An Analysis of Students’ Error in Learning Mathematical Problem
Solving: The Perspective of David Kolb’s Theory
Widodo Winarso
1
, and Toheri
1
1
Institut Agama Islam Negeri Syekh Nurjati Cirebon, Indonesia
Keywords: Student error; Learning styles; Problem-solving; Mathematics; The theory of David Kolb
Abstract: One of the urgencies of mathematics learning is how much students' ability to solve mathematical problems.
But in the process, not a few students who make mistakes in doing math tests. In addition, it turns out that
various types of errors also depend on the learning style possessed by students. then the focus of this research
is to analyze students' errors in solving mathematical problems based on differences in learning styles
according to David Kolb's theory. The study was conducted at the Vocational Middle School in Cirebon-
Indonesia. the type of research used is a qualitative research case study approach. The instrument used in this
study was a questionnaire (Kolb Learning Style Inventory refers to KLSI version 3.1) and tests. Whereas for
the analysis of research data using triangulation techniques. The results show that there is a proportional
diversity of students' learning styles. each type of learning style has its own unique errors. where the type of
diverger is procedural error and misunderstanding. The types of assimilator type errors are procedural and
conceptual errors, the type of convergent error type is a procedural error. The type of accommodator type
error is a conceptual error. so the type of conceptual is caused by the wrong understanding or deviated from
the existing provisions, so this affects the students to make mistakes in the process of math tests. Strategy
errors can be experienced when the students are stuck to continue the process of completing a math test.
procedural errors occur when the system uses a method that is not systematic in completing the test.
1 INTRODUCTION
Mathematics learning is about the concepts and
structures of mathematics contained in the material
being studied, as well as finding the relationship
between concepts and mathematical structures in
them(Bruner, 2017; Hiebert and Lefevre, 1986).
Furthermore, mathematics learning can also be
interpreted as a learning process that actively involves
students to build mathematical knowledge (Voigt,
2013). Therefore the learning of mathematics itself is
a process of interaction between teachers and students
which implies the development of thinking models
and elaboration logic in the learning environment.
The condition is created by teachers with various
methods so that the learning activities of mathematics
can grow and develop optimally and students can
carry out the learning activities effectively and
efficiently.
The purpose of learning mathematics itself consists
of; (a) Train thinking and reasoning in drawing
conclusions, for example through exploration,
experimentation, equality, diversity, consistency, and
inconsistency; (b) Developing creative activities
involving imagination, intuition, and discovery by
developing divergent, original thinking, curiosity,
making predictions and guesswork, and
experimenting; (c) Develop problem-solving skills;
(d) Developing the ability to convey information or
communicate ideas through spoken speech, charts,
maps, and diagrams in explaining ideas (Schoenfeld,
2016).
Seeing how important mathematics is, it becomes
ironic in the fact that many students do not like
mathematics (Hannover and Kessels, 2004; Tirta
Gondoseputro, 1999). Students assume that math is a
lesson that less favorable. According to survey data,
mathematics occupies the third position as the
subjects most hated by students (Rofalina, 2015).
Meanwhile, based on data from PISA (The Program
for International Student Assessment) in 2015, states
that the performance of Indonesian students is still
relatively low. Successively average Indonesian
achievement scores for science, reading, and math are
ranked 62, 61, and 63 of the 69 countries evaluated.
The ratings and average Indonesian score do not
differ much from previous PISA tests and surveys in
706
Winarso, W. and Toheri, .
An Analysis of Students’ Error in Learning Mathematical Problem Solving: The Perspective of David Kolb’s Theory.
DOI: 10.5220/0009914907060713
In Proceedings of the 1st International Conference on Recent Innovations (ICRI 2018), pages 706-713
ISBN: 978-989-758-458-9
Copyright
c
 2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

2012 which are also in the low material mastery group
(Stacey, 2015).
Based on the data, students' ability in
understanding mathematics is very low. The ability of
students in solving mathematical problems can be
known through the tests given when the evaluation of
mathematical learning. In the process of mathematics
learning, students often make mistakes. The number
of mistakes made in working on mathematical
problems into a hint of the extent to which student
mastery of the material. From the mistakes made, it
can be further investigated about the source of errors
committed by students. The cause of the mistakes
made by the student should immediately get a
complete solution. This solution is done by analyzing
the root cause of the error, and afterward identified
the types of mistakes that are commonly done by
students in crafting math tests.
The mistakes made by students are obstacles to
learning mathematics. According to Taylor Koriakin,
et al error is a form of deviation from the right, pre-
determined procedural or deviation from an
expected(Taylor, Bogdan and DeVault, 2015).
