> KMJM v,bjbj==!BWWv(lZrrrr4Z_*()))))))$M+ m*3*]=*]]])])]]9R@%)X?0Zr"))/*0_*@)1.o1.)]J$6Mathematics for Students with Special Educational Needs:
Touching and Shaping Mathematics withDeaf Students
Virginia MovilioChacn
SPECIAL EDUCATION SCHOOL FOR THE DEAF: UEEBMATURN
UNIVERSIDAD PEDAGGICA EXPERIMENTAL LIBERTADOR VENEZUELA
HYPERLINK "mailto:moviliov@gmail.com"moviliov@gmail.com
Deaf people can come to be understood not as a disability group but as the possessors and protectors of a great cultural heritage, a beautiful language, numerous art forms and an eloquent history.
Harlan Lane, 2003
Introduction
Just before the sixties, W. Stokoe commented with his colleagues at Gaulladet College on the possibility of the existence of a signed language used by deaf students. At the time, this idea was unacceptable to many deaf educators in the United States. According to his personal experience, the deaf students were using routinely a language, which was structurally different from English.
As a result of these observations, in 1960 he published an article titled Sign Language Structure and in 1965, with the help of two deaf colleagues, the first dictionary of American Sign Language (ASL) (Stokoe, 2004).
In Venezuela the education of the deaf and hard of hearing is done within a bilingual context. The deaf must acquire sign language at the earliest possible time as a first language then afterwards learn how to use written Spanish in order to guarantee their integration into the subsequent educational levels (Oviedo, 2000).
Venezuelan Sign Language and, in general, SpanishAmerican sign languages, have very few signs for mathematical concepts, terms and procedures (Larreal, 2006), so that frequently teachers must create or coin specific signs in order to teach Mathematics to Deaf students.
In this paper, we present some experiences in the creation of approximately 250 signs for mathematics. The experience began in 2003 with high school students whose ages ranged from 13 to 26 years, and was developed within the framework of constructivist learning principles at the special education school for the deaf at Maturn, Monagas, in eastern Venezuela. The creation process is developed during class with the help of the math teacher who is also a sign language interpreter. When there is a lack of signs in the mathematical subject studied, new signs are coined in a collaborative process with the active participation of the Deaf students.
Coining Mathematical Signs
In Spain, a very interesting experience in the creation of mathematical signs was carried out in 1999 when a team of educators composed of two mathematicians, one physicist and a biologist, coined a total of 350 signs related to mathematics and biostatistics (Fajardo, 2005). In the United States only experts in American Sign Language (ASL) and mathematics teachers have developed most sign coining experiences.
The coining of math terms at the School for the Deaf in MaturnVenezuela began in the classroom, so it is very important to arrange and decorate the classroom according to the mathematical terms under study (Lujan, 2007).
It is also necessary to take note that open doors or windows without curtains causing visual distractions for the deaf students could turn into obstacles in the communication process when discussing a particular sign.
Lets consider the coining process for the concept of the area of a plane figure. This concept does not have a sign listed in the Manual of Venezuelan Sign Language published by the Deaf Federation of Venezuela (FEVENSOR).
The teacherinterpreter begins the class whose goal is to calculate the area of certain polygons:
Places the word area on the blackboard and asks the students about its significance since the concept might exist already in their vocabulary. In this case, the response was negative.
The teacher begins by touching the surface of various objects, among them: the rectangular surfaces of the table, the blackboard, the eraser and the notebooks. Immediately, the eight deaf students begin to make signs of various forms. Two groups of students had a sign whereas the third group was still confused. One of the signs consisted of placing the dominant hand over the fixed upturned palm of the other and making a circular movement with it. The teacherinterpreter intervened noting that the other sign used had a different meaning in another related science. So the new sign began to be used in the context of the concept of the area for the different examples used and the third group of students began to understand the meaning of the new sign using it in the correct context. The acceptance of the new sign was therefore achieved through the spontaneous, creative and collective participation of all the students. Each expressed his or her opinion about the sign and all opinions were respected. The coining process took about one hour.
The teacherinterpreter then showed the students how to calculate the area of a few plane figures using graphing paper and coloring materials. They mentioned that the concept was also applicable to other situations such as calculating the amount of tiles needed to cover the floor of a house, the area of a plot of agricultural land, among others. This indicated that the coining process was effective and practical since the concept learned was applied to other contexts.
