Project title: SignEd|Math (Signs of mathematics: Fostering the development of conceptual gestures among deaf students)

Aim: Designing a mathematical learning environment that builds on sign language as a resource for learning while providing learning opportunities for inclusive and adaptive learning.

Funding: European Commission – Marie Skłodowska Curie Actions (Horizon 2020), Individual Global Fellowship (€264.669 / U Duisburg-Essen)

Project duration: Fall 2019 – Fall 2022 (2019-2021 at UC Berkeley, 2021-2022 at U Duisburg-Essen, Germany)

Team members: Christina Krause (UC Berkeley / Universität Duisburg-Essen, Germany), Dor Abrahamson (UC Berkeley), Florian Schacht (Universität Duisburg-Essen, Germany)

Undergraduate students involved in the project: Janaki Vivrekar, Cindy Chen, Chelsea Boyle

German website: https://www.uni-due.de/didmath/ag_schacht/signed_math.php

Background: As much as inclusive and accessible education has made big steps forward in the last years, deaf students are still mostly considered within a perspective of deficits and needs, instead of emphasizing also their diversity and strengths. SignEd|Math builds on research in mathematics education, the learning sciences, deaf education, and psycholinguistics and brings them together in a design based research project in which we seek to embrace sign language as resource for learning mathematics. Here, a mathematical learning environment is first developed and then iteratively tested and developed further, acknowledging and appreciates the Deaf learners’ differences in communicating and meaning making as influenced by the use of sign language.

Main guiding questions are:

- What can be effective design strategies for conceiving learning opportunities that stimulate conceptually fruitful discourse to negotiate new mathematical meanings in sign language?
- How can these strategies be put into practice to design learning opportunities that enable deaf learners to have epistemologically equitable access to the mathematical content to be learned by acknowledging their specific ways of thinking and learning.
- What else can we learn about the role of language and multimodality in the development of mathematical meaning from observing the students’ learning as based on their interaction with the learning opportunity?

Motivation: Deaf students experience the world differently and bring different learning conditions to the mathematics classroom. Studies in deaf education point to the so-called “math gap”, stating that deaf students’ competence in mathematics on average lags behind the performance of their hearing peers. While this is often explained by lacking informal knowledge of mathematics hearing children often encounter in everyday mathematical conversation (for example hearing fraction terms like “it is half past three” or even the GPS saying “turn right in a quarter of a mile”), difficulties with accessing and processing written language is also reported to play an important role. Recent research in psycholinguistics furthermore points out that the use of sign language influences the ways concepts and knowledge is organized and communicated, in turn also influencing individual understandings of mathematics. Responding to concerns in deaf education that deaf students are often still treated as “hearing students that cannot hear” (Marschark et al. 2011, p. 4), we question if traditional approaches of instruction are actually appropriate to accommodate deaf students’ way of learning mathematics.

SignEd|Math hence starts to re-imagine instructional approaches from the strengths of deaf students, integrating sign language as natural resource of Deaf learners in the design of mathematical learning opportunities. More concretely, the design encourage movement as solution to a dynamic interaction problem to bridge from action to signed mathematical discourse in a conceptually meaningful way.

First design approach: Embodied design has been considered a fruitful approach as it starts from learner’s existing resources, including their individual experiences and ways of making sense of the world. This embraces physically diverse ways of engaging with the designed interaction problem and linguistically diverse ways of talking about observations, strategies, and solutions.

To work towards the goal of SignEd|Math, we first re-design the Mathematical Imagery Trainer for proportions (MIT-p) a well-established design within the embodied design framework. The re-design encourages the integration of a handshape that resembles a meaningful component of ASL signs, a so-called classifier. This handshape can then carry meaning as grounded in action in the signed discourse of Deaf students when solving a related mathematical problem together.

Aside from providing a dynamic interaction problem that is hoped to foster the emergence of conceptual gestures as ‘pre-formal proto-signs’ for mathematical conversation, the design within the embodied approach furthermore minimizes barriers through written language as they can hamper initial access to new learning experiences.

Perspective for the second phase (Germany, 2021-2022): As much as the design is aligned to the specific preferences and practices of Deaf learners, we hope to carry the design as well as the results also beyond this specific group of learners. While accommodating a special group, the design should still provide fruitful learning opportunities for as many learners as possible as aiming for adaptive education. Being aware of the constraints of building on a linguistic feature of a specific sign language (of which there are many), in this case ASL, the second phase of the project will explore its usability in different contexts in Germany. This will include German Deaf students growing up with German sign language, hard-of-hearing students, and hearing students as they might constitute different learning setting in German classrooms. Furthermore, the educational value of the learning environment for students with low language proficiency will be tested, as fostering the development of conceptual gestures might help them overcome barriers to peer interaction and with that, to learning.

**Most Recent Publications:**

**Krause**, C. M., & Abrahamson, D. (in press). Modal continuity in deaf students’ signed mathematical discourse. In A. Isabel Sacristán & J. Carlos Cortés (Eds.), *“Entre Culturas / Across Cultures” — Proceedings of the 42nd annual meeting of the North-American chapter of the International Group for the Psychology of Mathematics Education (PME-NA).* PME-NA.

**Selected prior work in DeafMath (background):**

Krause, C.M. (2019). What you see is what you get? – Sign language in the mathematics classroom. Journal for Research in Mathematics Education, 50(1), 84-97.

Krause, C.M. (2018). Embodied Geometry: Signs and gestures used in the deaf mathematics classroom – the case of symmetry. In R. Hunter, M. Civil, B. Herbel-Eisenmann, N. Planas, D. Wagner (Eds.), Mathematical discourse that breaks barriers and creates space for marginalized learners (pp. 171-193). Rotterdam: Sense.

Krause, C. M. (2017). DeafMath: Exploring the influence of sign language on mathematical conceptualization. In T. Dooley & G. Gueudet (Eds.), Proceedings of the 10th Congress of the European Society for Research in Mathematics Education (pp. 1316-1323). Dublin, Ireland: DCU Institute of Education and ERME.

Krause, C. M. (2017). Iconicity in signed fraction talk of hearing-impaired sixth graders. In B. Kaur, W. K. Ho, T. L. Toh, B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology in Mathematics Education, Vol. 3 (pp. 89-96). Singapore, Singapore: PME.

Krause, C. M. (2017). What/How can we learn from the deaf mathematics classroom? In: J. Holm, S. Mathieu-Soucy, S. Oesterle (Eds.), Proceedings of the 2017 Annual Meeting of the CMESG (pp. 259-260). Canada: Montréal: CMESG.