Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 IOP Publishing

Journal of Physics: Conference Series 1778 (2021) 012011 doi:10.1088/1742-6596/1778/1/012011

Mathematical disposition of strategic thinking ability in

working on HOTS questions

E Firmansyah1, M P Mubarika2, L Saniah3

1,2
Magister Pendidikan Matematika, Universitas Pasundan
3
Universitas Putra Indonesia

E-mail: eka_firmansyah@unpas.ac.id

Abstract. This article contains the results of a study of the mathematical disposition of
strategic thinking skills in working on HOTS (High Order Thinking Skills) questions.
HOTS's problem in learning mathematics has recently become a trend. Therefore,
many educators have begun to learn about the characteristics of HOTS questions, and
some of them consider HOTS problems to be closely related to problems with a high
degree of difficulty. This study was made with the aim of looking at the relationship
between mathematical dispositions and the ability to think strategically in working on
HOTS questions. In learning mathematics, it is suspected that the mathematical
disposition has an important role in solving HOTS problems with the assumption that
if a student has a good mathematical disposition then he can do HOTS problems
easily. Working on HOTS questions is also closely related to the ability to think
strategically because the characteristics of HOTS questions require students to think
strategically in solving existing problems. The ability to think strategically, basically
run by personal characteristics, one of which is mathematical disposition. Therefore,
mathematical disposition has an important role in the ability to think strategically in
working on HOTS problems.

1. Introduction
The development of the school mathematics curriculum is very interesting to talk about, especially
regarding the implementation and aspects of learning theory that underlie it. This is the impact of
curriculum changes that over time continue to be done, in order to improve the quality of learning for
the achievement of educational goals. The national curriculum, or better known as the 2013
curriculum, requires mathematics teachers to have a broader view of mathematics learning, including
mastering mathematical material in accordance with the demands of the times. Teacher and student
perceptions are crucial to understanding classroom processes, and teacher efficacy interacts with class
difficulty to predict teachers' perceptions is an important thing in the demands of learning at this time.
In fact, there are other factors that influence learning in the present, namely: teacher self-reported
efficacy is related to student perceptions of teacher traits, and higher efficacy teachers rate remedial
students as increasing in effort [15].
The mission of the 2013 curriculum is to build student competencies ranging from elementary
school to high school to have: (1) abilities that can be used in solving problems related to mathematics,

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Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 IOP Publishing
Journal of Physics: Conference Series 1778 (2021) 012011 doi:10.1088/1742-6596/1778/1/012011

other subjects, and problems related to real life; (2) the ability to use mathematics as a communication
tool; (3) the ability to use mathematics as a way of reasoning that can be transferred in every
circumstance. These abilities are very useful in following higher education, and can become a
provision in social life, including in the world of work. In addition, with the abilities possessed by
these students, it is expected that students' mathematical thinking abilities will increase and arouse
curiosity and enjoy learning mathematics [1]. Real-life connections provide a deeper understanding to
the purposeof math concepts and skills [16]. this will happen if students understand the problem and
are diligent in solving it [17].

Mathematical thinking ability that is widely known that is about the ability to think critically and
think creatively. To carry out the mission of the 2013 curriculum, scientists developed questions by
emphasizing the HOTS (High Order Thingking Skills) approach. HOTS or higher order thinking
ability is an ability to think that not only requires the ability to remember, but requires other higher
abilities. The ability to think critically and think creatively includes the ability to think at a higher
level. However, in this study we will focus more on mathematical strategic thinking abilities. This is
done with the allegation that to work on HOTS questions students are not only required to be able to
think critically and creatively, but must be able to think strategically so that students can understand,
solve problems, and get solutions well. Instructional design developed generally include three main
components: (1) involve students in the activities non-routineproblem solving; (2) facilitating students
to develop the ability to analyze and evaluate (critical thinking) and the ability to create (creative
thinking); and (3) encourage students to construct their own knowledge (strategic thinking) [18].

