Students’ Errors in Resolving Set Item Test based on Watson’s

Criteria

Nursalam, Andi Dian Angriani, Kamariah, Andi Kusumayanti and Nur Yuliany

Department of Mathematics Education, Universitas Islam Negeri Alauddin Makassar, Indonesia

Keywords: Students’ Errors, Sets, Watson’s Criteria.

Abstract: The study aims to identify these types of students’ error in resolving set test item based on Watson’s criteria

(inappropriate data, inappropriate procedure, omitted data, omitted conclusion, response level conflict,

undirected manipulation, skills hierarchy problem, in addition to above other) and the factors caused the

students’ error in doing set test. The research used quantitative descriptive approach by taking a sample from

Grade VII Madrasah Tsanawiyah student of Gowa district. The test instrument used is a material description

test. The results showed that the percentage of student error in resolving set test item based on Watson’s

criteria that is not accurate (5.56%), inappropriate procedures (16.29%), missing data (2.59%), missing

conclusions (2.22 %), conflict response level (16.29), indirect manipulation (8.88%), skill hierarchy problem

(2.96%), and others above (64.81%). Based on the percentages related to some mistakes that were often made

such as ignorance in using the correct formulas to the questions, inappropriate completion steps, careless in

mentioning the members of the set, and even there were some students who did not answer the questions at

all. Therefore, concrete actions that can help the students to minimize errors in solving problems are by using

learning methods or approaches that involve the students actively during the learning process or when

answering questions such as using problem solving approaches.

1 INTRODUCTION

Science is an essential thing because by having it,

someone can correct all problems, whether they are

related to the world or the hereafter. Science is

likened to light because it is a guide and light for

people who are in darkness(Al-Abbasyi, Athiyah, M.,

2002). Therefore, science has a crucial role in a

person's life, because with human knowledge it is

easy to get the glory of the world and the hereafter.

The science of this world varies, ranging from

mathematics, physics, biology, economics,

astronomy, social science, sports, art, fikih (fiqh),

aqidah (faith), and others. In this case, what will be

discussed is mathematics.

Mathematics is the very significant part of human

life because in everyday activities people cannot be

separated from mathematical things Huljannah, M.,

2015. Mathematics is not a solitary knowledge that

can be perfect because by itself, but its existence is

primarily to help humans understand and master

social, economic and natural problems(Kiswanto,

Rahman, & Sulasteri, 2015). Mathematics is a

compulsory subject that starts to be SD/MI,

SMP/MTs, SMA/MA/SMK, even up to college

(Lipianto, Danang & Budiarto, M. T., 2013) which can

train students to be able to do calculations, understand

mathematical concepts thus learning becomes

meaningful (Mutia, 2017)develops and improves

logical, critical, and creative ways of thinking

(Nursalam, Angriani, A. D., Darmawati, Baharuddin,

2018)and builds quality human resources to develop

an advanced national civilization in science and

technology (Suharti, Latuconsina, N. K., Tasril,

Sriyanti, A., & Halimah, 2018).

The role of the teacher in teaching mathematics is

very important especially in the learning process. To

get the good learning evaluation results, each teacher

should be able to recognize various characters,

models, strategies, approaches, methods and learning

media which appropriate with the students.

Furthermore, one of students’ success in learning

mathematics is the ability of students to accomplish

mathematical problems through the evaluation of

learning. In evaluating, there must be clear objectives.

The goal of assessment in education is about

everything that related to educational activities or

processes that used as the center of attention or

Nursalam, ., Angriani, A., Kamariah, ., Kusumayanti, A. and Yuliany, N.

Students’ Errors in Resolving Set Item Test based on Watson’s Criteria.

DOI: 10.5220/0008523604550459

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 455-459

ISBN: 978-989-758-407-7

455

observation (Suharti, Latuconsina, N. K., Tasril, Sriyanti,

A., & Halimah, A., 2018).

