Higher Order Thinking Skills of Mathematics Education Department

Students of Hasyim Asy’ari University in Solving the Problem

of Generator Function in Discrete Mathematics Lecture

Novia Dwi Rahmawati, Gunanto Amintoko, and Siti Faizah

Department of Mathematics Education, Hasyim Asy’ari University

Keywords: HOTS, Problem Solving, Discrete Mathematics

Abstract: This research aimed at describing students’ higher order thinking skills in solving the problem of generator

function. Higher Order Thinking Skills (HOTS) in this research consisted of logic and reasoning, analysis,

evaluation, and creation skills. This research was a descriptive research by using qualitative approach.

Meanwhile, the research subject was three students of mathematics education department of Hasyim Asy’ari

University,one student with high ability, one student with medium ability, and one student with low

ability.The data collecting method used was test, scoring rubric, and interview. Then, the data validation

technique used was tie triangulation. To analyze the data, the researcher used Miles and Huberman concepts

consisting of data reduction, data interpretation, and conclusion making. The conclusion of this research

shows that one student do the skills of logic and reasoning, analysis, evaluation, and creation not very well

in solving the problem of generator function, so that, they are included in the medium level of high order

thinking skills. Next, two students cannot do the skills of logic and reasoning, analysis, evaluation, and

creation well in solving the problem of generator function, so that, they are included in the low level of high

order thinking skills.

1 INTRODUCTION

The abilities of learning, improving performance,

and reducing weaknesses belong to students with

HOTS because learning effectiveness, learning

speed, and learning ability are affected by the

thought of a person (Yee, Othman, Yunos, Tee,

Hasan, and Mohammad, 2011). Furthermore, Kings,

Goodson, and Rohani (2013) state that HOTS are

students’ ability to think not only by remembering

but also by encountering unfamiliar problems,

uncertainties, questions, or dilemmas. Moreover

Pogrow (2005) argues that students’ success can be

predicted by HOTS owned by them because by

having HOTS can make students face advanced

academic life and adult’s work and responsibility in

daily basis better.

Moore and Stanley (2010) state that Higher

Order Thinking Skill is the last three aspects of

Bloom taxonomy consisting of analysis, evaluation

and creation. According to Brookhart (2010), Higher

Order Thinking Skills cover skills of logic and

reasoning, analysis, evaluation, creation, problem

solving and judgment.

Anderson and Krathwohl (2001) say that analysis

skill in HOTS is a skill to find a problem, then it

needs to rebuild the thing becoming the problem

and identify the most important and relevant part of

the problem, next it is continued by building an

appropriate relation to the given information.

Meanwhile, evaluation skill consists of planning

how far a plan works well and criticizing to a

product or operation assessment based on external

criteria and standards. Next, creation skill in HOTS

is a skill to present the problem, finding of

alternative hypothesis needed and planning to solve

the problem given. Reasoning skill is thinking

proses and concluding in the form of knowledge.

HOTS in this researchare skills of logic and

reasoning, analysis, evaluation also creation.

Same researches deal with HOTS of student have

been conducted araund the world. Tajudin (2015)

conducted studies in mathematical knowledge and

higher order thinking skills for teaching algebraic

problem solving in Turkey. Next, Yen and Halili

260

Rahmawati, N., Amintoko, G. and Faizah, S.

Higher Order Thinking Skills of Mathematics Education Department Students of Hasyim Asy’ari University in Solving the Problem of Generator Function in Discrete Mathematics Lecture.

DOI: 10.5220/0008520402600264

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 260-264

ISBN: 978-989-758-407-7

 2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reser ved

(2015) conducted the study of effective teaching of

higher order thingking (HOT) in education.

Discrete mathematics is a part of mathematics

that studies different and separated objects.

Generally, discrete mathematics is used to count

many objects, study the relationship between finite

sets and analyze process that engages infinite steps

(Rahmawati, 2016). One material that is considered

difficult by students in discrete mathematics course

is generator function. The research that was

conducted by Podilito (2015) explains that students

have not been able to formulate the problem solving

steps correctly and systematically.

