Developing High Order Thinking Problem on Aplication of Cubes

and Cuboids

Eli Marlina, Ratu Ilma Indra Putri, and Darmawijoyo

Universitas Sriwijaya, Jalan Padang Selasa, Palembang, Indonesia

Keywords: Developing problem, application cubes and cuboids, high order thinking, development studies

Abstract: This research aim to develop a valid and practical problem High Order Thinking Type Application Volume

Cube and Cuboid for secondary school. This is a development studies with formative evaluation type. Data

collection technique include walk through, documentation, interview, test, and questionnaires. The prototype

is valid qualitatively by validators that are expert. In additional expert have also stated that prototype is

practical problem for. It has also been tested to eight grade student to know the quantitative validity and

reliability of each item. This study result fifteen item exam high order thinking type application volume cube

and cuboid for eight grade student.

1 INTRODUCTION

Mathematics literacy is often translated as the ability

to apply Mathematics in various fields. Mathematical

literacy plays an important role in the digital age

where information technology and knowledge

develops dynamically. It shows the need for a

learning approach that can shape the thinking patterns

needed to interpret and critically analyze everyday

situations, solve problems and evaluate the

information presented to us. But the approach done

by educators in schools has not been able to improve

students' ability in everyday situations in solving

problems. This is seen in the results TIMSS and PISA

2015 still below the average OECD that is equal to

386 (OECD, 2016)

The Trends in International Mathematics and

Science Study (TIMSS) and the Program for

International Student Assessment (PISA) is a test

system initiated by the OECD organization to

evaluate education systems from 72 countries around

the world. Every three years a 15-year-old student is

randomly selected to take the tests of three reading,

math, and science competencies once and every 4

years for TIMSS by examining the mastery of

Mathematics and science. The results of PISA and

TIMSS that Indonesia has followed since 2000 have

not shown good results. Indonesia still occupies the

lowest position of many countries in attendance

according to Lie Thien (2015) shows that the 6 levels

of ability formulated in the PISA and TIMSS studies

show that almost all Indonesian students are only able

to master lessons up to level 3 solving problems

according to the procedure in sequence and

selecting/implementing simple problem-solving

strategies, while other countries involved in this case

study reach level 4, 5 and 6. In PISA and TIMSS tests,

Indonesian state is categorized as still at low-level

thinking level that is to remember, understand and

apply but not to develop high-order thinking skills

that are analyzing, evaluating, and creating.

The low PISA and TIMSS results are certainly

caused by many factors. According to Zulkardi

(2010) the cause of Indonesian students have not been

able to resolve the problem of PISA well is that

students are not accustomed to work on PISA

problems that are different from the usual form of

questions tested in school based on real-world

problem. Thus, a change in learning approach and

problem-solving is needed to improve student's safety

in everyday situations in solving problems.

According to Suradijono (2004), problem-based

learning is a learning approach whereby students do

authentic problems with the intent to develop their

own knowledge, develop inquiry and higher-order

thinking, develop self-reliance and self-confidence.

Meanwhile, according to Yamin (2012) based

learning problem (problem-based learning) is one of

the innovative learning models that provide active

learning conditions to learners in real-world

conditions. With a good learning approach is

Marlina, E., Ilma Indra Putri, R. and Darmawijoyo, .

Developing High Order Thinking Problems on Application of Cubes and Cuboids.

DOI: 10.5220/0009993900002499

In Proceedings of the 3rd Sriwijaya University International Conference on Learning and Education (SULE-IC 2018), pages 171-177

ISBN: 978-989-758-575-3

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

171

expected to improve students' high-order thinking

skills.

High-level thinking according to the taxonomy of

bloom is the ability that includes analysis, evaluation,

and creation (Anderson & Krathwohl, 2001).

According to Heong et al. (2011) Higher-order

thinking is defined as the wider use of the mind to find

new challenges. This high-level thinking capability

requires a person to apply new information or prior

knowledge and manipulate information to reach

possible answers in new situations. High-level

thinking is thinking at a higher level than simply

memorizing facts or saying something to someone

just as something is delivered to us. Wardana (2010)

argues that high-order thinking is a process of

thinking involving mental activity in an effort to

explore complex, conscious and creative, conscious

experiences to achieve the goal of acquiring

knowledge that includes the level of analytical,

synthesis, and evaluative thinking. One of the most

widely used mathematical materials in everyday life

and including the content domain of TIMSS and

PISA is the volume of cubes and beams which is one

of the geometry material. In addition, the learning

objectives of cubes and cuboids volumes that exist in

the curriculum are limited to the students can

calculate the surface area and volume of cubes,

beams, prisms, and pyramids, but do not relate to

daily life in problem solving (Curriculum, 2006). So

it can be assumed that the problem of cube and cuboid

volume in the textbook has not included the demands

of problem based learning that include the ability to

find conjecture, analysis, generalization, connection,

synthesis, non-routine problem solving, and

justification or verification.

