The Ability of Mathematical Connections to Deaf Students in

Completing Math Test

Samuel Igo Leton

1,2

, Wahyudin

and Darhim

Universitas Pendidikan Indonesia, Jl. Setiabudhi No.229 Bandung, Indonesia

Universitas Katholik Widya Mandira, Jl. A. Yani No. 50-52, Kupang, Indonesia

Keywords: Mathematical Connections, Deaf Students, Math Test.

Abstract: The purpose of the study was to explore the ability of deaf students in grade VIII to complete math connection

test of inter-topics in mathematics. The type of research used is qualitative research with a case study and

grounded theory design. Data were collected by various methods from six subjects who were taken

purposively based on the characteristics of language and speech, intelligence and social-emotional. They were

spread in three schools namely; SMPLB Karya Murni Ruteng - East Nusa Tenggara (NTT), SMPLB Negeri

Semarang and SMPLB Don Bosco Wonosobo. The results of the analysis showed (1) in building an

understanding of the problem, deaf students tend to represent the problem in the form of images and concrete

objects. (2) in making initial plans to complete, students are inclined to use media related to the problem

given. (3) Deaf students tend to be able to make predictions to obtain a mathematical model of a given

problem, but the students are likely to be unable to provide a reason to validate the assumption. (4) if the deaf

students can solve the problem, they tend to use a way of counting to solve it.

1 INTRODUCTION

A deaf student is students who have impaired hearing

function, either in part or in a whole that has a

complex impact on their life. The deaf student

generally has normal or average intelligence, but

because their intellectual development is strongly

influenced by language development, the deaf student

will have lower intelligence compared to normal

students. This is influenced by the difficulty of

understanding the language, so that deaf student in

their acquisition of information and language is lack

of vocabulary, difficult to understand the expression

of language that contains the meaning of metaphor

and abstract words and it will result on the following:

deaf student needs more time to learn how to connect

the relationships between mathematical concepts and

to communicate them.

The results of a study conducted by Martin found

that deaf student lacked the cognitive potential

possessed by normal students to the maximum extent

in processing information (Martin, 1991). This causes

cognitive skills possessed by a deaf student to be

lower than normal students (Barbosa, 2014). Deaf

students are less likely to use their cognitive potential

to the maximum extent in processing information due

to limitations in communication and problem solving

(Foisack, 2003), since the deaf student has such a

deficiency above causing them to have a lower

learning achievement when compared to normal

students for materials lessons that are abstract

(Somad, 1996). In general, if the deaf student cannot

understand the problems presented orally, they will

not be able to solve them properly (Carrasumada,

1995).

Although deaf students have the limited listening

ability, it does not mean that they cannot participate

in learning process activities. Limitations in auditory

abilities can be overcome by their visual capabilities.

The best mathematical abilities possessed by children

who experience visual impairment related to visual

(Nunes, 2004). Visual is very useful for the deaf

student in building an understanding of a given

concept. Thus, hearing impairment possessed by

those students is not a direct cause of difficulty in

learning mathematics because of not all deaf students

have math scores more than normal students; about

15% of deaf students have an average or above

average standard test (Wood, 1983). In addition, the

results of previous relevant research reports found no

correlation or only a very small correlation between

hearing impairment levels and mathematical

432

Leton, S., Wahyudin, . and Darhim, .

The Ability of Mathematical Connections to Deaf Students in Completing Math Test.

DOI: 10.5220/0008523204320437

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 432-437

ISBN: 978-989-758-407-7

achievement. These results indicate that hearing loss

is not a direct cause of difficulties in learning

mathematics (Wood, 1983 and Nunes, 1998). From

the above description, this study examines

qualitatively to explore the ability of mathematical

connections on aspects of the connection between

topics in mathematics. The ability of a mathematical

connection is the ability to connect conceptual and

procedural knowledge, use mathematics on other

topics, use mathematics in everyday life activities,

and inter-topic connections in mathematics (Coxford,

1995). In expressing the ability of mathematical

connections in hearing impaired students, researchers

provide tests in the form of images that are

interesting, realistic and close to the environment of

everyday students.

2 RESEARCH METHOD

This research is included in qualitative research with

case study design. The researcher used a case study

design to explore in depth and detail on the subjects

to be studied using various procedures to collect data.

Data collection techniques used i.e.; provide tests

related to the interconnection of topics in

mathematics i.e. geometry (calculating extent of a

rectangle) and algebra (solving two linear equations)

and in-depth interviews on the results of work. The

number of subjects in this study was six people who

were taken purposively in 3 schools namely; 1 SLB

in East Nusa Tenggara (NTT) and 2 SLB in Central

Java. The following are the problems given to the

research subjects.