Thinking is one of the main components in learning mathematics. Therefore, mathematics is one of
the tools to develop human thought patterns. School mathematics is one of the instruments to train
students' mindset through its procedures with the aim that these students can easily provide solutions
to the real problems they face. Therefore, students' mathematical thinking habits need to be done
through mathematics learning which substantially challenges students to think at a higher level by
developing strategic thinking skills to make it easier to carry out existing procedures in solving
problems [2].
Learning mathematics is not only to develop cognitive aspects, but also affective aspects such as
mathematical disposition. Mathematical disposition is related to students' tendencies to reflect on their
own perspective. Mathematical disposition is one of the factors supporting the success of students'
mathematics learning. Mathematical disposition is also one of the factors that influence student
behavior in dealing with problems / problems. There was a positive relationship between mathematical
disposition and student mathematics achievement [3][12].
The above statement, we can conclude that in mathematics learning by giving HOTS questions in
addition to developing mathematical thinking skills also must develop mathematical dispositions. This
is allegedly because not all students are able to utilize all the material from mathematics learning, but
it is certain that students need a positive mathematical disposition to deal with problematic situations
in real life.

2. Method
Therefore, this study is made as a theoretical description of the relationship between disposition and
strategic thinking skills in working on HOTS questions. From this study it is also expected that every
teacher does not rule out affective competence in students, apart from the demands of the curriculum,
student affective competence is one of the most important factors in learning.

3. Result and Discussion

3.1 Mathematical Disposition
Mathematical disposition has a long-term effect in terms of students convincing toward mathematics
[13]. This relates to how students reflect on their own perspective that allows students to have a

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Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 IOP Publishing
Journal of Physics: Conference Series 1778 (2021) 012011 doi:10.1088/1742-6596/1778/1/012011

positive mathematical disposition or vice versa. Negative mathematical disposition, not because
students do not have the ability in mathematics only they have a negative perception of mathematics.
Teachers are challenged to transform their negative mathematical disposition into positive
(productive) mathematical disposition, so that they trust in mathematical power and function to solve
problems and for their future career progress [4].
Mathematical disposition is defined as one's belief or behavior about mathematics supporting a
tendency to observe mathematics as something logical, useful and valuable [5-6]. The mathematical
disposition of students develops when they learn other aspects of competence. For example, when
students build strategic competence in solving non-routine problems, their attitudes and beliefs as a
learner become more positive. The more concepts a student understands, the more confident the
student is that mathematics can be mastered. Conversely, if students are rarely given a challenge in the
form of mathematical problems to solve, they tend to memorize rather than follow the proper ways of
learning mathematics, and they begin to lose confidence as learners. The more assignments given to
students, it can be seen that commitment and challenges in learning will also be less good. How not,
boredom in dealing with learning tasks makes student commitment weakens. The number of
assignments that students often work on will increasingly reduce the challenges in themselves, as if
students are responding to these assignments as usual. When students feel themselves capable of
learning mathematics and using it in problem solving, they can develop skills using procedures and
adaptive reasoning [14]. The mathematical disposition of students is a major factor in determining the
success of their education [7].

3.2 Strategic Thinking Ability

In the previous discussion it was explained that in working on non-routine questions needed a strategic
ability that is nothing but the ability to think strategically. The non-routine question in question is a
matter of the HOTS approach. The ability to think strategically is the ability to take decisions in
undergoing procedures by placing focus and use of time in the process.
The ability to think strategically is needed by students in analyzing problems / problems.
Correspondingly, in a changing environment, strategic thinking abilities are needed in one's
competence about the more general analytical abilities that have been taught in schools. There are two
indicators of strategic thinking ability, including: (1) recognizing dependency, interrelation and
patterns; and (2) make consequential decisions using analytical skills and intuition. The two indicators
can be divided into three indicators, where the second indicator can be separated between those who
use analytical skills and intuition abilities in making consequent decisions [8].
Strategic thinking is creative, critical, and analytical, although using all types of thinking together
is difficult. From this statement, we can understand that someone who thinks effectively will show
complex mental skills compared to someone who does not think effectively. Mental or cognitive skills
enable the acquisition of knowledge by manipulating ideas and processing new information and
beliefs in our minds so that it is easier to find solutions to problems [8].

3.3.HOTS Questions in Mathematics Learning

HOTS (High Order Thingking Skills) is known as high-level thinking skills. In its implementation
HOTS is a development of Bloom's taxonomy theory. HOTS is the ability to apply knowledge or
methods to solve problems creatively, innovatively and consequently able to create new dimensions
based on knowledge that has been learned. The implementation of HOTS also refers to curriculum
changes and also assessment [10].
HOTS is implemented in an assessment framework so students can assess their ability to solve non-
routine questions. The implementation of HOTS in learning mathematics is very important to change
the community's stigma of difficulties in learning mathematics. HOTS can also attract students to
foster their mathematical disposition in mathematics.
One of HOTS's problems refers to the theory of constructivism. Therefore, students are given the
opportunity to build their understanding, attitudes, and creativity. It is expected that students can think

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Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 IOP Publishing
Journal of Physics: Conference Series 1778 (2021) 012011 doi:10.1088/1742-6596/1778/1/012011

if mathematics is an easy and fun subject. HOTS is consistent with this idea because one of the
indicators highlighted in HOTS is creating sustainable learning and instilling creativity among
individuals. This is in accordance with the understanding of HOTS which states that HOTS is able to
create a new dimension based on knowledge that has been learned so as to create sustainable learning
and instill creativity among individuals [11].

