ABSTRACT thinking skills are absolutely necessary for students



purpose of this paper is to describe about high order thinking skill in
matematic learning in primary school. High order thinking skills are absolutely
necessary for students to equip them in the context of 21st learning
century. In the primary school, the implementation is embedded in the
curriculum framework currently used to develop high order thinking skills in
the learning process. In addition, the competency of learning is also
affiliated with the achievement of 21st learning century skills. The
process of learning mathematics, is not purely only learn how to count in the
implementation of learning that done. This is in line with the high level of
expected competence related to the development of high order thinking skills by
referring to the development of 21st learning century contexts in
the primary school classes. This developed of high order thinking skills refers
to Bloom’s taxonomy that has been revised by Anderson, et.al. Based on these taxonomy, the high order thinking skills is
consists of from 3 levels of the 6 levels developed at levels 4 through 6.
These three levels among others, are: (1) analyze; (2) evaluation; (3) create.
These three levels in the cognitive domain are implemented through a series of
mathematics learning processes in primary school. In the process, the
development of cognitive abilities at such a high level can be implemented by
provising high order thinking skills challenges to enable meaningful learning
in the mathematics learning process in primary schools. The result of this
paper is we can know and understand at least about mathematical learning
process in primary school and how to develop high order thinking skill by
referring to the development of 21st century learning skills in
primary school classes.


Keywords: High order
thinking skill, mathematical learning, primary school




The context of learning based in the development of the 2013 curriculum
that has been revised on 2026 is implemented to develop high order thinking
skills that are also capable of developing and optimizing 21st century learning
skills better known as 4C’s (collaboration, critical thinking and problem
solving, communication, and creativity) (Halah Ahmed Alismail, Vol 6, No.
6, 2015).
The implementation of the learning process refers to how students are
independently able to develop and optimize both competencies. It becomes a
reference to how the learning is carried out. Learning estates are implemented
taking into account the circumstances and condition of students related to student’s
physical and psychological learning readiness from the student.

The learning of the 21st century has major implications for the current
series of educational processes. This is due to a shift in the paradigm of
learning that is run. Its as an implication of the 21st century learning
context developed impacts on how the learning is carried out. The development
of the revised 2013’s curriculum in 2016 provides flexibility for teachers to
develop the learning process in the skills into one learning development
estates implemented.

Mathematics is one of several other subjects that students learn in primary
school. Among other subjects, mathematics has different characteristics as well
that is carried out. The integrated thematic learning process in primary school
doesn’t include mathematics in units of particular themes or the whole. It
affects the learning of mathematics which is carried out separately in the
class itself.

Learning maths in the primary school is conducted as an effort to provide
students with learning experiences related to mathematical skills that can be
developed. The concept and context of the learning that is conducted leads to
how students are able to independently develop mathematical competencies
provide benefits and help them to apply in practical life processes. It is a
conceptual framework that is projected about how mathematical material can be
teoretically developed in practice in the learning process.

The optimization of high order thinking skills in the
series of math learning process in primary school is a deffinitive effort to
asnwers the challenges and the development of the current era. The context of
learning in the 21st century is answered by the actualization of math learning
to develop and optimize high order thinking skills in the classroom. The
process of learning mathematics that not only develop the cognitive aspect as
the implementation of kwonledge also needs to be followed up by the
presentation of learning that is able to optimize and actualize the development
of affective, psychomotor, and cognitive fields simultaneously and
synergistically among the sphere in a conceptual framework implemented in step
by step learning mathematics especially in primary schools. thus, the high
ideals of the future will create a golden generation of 2045 competent in the
face and identify various phenomena of globalization is very complex with a
comprehensive capital learning experience.


High Order
Thinking Skills

High order thinking skills are one of several development concepts that
focus on being optimized in today’s learning processes. It makes this aspect
one of the few priority development concepts when the learning process is
implemented. Currently developed 2013 curriculum that has been revised in 2016
after experiencing benchmarking process with global level and has resulted in
learning competency mapping on core competence and basic competence of primary
and secondary education based on the regulation of the minister of education
and culture of the republic of indonesia. All core competence and basic
competence after benchmarking processes with existing global standards have
improved and developed in terms of factual, conceptual, procedural, and
metacognition knowledge within the framework of the curriculum formulated through
core competencies and basic competencies of primary and secondary  schools.