Based on some of these opinions can be concluded

that high order thinking (High Order Thinking Skill -

HOTS) is a process of thinking that is not just

memorize and relay information that is known. High-

level thinking is the ability of students to solve new

non-routine problems in exploring complex,

reflective and creative experiences by using different

approaches to existing tasks by linking, manipulating,

and transforming existing knowledge and experience

to think critically and creatively in the effort to make

decisions and solve problems in new situations to

gain knowledge that includes the level of analytical,

evaluation, and creative thinking.

Some relevant researches include Lewy (2009),

which develops Problems to Measure Thinking

Ability to provide results of the problems which are

developed to be used to measure higher order

thinking skills in Number Sequence and Series.

Darwanto (2017) entitled Development of

mathematics teaching materials with PBL model to

develop the ability of creative thinking on high school

students with the results of research that students 10

grade MAN showed the average results of learning

test students showed good results that is beyond

KKM, and also data analysis in the form of a response

indicates that learners respond well, so that the

development by using teaching materials that have

been developed creative thinking of learners. In

addition Pertiwi (2016) The development of

mathematical problems characteristic of TIMSS type

problem solving on the topic of geometry measuring

cube volumes and

grade blocks shows that students

can understand the problem well, according to

TIMSS level with reliable questions of 0.7003. On the

basis of this, in an effort to improve the learning

process, researchers want to develop a matter of high

order thinking type of application of cube volume and

block based Problem Based Learning on the subject

of cubes and cuboids. This research combines from

some previous research, If Pertiwi (2016) develops

math problem that focuses on the characteristic of

TIMSS hence the researcher develops about high

order thinking type application to know the student's

mathematical literacy in the problem that is cut down

characterized by high level thinking. This study is

limited to the volume material of cubes and cuboids,

the researchers hope there will be other studies that

can develop this research.

2 RESEARCH METHOD

The type of this research is design research type

development study (Plomp & Nieveen, 2009). In this

study, researchers developed a matter of high order

thinking type of cubes and cuboids validation of valid

and practical volumes, and used to find out the

mathematical literacy in the development of this

problem using the stages of the popularized ADDIE

(Analysis-Design-Develop-Implement-Evaluate)

model in the 1990s by Reiser and Mollenda (Branch,

2009).

Stage analysis is a need assessment process (needs

analysis). In this stage, the researcher analyzes the

need for textbooks used by students and teachers in

learning, how teachers teach, and other learning

resources that teachers use in relation to study of

research materials. The technique is an interview with

a teacher of mathematics with the aim to know the

description of the characteristics of students and

know the approach taken by the teacher during the

learning process.

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The design stage is done after student requirement

analysis, by making a design (blueprint) about high

order thinking type of application. The problem

questioning aims to help students train high order

thinking skills especially in the cubes and cuboids

volume material. The design of the problem is made

on paper using the stages of Problem Based Learning

(PBL) learning. The design process uses three

aspects, namely: content/content, constructs, and

language. That is validated by an expert. Expert

advice is used for design problem revisions. The

responses and suggestions from experts on designs

that have been made are written on the validation

sheet like material for revision.

Development stage (Development) Development

is the process of realizing the blueprints into reality.

That is, at this stage everything that is needed or that

will support the learning process should all be

prepared.

Implementation and Evaluation. At the

implementation stage, the problem has been created,

set in such a way as to be ready to be implemented.

Prior to that, an assessment by the researchers

themselves, counselors, and peers on the problem

questioning was developed through problem-based

learning called the first prototype.

Evaluation stage is the process to see if the

problem being made is successful, in accordance with

the initial expectations or not. Once the product is

ready, then the problem can be piloted in a small

group then evaluated and revised. Then the test can

be done on large groups then reevaluated and revised

so as to produce the final product that is ready to be

tested on the subject of research. The evaluation stage

can be done using the formative evaluation stage as

follows:

a) Expert Reviews. The design results on the first

prototype developed on the basis of Self Evaluation

given to the expert (Expert Review). This stage is

named as a validity test to be evaluated in terms of

content, contrast and language to the problem to be

developed.

b) One-to-one. The prototype was tested against three

students having less, medium and high ability as a

tester. This is done in the hope of seeing the

practicality of design questions through observation

of students in the use of questions. The results of this

trial were analyzed to revise the first prototype.

