1. Introduction
Being an important instrument in our daily lives makes the mathematics necessary for each individual of a society to learn it properly. Although the studies dated before 2000s had focused mainly on the content of mathematics, in recent studies it has been tried to explain how mathematics should be thought and which methods should be used for teaching activities. There have been lots of studies on teaching mathematics to the students with learning disabilities with the “Everyone Can Learn Mathematics” principle.
The students with learning disabilities for mathematics are the students who have more problems for learning mathematics than the others, or ones who underperform than the others, or ones who need special education to give adequate performance (Bintas, 2007). There are individuals who have been reported as having at least 20% disability degree on their health certificates have resided intrastate Republic of Turkey [TUIK]. The hearing impaired individuals in Turkey have received their education in different schools at the elementary level (primary and middle schools for hearing impaired), and at the secondary and higher education levels, they have received inclusive education.
An effective education for mathematics to increase the success rate of the students with learning disabilities has been supported by National Council of Teachers of Mathematics (NCTM). The standards of NCTM emphasize that all of the students need algebra beginning from pre-school and proceeding to all levels (NCTM 2000). The new principles and standards on school mathematics have been prepared in order the students to progress with 5 simple goals. The 5 simple goals given below need to be gained by the students by adopting the principle of equality: “Mathematics is for all students without recognizing any personal characteristics, background information and physical characteristics of them”
[NCTM].
1. To learn the importance of mathematics 2. To be confident about mathematics skills 3. To be a problem solver in mathematics
4. To learn how to communicate in mathematics language 5. To learn how to think mathematical
It is necessary for disabled individuals to receive education or acquire a profession on an equal basis with the other individuals of the society. Hearing loss is loss of hearing due to the problems from birth or afterbirth. Hearing impairment is a situation occurs for an individual due to the hearing reduction. Hearing impaired individuals have a difficulty of learning since they have problems with the speaking, understanding and comprehension skills due to the hearing loss. Based on their speaking and language problems, they also have difficulties on cognitive, motor coordination, emotional-social, educational, professional and social areas. Although they use hearing instrument, hearing impaired individuals receive the frequency and intensity of the sounds only allowed by the instrument. Therefore they cannot hear some of the speech sounds or they confuse them. They have a difficulty to understand the things that have been spoken based on the distance between the speakers and them, the intensity or tone of the voice of the speaker or background noises. The factors such as the type, degree, configuration, cause of hearing loss and active usage of hearing instrument, the beginning age of the usage, the suitability and adjustment of the instrument for the hearing loss are important for language and speaking development of the hearing impaired individuals [MNE, educational support program for Hearing Impaired Individuals ].
Vygotsky (1965) stated that in development of thought and speech the way is not from individuality to community, it is from community to individuality in his “Thought and Language”.
Consequently Vygotsky brought into prominence to the children thought, which has been assumed primitive and far from reality from infancy by showing that it is for a purpose, in other words to communicate and socialize. And he also conduce education methods to be revolutionised by drawing attention to the success of a child with a help when the related education is above the maturation level of the child. Thus, the importance of socializing and communicating in the educational period was emphasized. Hearing impaired individuals have experienced delays and restrictions to acquire the information and skills which have been acquired by communication due to their disability on language and speaking. Accordingly, they have expressed their thoughts in written or they have not been able to understand mathematical concepts expressed verbally. For instance they have a difficulty to understand the words such as “below”, “right” and “left” in the expression of “Right and left viewpoints of the cube given below” which they encountered in a mathematical question. Concerning mathematics education, when compared to normal students it makes them disadvantaged to understand the words, considering they have no idea about the meanings of these words since they have not used them in their daily lives. Using the sign language for the words and terms, which are suitable for mathematics lessons, cause contradiction in terms. For instance the word “yuz” (a hundred) in Turkish expresses a number mathematically, in sign language it is expressed by showing human face (since the word “yuz”
has a number of meanings including “a hundred” and “face” in Turkish) and this makes it difficult for the students to think concepts such as natural numbers and digit value. The hearing impaired students have difficulties on thinking and reasoning, classification and association and explaining skills since the inabilities on their language development. Compared to the students of the same age, they have a difficulty on envisioning in abstract thinking skills. The hearing impaired individuals do not receive auditory stimuli in a similar way depending on the type and degree of the hearing loss. And this causes to have difficulties related to long-term memory and working memory. The hearing impaired individuals have a difficulty in listening and following the verbal directives. They can be distracted easily. They have made much more effort to understand the things in their environment and thus they have easily got tired mentally. Additionally, they can also have difficulties in some skills which require visual motor coordination. The failures which the individual experienced related to learning have created lack of motivation, and dependently those failures have affected the achievements related to learning social relations and academic skills of the individual negatively [MNE, educational support program for Hearing Impaired Individuals].