In mathematics learning, problem solving is a

way to think. It means that students cannot just rely

to what they learn to be able to solve a problem

without structured process. Even though, some

students may be able to solve the problem well, most

of them should learn how to find the reason and how

to solve the problem. Whereas according to

Rahmawati (2015), problem solving is a learning

approach that stimulates students to want to think,

analyze a problem so that it can determine its

solution. In line with this, Ersoy (2016) explains that

Problem solving plays an important role in

mathematics education since it increases the

students’ high level thinking by having self-learning.

The purpose of this research is to describe students’

HOTS in solving generator function problem based

on arranged indicators.

2 METHODS

This research on students’ HOTS in solving the

problem is a descriptive research with a qualitative

approach. This research includes descriptive

research because the researcher just analyzes up to

description step. It is analyzing and presenting the

facts systematically (Azwar, 2007). While according

to Sugiyono (2011), qualitative research method is

research method that is used to conduct the research

about natural object condition, the researcher as a

key instrument, triangulation as the data collection

technique, inductive/ qualitative data analysis, and

the emphasize of qualitative research result on

meaning more than generalization.

This research subjects are mathematics students

having taken discrete mathematics course. They are

3 students in the semester 5 of mathematics

education department, Hasyim Asy’ari University.

So, the data of Students’ HOTS in solving the

problem achieved is expected to be able to represent

the real condition in the field. Subject selection uses

purposive sampling technique based on students’

ability determination on their midterm test, final test,

and task score given by the lecturer of generator

function. Meanwhile, the research is conducted at

department of mathematics education classroom in a

conducive condition, so that the students focus to

explain what is to be a problem in solving the

problem at the generator function in detail.

In research there must be a valid research

instrument. Before the researcher conducts research,

the researcher must make a research instrument.The

main instrument and supporting instrument are used

to get HOTS category data. The main instruments

are the researchers themselves as planners, data

collectors, data analyzers, data interpreters, and

research result reporters. Supporting instruments are

test questions, assessment rubric and interview

guidelines. Test questions are given in this research

in the form of worksheet that is done by the students

individually. It is done to find HOTS description in

solving generator function problem from the

researchers. Then the instrument is validated to the

validator. In the results of the validation test, the

researcher conducted an analysis of the results to

determine the validity level.

Data validity technique that is used in this

research is time triangulation. Data analysis

technique used in this research is Miles and

Huberman concepts; such as reduction, data

presentation and conclusion making. HOTS score

from each student is the students’ total scores gained

based on the number of reactions to the problem/

question that occur when they complete the test

question and interview. Maximum score is the

highest score of assessment rubric on every HOTS

multiplied by the number of test question, while

minimum score is the lowest score of assessment

rubric on every HOTS multiplied by the number of

test question. If the maximum and minimum score

have been gained, so the step to categorize the

HOTS in high, middle and low level is by

determining data range and dividing it into 3 parts,

so that high, middle and low class interval is got in

sequence reflecting high, middle and low level

students’ HOTS categories.

3 RESULTS AND DISCUSSION

Score result gained from generator function solving

problem and interview answers, is used in

determining students’ HOTS level. From the

Students’ HOTS test and interview results covering

logic and reasoning, analysis, evaluation and

Higher Order Thinking Skills of Mathematics Education Department Students of Hasyim Asy’ari University in Solving the Problem of

Generator Function in Discrete Mathematics Lecture

261

creation aspects, the lowest and highest score are

obtained in sequence; 30 and 42. The score is used

to determine students’ HOTS level categories

presented in the table 1.

Table 1: Students’ HOTS score categories.

