Errors Identification In Solving Arithmetic Problems
Sri Hariyani
Department of Mathematics Education, Kanjuruhan University, Street S. Supriadi No. 48, Malang, Indonesia
Keywords: Identification, Errors, Problem Solving, Arithmetic.
Abstract: The aim of this research is to identify students’ errors in solving arithmetic problems. This qualitative
research uses case study approach. The methods used to obtain the data are observation and semi-structured
interview. The result of this research shows that the subject could solve arithmetic problems in reading,
comprehension, transformation, and process skill stages. The subject made some errors in encoding stage.
Encoding errors are often made by students. Moreover, encoding errors are not considered as errors when
solving problems. This research contributes in the importance of encoding stage in solving problems.
1 INTRODUCTION
Errors in solving arithmetic problems are caused by
students’ inability to recall the lecturer’s problem
solving procedures. Arithmetic problem solving in
class tends to be monotonous. Students solve
problems by copying the lecturer’s problem solving
procedures. Students regard the lecturer’s problem
solving procedures as the most correct solution. It is
the easiest way for the students to solve a new
problem by copying the example of problem solving
procedures given by the lecturer. Solving a new
problem is easier to be done when the procedure
refers to a successful problem solving (Wareham et
al., 2011). Competitive and cooperative learning
style as a learning strategy is very important to
enhance the ability to solve mathematic problems
(Özgen, 2012). Creativity is needed not only when
learning in class, but also when solving problems.
The use of APOS theory as a framework
revealed that several students’ errors might be
caused by over-generalisation of mathematical rules
and properties (Siyepu, 2013). Difficulties in
applying mathematical rules are caused by the
inaccuracy of mental structure on the process,
object, and scheme level (Maharaj, 2013). Students
show low ability of solving problems in the stages of
problem modeling process and applying
mathematical procedure (Wijaya et al., 2014).
Student who has creative idea in solving a problem
is not necessarily correct in writing the problem
solving systematics. The students’ lack of creativity
is affected by many factors, such as the mastery
level of mathematic concept, the accuracy in using
symbols, the confidence (Karwowski, 2009), and the
openness towards an idea. Students who can solve
routine problems show their level of ability only on
one level, which means that although they can solve
a problem correctly, they are still lacking in
conceptual understanding (Brijlall and Ndlovu,
2013). Errors in solving mathematic problems are
usually influenced by the previous learning habit
that is by memorizing (Siyepu, 2015). According to
the previous research, errors in solving mathematic
problems happen in the mathematic problem
modeling process stage (transformation) and in
applying mathematic procedure (process skill). But,
those researches ignore the errors in solving
mathematic problem on the encoding stage.
However, Newman in White (2009; 2010) defined
five main abilities of literacy and numeracy, i.e.
reading, comprehension, transformation, process
skills, and encoding. Thus, this research aims to
identify the errors in solving mathematic problems
on the encoding stage. The focus of mathematic
problem in this research is arithmetic problems. The
data collecting in this research are done through
observation and semi-structured interview. The five
literacy abilities are the indicators of successful
problem solving, one of which is the encoding stage.
2 RESEARCH METHODS
This qualitative research uses case study approach.
The subject of this research is the students of
Hariyani, S.
Errors Identification In Solving Arithmetic Problems.
In Proceedings of the Annual Conference on Social Sciences and Humanities (ANCOSH 2018) - Revitalization of Local Wisdom in Global and Competitive Era, pages 357-360
ISBN: 978-989-758-343-8
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
357

Mathematics Education of Kanjuruhan University,
the odd semester of academic year 2017/2018. The
students were given contextual problems. These
problems were related to daily life, so that the
students were familiar with them. Solving contextual
problems enable the mind to actively involve in
searching and constructing new ideas (Lubart and
Mouchiroud, 2003). The methods used to obtain the
data are observation and semi-structured interview.
The research data are the observation result and
interview result. Observation were conducted to the
students solving the problems. Students wrote down
the steps of problem solving. The data from this
observation result was completed by the data from
the interview. The researcher conducted an interview
to explore the problem solving process. All of the
data were then analyzed according to the problem
solving stages.
The data analysis in this research were done
simultaneously with the data collecting process,
interpretation, and drawing conclusion. Every data
obtained was directly analyzed, interpreted, and
concluded. The process conducted in the data
analyzing stage included data presentation, the
whole data were thoroughly read, irrelevant data
were ignored, and then conclusion were drawn from
the reduced data. .