Prototype 1 was also validated quantitatively and

given to 15 students with varying abilities. Then the

researcher analyzes the items to test the validity and

reliability of the problem grains. From the revision of

expert review and one to one, and analysis of the item

on the 15 students is called the second prototype.

c) Small Group. At this stage the second prototype

was tested on a group of students outside the class

studied (consisting of 6 peer students non subject

research). Furthermore, the results of these trials are

analyzed and discussed in such a way as to produce

suggestions for revision in the form of student

comments on the questions. The revised result is

called the third prototype.

d) Field Test. At this stage the third prototype as the

final product tested to 21 students at

as research

subjects. In this study is expected to see the potential

effects of problems that have been developed.

Products that have been tested in the field test must

meet the quality criteria that is valid in terms of

content, constructs, and language as well as practical

which means easy to use by students

3 RESULTS AND DISCUSSION

3.1 Preliminary Stage

In preliminary stage we are student analysis,

curriculum and about the volume of cubes and

cuboids are developed. At all stages of the prototype,

the researcher used a different

grade students. The

goal is to avoid leakage of problems or repetition of

the problem on the same student. Subsequent

completion of draft initial prototype (Table 1) of the

problem to be developed. In stage one to one,

researchers used 3 students of

grade with various

capabilities. Then at small group, the researcher uses

6 students of

grade with different students and with

various capabilities as well. Next in the field test the

researchers used 21 students of

grade. In this early

stage also produces the instrument development tools

that problem, the problem grid, problem device,

problem cards, and the rubric of value that shown in

Table 1 problem before revision

Table 1: Problem before revised

Proble

Before Revise

An entrepreneur knows to make 10kg

of tofu, if the wooden blocks are 40cm

long, 40cm wide, and 2cm high, how

many pieces of maximum tofu can be

roduced?

Developing High Order Thinking Problems on Application of Cubes and Cuboids

173

3.1.1 Expert Review

Expert review or expert test is a validation phase of

prototype 1 qualitatively in terms of content, content,

constructs and language. The problem device is

consulted to experts and friends who have

experienced in mathematics education as a validator.

The prototype 1 a validator process is done through

two ways: face to face review and mail review. Mail

review involves one expert while the face to face

review of the expert involved is the teacher of

mathematics at school. Result from expert review

and one to one use to revision prototype 2.

3.1.2 One to One

One to one test is tested after expert review. about

prototype 1 was tested on three students with

heterogeneous ability. Students are required to work

on the initial prototype. After doing the questions,

students are given a questionnaire consisting of

several questions about the problem that is done. The

researchers then interviewed the students to confirm

the questionnaire answers. In addition to validation

on the expert and one to one, Prototype 1 is also

validated quantitatively and given to 15 students with

diverse capabilities. Analysis of the item using

Microsoft Excel. Grain validation test using product

moment correlation from Karl Person and reliability

using Spearman Brown. One to one result will be

analyzed again in the small group to get the final

result of the preliminary stage. Data and test result of

validity of item is shown table 2.

Based on the results of the expert review and one to

one test that has been done in parallel, and the

analysis of item (test of validity) quantitatively, then

the matter of prototype 1 revised again and produce

prototype. The result of the revision is shown in Table

3.1.2 Small Group

In the small group stage, the problem of prototype 2

is tested to 6 students. Students involved at this stage

are students of varying abilities. During the process

of working on the problem being done the researcher

records the things that become student questions

about the problem being done and researchers also

interview students to find out what difficulties

experienced by students. Then the students are given

a questionnaire containing questions about the

problem that has been done. The results of the

revision of the questions based on the suggestions

Table 2: Test results validity item problem

Problem r-table r-count Explanation

0,482

0,806

0,97

0,86

0,78

0,700

0,712

0,977

0,865

0,59

0,879

0,95

0,85

0,86

0,92

Valid

No valid

Valid

Based on the results of the expert review and one to

one test that has been done in parallel, and the analysis

of item (test of validity) quantitatively, then the matter

of prototype 1 revised again and produce prototype.

The result of the revision is shown in Table 3.

Table 3: Problem prototype 2

Proble

After Revision

An entrepreneur knows to make 10kg

of tofu, if the wooden block is 40cm

long, 40cm wide, and 2cm high, how

many pieces of cube-shaped tofu can

roduced?

