Grade 7th Kinesthetic Student Mistakes in Mathematics Problem Solving

about Quadrilateral

Yusuf Adhitya, yusufadhitya@upi.edu , Indonesia University of Education

Abstract

The purpose of this research is to obtain type of mistakes and its reason of 7th

grade kinesthetic student in mathematics problem solving about quadrilateral. The mistakes of this study is based on Newman’s Error Analysis that are reading, comprehension, transformation, process skill, and encoding. Kinesthetic is the least of learning style composition in this class. The main characteristics of kinesthetic student are more physical and more moving. It makes a curiosity about how the kinesthetic student in mathematics problem solving. This research uses purposeful sanpling that there are three student as subjects. The subjects selected are three student indicated many mistakes. To collect data in this research is based on problem solving test and interview. Problem solving data are confirmed by interview as triangulation step. The analysis data are done by the following steps: data reduction stage, data presentation stage, verification stage and conclusion. The results showed that kinesthetics learning style student don’t have tendecy on type of mistakes. The mistakes are various but indicated kinesthetic students make first mistake in comprehension. Another mistakes are caused by comprehension mistakes. The reason is inability to undestand the problem solving test as narrative text. There are solutions to minimize the mistake such as using a mathematical props and doing outdoor learning to activate the kinesthetic movement.

Keywords: Newman’s Error Analysis ; Kinesthetic ; Quadrilateral

Introduction

Mathematics is one important science in building concepts and applications

of other sciences. Mathematics is considered so important that it has been included

in the primary school learning curriculum. Sumarmo (2006) says that one of the

important mathematical characteristics is the deductive process which requires

students to think logically and axiomatically. This makes the science of

mathematics also influence human cognitive development. Mathematics also has

the regularity seen from several rules, axioms, and formulas contained therein. The

rules in mathematics are interrelated and form a complete mathematical concept.

Studying mathematics must begin with understanding mathematical

concepts. Learning mathematical concepts is fundamental in understanding

mathematics (Monariska, 2016). Concepts of mathematics are often so complex

made students feel difficult. That matter makes an asumption that mathematics is

difficult (Ompusunggu, 2014). The difficult assumption can be found in the fact

that students often make mistakes in solving math problems (Satoto, 2012;

Nuroniah, 2013, Bintari & Chadra, 2013). The number of mistakes can be analyzed

and used as a guide to the evaluation of students' undestanding of the topic.

Futher, analysis of students’ mistake is going to lead to an explanation of the

source of the problem. Sources of misatakes by students should immediately get a

complete solution. One method of analysis is Newman's error analysis method.

Newman's error analysis method was first introduced in 1977 by Anne Newman.

According to Newman as quoted from the study (Singh, Rahman, & Hoon, 2010)

defines that there are 5 hierarchies that a person needs to solve a mathematical

problem description. The five hierarchies are reading, comprehension,

transformation, procces skill, and encoding.

The analysis can be used for making a prediction why the student make

mistakes in math problem. Teachers must understand students' attitude and

mistakes in learning math (Buckley, Reid, & Thomson, 2016; Tambychik &

Meerah, 2010). Teachers have to handle the problem. The teacher is responsible

for adapting the learning situation to the students' interests, background and

maturity. Therefore, the teacher should desaign the teaching material and

techniques according students’ characteristic (Ismail, Hussain, & Jamaluddin,

2010).

Based on the psychological aspects, the characteristics of students in

understanding the concept of a subject matter are also potentially in the mistakes.

One of the characteristics of the student is the student's learning style. The learning

style has very significant relationship with the child's attitude toward mathematics

(Sirmaci, 2010) . Learning styles are a way that people tend to choose to receive

information from the environment and process information. Each student must

have their own learning style. By looking at their students' learning styles and

teaching according to their learning styles, teachers are more likely to improve

teaching effectiveness and increase student learning outcomes (Oflaz & Turunc,

2012).

Deporter & Hernacky (2008) classifies three types of learning style. learning

styles are divided into three types. These three types of learning style are visual,

auditorial, and kinesthetic. These three types of learning styles that are

distinguished based on their tendency to understand and capture information more

easily using penglihtan, hearing, or do it yourself. One of the unique learning styles

is kinesthetic. Kinesthetic students prefer things that are physical (Fleming &

Mills, 1992). Many mathematics lessons in schools don’t support physical-based

activities. This certainly makes it a potential that kinesthetic students will find it

harder to understand math.