Identifies the type of miscalculation of the count
operation performed by the student(Mercer and
Mercer, 1989). The types of mistakes made by
students are divided into operating errors,
computational errors, algorithmic errors, and random
answers. This is similar to what is described by
Radatz, there are 3 indicators of the type of error that
is: a) misconceptions, mistakes made by students in
using the concepts related to the material, b) Errors of
principle, errors in using the rules or mathematical or
incorrect formulas in the use of principles relating to
the material, c) Operational error, errors in operation
or calculation. Certainly, the student's mistake will
have an impact on the outcome of the learning process
(Radatz, 1980).
The factors that influence student learning
outcomes are two factors, among others internal
factors, namely the lack of special talent in doing
certain situations, lack of basic skills possessed by
students, lack of motivation and motivation to learn
and physical factors which does not support learning
activities (Lim and Morris, 2009). Another factor is
about how the character of students in the learning
process, as well as learning styles owned by each
student. Mistakes in mathematical problem solving
can also be observed from student learning styles
(Ryan and Williams, 2007). In line with that opinion,
Eugene A Geist, and Margaret King suggests that
students' mistakes can be seen from the student's
learning style, of course, because every individual has
different characters, so in the case of any questions
the factors can cause students to make mistakes(Geist
and King, 2008).
Learning styles are a combination of how one
absorbs, and then organizes and processes
information (Schmeck, 2013). Learning styles are not
just aspects of facing information, seeing, listening,
writing and saying but also the aspect of information
processing, analytical, global or left-brain right brain,
another aspect is when responding to something in the
learning environment (abstractly and concretely
absorbed). This is in line with the view of Riding &
Rayner, which suggests a student learning style that
is the consistent way in capturing stimulus or
information, how to remember or think and solve
problems(Riding and Rayner, 2013). Learning styles
are the way students tend to react and use incentives
to absorb and then organize and process information
in the learning process.
David Kolb's learning model is a learning style
that involves new student experiences, develops
observation/reflection, drafts, and uses theories to
solve problems. Student learning styles are influenced
by personality types, habits, and develop over time
and experience. The model is built on the idea that
learning preferences can be explained by the active
observations of experiments-reflections and
experiences of abstract concrete concepts. The result
is that there are four types of learners: convergent
(experimental experimental-experimental abstract),
accommodator (experimental - active experience),
assimilation (conceptualization of abstract - reflective
observation), and divers (reflective viewing
experience)(Kolb, 1981).
Based on observations in one of the Vocational
High Schools, many students complained that they
had difficulty in understanding math problems. The
mathematics whose primary purpose is to form
students with the first critical, logical and systematic
ability is fortified with the mathematical fears
themselves. In addition, mathematics teachers argue
that during this time students have a variety of
learning styles that have not been known for sure, of
course, this is correlated with the learning process
conducted in the classroom. Thus, the researchers are
interested in learning styles according to David
Kolb's theory. where individual differences are
mapped into different types of learning styles.
Observing the problem, in previous studies have
not paid attention to the analysis of student errors on
differences in learning styles that students have. In
addition, the analysis of student error in solving
mathematical problems can be detected through the
answers to exercise questions. Thus, researchers are
encouraged to analyze student errors.
An Analysis of Students’ Error in Learning Mathematical Problem Solving: The Perspective of David Kolb’s Theory
707

2 METHODS
Based on the objectives to be achieved in this study,
namely to analyze student errors. then the type of
research used is qualitative with case study approach
(Taylor, Bogdan and DeVault, 2015; Creswell and
Creswell, 2017). it is necessary to acquire knowledge
or solve problems encountered and carried out
carefully and systematically and can give a specific
picture of the problem.
2.1 Procedure
This research was conducted at SMK Patriot Cirebon
with the subject of the research of students class X.
The research subjects were grouped according to the
learning style according to the theory of David Kolb.
Selection of subjects based on the following criteria:
a) Students who complete the math test with the most
questions and b) Students who make more mistakes
in working on math problems. While the object of the
research is students error make in solving math
problems. The math test was performed using the
system of linear equations with two variables
(SPLDV).
2.2 Data Collection and Analisis
Technique
The tools used in this study are questionnaires and
tests (Cohen, Manion and Morrison, 2013). The
questionnaire and the test tools, both created and
developed by the author. The questionnaire
development process adopted the Kolb Learning
Style Inventory concept and refers to KLSI version
3.1 (Kolb, 1976; Manolis et al., 2013). There are 48
items used in the questionnaire. The 12 grains
represent the dimensions of the CE (Concrete
Experience), 12 elements describe the dimensions of
RO (Reflective Observation), 12 items describe the
dimensions of AC (Abstract Conceptualization) and
12 items describe the size AE (Active Experimental).
