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
Copyright
c
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
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.
REFERENCES
Al-Abbasyi, Athiyah, M. (2002). Dasar-Dasar Pokok
Pendidikan Islam. (P. B. Bintang, Ed.). Jakarta.
Huljannah, M. (2015). Analisis Kesalahan Siswa dalam
Menyelesaikan Soal Persamaan dan Identitas
Trigonometri Berdasarkan Kriteria Watson di Kelas X
SMA Al-Azhar Palu. Pendidikan Matematika
Universitas Tadulako.
Kiswanto, K., Rahman, U., & Sulasteri, S. (2015). MaPan:
Jurnal Matematika dan Pembelajaran. MaPan : Jurnal
Matematika dan Pembelajaran (Vol. 3). Universitas
Islam Negeri Alauddin Makassar.
Lipianto, Danang & Budiarto, M. T. (2013). Analisis
Kesalahan Siswa Dalam Menyelesaikan Soal yang
Berhubungan dengan Persegi dan Persegi Panjang
Berdasarkan Taksonomi Solo Plus pada Kelas VII.
MATHEdunesa, 2(1).
Mutia. (2017). Analisis Kesulitan Siswa SMP dalam
Memahami Konsep Kubus Balok dan Alternatif
Pemecahannya. Beta Jurnal Tadris Matematika, 10(1),
83102.
Nilasari, Tristian F., Hobri, & Lestari, Nurcholif, D. S.
(2014). Analisis Kesalahan Siswa Berdasarkan
Kategori Kesalahan Watson Dalam Menyelesaikan
Soal-soal Himpunan di Kelas VII D SMP Negeri 11
Jember.
Nursalam, Angriani, A. D., Darmawati, Baharuddin, & A.
(2018). Developing Test Instruments for Measurement
of Student’s High-Order Thinking Skill on
Mathematics in Junior High School in Makassar City.
Journal of Physics Conf. Series 1028.
Suharti, Latuconsina, N. K., Tasril, Sriyanti, A., &
Halimah, A. (2018). The Effect of the Realistic
Mathematical Approach Towards the Result of
Learning Mathematics Reviewed from the Ability of
Numerical Students. Journal of Physics Conf.
Wildana, Mustamin, S. H., & N. F. (2016). Analisis
Kesalahan Peserta Didik dalam Menjawab Soal
Program Linear Kelas XII IPA MAN 1 Makassar.
MaPan : Jurnal Matematika Dan Pembelajaran, Vo. 4
No., 7582.
Winarsih, Kurniya A., Sugiarti, T., & K. (2015). Analisis
Kesalahan Siswa Berdasarkan Kategori Kesalahan
Watson Dalam Menyelesaikan Permasalahan
Pengolahan Data Siswa Kelas VI SDN Baletbaru 02
Sukowono Jember Tahun Pelajaran 2014/2015.
Zakaria, E. (2010). Analysis of Students’ Error in Learning
of Quadratic Equations. International Education
Studies.
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