The following are the problems given to the

research subjects.

Figure 1.

3 RESULTS

There are several findings obtained by the researcher

when subjects completed a connection test related to

the interconnection of topics in mathematics. These

findings refer to three indicators of interconnection on

topics in mathematics (a) determine the same concept

representation, (b) determine the mathematical

concepts to be used, and (c) use predetermined

concepts to solve the problem. The results of the

analysis of each indicator are presented as follows;

3.1 Determine the Same Concept

Representation

Based on the findings it is known that all subjects (S1,

S2, S3, S4, S5 and S6) determine the same concept

representation of the problem in terms of equations

i.e.; 2p + l = 96 cm, p + 2l = 84 cm, 2p + 1l = 96 cm,

1p + 2l = 84 cm, p + p + l = 96 cm, p + l + l = 84 cm,

p + p + l = 96, and p + l + l = 84. To obtain the

equation, each subject works in several ways i.e.;

3.1.1 Make a Picture

S1, S2, S5, and S6 illustrate the problem by creating

a rectangular image. From the interview, the subject

said that the three possible sides that can be measured

from a rectangle are the length, length, width, and

length, width, width. S1 uses a finger to cover one

side (side 1) on the rectangle so that the visible sides

are p, p, and l. Furthermore, s1 closes one side

(length/p) of the rectangle, so that the visible sides are

width l, l, and p. From the activity, s1 wrote in the

form of equation 2p + l = 96 cm and p + 2l = 84 cm.

S2 makes a rectangular image and writes three sides

to the rectangle i.e; p, p, l and write the equation 2p +

ll = 96. Next, he write l on the other side and obtained

the equation 1p + 2l = 84, while s5 and s6 had the

same way of obtaining equations in which the

representation with the problem given was making 2

images in rectangles. In the first picture, he made an

arrow that starts from the length, width, length, and

writes the equation p + p + l = 96 to show the three

sides measured by Melki. In the second picture, it also

creates an arrow line starting at the width, length,

width and writing the equation p + l + l = 84.

Figure 2: Picture based category.

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With respect to three sides each measured, the

four subjects had the same opinion that Melki & Berto

measured three different sides on the same

whiteboard surface. This can be seen from the

mathematical sentences written by each subject i.e. 2p

+ l, p + 2l, 2p + ll, 1p + 2l, p + p + l, and p + l + l, and

it is also seen from the total size which is different

obtained by each subject in the form p + p + l = 96

and p + l + l =84. In relation to the form of equation

obtained S1 i.e. 2p + l = 96 and p + 2l = 84 is different

from the equation obtained S2 i.e. 2p + ll = 96 and 1p

+ 2l = 84. S1 obtains 2p + l of p + p + l by adding the

same variable, p + p, to get 2p. Likewise with p + 2l

from p + l + l and summing the same variable that is

l so as to get l + l = 2l. This differs from the form of

the equations obtained by S2 i.e. 2p + ll = 96 and 1p

+ 2l = 84. S2 does not multiply constants 1 on l and

constant 1 on p. In case, multiplication 1 with any

number results in the number itself so that ll = l and

1p = p. Thus, S2 knowledge of multiplication with

number 1 is not applied in the form of 2p + ll and 1p

+ 2l, although the form of equation obtained by S2 i.e.

2p + ll = 96 and 1p + 2l = 84 is true but the form of

the equation can still be simplified to 2p + l = 96 and

p + 2l = 84. Similarly to the form of the equation

obtained by S5, the result is the same as that obtained

by S6 i.e. p + p + l = 96 and p + l + l = 84. In the

equation p + p + l = 96, there are two equal variables

p whose sum equals p + p = 2p, whereas the equation

p + l + l = 84 also has two equal variables l and can

be summed i.e. l + l = 2l. Although the form of

equations obtained by S5 and S6 are true, but the

equation p + p + l = 96 and p + l + l= 84 can still be

simplified to 2p + l = 96 and p + 2l = 84. The

understanding of S5 and S6 relates to summing the

two same variables in this case is not used.

3.1.2 Rewrite

In this category, there are two subjects namely S3 and

S4 which illustrate the problem by rewriting the

problem. According to S3 and S4 that measuring

three sides on a whiteboard surface is similar to

calculating the surface area of the board. S3 writes in

the form L = p + p + l = 96 cm and L = p + l + l = 84

cm. This is the same as the one written by S4 that is

the area of rectangle = p + p + l = 96 cm and the area

of rectangle = p + l + l = 84 cm. This shows that there

is a misunderstanding by S3 and S4 on the concept of

the area and the circumference of the rectangle.

Figure 3: Rewriting Category.