The test used in this study is a test essay(Mohamad et
al., 2015). The grid of this evaluation of the assay
uses the achievement of the learning of the system of
linear equations with two variables (SPLDV). The
reference used in the preparation of this essay adopts
the cognitive aspects of Bloom's taxonomy, namely
the categories C4, C5 and C6 (Bloom, 1956). While
for data analysis, using the triangulation technique
(Leech and Onwuegbuzie, 2007).
3 RESULTS AND DISCUSSION
The first stage in this study was to classify the
learning styles of students. Based on the results of the
questionnaire distribution Kolb Learning Style
Inventory to 24 class X students of Cirebon Patriot
State Vocational School, the grouping of learning
styles was obtained as follows.
Table 1:The Proportion of Student Learning Styles
Type of Learning
Style
(%) Subject Code
Diverger 12,5 PM04, PM18, PM19
Assimilator 16,7 PM01, PM11, PM14,
PM22
Converger 33,3 PM02, PM03, PM05,
PM07, PM09, PM16,
PM20, PM21
Accommodator 37,5 PM6, PM8, PM10,
PM12, PM13, PM15,
PM17, PM23, PM24
Based on Table 1. Type of the more dominant
accommodator (37.5% of students). While the
Diverger type is less than four other learning styles
(12.5% of students). After classifying students based
on the Kolb modeling style, only a total of eight
subjects were eligible for further analysis. Then the
subject of the study was given a math test to find out
what kind of error occurred. The following in the
second stage in this study dissects several cases of
errors made by students based on differences in
learning styles.
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Tabel 2: Characteristics of Student Error in Learning Mathematical Problem Solving
Type of Learning
Style
Students' answers and errors in problem-solving
Diverger
PM04
Answer no 1 Answer no 3
The subject of PM04 encountered an error on the
use of the number operation sign, this is due to
the inability of the subject to solve the problem.
The subject of PM04 also performs
procedural errors in terms of division of
positive and negative numbers
PM18
Answer no 3 Answer no 6
Subject PM18 performs on erroneous operation
number
Subject PM18 has two operation count
errors in integers
Assimilator
PM01
Answer no 4
PM22
Answer no 4
Subject PM01 made a mistake that does not
work the completion process to completion
Subject PM22 made a error in placing the
variable
Converger
PM03
Answer no 4 Answer no 6
Subject PM03 performs in placing variables x
and y
The subject of PM03 makes error that is
wrong in determining the variables x and y
An Analysis of Students’ Error in Learning Mathematical Problem Solving: The Perspective of David Kolb’s Theory
709

Answer no 8
The subject of PM03 made a mistake in
transforming the story into the form of
mathematical modeling
PM07
Answer no 4
Subject PM07 made a mistake not to do the
work to completion, other than that the
subject also made a redaction error
Accommodator
PM08
Answer no 4
The subject of PM08 has errors in the procedure that is wrong in entering the data that has been
known
PM24
Answer no 6 Answer no 8
The subject of PM24 encountered an error for
not continuing the work
The subject of PM24 has an error in placing
the variable
Based on table 2. The next study continued with
the third stage, namely classifying the types of student
errors. Explanation will describe the type of student
errors that are made and provide an explanation of the
factors that cause student errors. The detailed
explanation as follows.
Type of conceptual error-The first type of error
students make is a conceptual error. According to
James Hiebert and Patricia Lefevre, a conceptual
error is a mistake in determining and using the
theorem or answering the problem (Hiebert and
Lefevre, 1986). Correspondingly, Sahriah (2012)
explains that the conceptual error indicator includes:
a) wrong in determining formula or theorem or
definition to answer the problem; b) incorrect use of
formulas, theorems or definitions which are
inconsistent with the conditions under which
formulas, theorems or definitions apply; and c)
incorrectly not writing formulas, theorems or
definitions to answer the problem (Riccomini, 2005).
The conceptual error is done by the subject of
PM08, PM22, and PM24. The subject of PM08 makes
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the mistake of not changing the known information to
the definition to make it easier to the next stage.
Subjects in the stage of creating mathematical
equations without making variables available. This
causes the subject to not complete the job. Based on
the interview, the subject did not quite understand that
he made a mistake. The subject of PM22
misinterpreted the problem at number 4, the subject
answered does not match the existing or already
taught definition. The subject does not yet understand
correctly, but the subject takes the initiative to solve
the problems he faces by creating his own theory.
interview results state that the concept known to the
subject is a searched variable first. but the concept is
wrong, so make the subject make a mistake.
This case also occurs on the subject of PM24, not
understanding the existing material makes the subject
create his own theory based on his feelings. The
subject experienced an error when turning the story
into a mathematical modeling. In the interview quote,
the variable equation should start from the variable
(x) without considering the information contained in
the problem or regardless of the occupation that has
been occupied. The subject has a misconception
about the concept. So it made him make a mistake.