Factual knowledge is a basic element that experts use in conveying,
understanding, and embracing their academic discliplines. Conceptual knowledge
os schemes, models, and explicit or implicit theories that demonstrate one’s
own knowledge can also be assumed as knowledge to solve problems. Procerural
knowledge involves specific skills, algorithms techniques, and methods. The
knowledge of metacognition is a personal awareness of a person, where more
emphasized to the students to always be aware and responsible for their
thinking independently (Penyusun, 2016).

Based on the development of the revised 2013 curriculum in 2016, the
development of a high order thinking skills context refers to Bloom’s taxonomy
revised by Anderson and Krathwohl in 2001. Based on cognitive levels, Bloom (as
Anderson and Krathwohl revised) (Krathwohl, 2001) divide cognitive level in six level,
including: (1) remembering; (2) understanding; (3) application; (4) analysis;
(5) evaluation; (6) create. From these six levels, identified into two types of
levels thinking is low order thinking skills (LOTS) and high order thinking
skills (HOTS). Hierarchically, the concept of high and low level thinking can
be seen in the following chart.

            LOTS                           HOTS

1. Cognitive level based on the Bloom’s taxonomy (image only illustration)
(Revision Anderson, 2001).


Development of high order thinking skill can be developed
through a learning processes that stimulate student’s cognitive abilities
continually. The process is absolutely done through a series of of lessons that are
capable of delivering challenges and higher levels of thinking or above the
standard of thinking of existing student competencies. Thus, students will be
more accustomed to developing higher-order thinking skills in the context of
learning through the correlation of reality in the life processes they
experience. In this process, students should always be given a learning
presentation that is able to develop and optimize their analytical, evaluative,
and creative skills by adjusting the targeted learning competencies. In addition,
students also need to be given a variety of learning experiences that can enter
into their long-therm memory. So that, the learning process that can optimally
develop and optimize high order thinking skills through meaningfull learning

The domain of cognitive ability development in high order
thinking skills is optimized through a process of learning that has a higher
level of thinking. In the process undertaken, students must be able to
independently perform the process undertaken, students mus be able to
independently perform the process of analysis, evaluate, and creating all
matters relating to the material that is currently being studied. For example,
at level C6 (creating) in the process of learning mathematics in the primary
school, students
are able to independently determine and find a solution to a mathematical
problem in its own way but still pay attention to the realm of completion of a
comprehensive problem. This is as can be found in the open-ended model that has
an alternative answer more than one. Of course there are many others atlernatives that can be
done to develop and optimize learning process that leads to the improvement and
development of high order thinking skills.


Math Learning in The Primary Schools

Learning process is carried out
to be able to provide learning experiences to students to be able to master and
optimize targeted learning compeencies. In primary school, math learning in one
of its development studies the concept of mathematics through conceptual investigation
(Frei, 2008). Nevertheless, the
praxis in mathematical learning concepts is developed in a step by step
learning that students learn praxis as learning.

In different concepts on
learning mathematics, if learning in the context of teaching by teachers, math
learning only gives one side of the idea in terhs of mathematical thinking.
That’s as Polya’s assumption in Cowan (Cowan, 2006) which states that
overall the activity of guessing nad developing math concepts of things not
seen arround students. It’s sometimes that makes the teacher neglectful to be
able to develop a variety of mathematical skills that can be actually be made
something interesting as a student’s learning experience. The math concept is
also useful  for students as a provision
of experience in living and facing real life processes in life later. Thus,
learn math is not only limited to memorizing and applying math formula but
rather to how students with math knowledge and understanding are able to apply
in the process of daily life of math concepts in practical life in the real
life. It’s same as habituation process to make math as something include in
real life to help and solve their life’s problem and trouble.