Score

Categories

20 ≤ skor ≤ 34

Low

34 ≤ skor ≤ 48

Middle

48 ≤ skor ≤ 62

High

The research result that is gained from 3 research

subjects is that there is no student with high level of

HOTS, one student with middle level of HOTS, who

has less ability in doing logic and reasoning,

analysis, evaluation and creation skills well in

solving generator function problem, and two

students with low level of HOTS, who cannot do

logic and reasoning, analysis, evaluation and

creation skills in solving generator function problem.

Based on interview transcript results, they can

represent middle and low level of HOTS.

3.1 Middle level of HOTS

The result based on data analysis is that a student

with middle level of HOTS is good at analysis skill

of both first and second problems; this student can

identify the main idea by stating thing known and

asked on the questions clearly, shortly and

appropriately. Next, she can give theoretical reason

in every answering step to the last answer correctly.

Additionally, she can give the similarity, difference

and usage known to answer the question correctly.

The following is the example of answer sheet from

students:

In evaluation skill of both first and second

problems, the student is able to give assessment to

the solution and method used in answering the

questions appropriately. Next, the student criticizes

the arguments appropriately to the questions. The

student is also able to recheck starting from the thing

known to the conclusion of the answer by

considering theoretical aspects of answering steps

appropriately to the questions.

In creation skill of both first and second

problems, the student can design how to answer the

questions correctly. The following is the example of

answer sheet from students:

Then, the student designs the way to answer the

question correctly by considering the first analysis

on the thing known and asked in the questions. The

student is also able to make new answering step by

combining previous answering steps logically and

theoretically on the questions. The following is the

example of answer sheet from students:

In logic and reasoning skills, both the first and

second problems, student can write the answer

content, evidence and reason, and language style

clarity effectively, well and logically in finishing the

questions.

3.2 Low Level of HOTS

The result based on data analysis is that students

with low level of HOTS in analysis skill of both first

and second problem, the two students have not been

able to identify the main idea by stating the thing

known and asked on the questions clearly, shortly

and appropriately. Next, they are not able to give

similarity, difference, and usage known to answer

the questions correctly. The following is the

example of answer sheet from students:

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262

In evaluation skill of both the first and second

problems, they are also not able to give evaluation

on the solution and method used in answering the

questions correctly. But, they criticize the argument

the questions correctly. Then students also are not

able to recheck the answer from the start to the

conclusion by considering theoretic al aspect of

answering steps correctly to the questions.

In creation skill of both the first and second

problems, they cannot design how to answer the

questions appropriately. The following is the

example of answer sheet from students:

Next, the students are not able yet to design the

way by considering the first analysis on the thing

known and asked of questions. They cannot make

new answering steps by combining previous

answering steps logically and theoretically on the

questions.The following is the example of answer

sheet from students:

In logic and reasoning skill of both the first and

second problems, the students cannot write the

answer content, evidence and reason, as well as

language style clarity effectively, well and logically

to answer the questions.

The test and interview results show that there is

correlation between analysis, evaluation, and

creation skills. Creation skill is affected by analysis

and evaluation skills. So, the requirement for the

students to be able to do creation is if the students

have been able to do the analysis and evaluation

skills at first. This is in line with Anderson’s

opinion in A Taxonomy for Learning, Teaching and

assessing: A Revision of Bloom’s Taxonomy of

Educational Objectives (2001), creation as the

highest part of cognitive domain.

4 CONCLUSIONS

Based on the research result, the research

conclusions are as follows:

First, the student with middle level of HOTS is

able to identify the main idea, analyze an argument,

and show the usage of the thing known to answer

some questions, so she has quiet good analysis skill.

She is also able to give assessment to the solution

and methods used and recheck the questions, it

means that the student has quite good evaluation

skill. The student also can design how to answer and

show well to the questions. Thus, it can be said that

she has good creation skill. While on their logic and

reasoning skill, the student can write the answer

content, evidence and language style clarity

logically, well and effectively.