So, conceptual mistakes are errors that are made
because of wrong understanding or deviate from the
existing provisions, so this affects a person to make
mistakes in the process of workmanship. The
indicators of conceptual error are a) wrong in
changing the problem into a mathematical equation;
b) wrong in using data.
Type of strategy errors-The second type of
errors students make is a strategy errors. According to
Nancy C. Jordan and Teresa Oettinger Montani, a
strategy error is an error that occurs if the student
chooses an inappropriate path and leads to a deadlock
path (Jordan and Montani, 1997). This is related to
what Ivan Watson said, that the category of errors in
problems is related to the problem of hierarchy of
skills(Watson, 1980).
The strategy error is done by PM18 subject. Subject
PM18 basically make a mistake on operation number,
where the answer obtained results for apple unit price
is Rp. -20,000. The subject is aware of the error
because there is no rupiah value that is negative. But
the subject does not have the motivation to re-check,
so, with the beginning of the process is wrong, the
subject experience deadlock, the subject prefers not
to solve the problem where it affects the final result.
Thus, a strategy error is an error in the process
experienced by someone experiencing a deadlock to
continue the settlement process.
Type of procedural error -The third type of
errors students make is a procedural error. a
procedural error is an error in preparing the steps.
Further explained, procedural error indicator is: a)
wrong not write problem in process of settlement; b)
incorrectly discontinuing the settlement process; c)
wrong in understanding and observing the purpose of
the question; d) wrong in performing addition and
subtraction operations; e) wrong in multiplication and
distribution operations; f) incorrectly unable to
manipulate steps; g) is false for concluding without
reason; and h) false because the settlement step is not
systematic (Rittle-Johnson and Alibali, 1999).
The procedural error is done by a subject of
PM01, PM03, PM04, and PM07. The subject of
PM01 encountered an error because it did not
complete until the final process. Subject understands
concepts and solutions but does not solve them due to
environmental factors (disturbed concentration). Still,
this has an impact on errors in solving a problem. The
subject of PM03 makes a mistake in placing the
variables (x) and (y). But this is based on no reason,
not because it has its own concept. But the cause is
because the subject still does not understand the
material that is complex.
The subject of PM04 makes an error in the
operation of integers. Of the two questions resolved
by the subject, both are the same in the type of error
that is caused by the crowd around him that makes
him unable to focus.
The subject of PM07 has an error in looking at the
problem. The information written by PM07 does not
match what is asked in the question. This is because
the physical condition is being experienced by the
subject so as to make it not careful with what is asked.
Thus, a procedural error is an error in using an
unsystematic way to perform a settlement that affects
the outcome. The procedural error indicator is a)
wrong not writing down what is known and asked; b)
wrong does not solve the problem to the end; c) wrong
in the placement of known data; d) wrong in counting
operations that impact on the final result.
4 CONCLUSIONS
Starting from the discussion of the previous chapter,
the authors present some conclusions as follows;
Student learning styles in SMK Patriot Cirebon vary
greatly. Based on David Kolb's theories used in this
study, the distribution of learning styles of students as
follows: there are three students who have divergent
type learning style, 4 students have learning style of
assimilation type, 8 students have Converger style
learning style, and 9 students have of learning style
the accommodator. Types of errors made by diverger
types are procedural errors and misconceptions,
Types of assimilator type errors are procedural and
conceptual errors, Types of converger type errors are
An Analysis of Students’ Error in Learning Mathematical Problem Solving: The Perspective of David Kolb’s Theory
711

procedural errors. The type of accommodator type
error is a conceptual error. Furthermore, the data
show that there are three types of errors made by
students in completing the math test. The three types
are; 1) The errors of the first type is the conceptual
error, where the error is done because of a wrong
understanding or deviated from the existing
provisions, so this affects the students to make errors
in the process of math tests. 2) The second type of
mistake is a strategy error, experienced because
students are stuck to continue the process of
completing the math test. and 3) The third type of
error is a procedural error, an error in using an
unsystematic way to perform a settlement that
impacts the final result of the test
5 RECOMENDATIONS
To overcome the obstacles found at the time of the
study, the authors propose some recommendations as
follows: The teacher must determine the
comprehensiveness of the material understanding of
the student's mathematical achievement.
Furthermore, teachers should also familiarize
students with systematic issues. While suggestions
for students, students should often practice
elaboration of complex mathematical tests and
practice solving math problems in a systematic and
effective way.
ACKNOWLEDGEMENTS
The authors wish to thank Faculty of Tarbiyah and
Teacher Science (FITK) IAIN Syekh Nurjati
Cirebon-Indonesia.
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