Against the form of equations obtained by S3 and

S4, i.e. p + p + l = 96 and p + l + l = 84 wherein the

equation p + p + l = 96, there are two equal p variables

which can sum up i.e. p + p = 2p, whereas in the

equation p + l + l = 84 there are also two variables l

which are the same and can be summed up that is l +

l = 2l. Although the equations obtained by S3 and S4

are true, the equations p + p + l = 96 and p + l + l =

84 can still be simplified to 2p + l = 96 and p + 2l =

84. Thus, and S4 corresponds to summing the same

two variables in this case which is not used. To obtain

a mathematical model, the six subjects made a

conjecture by saying that the total size of the three

sides as measured by Melki is greater than the total

size of the three sides as measured by Berto. The

researcher sees that the allegation is built with the

argument that the length (p) is larger than the width

(l), since p>l then 2p> 2l is consequently 2p + l >p +

2l. From this process, all six subjects suspected that

2p + l = 96 cm and p + 2l = 84 cm. The allegations

made by each subject are not supported by

mathematically strong arguments based solely on the

logical principle and the understanding of each

subject that in the rectangular image, the length of the

sides is always longer than the width of the sides. The

researcher views that there is a misconception of the

concept of understanding that the size of the long side

is always longer than the size of the width of a

rectangle. In fact, the size of the side of a rectangle

only expresses a dimension of the two-dimensional

figure.

3.2 Determine the Mathematical

Concepts That Will be Used

In the indicators determine the mathematical concepts

that will be used in connection with the connection

between topics in this problem, which the subjects in

searching for p and l values are not yet known, the

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434

researcher makes in 2 categories namely; counting

and guessing.

3.2.1 Counting

S1, S2, S5 and S6 use numerical methods (counting

one by one), adding up, and substituting to find the

value of p and l;

a Summing Up

The four subjects summed the equation 2p + l = 96

with the equation p + 2l = 84. They add up the same

variables i.e 2p + p = 3p and l + 2l = 3l, but there are

differences in the way S5 and S6 do; S6 creates a line

and S5 creates a circle-shaped curve to group the

same variables and calculates the number of

variables. S5 and S6 have a creative way of grouping

the same variables and counting them. In the end, the

four subjects obtained the same result, namely 3p + 3l

= 180.

Figure 4: Categories based on how to add (sum up).

Based on Figure 4, it appears that the four subjects

simplify the equation 3p + 3l = 180 by multiplying

by1/3. S1, S5 and S6 write in the form of 1p + 1l =

60. The equations obtained by S1, S5, and S6 are true,

but the form of the equations can still be simplified to

p + l = 60. Figure 4: Categories based on how to add

(sum up). Based on Figure 4, it appears that the four

subjects simplify the equation 3p + 3l = 180 by

multiplying by 1/3. S1, S5 and S6 write in the form of

1p + 1l = 60. The equations obtained by S1, S5, and

S6 are true, but the form of the equations can still be

simplified to p + l = 60.

b Substitution

The second step taken by the S1 to obtain the length

and width of the rectangle is a substitution. From the

equation obtained, p + l = 60, written to 1p = 60 - 1l.

The researcher sees that what is written by S1 is true

because equation 1p = 60-1l if simplified will be p =

60 - l is a form of equation equivalent to the equation

p + l = 60.

Figure 5: Substitution by S1.

According to Fig. 5, S1 obtains l = 24,

subsequently subordinates the value of l = 24 to the

equation p = 60-l and obtains a value p = 36

c Subtractions

The second step carried out by the subjects S2, S5 and

S6 are to reduce the equation 2p+l = 96 with the

equation p+2l = 84. The three subjects performed a

reduction operation as usual. They subtract the same

variables i.e. 2p-p = 1p and l-2l = -1l. However, there

is a difference in the way S6 makes it that it creates a

line to cross out two variables p and 2 variable l (make

it 0). In the end, S2, S5 and S6 get the same result, p-

l = 12

Figure 6: Categories based on reduction method.

According to Figure 6, the three subjects obtained p-

l=12, and wrote p = 12+l. The researcher sees what

the three subjects are writing is true because the

equation p=12+l is equation equivalent to the

equation p-l=12. In Figure 7, the three subjects have

different ways of obtaining p and l values. S2 obtains

the equation p = 60 - l and p = 12 + 1, so that it is

solved by writing together 60 - l = 12 +l. The

interview result obtained that S2 wrote thus because

"equally p". Next, form 60 - l = 12 + l it completes

and obtains l = 24. From that result it is substituted to

the equation p + l = 60 and obtains the value p = 36.