In conclusion, the mathematically disabled students with need special attention in order them to acquire skills for basic mathematical operations, various conceptual methods and automation.
Therefore the direct educational method should be used, especially clear and straight education (Carnie, 1997).
Teacher Education on Educating The Hearing Impaired Students
Council on Teachers of The Deaf, CED prepares teachers with hearing impairment or for hearing impaired students and cooperates with national, provincial or local associations and agencies for various activities, committees and working groups, and accredits university programs. In our country, it has been emphasized at Higher Education Council in 2015 that the necessity for teachers in the fields of teaching mentally disabled, hearing impaired, visually impaired and for the students with multiple disabilities or with superior intelligence under special education has been increasing. In this meeting, it is indicated that the importance of the adequate education which should be received by the teacher candidates in Special Education Field Teaching departments regarding to the education of mentally disabled, hearing impaired, visually impaired, the students with multiple disabilities or with superior intelligence in accordance with the recent developments in special education. Dating from 2016-2017 academic year, courses conforming the international standards for teacher education have been added on the special education teaching programs.
The Objective Of The Study
There are limited studies in the literature of mathematics education for hearing impaired children in Turkey (Kot, M., Sonmez, S., Yikmis, A. & Ince, N. C., 2016). The topics of the studies in this field can be classified as below:
- Comparison of performances of the hearing impaired students and normal students in mathematics,
- The effect of educational environment for the success rate of the hearing impaired students, - The relationship between teaching mathematics, reading and comprehension and
problem-solving performances of the hearing impaired students.
Guldur (2005) has evaluated the behaviours of hearing impaired students for solving mathematical problems depended for operations and observed features of hearing loss, duration of using hearing instrument and chronological age which are thought to affect the problem-solving skill of the students. According to the findings of the study, it was observed that the degree of hearing loss, duration of hearing instrument and chronological age are not the factors which affect the problem-solving skill alone and concluded that the hearing impaired students do not have adequate experiences related to problem-solving skill (Kot, M., Sonmez, S., Yikmis, A., & Ince, N. C., 2016).
The technological advancement in the recent era makes importance increased placed on education. The effort for changing the system of education and the qualification of human power have gained importance. The approaches which focus on disabled individuals and put the individuals in the center have come into prominence with the greater value for humanity. It is necessary to improve quailites and quantities of the teachers who will work in this field since the special education is a special major branch (Ozturk, 2008). Individual works or teamworks can be performed for the education of hearing impaired students. The important thing here is the methods and classroom tasks which the teacher applies. Therefore, the importance should be placed on developing new methods and equipment for disabled individuals in Special Education Undergraduate Programs or material producing courses.