Set is one of the mathematical materials taught in

class VII in junior high school (SMP). This material

is still considered difficult by several students

because it requires high solution and understanding to

get the answer. As a teacher who teaches in school

every day, of course, it is not uncommon to handle

students who experience learning difficulties

(Wildana, Mustamin, S. H., & N. F., 2016). The results of

interviews by researchers with math teachers at class

VII MTs Syekh Yusuf Sungguminasa, Gowa

Regency which revealed students’ difficulties in

learning. Some students could not interpret the

questions using mathematical notation; they did not

understand the use of symbols in the set material,

grouping members in the set and understanding the

item if in the form of a story. This statement is

supported by the results of the daily tests of the set

material at 2017/2018 academic year, only 30% of

students received scores above the KKM. Regarding

this result, the conclusion is the students' ability to

solve the set items of the seventh-grade students at

MTs Syekh Yusuf Sungguminasa in Gowa Regency

was still low, and an action was needed to overcome

these problems. Therefore, further research is needed

to explore the mistakes made by the students using

Watson's criteria including looking for the causes.

Some research related to the analysis of students'

errors in solving the items based on Watson's criteria

has been carried out by (Huljannah, 2015);(Nilasari,

Tristian F., Hobri, & Lestari, Nurcholif,

2014);(Winarsih, Kurniya A., Sugiarti, T., 2015);

(Lipianto, Danang & Budiarto, 2013); (Wildana,

Mustamin, S. H., 2016);(Zakaria, 2010). From

several of these studies, explained the analysis of

students' errors in solving math items based on

Watson's criteria. As we all know that the purpose of

the analysis is to find out the real situation and can

develop new insights in teaching. Meanwhile,

Watson in, expressed that the criteria for errors in

accomplishing the questions contained eight

classifications, such as:

a. Inappropriate data; the data was not appropriate

or in other words was incorrect in entering values

into variables.

b. Inappropriate procedure; in this category,

students tried to solve the problem with the

correct system, but it used incorrectly. As wrong

in using formulas, number operations, and

operation marks.

c. Omitted data; resolving the problem incorrectly

because the data was lost or more.

d. Omitted conclusion; in this category students

shown appropriate procedures but failed to

conclude.

e. Response level conflict; in this category student

worked on a problem not using concepts or

directly reaching without a logical way.

f. Undirected manipulation in this category

students got the final answer without the

providing the right reasons.

g. The hierarchy problem of skills; in this category

students could not solve problems because they

were less skilled in using formulas and less

accurate in calculations.

h. In addition to the seven types above, in this

category students did not call questions or items

Therefore, the analysis of students' errors in

accomplishing the questions set using the Watson

criteria can be used as an alternative that is useful

enough to improve mathematics learning at MTs

Syekh Yusuf Sungguminasa in Gowa Regency. The

objectives of this study were to find out the kinds of

mistakes made by students in solving set test based on

Watson's criteria and to find out the causes of the

students' error in answering those questions in class

VII MTs Syekh Yusuf Sungguminasa Gowa

Regency.

2 METHODS

This research was a qualitative approach by using

descriptive qualitative as a research design. This

research was carried out at MTs Syekh Yusuf

Sungguminasa in Gowa Regency as many as 27

students as research subjects and the researcher

selected several students to be interviewed to find out

the causative factors of students’ errors. The methods

used to collect research data were diagnostic tests

such as an analysis of the set questions, interviews

related to the students’ error, and documentation

including the records of the interview, photos of the

researcher’s activities, and others supporting data.

The inspection of the validity of the findings data

in this study used triangulation techniques.

Triangulation is a technique to test the credibility of

the data by checking data to the same source using

different techniques (Sugiyono, 2014: 338-345). This

study used triangulation techniques to test the

credibility of the data by checking the data with the

same source with different methods. The data analysis

technique used qualitative descriptive analysis with

aims to describe and summarize the meaning of

collected data by giving attention and recording as

many aspects of the situation as possible to obtain a

ICMIs 2018 - International Conference on Mathematics and Islam

456

general and overall picture of the actual situation. The

results of the data received from the tests and

interviews have not existed in the form of scores so

that the data analysis techniques used were reduction

and presentation data, and verification.