Based on the above background, the problems to be studied in this research

are as follows.

1. What are some types of mistakes made by a class VII class kinesthetics

student in solving quadrilateral math problems?

2. What are the causes of the mistakes made by the class VII junior kinesthetics

students in solving quadrilateral material math problems?

Literature Review

Definition and Characteristics of Kinesthetics Student

Kinesthetic learning style is a learning style in which a person is more

physical than visual and auditory (Ayala, Mendivil, Salinas, & Rios, 2013;

Ocampo, Silva, & Salinas, 2015; Touval, 2011; Tse, Thanapalan, & Chan, 2014;

Yahya & Noor, 2015). Based on DePotter & Henacky (2008) characteristics of

kinesthetics as follows (1) speak slowly, (2) responding to physical attention (3)

touch people to get their attention, (4) stand close when talking to people, (5)

always physically oriented and moving a lot and (7) learning through manipulation

and practice.

Newman Analysis Procedure

Error analysis used is Newman's Error Analysis consisting of five types of

errors: reading, comprehension, transformation, process skill, and encoding.

According to (Singh et al., 2010) the criteria of errors can be detailed as follows:

1. Reading error occurs if the student is unable to read the words or symbols

contained in the problem. This error can be detected by interview method.

2. Comprehension error occurs when the student is able to read the problem but

fails to understand what is needed to correct the problem.

3. Transformation error occurs if the student has understood what is needed in

the problem but fails to identify what mathematical operations are being used

to answer the solution of the problem.

4. Process skill error occurs when the student is able to determine the operation

used but the student has miscalculated or the wrong step is used.

5. Encoding error occurs when the student has been able to solve the problem but

the student is unable to restate what the question asks.

Method

The type of research used is qualitative research. In the opinion of Moleong

(2013) and Hatch (2002), qualitative research is a study aimed at understanding

things experienced by research subjects in their daily life, such as behavior,

perception, motivation, etc., described descriptively. The purpose of this research

is to obtain type of mistakes and its reason of 7 th grade kinesthetic student in

mathematics problem solving about quadrilateral The type of error to be

investigated is based on Newman's error procedure.

Determination of research subjects based on the results of observation and

suggestion of teachers (teacher grade VII). This is in coresponding with the

opinion Moleong (2013) that in qualitative research uses purposive sampling.

Researchers chose one class as a research subject with 32 class student. For

selecting the subject, researcher used some of instrument.

The instruments used in this study were researchers, questionnaire learning

styles adopted from Deporter & Hernacky (2008), problem solving test (6 word

problem), and interview questionnaires. Researchers used a questionnaire

instrument used to determine specifically how many children had an auditorial

learning style. The results of the questionnaire will serve as the basis for selecting

selected subjects that will be the focus of the analysis of error analysis and

interviews. Data analysis results of kinesthetics student error sorted from the

largest and smallest value. Data sorting aims to see how many errors they made.

After the selection process, three students represented the class of the kinesthetics

style learning style were selected. The three subjects were obtained from high-

ability, medium-ability, and low-ability students.

Data collection techniques used in this research are problem solving and

interviewing test. For data validity, triangulation is required. Triangulation used on

this test is triangulation method comparing test data and interview. The result of

problem solving test and data of interview result will be analyzed. Newman's error

procedure requires an interview. This is consistent with what has been done by

(Prakitipong & Nakamura, 2006; White, 2005), they use interviews to explain what

causes the mistakes of students in solving mathematical problems.

Result and Discussion

Based on the learning style questionnaire, kinesthetic-style students are the

smallest compositions among the three types of learning styles. The full results can

be seen in Figure 1.

Based on figure 1 it is seen that the number of students who have

kinesthetic learning style is five students. The percentage of kinesthetic students in

the class is 16.67%. This becomes a unique and interesting thing to examine the

extent to which the characteristics of kinesthetic students in understanding

mathematics. Based on Deporter & Hernacky (2008), kinesthetic people have the

main characteristic that is active and more relies on the physical. Based on this

physical tendency that makes kinesthetic students dominated by men (Kholid,

Pangestika, & Harta, 2016; Klement, 2014).