S5 sums the equation p + l = 60 with p - 12, to obtain

p = 36. To obtain the value of l, S5 substitutes the

value p = 36 to the equation p + l = 60, and obtains l

The Ability of Mathematical Connections to Deaf Students in Completing Math Test

435

= 24. While S6 subtracts the equation p + l = 60 with

p - l = 12, and the result obtained is l = 24. To obtain

a p-value, he substitutes the value of l = 24 in the

equation p + l = 60, thus obtaining p = 36

Figure 7: Solve the problem with subtraction.

From the way of S1, S2, S5, and S6, the researcher

sees that the concept of finding the value of p in l is

the same, but there are differences in the procedure.

The difference in procedure shows the creative

thinking of each subject in solving problems.

3.2.2 Guessing

There are 2 subjects i.e. S3 and S4 have different

ways of finding p and l values. S3 writes in the form

of the equation L = p + p + l = 96 cm and L = p + l +

l = 84 cm and makes a guess by taking the value p =

36, l = 24. In Figure 8 below, shows that S3 replaces

the value of p = 36, l = 24 to equation 2p + l = 96 and

equation p + 2l = 84 so that the equation becomes true

(the value on the right-hand side is the same as the

value on the left-hand segment. From the interviews,

it is obtained that S3 takes p-value = 36, l = 24 by

"guessing." Although "guessing" is one of the

strategies for solving problems, it needs mathematical

argumentation to strengthen the validation of the

alleged/guessed evidence. While S4 has a different

way with S3. S4 adds the equation 2p + l = 96 with

the equation p + 2l = 84. From the sum, he got the

value on the right-hand side which is 180, then he

calculated 180 ÷ 3 = 60. From the results obtained,

then he calculated 96 - 60 = 36, and he obtains a value

of p = 36. The process performed by S4 in making

mathematically incorrect allegations. Next, to obtain

a value of l, S4 subtracts the equation 2p + l = 96 with

the equation p + 2l = 84. The result obtained in the

process is l = 24.

Figure 8: Guessing based category.

From the process carried out by S3 and S4 in Figure

8, the researcher saw that the two subjects did not

have an initial plan to find the length and width on

the surface of the blackboard. However, both

subjects have good ability to make guesses even

though they cannot provide mathematical

arguments to strengthen the validation of such

alleged evidence

3.3 Use Predefined Concepts to Resolve

the Issue

From the result of the work and the interview result,

it was found that all subjects knew that the formula

for the area of the rectangle is p × l. From the results

obtained, where p = 36 and l = 24, the six subjects

substitute into the formula and obtain the area of the

rectangle. From the results of the work, S1 and S2

obtained 864 cm2, S3 obtained 864 cm, S4, S5, and

S6 obtained 864. From the calculation of 36 × 24, all

subjects who answered correctly that 864. S3, S4, S5,

and S6 did not know by both that the unit area of the

rectangle is centimeter squared (cm

4 DISCUSSION

In building an understanding of the problem, there is

a tendency that deaf students illustrate the problem in

the form of images. Illustrating the problem in the

form of images shows that the thought process

constructed by the subject starts from the semi-

concrete to the abstract. Deaf students find it easier to

understand the problem if the problem presented in

Visual form is very beneficial for a deaf student

(Frostad, 1999). In addition, illustrating in the form of

images is the best mathematical ability possessed by

deaf students (Nunes, 2004). To solve the given

problem, there are two categories of ways done by the

six subjects to say and guess.

Summing up is counting one by one. Deaf student

performs oral calculations and written calculations

using sign language which is a simple arithmetic skill

possessed by a deaf student (Merrienboer, 2005).

Limitations do not become an obstacle to the six

subjects in doing the exploits through images, doing

algebraic engineering by summing and subtracting

the equations that have been obtained. The way in

which the subjects are used is not one of the methods

taught in solving the two-variable linear equation

system. This way arises as a result of the creative

thinking by the subject and also because of the

knowledge that has been stored in the form of a

schema in long-term memory, not from its ability to

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436

engage itself with unorganized information elements

in long-term memory (Nunes, 2002).

Thus, hearing loss possessed by those students is

not a direct cause of difficulties in learning

mathematics. Deaf students have elaborated the

linking of existing information on the problem with

the knowledge that has been formed to obtain ideas

and communicate them through images and writing

them to solve the problems given.

5 CONCLUSIONS

Based on the result of mathematical connection

ability analysis to deaf students in completing tests

related to the connection between mathematics topics

concluded that deaf students can solve non-routine

problems with high difficulty level visualized in the

form of images by following the steps of problem-

solving according to Polya.

ACKNOWLEDGEMENTS

For Directorate of Research and Community Service -

Directorate General for Research and Development -

Ministry of Research, Technology and Higher Education

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