3 RESULTS AND DISCUSSION

Based on the results of the test, it found that students

made mistakes in working on set items based on

Watson's criteria as follows.

Inappropriate data (incorrect data), this error

category occurs in each item of the question from 27

students, namely five students on question number 1,

five students on number 5, two students on number 6,

two students on number 7 and one student in question

number 8. The error data category of inappropriate

data occurs in the questions number 1 and 5. The

students did the test by counting the number of

students who were interested in math and English

then reduced the number of the students who were not

interested of both. In the Venn diagram, the students

were not accurate in entering the members of the set,

it showed how the students only directly put the data

contained from the question. In this category, students

tried to operate a problem correctly, but the students

chose inappropriate information or data. It meant that

the students used the wrong data, forgot the correct

formula, and entered the incorrect data into a set.

Inappropriate procedure (procedure is not right),

this error category occurs in each item of question

from 27 students, namely sixteen students at number

1, six students at number 2, four students on number

3, seven students on number 5, four students on

question number 6, four students on question number

7, two students in question number 8, and one student

on question number 9.The students wrote the

members of set K and members of set L. Then, the

students matched the members of set L with the

members of set K that both had, then the students

concluded that the members of the set of 𝐾 ∩ 𝐿 were

2 and 8. In this category, the students tried to solve

the problem with the correct procedure, but they used

the incorrect formula because of lack in

understanding set.

Omitted data (data missing), this error category

occurs in each item of the question from 27 students,

namely one student on number 1, four students on

number 5, and two students on number 7. Missing

data errors occur in questions number 5. The students

solved the problem incorrectly because of one or

more missing data. The students were right in

mentioning the members of set L and not accurate in

mentioning the members of set K. On the diagram

Venn, the students then tried to complete by entering

the members of the set K and L. There were also

members of the new set which did not include as the

members of set K and L, and several missing

members of the set. In this category, students solve

problems incorrectly because there were one or more

missing data. It happened because the students were

careless put the data. Thus, data or members of the set

that should be the settlement were not included in the

set.

Omitted conclusion (the missing conclusion), this

error category occurs in each item of the question

from 27 students, namely three students in number 3,

one student on number 5, one student on question

number 7, and one student on question number 9. The

students solved the problem by showing the right

procedure and mentioning the members of sets A, B,

and C but failed to conclude it or the students solved

the problem but forgetting to write the conclusion, so

that the students' answer were considered incomplete.

In this category, the students answered the questions

by showing the right procedure, but they did not give

conclusions.

Response level conflict (conflict level response),

this error category occurs in each item of the question

from 27 students, twelve students on question number

1, five students on question number 2, nine students

on question number 3, seven students on question

number 5, three students in question number 6, six

students on question number 7, one student on

question number 8, and one student on question

number 9. The students showed an operation at a high

level then decreased to a lower operation to give a

conclusion. The students directly wrote S, M, and B

members. On the Venn diagram, they seemed

entering the data from the question. In this category,

the students have shown an operation at a high level

and then decrease to a lower activity to conclude. In

other words, conflict response level was where the

students answered a question, but they did not use

concepts, or the students directly end their conclusion

without using a logical way.

Undirected manipulation, this error category

occurs in each item of the question from 27 students,

namely eleven students on number 1, one student on

number 2, six students on number 3, one student on

number 4, three students in question number 6, one

student in question number 8, and one student on

problem number 10. The students counted the number

of the students who were interested in math and

English and who were not interested of both. Then,

the students reduced them with the number of the

students of VII grade in MTS Sheikh Yusuf

Students’ Errors in Resolving Set Item Test based on Watson’s Criteria

457

Sungguminasa Gowa Regency. In this category,

students got the final answer without providing the

right reasons, or the students' responses were correct

but using straightforward and illogical or random

ideas.

