MATHEMATICS THROUGH ART:
developing spatial skills and digital literacy through visual arts education
Coordinator: Erika Kugler
School: Szent István primary and Secondary Grammar School with Sport Specialisation, Jászberény, Hungary
School: Szent István primary and Secondary Grammar School with Sport Specialisation, Jászberény, Hungary
Context
In public education, it is expected from schools to cater for student diversity, and support those who are challenged with social disadvantages, learning deficits or mental, behavioural problems. Our institution also strives for educational equity. However, when behavioural or developmental problems are identified, the role of the family is crucial: children who are diagnosed with such challenges, are mostly given special treatment by speech therapists, special educators, or psychologists, for example, due to the caring attitude of their parents. There are, however, children deprived from appropriate parental care, who will receive remedial education at school only. It is not easy to accommodate these developmental programs, as the curriculum is overburdened with special classes for sport, languages, or high-level arts, according to the focus of the institution.
Teachers face the problem of individualised instruction: they must cater for those lagging behind, due to their special needs, and average performers, or the talented ones in need of nurturing. Those who are less successful in the race for better learning results because of their challenges, will develop aggressive behaviour or sink into depression, even entertain suicidal thoughts. Struggling with the task of teaching these children, teachers often leave the profession for the lack of competence to face students with special learning needs. Therefore, there is a burning need for teaching methods and aids for the development of students with attention deficit disorder (ADD) and attention deficit hyperactive disorder (ADHD), to name only the most frequent challenge. Art education in Hungary is not one of the major disciplines. With one, 45-minute lesson hour per week, the developmental potentials of the arts are hard to realise. However, this discipline may be instrumental in supporting the cognitive and emotional development of challenged learners through scientific visualisations and arts-based interventions.
In public education, it is expected from schools to cater for student diversity, and support those who are challenged with social disadvantages, learning deficits or mental, behavioural problems. Our institution also strives for educational equity. However, when behavioural or developmental problems are identified, the role of the family is crucial: children who are diagnosed with such challenges, are mostly given special treatment by speech therapists, special educators, or psychologists, for example, due to the caring attitude of their parents. There are, however, children deprived from appropriate parental care, who will receive remedial education at school only. It is not easy to accommodate these developmental programs, as the curriculum is overburdened with special classes for sport, languages, or high-level arts, according to the focus of the institution.
Teachers face the problem of individualised instruction: they must cater for those lagging behind, due to their special needs, and average performers, or the talented ones in need of nurturing. Those who are less successful in the race for better learning results because of their challenges, will develop aggressive behaviour or sink into depression, even entertain suicidal thoughts. Struggling with the task of teaching these children, teachers often leave the profession for the lack of competence to face students with special learning needs. Therefore, there is a burning need for teaching methods and aids for the development of students with attention deficit disorder (ADD) and attention deficit hyperactive disorder (ADHD), to name only the most frequent challenge. Art education in Hungary is not one of the major disciplines. With one, 45-minute lesson hour per week, the developmental potentials of the arts are hard to realise. However, this discipline may be instrumental in supporting the cognitive and emotional development of challenged learners through scientific visualisations and arts-based interventions.
OBJECTIVES
In the framework of the AMASS project, we develop programs that enhance mathematical skills of students with learning difficulties.
In the framework of the AMASS project, we develop programs that enhance mathematical skills of students with learning difficulties.
- We personalise instruction to include hearing impaired, lefthanded, hyperactive, depressive, even suicidal children in the teaching-learning process
- We motivate learners through arts-based activities that give them a new and flexible channel of expression
- We facilitate student learning through experience-based instruction: hands-on tools for problem solving, visualising concepts and rules, and offer carefully structured, meaningful manual activities to develop cognitive skills
- We encourage visualisers to use their skills in a predominantly verbal instructional culture and teach them how to make meaning through images
PARTICIPANTS
Program development and realisation: Erika Kugler, MA in art and design education, Master Teacher, lecturer in teacher education
Research consultant: Andrea Kárpáti, Prof. Dr., art historian and educational researcher, Corvinus University Budapest
Program venue: Szent István primary and Secondary Grammar School with Sport Specialisation, Jászberény, Hungary. (Director: Imréné Pomázi)
Students: this longitudinal developmental program is realised in afternoon sessions, at school, in the optional stream of the timetable. Students opt for the arts-based, mathematics focused experiment for a semester only, but most of them stay. The program started in September 2020, with students in Grade 5 (average age: 11 years) and is now in its third semester (November 2021) with students in Grade 6 (average age: 12 years).
Program development and realisation: Erika Kugler, MA in art and design education, Master Teacher, lecturer in teacher education
Research consultant: Andrea Kárpáti, Prof. Dr., art historian and educational researcher, Corvinus University Budapest
Program venue: Szent István primary and Secondary Grammar School with Sport Specialisation, Jászberény, Hungary. (Director: Imréné Pomázi)
Students: this longitudinal developmental program is realised in afternoon sessions, at school, in the optional stream of the timetable. Students opt for the arts-based, mathematics focused experiment for a semester only, but most of them stay. The program started in September 2020, with students in Grade 5 (average age: 11 years) and is now in its third semester (November 2021) with students in Grade 6 (average age: 12 years).