Although the coining process usually begins in the classroom, the deaf students will continue to propagate and validate the signs with the students from other grades. It has also been observed that they share and transmit the signs to the deaf community both schooled and also the uneducated.
The coining experiences indicate that in some cases a math sign can be created in an immediate and permanent form, whereas in other cases the coining process can be slow and the signs need to be modified later on (Movilio, 2005).
The authors experience indicates three distinct paths to creating a math sign:
Writing in Spanish the word that corresponds to the concept, term or mathematical procedure that lacks a corresponding sign in LSV;
Using an existing sign from everyday language;
Selecting without discussion a sign, which spontaneously emerged within the group in an unanimous fashion.
INCORPORATING MATH SIGNS INTO SIGN LANGUAGE
One of the most experienced authors in the formation of database in sign language in various fields of knowledge is Frank Caccamise, who indicates that the process of selection and acceptance of a particular sign follows the scheme presented in the following diagram:
Need to communicate ideas, etc.
Users/communicators develop sign vocabulary
Sign user selection
Standard sign usage
Collection
Evaluation Sharing
Selection Recording
Caccamise, et al. (2003)
The new signs later are used for teaching math to new Deaf students, which eventually modify them to better approach the signed concepts. According to the Caccamise (2003) model, the fifth step will include a validation process, which will be carried out by a multidisciplinary research team. After that process, the signs will be registered in video, shared with colleagues and diffused across Venezuela in conferences, workshops and also using the web page HYPERLINK "http://www.cienciaensenas.org" www.cienciaensenas.org dedicated to the coining, registration and evaluation of signs in science.
Mathematics uses universal symbolism, since we can see mathematical publications written in different languages, even in ideographic languages, and still all use common math symbols. This leads us to think that we can achieve a set of standard math signs in a manner independent of the linguistic variations between the different sign languages.
Coining of signs has covered, among others, the need of signs in the following areas:
Whole numbers and their operations;
Rational numbers and their operations;
Prime, composed, odd and even numbers;
Radicals and exponents;
Some geometrical figures;
Some geometric solids;
Elemental statistics.
Our goal is to build a wide technical sign vocabulary, which will stimulate the inclusion of Deaf students in all educational and professional levels.
References
Caccamise, F; Basile,M; Ortolani, V; Aidala, C; Dorn, C; Feigel, D (2003). Administrative Support Technology (AST) Sign Vocabulary CDROM Project: A SelfInstructional Sign Language Resource for Faculty, Staff and Students. International Symposium on Instructional Technology and Education of the Deaf: Supporting Learners, PreSchoolCollege. Rochester, NY. June 2527.
Fajardo, L. (2005). Personal communication.
Lane, H. (2002). Do Deaf People Have a Disability? Sign Language Studies, 4(2), 356379.
Larreal, E. (2006). Mathematical Significance and Sign language. Unpublished master thesis. Zulia University. Venezuela.
Larreal, E. (2006). Significados Matemticos y la Lengua de Seas Venezolanas. Unpublished master thesis. Zulia University. Venezuela.
Lujan, M. (2007). Los nuevos recursos: estrategias para lograr la inclusin de alumnos hipoacsicos en las aulas regulares de Matemtica. En R. Abrate y M. Pocholu (Eds). Experiencias, Propuestas y Reflexiones para la Clase de Matemticas. Universidad Nacional de Villa Mara: Argentina. 91109.
Lujan, M. (2007). New Resources: Strategies to Include Deaf Students in Regular Math Classes. In R. Abrate and M. Pocholu (Eds). Experiences, Proposals and Reflections on Math Classes. National University of Villa Mara: Argentina. 91109.
Movilio, V. (2005). Coining math signs for the teaching of some topics in geometry and arithmetic to students with hearing deficiencies at the 7th and 12th semester of the IRFAUEEBM collaboration. Unpublished, UPELVenezuela.
Movilio, V. (2005). Acuando seas matemticas para la enseanza de algunos tpicos de la geometra y aritmtica a educandos con Deficiencias Auditivas del 7mo al 12do semestre del Convenio IRFAUEEBM. Trabajo no publicado UPELVenezuela.
Oviedo, A. (2000). Contando cuentos en Lengua de Seas Venezolana. Mrida: Consejo de Publicaciones. ULA.
Oviedo, A. (2000). Telling Stories in Venezuelan Sign Language. Mrida: Consejo de Publicaciones. ULA.
Stokoe, W. (2004). El Lenguaje en las Manos. Por qu las seas precedieron al habla. Fondo de Cultura Econmica: Mxico.
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