Skills hierarchy problem (the problem of the

hierarchy of skills), this error category occurs in each

item of the question from 27 students, namely three

students in question number 2, one student in question

number 5, and four students on question number 10.

The students could not solve the problem after the

students wrote the formula. The next step, the

students wrote P + Q = 38. In this category, students

could not complete the question because they were

less skill in using formulas and less accurate in

calculations.

Above other (in addition to the seven categories

above), this error category occurs in each item of the

question from 27 students. Five students on question

number 1, eighteen students on question number 2,

fourteen students on question number 3, twenty-six

students on question number 4, twelve students in

question number 5, twenty students on question

number 6, ten students on question number 7, twenty

four students on question number 8, twenty four

students on question number 9, and twenty two

students on question number 10. In this category, it

contained students’ errors that did not included in the

seven categories above. The mistakes that fell into

this category was the students did not respond;

thereby the students chose not to answer.

Based on the students’ errors in accomplishing the

questions, the most students made a mistake other

than the seven categories above (above other / ao) of

64.81%. The reason behind it because the students did

not understand the set material; the answers of

students who mostly choose not to answer some of the

given questions. Teachers should provide more issues

related to the content of the set, and then students can

be trained and able to complete the concepts of the

set.

Several factors influence the errors made by

students, namely internal and external factors. The

internal factors were 1) motivation, this factor

explained that the students lack a lot of practicing

their skills by working on set questions; 2) Interest,

this factor explained that during the learning process,

several students did not pay attention to the teacher's

explanation, there was interference from other

students, when they faced difficulties they prefer to

ask their friends rather than the teacher, and several

students did not like math; 3) Talents, this explained

that the students had tried to pay attention but still did

not understand and quickly forgot the teacher's

explanation. Based on this, it could be concluded that

the condition of the students who did not care the

material explained by the teacher so that the students

did not understand the material. In addition, the

students are less motivated to relearn material and

practice answering questions about the set. The

external factors included teachers and students. This

factor explained the way the teacher taught material

was not clear enough and the students preferred to

play with friends around him.

4 CONCLUSIONS

Based on the results of the research and discussion

that has been explained, it could be concluded that

several types of errors were made by the students in

the seventh grade of MTs Syekh Yusuf

Sungguminasa Gowa Regency in answering set

material questions, namely 1) inappropriate data/id;

i.e. incorrect in using data and forgetting formula that

must be used and wrong in entering data into a set. 2)

inappropriate procedure/ip; i.e. to solve the problem

with the correct procedure but the procedure used was

not accurate because of lacks understanding of set

material. 3) missing data (omitted data/od), i.e.

careless in entering data, the data or set members that

should be resolutions were not included in the set. 4)

missing conclusions (omitted conclusion/oc) which

was solving the problem by showing the right

procedure, then failing to conclude or the students

complete a problem but forgetting to write the

conclusion. 5) response level conflict/rlc that was the

students working on a problem not using the concept

or directly concluding without a logical way. 6)

undirected manipulation/um i.e. the students got the

final answer without the right reasons, or the students'

answers were correct by using very simple and

illogical or random reasons. 7) skills hierarchy

problem (shp), the students could not solve the

problems because they were not skilled in using

formulas and careless in calculating. 8) in addition to

the seven categories (above other/ao), the students

lack understanding of set material, they did not know

what to write and where to start from. The factors

caused the students to make mistakes in solving the

set problem were internal factors and external factors.

Internal factors include 1) motivation, lack of

developing abilities. 2) interest which included less

attention, disliking math, being disturbed, and lazy to

ask. 3) talent; the students were difficult to understand

even though they have been tried. The external factors

included the teacher and the students, the way the

teacher explained material that was not clear enough

ICMIs 2018 - International Conference on Mathematics and Islam

458

and the student preferred to play with friends around

him.

ACKNOWLEDGEMENTS

The writers address incredible thanks to A. Halimah,

Sri Sulasteri, and A. Miftah Ainun who have been

involved in this research.

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