In accordance with all the information given above the objective of this study is to improve problem analysing, comprehension and problem solving skills of the hearing impaired students by making them use basic mathematical skills which should be used in daily life. In line with this objective, a number of activities for hearing impaired students have been prepared. The mentioned activities have been prepared in accordance with the understanding, listening, writing, following instructions, expressing and writing thoughts, working and long-term memory problems derive from hearing loss and for the activities, it has been aimed to present alternative methots / techniques. And it has been also aimed to find solutions for the problems derive from teaching and using materials for hearing impaired individuals. The experiences and observations gained with this study have been expressed for following studies. As a consequence of this study, it has been aimed to popularize the learning environments prepared for the hearing impaired students to learn mathematics all around Turkey. With the study applied, it has been also aimed to make the individuals reach the below goals indicated in the Ministry of National Education educational support program for Hearing Impaired Individuals:
1. Using the hearing residuals at a maximum level,
2. Improving language and speaking skills at the level of the individuals at the same age by using auditory perception skills,
3. Using communication skills in daily life by improving them, 4. Improving reading comprehension, reading and writing skills, 5. Gaining basic mathematical skills,
6. Improving reasoning skills.
The material teaching has an important role for the disabled children since they learn by seeing and touching things. By realizing this fact, M. Montessori, who is one of the influential representatives of pedagogics, has developed several materials related to the different areas of development in order the disabled children to gain some behaviours easily and has concentrated on the education of sense organs of the disabled children (Basaran, 2004). With this object in the study, it has been tried to be
determined whether the activities prepared for this study are effective on the visual perception of the hearing impaired and mentally disabled children from their receptive language skills. The materials prepared for the hearing impaired students are paid attention to be easily found, portable, clear, performable, affordable and suitable for seeing and touching materials.
Being a master in simple operations is somewhat not enough. In addition to the simple operations (Automation Development; Carnie, 1997; Goldman, 1989), the students shoul also gain problem-solving skills (such as flexibility and adaptation). In this study, it has been aimed for the hearing impaired students to automatise preparatory arithmetics and simple operations and to comprehend mathematical problem-solving methods. Besides, it is also not enough that the students have only mathematical skills to solve mathematical problems; they should know how and when they apply this kind of information when they encounter a new and a similar situation. It has been aimed for solving word problems to teach which operation or method should be applied when and how.
Method
In this study, case study method from scientific research metods (Cepni, 2010) has been adopted. This approach aims to describe the details of the research subject and reveal cause and effect relationships.
In this study, the students with individual differences have been also observed by following the development process of their performances on group works and individual works.
The practice prepared in this direction had been performed in Izmir Tulay Aktas Hearing Impaired Secondary School as 10 course hours for 2 weeks in the spring term of 2017-2018 academic year. The activities prepared for the students had been performed by the 5th and 8th grade hearing impaired students in company with a special education mathematics teacher. The natural description processes of the students had been observed by preparing them a classroom environment which they can express themselves easily in the research process.
In this study which had been done on the hearing impaired students, it has been aimed perform achievements determined by Ministry of Education. Depending on this objective, the answers have been sought for the problems given below:
- Can he/she count by ones, twos, threes, fours, fives, sixes, tens rhythmically?
- Can he/she comprehend the natural numbers of 1, 2, 3, 4, 5, 6 ,7, 8 and 9?
- Does he/she know numerical axis and numerical order?
- Does he/she know two-digit natural numbers and digit values?
- Can he/she add or subtract numbers without carry?
- Can he/she add or subtract numbers with carry?
- Can he/she solve the problems related to addition/subtraction/mulliplication/division?
The preliminary test which belongs to the achievements indicated above was performed on 10 hearing impaired 5th grade students and 4 hearing impaired 8th grade students. After the preliminary test, it was determined that these students have problems on the achievements of;
1. Learning natural numbers and concept of digit, writing the digits properly, showing the numbers on the numerical axis,
2. Analysing the natural numbers,
3. The largeness-smallness relationship between the numbers and numerical patterns, 4. Using skills for four operations while solving problems.