Based on the data source of the students' work in the problem-solving test

and the interview questionnaire results, 3 students were selected representing the

kinesthetic type learning style students. The three subjects were obtained from

high-ability, moderate, and low-ability students. The selected research subjects of

the students of the auditorial learning style are G24, G01, and G30. The problem-

solving and interviewing tests completed by the three subjects were analyzed by

Newman's error procedure. Analysis of G24, G01 and G30 subject data on problem

solving and interviewing tests can be seen in Table 1

Visual Auditorial Kinestetik05

101520

9

16

5

FIGURE 1. Comparison of Learning Styles

Table 1. The tendecy of the kinesthetics learning style students error

No SubjectError Accumulation

TendencyR C T PS E

1 G24 0 0 2 2 2 Tranformation, Process

Skill,and Encoding

2 G01 0 1 4 0 0 Transformation

3 G30 0 3 3 0 0 Comprehension and

Transformation

Note:

R : Reading PS : Process skill

C : Comprehension E : Encoding

T : Transformation

Based on Table 1, it is found that kinesthetic student don’t misread reading.

Students have been able to read the symbols and information contained in the

question. However, after being able to read, kinesthetic students tend to make the

main mistake in all the next steps. There is no trend at which stage kinesthetic

students are more dominant in error. The error begins with the student not being

able to complete at all (no understanding of the problem) mistaken for

comprehension until found carelessness in writing the final answer (encoding

error).

Comprehension Error

Based on Table 1, the comprehension error is done by G01 and G30. G24 is not

indicated to make a mistake. Among the two subjects who made the mistake it was

seen that the G30 made more mistakes. G20 made a mistake 3 times in the question

numbers 4, 5, and 6. Meanwhile, G01 made a mistake in the number 4. It appears

that the number 4 to be the location of the same error. G30 doesn’t even answer at

all about the number 4. Question in number 4 is as follows

“What happens to the area of a new parallelogram if a new parallelogram model is reduced to ¾ from the previous height but the base is magnified in size 4 times than before? Describe your opinion and prove it by including a logical step!”

Based on the description of the above questions it requires students to

understand the form of a story that contains material comparison and quadrilateral.

Because G30 did not work so the researcher focused more on analyzing the work

result of G01. G01 has tried to work but he made a mistake that needs to be

analyzed further. Here's the answer to the work of number 4 of G01

Figure 2. The result of G01work on problem number 4

Based on Figure 2, it shows that G01 only answers simply. Researchers

make the initial guess is the numbers contained in the question. When referring to

the problem, it shows that question number 4 is the word "¾ times and 4 times".

G01 has not been able to understand the problem and only multiplies it ¾ by 4 so

that it is obtained 3. G01 also doesn’t mention what that 3 means. To explore more

information, researchers conducted interviews to validate these assumption. The

following transcript of the interview has been translated from Indonesian to

English.

Q : What is being asked in this question?G01 : Area changingQ : How is the change?G01 : I don’t understand sir, I just multiply the numbers in the matterQ : Then what is the result?G01 : 3 SirQ : 3 What does that mean?G01 : (silent)P : OK. Which one is true, is it 3 times old area or 3 times new area?G01 : (silent)Q : Let's read the question again, this question is about the change of

area, if changed may be small or bigger, do you think it's getting bigger or smaller?

G01 : getting bigger Sir

Q : Which on is bigger?G01 : New area SirQ : So what's the conclusion?G01 : New area is 3 times the old area

Based on the results of the interview, it appears G01 error doesn’t write down what

is known and what is asked. In interview G01 claimed not to understand this

matter. G01 doesn’t do a wide comparison process old and new area. The visible

process is the multiplication between change of base and height. After doing

interview with guided questions, finally G01 understand the meaning of answer 3

having been obtained. This indicates G01 is less understanding of the concept of

comparison. Based on the results of work and interviews, G01 has difficulty

understanding the problem and has been wrong in the comprehension step.

To make the analysis is valid, researchers conducted interviews on the

G30. Although the G30 only writes what is known and there is no continuation,

the researcher considers there is information needing to be deepened from the G30

to strengthen kinesthetic student analysis. The following transcript of the interview

has been translated from Indonesian to English

Q : Why? Not understanding or lack of time?G30 : Do not understand sirQ : Try what is known from the problem?G30 : Do not understand sir, that's the base changed and height

changed Q : Why do not you understand?G30 : The language on the subject I can not understand. So I do not

know the point is what it is.Q : Do you know the size formula of parallelogram?G30 : base times height

Based on interviews and work results, G30 made a major mistake in the

step of comprehension. Comprehension errors caused by G30 less understanding

of language and what is meant in question. Kinesthetic students tend to be less

fond of reading (Tse et al., 2014). It also supports that kinesthetic students have

difficulty in the stage of comprehension or understanding problems.