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3.1.3 Small Group

In the small group stage, the problem of prototype 2

is tested to 6 students. Students involved at this stage

are students of varying abilities. During the process

of working on the problem being done the researcher

records the things that become student questions

about the problem being done and researchers also

interview students to find out what difficulties

experienced by students. Then the students are given

a questionnaire containing questions about the

problem that has been done. The results of the

revision of the questions based on the suggestions /

comments of students in small group stage, then

produced a third prototype consisting of 14 questions

that will be examined at the field test stage

3.1.4 Field Test

The field test stage, prototype 3 was tested on the

subject of the research 8

grade as many as 21

students. After working on the problem of students to

inscribe students fill out a questionnaire to determine

the response of students to the problems that have

been done and select some students to be interviewed

directly by researchers. Then, the researchers

analyzed the results of students' answers to determine

what potential effects arise from the problems

developed by researchers. Table 4 is prototype 3 is a

revision of prototype 2 whether the problem is revised

or maintained without revision.

From the result of analysis of the question for

measure thinking ability the height of student in the

subject volume cube and cuboid can be see that 14

student (66,6%) include in the category of having

high level thinking skill is good category out of 21.

From the result of the tests in these 2 meeting, it is

knows that student’s analytical skill are enough good,

most student have been able to analyze the incoming

information and divide or structure information into

smaller parts to recognize patterns or relationships, be

able to recognize and distinguish factor cause and

consequence of a complex scenario and has been able

to identify/formulate questions.

Student ability to evaluate in good category.

Student have been able to provide an assessment

towards solution, ideas, and methodology using

suitable criteria or exiting standard to ensure the value

of effectiveness or benefits. Student have also been

able to hypothesize, criticized, and test even though by

means of testing by entering several variable. Only a

few student have to ability to evaluates with inductive

proof.

Table 4: Problem prototype 3

Problem After Revision

An entrepreneur knows to make

10kg of tofu, if the wooden block is

40cm long, 40cm wide, and 2cm

high, how many pieces of cube-

shaped tofu can be produced?

The question given written succeeded in creative

abilities by creating creative several new strategies in

solving problem. Question number 10 is developed

requires students' understanding of the information

provided in solving the problem. Student can

generalized an idea perspective on something, design

a way to solve a problem and organize element or part

into new structures that have never existed before.

Here are some question and answer to student

Problem 3.Prove the volume of the six pyramids

below s x s x s! Student’s strategy in this problem is

shown in Figure 1

Figure 1: The student's strategy answers

The strategy student’s accordance with the result of

(Lewy, 2009) that the strategy students can evaluated

formula and shown argument. The answer strategy

employed show that students are able to reason, and

communicate/ implement answer correctly, student

are also able to reason and argue with. The result of

the analysis of student answers there are 86% of

students have been able to communicate, season. And

argue correctly in answering question.

The Problem number 10, an entrepreneur knows

to make 10 kg of tofu, if the wooden block is 40 cm

long, 40 cm wide, and 2cm high, how many pieces of

cube-shaped tofu can be produced. The student’s

strategy accordance with the result (Lewy, 2009)

Developing High Order Thinking Problems on Application of Cubes and Cuboids

175

shown succeeded in giving rise to creative abilities by

making new strategy in problem solving. Students

can generalize an idea or perspective on something,

devise a way to solve problem and organize elements

or part into new structures that have never existed

before.

Student’s strategy in this problem is shown in

Figure 2

Figure 2: The student's strategy answers

From the answer, student do the reasoning and

planning an effective settlement strategy. Students are

required to estimate the size of a piece of cubic shape.

This problem include simple problem solving and

students can carry out the procedure well, including

procedures that require decision on a gratuity. Even

the matter is classified as many students who can not

solve the problem well. Only 7 student (34%) of

students can answer the question correctly.

In Problem number 13 Describe other shapes that

can be made into cubes or cuboids with the condition

that each size of the building must the same. Student’s

strategy in this problem is shown in Figure 3

Figure 3: The student’s strategy answers

From the strategy that is done by students shows

students have been able to crate by making some new

strategies in solving problems. Students have been to

generalize an idea or perspective on something to

design and organize or point part in a new structure.

4 CONCLUSIONS

Based on the results and discussion about the

development of cubes and cuboids volume problems

in the students

grade, it can be concluded that the

question of high order thinking type of application of

cubes and cuboids is valid and practical. The validity

has been tested qualitatively and quantitatively.

Qualitative validation is shown from the result of the

validator assessment at the expert review stage stating

that the problem has been good in terms of content,

constructs and language. For practicality, the experts

/ practitioners have stated the matter is appropriate to

be given to the students of

grade. It is also seen in

the stages of one to one and small group that students

can use the problem device well. The resulting field

test results state that the developed.

problem has a

potential effect on students' mathematical literacy

skills in high-level thinking.

Based on the results of the research and

conclusion, then if the results of this study can be

input for other researchers in developing a matter of

high order thinking type application of cubes and

cuboids for junior high school students

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