3.4 Illustration Example HOTS Problem

To give an idea of the ability to think strategically in working on HOTS problems, an example of a
problem that can be adjusted to the indicators of strategic thinking ability can be illustrated as
follows:Examples of questions used to measure ability to recognize dependencies, interrelationships
and patterns:

In a class there are 22 students. The teacher holds a Math test. The results of student tests were
obtained an average of 5 and a range of 4. If a student's lowest grade and the highest student's
grade were not included, the average grade changed to 4,9. The lowest and highest values in a
row are ...

Examples of questions used to measure the ability to make consequential decisions using
analytical skills:

Figure 1. Rectangle

It is known that the ABCD rectangle is 12 cm long and 8 cm wide. On each side, a point x cm
is determined from each vertex, so that a rectangular PQRS is formed as shown in the figure.
The smallest possible area of the PQRS square is ... cm2
(a) 40
(b) 46
(c) 64
(d) 72
(e) 85

Examples of questions used to measure the ability to make consequential decisions using
intuitive ability:

In a soccer competition participated by 38 teams, the determination of the winning team was
based on the most points gained, with the following points being set: (1) The winning team
gets 3 points; (2) If a match is a draw, each team gets 1 point; (3) The losing team gets 0
points. The following table contains the temporary positions of the top 6 teams from a total of
38 teams with 5 matches remaining.

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Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 IOP Publishing
Journal of Physics: Conference Series 1778 (2021) 012011 doi:10.1088/1742-6596/1778/1/012011

Table 1. Ranking of Match Teams

Ranking Team Points
1 K 74
2 L 72
3 M 70
4 N 64
5 O 63
6 P 60

Each team will meet each other in the remaining 5 matches. The exact statement based on that
data is ...
(a) Team K will win only 3 times in the remaining matches and one of them wins against
Team L
(b) Team L will win only 4 times in the remaining matches and one of them wins over Team
K
(c) If Team M wins all remaining matches, then Team L's position may still be above Team
M
(d) If Team L always draws in all remaining matches, then Team O may not be above Team
M
(e) Team P will win if it wins all the remaining matches and Team K always loses all
remaining matches

Based on the results obtained through such thought processes, it has become a necessity to
provide non-routine questions to students so that they are accustomed to new problems that
may correspond to what is happening in their lives. In this case, the process of learning
mathematics that can lead to situations that can encourage students to think strategically, of
course, by giving non-routine questions that are nothing but HOTS problems. To improve
their strategic thinking abilities, students are expected to have a good mathematical disposition
so that they can reflect on their perspective through these strategic thinking abilities.

4. Conclusions
Mathematical disposition is related to students' tendencies to reflect on their own perspective. The
mathematical disposition of students develops when they learn other aspects of competence. For
example, when students build strategic competence in solving non-routine problems, their attitudes
and beliefs as a learner become more positive. The more concepts a student understands, the more
confident the student is that mathematics can be mastered. Conversely, if students are rarely given a
challenge in the form of mathematical problems to solve, they tend to memorize rather than follow the
proper ways of learning mathematics, and they begin to lose confidence as learners. The ability to
think strategically includes three indicators, including: (1) recognizing dependencies,
interrelationships and patterns; (2) make consequential decisions using analytical skills; and (3) make
consequential decisions using intuitive abilities. HOTS is the ability to apply knowledge or methods to
solve problems creatively, innovatively and consequently able to create new dimensions based on
knowledge that has been learned so as to create continuous learning and instill creativity among
individuals. HOTS is implemented in an assessment framework so students can assess their ability to
solve non-routine questions

Acknowledgments
We would like to express our gratitude to our institutions, namely the Postgraduate of Pasundan
University and Universitas Putra Indonesia who have given us a lot of support in publishing this
article.

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Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 IOP Publishing
Journal of Physics: Conference Series 1778 (2021) 012011 doi:10.1088/1742-6596/1778/1/012011

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