Periodic Reporting for period 2 - SignEd.Math (Signs of Mathematics: Fostering the Emergence of Conceptual Gesture Among Deaf Students)
Période du rapport: 2021-10-01 au 2022-09-30
Inclusive education has made big steps forward over the last years. Still, deaf students are mostly considered within a perspective of deficits and needs without acknowledging their specific resources and strengths. The project SignEd|Math built on research in math education, learning sciences, deaf education and psycholinguistics and brought them together to embrace sign language (SL) as a resource for learning mathematics. Developing and testing a learning environment that uses Deaf learners’ use of SL to support mathematical understanding, we sought to contribute to math education for Deaf students, to build theory on learning mathematics more generally and to innovate methodology for designing for Deaf students and beyond.
Acknowledging the influence of the use of SL on cognition, conceptual understanding and social learning, the learning environment (LE) was designed to help the students leverage their potential for learning mathematics by building on their embodied and linguistic resources. By testing the LE with Deaf students and also with learners with other linguistic and sensory backgrounds to learning, the project was supposed to reach beyond the context of Deaf learners to enrich knowledge about designing for inclusive learning, enhance methodological knowledge for design and research, and to develop theory about what constitutes mathematical thinking and learning and how it relates to embodied experiences and language.
Because of the Covid-19 pandemic, the actions concluded in the development of the LE and related methodological innovations on designing for special education populations as well as theoretical contributions to gestures in bilingual mathematics education.
Acknowledging the influence of the use of SL on cognition, conceptual understanding and social learning, the learning environment (LE) was designed to help the students leverage their potential for learning mathematics by building on their embodied and linguistic resources. By testing the LE with Deaf students and also with learners with other linguistic and sensory backgrounds to learning, the project was supposed to reach beyond the context of Deaf learners to enrich knowledge about designing for inclusive learning, enhance methodological knowledge for design and research, and to develop theory about what constitutes mathematical thinking and learning and how it relates to embodied experiences and language.
Because of the Covid-19 pandemic, the actions concluded in the development of the LE and related methodological innovations on designing for special education populations as well as theoretical contributions to gestures in bilingual mathematics education.
We developed a digital LE that built on a specific feature of SL: its potential for iconicity, that is representing aspects of the idea in similarity. Following research in psycholinguistics, these aspects come to stand for the idea and become more strongly associated with it, while those not represented might fade to the back. Of particular importance for us, mathematical SL signs might incorporate mathematical activity in which conceptual understanding is grounded, linking both the concept and the corresponding sign to manual action.
A second aspect relevant for our design concerns the consideration that all our conceptual understanding is grounded in embodied experiences with the world. Assuming that, we can design problems for embodied interactions to develop movement schemata fruitful for conceptual understanding.
SignEd|Math considered these aspects and reimagined an established embodied design for establishing students’ proportional reasoning. It is programmed on a tablet interface and works with bimanual movement that picks up linguistic characteristics of American SL, in particular a handshape that can carry the idea of a generic number or quantity (Fig. 1). We modified the original design to integrate the development of manual movement schemes that can be used for talking about ideas around proportionality in transfer tasks, bringing manual action into mathematical discourse. A detailed description of the design and its background can be found online: https://youtu.be/tSquVe9LvXY
The pandemic impacted the implementation of the project in its core and forced some changes on it that were impossible to predict in advance. These changes concerned the very nature of the approach, in that the empirical part had to be reimagined several times before it was canceled eventually. We adapted by concentrating on aspects of theory and design.
For example, we focused on the methodology of design by considering SignEd|Math as part of a new innovative genre for educational design for special education populations from a perspective on resources and preferences, rather than deficiencies. As this, SignEd|Math became part of the research program SpEED - Special Education Embodied Design. SpEED understands itself as an approach to designing for special education populations, based on an embodied approach to thinking and learning. In SpEED, the embodied resources and preferences the students bring to learning are the basis from which the design process starts. In particular, this approach considers the peculiarities of the learning process instead of comparing the learners with typical students. It thereby goes beyond providing access to learning content but seeks to allow for equitable opportunities to conceptual learning, based on the special ways of learning that are related to special sensory-motor profiles.
SignEd|Math is one of three design projects of the first generation of SpEED, the other two dealing with social interaction of students on the autism spectrum, and the learning of mathematical concepts targeting students with a high sensory threshold. By comparing, contrasting and relating these projects and the underlying theoretical and methodological approaches, a design research genre for equitable inclusive design has been developed.
Results have been published in a book chapter and a peer-reviewed journal paper and have been presented at various talks and conferences.
SpEED is currently in its second generation, with further publications in preparation that include reflections integrating four new design research projects.