Transformation Error

Based on Table 1, the transformation error is performed by all subjects.

G24 made a mistake in the two number of questions that is about 5 and 6. G01

made a mistake in four questions that is 1,3,5, and 6. Meanwhile, G30 made

mistakes in three numbers of questions that are 1,2, and 3. Trasnformation error

seen spread in all the questions. Subject G24 which is representative of high ability

students also make mistakes in questions 5 and 6. Problem number 6 is interesting

because G01 also make mistakes in the matter. Therefore, the researchers focused

on discussing G24 in the number 6. Question number 6 is written as follows

“Mr. Bayu's land is square-shaped with a circumference of 200 m. Some of the land will be used as agricultural land where the farmland is also square. If the ratio of the circumference of the land and the circumference of agricultural land is 5: 3, determine the land area that is not used as agricultural land!”

To start the analysis, here are the results of G24 work

Figure 3. the result G24 work result on problem number 6

According to Figure 3, it is seen that G24 uses numerical values and uses

only square circumference formulas. Initial suspicion, G24 made a tranformation

error that is not able to determine the correct strategy. The strategy that should be

done is to find the size of the agricultural land using the roving ratio and then look

for the area after the side is known. To explore more information, researchers

conducted interviews to validate these allegations. The following transcript of the

interview has been translated from Indonesian to English

P : Okay, try to explain how you do it?G24 : I multiplied Mr. so I got 120Q : Is that what? Is it wide or around?G24 : Area of SirQ : What's that 200?G24 : CircumferenceQ : Why are you doing the circumference minus the area?G24 : (silent)Q : How are you doing?G25 : 80 m...Q : Try that there is a square, what is the general formula? What is

the circumference formula?G24 : Area is s x s and circumference is 4s.Q : Why do not you use it? Do you now understand?G24 : Not yet sir

Based on the interview results, it appears that G24 uses the numbers in the

comparison and only multiplies them with circumference. It also appears that G24

does not understand the concept of fractional division by explaining the process of

dividing the fractions into the multiplication. In addition it is seen that G24

performs the calculation process 200-120 = 80. This is because G24 considers the

circumference as wide so as to find the difference. This shows G24 is less

understanding of the area and circumference of the square.

Transformation error is indicated by the use of the wrong strategy. Judging

from the work, kinesthetic-style students often try to solve problems using their

own strategies. Although their "trial and error" strategy is often a misconception, it

is in the opinion of De Porter & Hernacky (2008) that students of kinesthetic

learning style have the nature of wanting to do everything (try new things) and

learn through manipulation and practice. The cause of this error is the lack of

comprehension material and the concept of the relationship between the area and

the circumference of the quadrilateral so that after understanding what the question

is, the subject does not know how to solve it.

Process Skill Error

According Table 1, the process skill error is only done by G24. The other

two subjects have been misplaced in the tranformation step so that their error skill

process is more due to an error in the previous stage. G24 is indicative of a process

skill error in numbers 3 and 4. G24 which is a representative of high ability

students made a mistake at this stage. The researcher gives an example of the G24

work in number 3. Here's the number 3.

"An athlete ran around a square-shaped square with an area of 8100 m2. If the athlete is able to surround as many as 5 times within 6 minutes, what is the speed of the athlete's run? (in km / h)”

Based on the description of the above problem, the calculation that will

appear is the calculation of looking for the sides of the field and the circumference.

After that, the circumference information can be used to find the distance and

speed. To start the analysis, here are the results of G24 work on question number 3

Figure 4. the result G24 work result on problem number 3

Based on Figure 4, it appears that the selection strategy is correct. A new

error arises when calculating the total distance and speed. G24 still writes K = 360

then writes K = 360 x 5. This shows there is an error that 360 x 5 is still regarded

as a circumference instead of jaeak travel. In addition, the speed calculation

process is also wrong because 1800

6=300 km /hour. G24 does not convert unit m

to km. The division of 1800 by 6 also makes the researchers' confusion because 6

here does not represent anything. The researchers asumption is G24 intends to

write 60 instead of 6 which is likely to represent the number of minutes in an hour.

To explore this allegation, here are the results of interviews with G24 for question

number 3.