Second, the students with low level of HOTS

have less ability in identifying the main idea,

analyzing the arguments, and showing the usage of

the thing known to answer some questions, so they

do not have good analysis skill. The students also

have less ability in giving assessment to the solution

and method used also rechecking to the questions, so

they do not have good evaluation skill. The students

also are not able to design how to answer and show

well to the questions, so they have less good creation

skill. While on their logic and reasoning skill, the

students have less ability in writing the answer

content, evidence and language style clarity

logically, well and effectively.

This research was conducted in Hasyim Asy’ari

University which still has few students so that it is

suggested to do the research with more research

subjects because the more subject collection, the

Higher Order Thinking Skills of Mathematics Education Department Students of Hasyim Asy’ari University in Solving the Problem of

Generator Function in Discrete Mathematics Lecture

263

more possible to describe HOTS on students in

solving generator function problem.

ACKNOWLEDGEMENTS

This work is supported in part by the Beginner

Lecturer Research under grant DRPM Ristekdikti.

REFERENCES

Azwar, S., 2007. Metode Penelitian. Yogyakarta: Pustaka

Pelajar.

Anderson, L.W., and Krathwohl, D. R., 2001. A Taxonomy

for Learning, Teaching, and Assessing: A Revision of

Bloom’s Taxonomy of Educational Objectives. New

York: Addison Wesley Longman, Inc.

Brookhart, S. M., 2010. How to Assess Higher-Order

Thinking Skill in Your Classroom. Alexandria: ASCD.

Ersoy, E., 2016. Problem Solving and Its Teaching in

Mathematics. Journal of New Horizons in Education.

6 (2), 79-87

King, F. J., Goodson, L., & Rohani, F., 2013. Higher

Order Thinking Skills. [online] [12 April 2017]

http://www.cala.fsu.edu/files/higher_order_thinking_s

kills.pdf

Podilito, A. S., 2015. Deskripsi Kemampuan Pemecahan

Masalah Matematika Mahasiswa Pendidikan

Matematika dalam Mata Kuliah Matematika Diskrit

Materi Fungsi Pembangkit. Unpublished Article.

Gorontalo: Pendidikan Matematika Universitas Negeri

Gorontalo.

Pogrow, S., 2005. HOTS revisited: A Thinking

Development Approach to Reducing the Learning Gap

after Grade 3. Phi Delta Kappan, 87, 64-75.

Moore, B., & Stanly, T., 2010. Critical thinking and

formative assessments. Larchmount, NewYork: Eyeon

Education, Inc.

Rahmawati, N. D., 2016. Peningkatan Kualitas

Pembelajaran Matematika Diskrit melalui Problem

Based Learning pada Mahasiswa Semester IV Prodi

Pendidikan Matematika Universitas Hasyim Asy’ari.

Unpublished Article. Universitas Hasyim Asy’ari

Jombang. Indonesia.

Rahmawati, Novia D. 2015. Profil Siswa SMP dalam

Pemecahan Masalah yang Berkaitan dengan Literasi

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APPENDIX

Indicators to measure students' high-order thinking

skills can be seen in the following table:

Component

of High level

thinking skill

Indicator of high-level thinking skills

in solving problems

Analysis

1. Students are able to identify the main

ideas by stating things that are known

and asked about the questions clearly,

concisely, and precisely.

2. Students provide theoretical reasons for

each step of the work until the final

answer is correct.

3. Students provide similarities, differences

and uses of things that are known to

answer questions correctly.

Evaluation

1. Students provide an assessment of the

solutions and methods used in

answering questions correctly.

2. Students criticize the argument correctly

on the question

3. Students re-check starting from the

things that are known to the conclusion

of the answer by paying attention to the

theoretical aspects of the work steps

right on the question.

Creation

1. Students design work methods to

answer questions correctly.

2. Students design ways by considering the

initial analysis in terms of known and

asked questions.

3. Students make a new step in the process

by combining the previous work steps

logically and theoretically into the

problem

Logic and

reasoning

1. Students write the content of the

answers, evidence and reasons and

clarity of the language style effectively,

well and logically in solving the

problem.

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