THEORETICAL BACKGROUND
The development of students is supported in a holistic, reflective way, considering student development in social behaviour, interpersonal skills, task-centeredness as well as in digital literacy, numeracy, scientific visualisation and spatial skills. Visual competence is also enhanced and assessed through the process-oriented portfolio method. The theoretical foundation of the methods employed are arts-based inquiry
Arts-based interventions address two major societal challenges:
1. Negative attitudes to leaning: encouraging students to develop their learning skills, attitudes and interests towards science and art disciplines and deepen their knowledge and critical skills. Art and arts education are perceived as a way of enhancing the agency of students at risk of alienation from school and the wider society (Ahonen et al, 2008).
2. A lack of transparency in knowledge production: we exploit the role of arts for innovating knowledge acquisition and overcome barriers between scientific and artistic domains. We intend to create conditions for long-term educational change and developmentand play an active role as agents of change (c.f. De Piccoli et. al. 2019).
Methodology
The learning program focused on the development of spatial abilities and numeracy, to support the most difficult thematic areas in Mathematics for the students with special needs. The interdisciplinary learning content was developed in collaboration with the teachers of Mathematics and Art (E. Kugler, the project co-ordinator). Intersecting areas of Mathematics and Visual Culture were identified:
The art educator gave tasks from everyday life that needed the utilisation of geometrical concepts and rules. Mathematics teachers coached students with special needs on a conceptual level. Construction of objects and spaces, building complex spatial ensembles and modelling based on images were well received even by students with short attention spans because the tasks provided a chance for individual solutions. After the development of basic spatial skills like orientation and manipulation in space, sign systems depicting space was acquired. Learning Monge axonometry was preceded by a series of constructing and depicting tasks. The image of a spatial object from different angles was carefully studied through 3D models, and only then was represented in a realistic way, and finally drawn using the Monge system. This long process of spatial imaging development will continue all through the four years of the program.
Semester 2. Art and ICTs integration
This part of the program focused on the integrated development of visual and digital skills. Students acquired the techniques of digital imaging and produced animations, video clips, photo sequences, photo collages and learnt about digital editing and postproduction. During the quarantine resulting from the COVID pandemic, children continued developing their media pieces:
Film 1: Music-image, photocollage
https://www.youtube.com/watch?v=sIK5bXbVhLc
Film 2: Dancers
https://www.youtube.com/watch?v=vgoGc3kgnsQ
Film 3: A puzzle of images
https://www.youtube.com/watch?v=25mvzxmv09U
- Semester 1. Art and Mathematics integration
We employ the arts as expressive means but also as agents of meaning making. Students develop spatial skills and thus enhance their understanding of mathematical problems. Information and Communication technology (ICTs) are constantly employed to create an authentic imaging environment. Informal (after-school) arts programs will interact with formal arts education and beneficially influence learning results of students.
The program started with the identification of students with multiple behavioural and mental challenges and their invitation to join the program “Mathematics through Art”. Ten students were selected from the two parallel classes (Grade 5, average age: 11.3 years) and their background folder was drawn up. Homeroom teachers characterised the students: - creativity and problem-solving skills (as diagnosed in previous assessments)
- areas of interest, preferred activities
- skill deficits, learning problems
- current mental state and behaviour
- social background
- any other information relevant for development
- Double self-portrait: in favourite dress and happy mood / in a dress you dislike, being sad
- Art map about a place you liked or one you want to visit
- Free expression: a painting entitled “Storm”
- Spatial representation: 2D representation of a house from 3 angles, based on a photo
The learning program focused on the development of spatial abilities and numeracy, to support the most difficult thematic areas in Mathematics for the students with special needs. The interdisciplinary learning content was developed in collaboration with the teachers of Mathematics and Art (E. Kugler, the project co-ordinator). Intersecting areas of Mathematics and Visual Culture were identified:
- space and plane geometry
- the concept of distance
- radius, diameter, arc of a circle, annulus, and tangent
- constructing a triangle
- splitting a section by half
- characteristics and construction of rectangle and quare
- perpendicular and parallel lines
- diagonals of plane figures
- examination of symmetry
- types of angles
- network of space figures (cube and cuboid), rules of frontal axonometry, overlay
The art educator gave tasks from everyday life that needed the utilisation of geometrical concepts and rules. Mathematics teachers coached students with special needs on a conceptual level. Construction of objects and spaces, building complex spatial ensembles and modelling based on images were well received even by students with short attention spans because the tasks provided a chance for individual solutions. After the development of basic spatial skills like orientation and manipulation in space, sign systems depicting space was acquired. Learning Monge axonometry was preceded by a series of constructing and depicting tasks. The image of a spatial object from different angles was carefully studied through 3D models, and only then was represented in a realistic way, and finally drawn using the Monge system. This long process of spatial imaging development will continue all through the four years of the program.
Semester 2. Art and ICTs integration
This part of the program focused on the integrated development of visual and digital skills. Students acquired the techniques of digital imaging and produced animations, video clips, photo sequences, photo collages and learnt about digital editing and postproduction. During the quarantine resulting from the COVID pandemic, children continued developing their media pieces:
Film 1: Music-image, photocollage
https://www.youtube.com/watch?v=sIK5bXbVhLc
Film 2: Dancers
https://www.youtube.com/watch?v=vgoGc3kgnsQ
Film 3: A puzzle of images
https://www.youtube.com/watch?v=25mvzxmv09U