Q : Please explain!G24 : I use the area formula , s x s so to look for x. I got from √8100

then s = 90 P : Good. What is thecircumference formula?G24 : 4s SirQ : So how many results are there?G24 : 360Q : How many times round?G24 : 5 SirQ : What does it mean?G24 : 360 x 5, that is the total distance so it is obtained 1800Q : Then what is the speed formula?G24 : Divide time divided SirQ : What's your result?G24 : 1800 divided by 6 so obtained 300Q : 6 This is the unit of the minute why it turns into a clock?G24 : (silent)...Q : How about meter to km?G24 : I know 1 km = 1000 m SirQ : Then how about 1800m how many miles?G24 : (confused)

Based on interview results, G24 made a mistake. The error is that G24 does

not convert m to km and minute to hour. This supports the fact that G24 lacks

understanding of conversions between units. This error is a process skill error

Encoding Error

Based on Table 1, there is G24 made a mistake in the encoding stage.

Based on the above definition explained that the encoding error occurs when it is

able to understand, determine the appropriate steps and calculations but can not

reproduce what has been asked by the problem. G24 is a subject that represents a

high mathematical ability. It also becomes a unique discovery that needs to be

studied separately. The subject of G24 indicated an encoding error in Problem 1

and 2.

The error that will be more discussed is the G24 subject error at number 1

because it is more complex and error number 2 is similar to the error in number 1.

Question number 1 is written as follows

A rectangular painting with a length and width of 6: 5. If you know the extent of 750 cm2, determine the circumference of the painting!”

To start the analyst, the following shows the result of the work of subject

G24

Figure 5. the result G24 work result on problem number 2

Based on Figure 5, G24 has been able to solve the problem correctly. A

new error is visible when the subject of G24 does not rewrite with a conclusion

like "So the circumference of the rectangle is ....". In addition, the use of the wrong

unit is K = 110 cm2. The researcher's initial assumption was that G24 made a

writing error and lack of accuracy.

The next step is to conduct interviews to get valid facts and information.

The transcripts of interviews on G24 subject for number 1 are as follows

Q: How many results did you get?G24: 110 cm2

...Q: Is the unit correct?G24: Yes sirQ: If the circumference of the unit is cm2, what is the unit area?G24: (confused and start to realize if he is wrong

Based on the results of the interview, it turns out that the error of using cm2

as a circumference unit is not a mistake, but it is true that the subject of G24 does

not understand the correct circumference unit. Based on the triangulation process

obtained the facts and the conclusion that G24 made a major error in the encoding

step. This error is due to the inability of G24 to select the exact circumference unit

Conclusions and Suggestions

The results of the study concluded that kinesthetic student make a major

mistake in the steps of comprehension, transformation, process skill, and encoding.

This suggests that kinesthetic-style students don’t have a tendency in one type of

error. In general the cause of error is a poor understanding of the prerequisite

materials such as comparison, algebra, and linear equations of one variable.

Suggestions and solutions to minimize these errors can originate the teacher

or the students themselves. Students will learn more effectively if teachers provide

different learning activities in accordance with the trend of learning styles

(Alkhasawneh, Mrayyan, Docherty, Alashram, & Yousef, 2008). The suggested

activities to teachers to enhance student understanding of the concept and the

material so that it can minimize mistakes are (1) always using visual aids or props

or media that can be seen, touched, and manipulated the students as they learn to

stimulate curiosity, (2) getting used to standing/sitting next to students in guiding

students individually, (3) making the rules of the game so that the students could

be doing a lot of motion in the classroom, and (4) using the drama/simulation

concept concretely. Meanwhile, students in activities to minimize his mistakes

include learning by making use model and practice find the strategy completion

problem itself without having to memorize the formula of raw.

This study is still limited in the process of exploring the errors and

causes of kinesthetic student errors. Further research is needed such as research

related to other factors that may cause errors. Other factors can be viewed from

the aspects of students, aspects of teachers, aspects of learning, and aspects of

learning facilities. In addition, studies related to the effectiveness and effect of a

suitable learning model and minimizing errors are considered necessary to deepen

the results of this study. The kinesthetic aproach to teaching has an advantages

and can be adopted to the teaching mathematics(Touval, 2011).

Acknowledgements

The researcher would like to thank the Lembaga Dana Pendidikan (LPDP) so that

researchers can attend this conference.

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