Music used practices significantly more frequently and had more investigative classroom cultures than did more skeptical teachers.
“The topics, which were taught individually and unlinked have to be consolidated in
order to see the relevance, between them, and understand the nature of being”
(Plato: Republic 573C)
Sounding Ways into Mathematics: Working in the English Primary School Context
Professor Graham Welch on behalf of the research team,
Caroline Hilton and Dr Jo SaundersUCL Institute of Education
According to Marcus du Sautoy:
‘Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry’.
The project has sought to explore some of these ideas in our learning and teaching.
Music and maths both use patterns and structures such as progression and symmetry
Models of IntegrationBarnes (2015) identified at least five common and contrasting ways of using more than one subject to respond to a problem, theme or issue.
These styles of cross-curricular teaching and learning have different aims, depend upon a range of planning strategies and result in different learning opportunities:
• Tokenistic
• Hierarchical
• Multidisciplinary
• Interdisciplinary
• Opportunistic
Experiences of integrated music and mathematics activities (School 1, Year 3 pupils)
Observations of integrated music and mathematical learning and teaching activities revealed greater opportunities for inclusion for those pupils who may otherwise have struggled to engage with mathematical learning
• 3 children with special educational needs, who usually receive 1:1 support from a classroom assistant, were able to participate independently
• The language barriers which were often a problem for children with English as an additional language, were less problematic when the children had another way of expressing their thinking
Experiences of integrated music and mathematics activities (School 2, Year 5 pupils)
Observations of these learning and teaching activities revealed greater opportunities for a range of learning styles (as well as some challenges).
• Children had little experience of music and inititially found it hard to keep a rhythm going
• Issues linked to multiplicative relationships were represented through musical activity and provided the children with a meaningful context within which to discuss the issues raised
• The introduction of musical instruments added another dimension and made it easier to see and hear the musical/mathemtical patterns
Primary teachers in England: Investigating transformations through Music and Maths
Primary teachers (from early years, special educational needs and mainstream primary settings) created graphic scores with 3D shapes. The musical material was manipulated using transformations and the compositions performed. The symbolisation represented pitch, rhythm, dynamic and duration amongst other musical elements.
Primary teachers in England: reflecting on the first day of the National Workshop
Sixteen teachers took part in the first of two day-long national workshops. An evaluation was completed at the close of the workshop. Participants responded to a series of statements using a 7 point Likert scale.
Teachers positively engaged with the activities and were given opportunities to talk through how to adapt the tasks to the particular needs of their pupils.
The teachers reported that they felt more confident to approach these activities within their classrooms and that their knowledge about how to approach Music and Mathematics in an integrated approach had increased.
Primary teachers in England: reflecting on using Music and Maths in the classroom
Following the first workshop, teachers experimented with the activities in their own classrooms. During the second workshop, they shared their experiences and further learning.
• Greater awareness of ‘where the Maths is’ in an activity, for example explicit use of patterns to support a composition activity, or using number lines and prediction to create polyphonic rhythms
• Reflecting upon current practice and better of understanding how integrated Music and Maths can be used to include those pupils who are often excluded
• Gaining a shared language that begins to bridge the musical and mathematical learning in the curriculum
• Working more closely with colleagues with different strengths to plan and deliver interdisciplinary activities.
Sounding Ways into Mathematics: Working in the English Primary School Context
Professor Graham Welch on behalf of the research team
Caroline Hilton [email protected] Dr Jo Saunders [email protected]
UCL Institute of Education
Impacts of International and Interdisciplinary Collaborations onthe Concept of Music Education
Samuel Inniger
The Intertwining of Research and Practice in Music Education
Helmut Heid (2015):
• There is neither a practice withouth theory nor a theory that is not connected with educational practice
• Educational research refers and builds on educational practice
• Educational practice is dependant on the educational-scientific research in order to develop and improve education
Heid, Helmut: Bildungsforschung im Kontext gesellschaftlicher Praxis, in: Zeitschrift für Pädagogik, Heft 3/2015, Beltz Juventa, Weinheim, p. 390-409.
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Impact of Inderdisciplinary International Projects
European Music Portfolio: Maths (2013-2016)
Challenges:
• Different scientific, disciplinary and educational cultures
• Different working cultures
• Different terms of employment, payment and financial possibilities
Creativity and openness are required to find a common understanding
Benefits:
• great variety of expertise (7 European countries, around 30 involved researchers)
• new methods and approaches in solving problems and doing research
Impact on our Institution: the Teachers of Today
Continuous Professional Development Courses (CPDs)
• Collaboration projects such as EMP-L (languages) gives us
the competences and tools to design and perform both
national and international CPD courses with interdisciplinary
settings
What we learned:
• teachers generally respond to interdisciplinary topics
• Theory and new interdisciplinary teaching methods must be explained with practical examples
• It needs time for the teachers to implement an interdisciplinary understanding in their every-day teaching
Impact on our Institution: the Teachers of Tomorrow
Developing a new Master Programme for integrated music and art teaching
• Music Pedagogy department & Art Design and Technical Design department
Impact on research preferences of our students
• Brainstorming, building from scratch
• Finding solutions needs dialogs
• Crossing borders
Impact on our Research: new Projects
• Educational tools developed by students of other departments
• Own research projects
“Sonic Classroom”(BA thesis IT- Department)
“Sonic Playground”iOS App “Soundoscope”80´000 Downloads
Conclusions
• We benefit a lot from international and national interdisciplinary collaboration
• Impact on our master and bachelor curriculums
• Ties the bonds to other departments of our institution
• New projects lead to new networks, (shared) funds
• New forms of public appearance, new audience
Thank you very much!