Another new focus has been set on deepening the understanding of relationships between gesture and language with respect to mathematics thinking and learning. This was supposed to prepare a fundament for the third year of the project, during which the learning design was to be tested with bilingual students and students with low language proficiency. Through this, we planned to explore how meaningful gestures aside from the signs of sign language might be grounded in the sensorimotor engagement with the learning opportunity and how these might enhance the learning processes of bilingual students. Together with a colleague, I established a framework that integrates gestures as part of language in a model of gestures’ role in mathematical thinking and learning. This was supposed to set the groundwork for observing the gestures elicited in bilingual students through the LE to compare with the gestures and signs of Deaf students. Through this, we submitted, we will be better able to understand the potential of the LE to bridge language barriers through fostering the development of conceptual gestures in all students.
A second aspect relevant for our design concerns the consideration that all our conceptual understanding is grounded in embodied experiences with the world. Assuming that, we can design problems for embodied interactions to develop movement schemata fruitful for conceptual understanding.
SignEd|Math considered these aspects and reimagined an established embodied design for establishing students’ proportional reasoning. It is programmed on a tablet interface and works with bimanual movement that picks up linguistic characteristics of American SL, in particular a handshape that can carry the idea of a generic number or quantity (Fig. 1). We modified the original design to integrate the development of manual movement schemes that can be used for talking about ideas around proportionality in transfer tasks, bringing manual action into mathematical discourse. A detailed description of the design and its background can be found online: https://youtu.be/tSquVe9LvXY
The pandemic impacted the implementation of the project in its core and forced some changes on it that were impossible to predict in advance. These changes concerned the very nature of the approach, in that the empirical part had to be reimagined several times before it was canceled eventually. We adapted by concentrating on aspects of theory and design.
For example, we focused on the methodology of design by considering SignEd|Math as part of a new innovative genre for educational design for special education populations from a perspective on resources and preferences, rather than deficiencies. As this, SignEd|Math became part of the research program SpEED - Special Education Embodied Design. SpEED understands itself as an approach to designing for special education populations, based on an embodied approach to thinking and learning. In SpEED, the embodied resources and preferences the students bring to learning are the basis from which the design process starts. In particular, this approach considers the peculiarities of the learning process instead of comparing the learners with typical students. It thereby goes beyond providing access to learning content but seeks to allow for equitable opportunities to conceptual learning, based on the special ways of learning that are related to special sensory-motor profiles.
SignEd|Math is one of three design projects of the first generation of SpEED, the other two dealing with social interaction of students on the autism spectrum, and the learning of mathematical concepts targeting students with a high sensory threshold. By comparing, contrasting and relating these projects and the underlying theoretical and methodological approaches, a design research genre for equitable inclusive design has been developed.
Results have been published in a book chapter and a peer-reviewed journal paper and have been presented at various talks and conferences.
SpEED is currently in its second generation, with further publications in preparation that include reflections integrating four new design research projects.
Another new focus has been set on deepening the understanding of relationships between gesture and language with respect to mathematics thinking and learning. This was supposed to prepare a fundament for the third year of the project, during which the learning design was to be tested with bilingual students and students with low language proficiency. Through this, we planned to explore how meaningful gestures aside from the signs of sign language might be grounded in the sensorimotor engagement with the learning opportunity and how these might enhance the learning processes of bilingual students. Together with a colleague, I established a framework that integrates gestures as part of language in a model of gestures’ role in mathematical thinking and learning. This was supposed to set the groundwork for observing the gestures elicited in bilingual students through the LE to compare with the gestures and signs of Deaf students. Through this, we submitted, we will be better able to understand the potential of the LE to bridge language barriers through fostering the development of conceptual gestures in all students.
Even though the project was not carried out as planned, the change of perspective from empirical work to theoretical and methodological work turned out to be fruitful and bear potential for becoming highly significant for future work in inclusive education. This concerns the theoretical work for integrating the role of gestures in mathematics education of bilingual students, but especially the development of a new design genre for equitable inclusive education as providing a significant contribution to the work on educational design.
The work of SpEED - of which SignEd|Math is one of the founding projects - has been presented to educational researchers and practitioners at conferences, in colloquia and in workshops. With this, SpEED seeks to not only reinvent the way we design for populations that differ in abilities, sensory-motor profiles and preferences to those of typical learners, the project also aims at transforming the discourse about non-typical learners in educational contexts in research as well as in practice.
The work of SpEED - of which SignEd|Math is one of the founding projects - has been presented to educational researchers and practitioners at conferences, in colloquia and in workshops. With this, SpEED seeks to not only reinvent the way we design for populations that differ in abilities, sensory-motor profiles and preferences to those of typical learners, the project also aims at transforming the discourse about non-typical learners in educational contexts in research as well as in practice.