And it was also determined that the students do not know the words and phrases related to the mathematical concepts such as “range the numbers from lowest to highest and from highest to lowest”,
“even natural numbers”, “find the number which disrupts the numerical pattern”, “forward, backward”,
“after-before”, “to find the difference”, “to share equally” etc., since they are insufficient on using language. In order to teach these mathematical concepts and the terms related to these concepts; a hundred cards, a numerical axis, activities for ordering, counting normal and rhythmically and materials for them were designed (Figure 1: a-b-c). These activities were performed by using methods of showing and making them perform the activities, being a model, showing, clear expression, discussion, drama, induction, deduction, games, repeating, concretion and generalising. The special
attention was paid on increasing the activities as many as possible since the achievement of natural numbers is the precondition for the achievement of the four operations skills of the individual (Figure 2: a-b-c).
Figure 1: a-b-c: Activities for counting normally and rhythmically
Figure 2: a-b-c: The materials used
In order to provide effective education, steps for educational method was followed. The researchers have found out that following these steps affects students with learning disabilities to model the patterns, to practice with or without a guide, to receive correct and positice feedacks with frequent repetitions (Maccini et. al., 1999; Maccini & Hughes, 2000; Maccini &Ruhl, 2000; Mercer &
Miller, 1992). Therefore, the works consist of individual works, group works and guided works (Figure 3: a-b-c and Figure 4: a-b-c).
Figure 3: a-b-c: The individual activities of the students
Figure 4: a-b-c: The group activities with the students
The biggest problems for disabled students are lack of self-confidence and self-expression. To this respect it was tried to receive feedbacks by calling them to the board and making them attend the activities (Figure 5: a-b-c).
Figure 5: a-b-c: The Active Attendance Environment of The Students
In order to attract students’ attention and provide motivation for them, each lesson under this study was started with games. And also, each lesson was started with activities which include the former lesson’s achievements. According to the rules of the games, group works was performed in twos, in fours and when necessary with all of them. Besides, the games had been prepared as learning-oriented, interesting, exciting and motivation increasing games (Figure 6: a-b-c).
Figure 6: a-b-c: The Work and Game Environment STAR Method
For the second phase of the study, STAR problem-solving technique was used. This method makes students complete the general problem-solving steps and also makes them link between the intermediary steps as a problem solver (Maccini & Hughes, 2000; Maccini & Ruhl, 2000). Although this method generally have been used with integers, it can be also used in different fields in order to improve problem-solving skills. This method was adopted from Mercer and Miller’s Strategic Math Series (1991).
The main steps of this method are; Search the problem, Translate the words into an equation in Picture form, Answer the problem, Review the solution
The intermediary steps of STAR method are;
1. Search the problem
• Read the problem carefully
• Ask yourself “Which facts do I know?””
2. Translate the words into an equation in Picture form
• Choose a variable
• Determine the operations
• Present the problem (concrete part)
• Present the problem by drawing it (semi-concrete part)
• Write an algebraic equation (abstract part) 3. Answer the problem
4. Review the solution
• Reread the problem
• Ask the question “Is the answer meaningful?”
• Check the answer
The steps of this method consist of these stages; prepare the regulators (they should make students to be able to identify new skills and also make them think for learning) identify and model, conduct the guided learning, conduct independent learning, perform the last tests, provide positive and decent feedbacks.
After the preliminary test, it was determined that the hearing impaired students are insufficient for presenting problems and finding soluitons. The STAR problem-solving technique was reregulated for the hearing impaired students (Table 1). Therefore it was deduced that teaching both presenting the problem (reorganizing the problem which is in the informative format as a visual representation) and solving the problem is necessary for the students. The first two steps of the STAR technique show
the representation of the problem. However, the problems was prepared by dramatizing and drawing pictures since the students was found insufficient to understand the problem due to their insufficiency for vocabulary. For the first problems, some hints (about the operations needed) related to the soluitons were given. After the students adopted the method, any kind of hint were not provided. Both the
the representation of the problem. However, the problems was prepared by dramatizing and drawing pictures since the students was found insufficient to understand the problem due to their insufficiency for vocabulary. For the first problems, some hints (about the operations needed) related to the soluitons were given. After the students adopted the method, any kind of hint were not provided. Both the