Data presentation was started by preparing the
data. The data were the transcript of observation
result, interview, and field notes. The researcher
read the whole data and marked the errors in the
students’ work. Next, the data from the solution
writing, observation, interview, and field notes were
segmented into categories of problem solving stages.
The data reduction were done continuously during
the research. The researcher then described the
categories and theme to be analyzed. The theme
which were going to be analyzed in this research is
the students’ errors in writing the solution. The
analysis result was a description of students’ errors
in solving problems. The researcher interpreted the
result of students’ errors and drew a conclusion.
3 RESULTS AND DISCUSSION
The subject of this research was given a mathematic
problem. The solving of arithmetic problem in this
research met the rules of problem solving stages.
Figure 1 shows the arithmetic problem solving.
Figure 1: Arithmetic problem solving.
Subject wrote number sequence:
25, 35, 50, 70, 95, 125
Subject named each number in the number
sequence:
Subject named 25 as
Subject named 35 as
Subject named 50 as
Subject named 70 as
Subject named 95 as
Subject named 125 as
Subject determined the numbers which had the
following rule: “if the number is added with the
number in the previous term, it will be the number in
the next term”. The numbers were:
10 and 10 + 25 = 35
15 and 15 + 35 = 50
20 and 20 + 50 = 70
25 and 25 + 70 = 95
30 and 30 + 95 = 125
He obtained numbers formed a new sequence:
10, 15, 20, 25, 30
Using the same step, subject determined the
numbers with the following rule: “if the number is
added with the number in the previous term, it will
be the number in the next term”. The numbers were:
5 and 5 + 10 = 15
5 and 5 + 15 = 20
5 and 5 + 20 = 25
5 and 5 + 25 = 30
The difference between the numbers in a term
with the previous term showed constant numbers.
Then subject added up the numbers in the sequence:
25 + 35 + 50 + 70 + 95 + 125 = 400
ANCOSH 2018 - Annual Conference on Social Sciences and Humanities
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The result of the addition of the sequence was
named. Expressing the sum of the first 6 terms.
Subject made the following conclusion:
“Thus, there are 400 chairs in the building.”
The arithmetic problem given to the students was
in the form of number sequence. It only showed the
amount of chair in the first row, that was 25; the
amount of chair in the second row, that was 35; the
amount of chair in the third row, that was 50; and
the amount of chair in the fourth row that was 70.
However, the amount of chair in the next rows was
not determined. The amount of chair in the fifth and
sixth row could be determined by the number
sequence pattern.
In the reading stage, the students read the
arithmetic problem sentence in detail. They were
able to understand the situation. In the
comprehension stage, they related the part of one
sentence to the other part of the sentence. The
correct understanding about the situation of the
problem minimizes the errors in solving a problem
(Jitendra et al., 2013). The understanding about the
situation of the problem can help the students to
develop their understanding, so that they can design
the strategy to solve the problem (Capraro et al.,
2012). In the transformation stage, the students
wrote the arithmetic problem in numbers and
mathematical rules. In the process skill stage, they
applied the mathematic procedure. They could
determine the number pattern. However, they did not
go through the encoding stage. They did not write in
detail the arithmetic problem solving. Therefore, the
information in the arithmetic problem solving did
not illustrate the full solution, although the end result
was found.
The error identification in the encoding stage are:
(1) students did not rewrite the new number
sequence: 10, 15, 20, 25, 30; (2) students did not
name the new number sequence; (3) students did not
specify the term that was determined by the new
number sequence; and (4) students did not specify
that the term determined was the solution of the
number sequence.
4 CONCLUSIONS
Five main abilities of literacy and numeracy are
reading, comprehension, transformation, process
skills, and encoding. Students were able to
understand the problem situation by relating one part
of the sentence with the others. The correct
understanding towards the problem situation given
can minimize the errors. This situation shows that
students were able to do reading, comprehension,
transformation, and process skill. However, they
made errors in the encoding stage.
ACKNOWLEDGEMENTS
I would like to express my gratitude to LPPM
Kanjuruhan University that have given their support,
thereby this research could be done. I would also
like to thank the students of Mathematics Education
who had been willing to be the subject of this
research.
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