Math learning sequences in
primary schools are developed with reference to some math concepts and skills.
The conceptual framework of own math learning in primary schools is developed
with the result of developing students’ math thinking skills. This ability is
an accumulation of the concept of thinking which indicates the development of
the ability: (1) understanding of math; (2) mathematical problem solving; (3)
mathematical reasoning; (4) mathematical connection; (5) mathematical

Learn math can make students
able to face their real life’s trouble. This concepts can be used practically
when student understanding math comprehensive. Math understanding is concerned
with the student’s ability to answer a math question accompanied by the reason
for the answer (why the student concerned assumes that the answer is true on a
logical basis). These reason can be definition of a concept, the use of models
and symbols to present concepts, the application of a simple calculation, the
completion of an algorithmic problem is done correctly and realized step by
step is done. According to Adjie and Maulana (Adjie, 2006), problem solving is
a process of acceptance of challenges and hard work to solve problem. Similar
disclosed Wahyudin (Wahyudin, 2012) states that probelm
solving is an integral  part in learning
proces of math. Thus, problem solving can’t be made as a separate part of the
learning process undertaken. In learning math in particular, problem solving is
not only a goal of learning, but also as a way to do the learning process

Math connections were
popularized by NCTM in 1989 which stated that mathematics is not a partially
separate set of partially separate 
topics and abilities. Although in reality mathematics is often partitioned
and studied in several brances ( (NCTM, 2000). Math is an integrated
science. With this assumption, math need to be viewed as a holistic whole. Looking
math as a whole is very important in learning and thinking about the connection
structure between topics in mathematics itself. The connection structure
between the branches of mathematics allows students to make analytical and
analytical mathematical reasoning.

Gilarso in Setyono (Setyono, 2008) states that reasoning is an explanation that shows the connection or
relationship between two or more things on a certain basis and with a certain
step up to one conclusion. The same thing is said Nico (Nico,
2012) which
states that reasoning is a thought to be able to produce a conclusion.

Mathematical communication is one
of the mathematical skills that are expected to be mastered by students.
Mathematical communication involves 3 aspects (Education, 2017), among others: (1)
using mathematical language accurately and using it to communicate aspects of
problem solving; (2) using accurate mathematical representation to communicate
problem solving; (2) present a well-organized and well-structured problem


Optimization of High-Level Thinking Skills in
Elementary Mathematics Learning

The optimal learning process can lead the students to understand the
targeted competencies as set forth in the learning objectives. Achievement of
quality learning process is created by all components of learning as whole
unity that has synergicity. Between components to create a series of optimal
learning process and quality. In that context, each learning component has its
own duties and roles in order to create a quality of educational process.

The consequence of learning process undertaken is need for the development
of learning material that really can develop high order thinking skills of
students. In addition, the cognitive dimension associated with the concept of
matter can be developed theoretically in the context of classroom chronological
learning praxis. So the ability to be developed by students is not only limited
to knowing and mastering math concept theoretically, but rather to how students
are abel to apply and implement the theoretical concepts of math material
learned in the context of field praxis as the process of life they experience
daily. Thus, the learning process that meaningfull learning really can be
implemented in real class in an optimal manner.

Learning is done to optimize the ability to analyze, evaluate, and create
is developed through the learning steps are compiled and implemented through
the steps of math learn in the classroom with a focus on learning affiliated
with the characteristics of developmental psychology and learning from the
students themselves. The factual and actual implementation of learning will
provide a valuable learning experience for students in order to make the
learning process meaningful.



learning that provides valuable experience to the students is the estuary of a
meaningful series of learning processes. This leads to how the development of
learning is implemented in order to create a 2045 gold generation that is ready
to face the reality and global phenomenon later. The development and
optimization of high-level thinking skills in the learning process of
mathematics brings new paradigm in the learning process undertaken. This
implies how the learning process is carried out with reference to the
development of students physically and psychologically. In addition, the
readiness factors of students both physically and psychologically need to be
considered related to how the learning process is implemented.

learning in primary schools as it is, is carried out by observing how students
are able to develop the process of thinking mathematically. In that context,
there is a wedge between what is developed in terms of high-level thinking
skills with students’ mathematical thinking. The development and optimization
of students’ ability to analyze,
evaluate, and create is aligned with how students are able to develop math
comprehension skills, mathematical problem solving, mathematical reasoning,
mathematical connections, and
mathematical communication.