Profile of Learners Who Have High Early Ability in Algebra Subject

with Problem Based Learning

Diana Tri Purnamasari

, Riyadi

, and Sri Subanti

Department of Magister Mathematics Education Faculty of Teacher and Education, Universitas Sebelas Maret, Surakarta,

Indonesia

Keywords: High Early Ability, Problem Based Learning, Algebra.

Abstract: Learners already have various levels of initial abilities when they have learned at the first time. High initial

abilities belong to the leaners will be very important in the learning teaching process. Due to the distinction

of initial high abilities which the learners have so that the research has been done to describe about the

learners who already have early high abilities in the learning mathematics with Problem Based Learning

model. The subject of this research is the learners whose high initial abilities. Data of the learners whose

high initial abilities have been obtained through interview and written test. Learners have been obtained

learning with Problem Based Learning model after gaining the results of the written test before. Steps away

from the model of Problem Based Learning is first, orientation of learners to the problem; second, define the

problem and organize learners to learn; third, guiding independent investigation or group investigation;

fourth, develop and present the work; and fifth, reflection and assessment. The sample is using purposive

sampling technique. The results showed that: the use of the right model of Problem Based Learning can

facilitate learners in understanding the material of learners who have a high initial ability above learners

who have the initial ability to understand the material.

1 INTRODUCTION

The rapid development of science and technology

has a major impact on various aspects of life,

including education. Education can be categorized

successfully if it can change the habits or basic

ability of the individual to be better. This is in

accordance with the opinion that “education is the

environmental influence of individuals to produce

constant changes in habits, thoughts, attitudes and

behaviors” (Thompson, 1957). There are three kinds

of educational paths, namely formal, non- formal,

and informal education. This is in accordance with

article 13 paragraph 1 of Law no. 20 Year 2003 on

the National Education Stem mentions that the

educational path consists of formal, non-formal and

informal education that can complement and enrich

each other. In accordance with article 1, paragraph

11 of Law Number 20 Year 2003 regarding National

Education System, clarified by Article 1 paragraph 6

of Government Regulation No. 17 of 2010 on

Management and Implementation of Education,

states that what is meant by Formal Education is a

structured and leveled education path which consists

of basic education, secondary education, and

college.

In the academic year 2017/2018 most schools in

Indonesia have implemented the curriculum 2013 to

increase the potential of learners. In accordance with

the Permendikbud No. 103 of 2014 states that

learning in the curriculum 2013 aims to develop the

potential of learners to have the ability to live as

individuals and citizens who are faithful, productive,

creative, innovative and effective, and able to

contribute to the life of society, nation and civilized

nation. Basically, every school always make new

innovations in learning in order to improve the

ability possessed by learners become qualified

human resources . In the learning process, teachers

often use learning models to improve student

achievement, especially mathematics subjects.

Many learners consider that mathematics is an

abstract subject and difficult to understand. This is in

accordance with the opinion saying that “it is a fact

that, despite its utility and importance, mathematics

is perceived by most pupils as difficult, boring, not

very practical, abstract, etc., and its learning as

requiring a “special ability” that is not always

410

Tri Purnamasari, D., Riyadi, . and Subanti, S.

Proﬁle of Learners Who Have High Early Ability in Algebra Subject with Problem Based Learning.

DOI: 10.5220/0008522704100414

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 410-414

ISBN: 978-989-758-407-7

within everyone’s reach” (Ignacio, 2006). One of

the subjects of mathematics that require more

comprehension is algebra. According to Lins states

that “algebraic thinking was an intentional shift

from context (which could be real, or a particular

mathematical case) to structure. Thus, algebraic

thinking arises when people are detecting and

expressing structure, whether in the context of

problem-solving concerning numbers or some

modelled situation, whether in the context of

resolving a class of problems, or whether in the

context of studying structure more generally”

(Watson, 2007). “Algebraic thinking promotes a

particular way of interpreting the world. It employs

and develops a variety of cognitive strategies

necessary to understand increasingly complex

mathematical concepts and builds upon students’

formal and informal mathematical knowledge.

Essentially students are using, communicating and

making sense of the generalities and relationships

inherent in mathematics, rather than just the

identification of a single numeric answer or

objective fact” (Windsor, 2009). Most mathematics

teachers still use a teacher-centered, conventional

learning model, so the learning-centered learning

model is expected to improve the initial capabilities

already possessed.

The application of the Problem Based Learning

model was chosen because it requires active learners

in the investigation and problem-solving process in

learning. “PBL is an instructional (and curricular)

learner-centered approach that empowers learners

to conduct research, integrate theory and practice,

and apply knowledge and skills to develop a viable

solution to a defined problem” (Savery, 2006). PBL

is a model of learning that begins by confronting

students with mathematics problems. “Problem-

based learning (PBL), aims students to gain

autonomous learning, independent study, inquisition

and problem-solving skills; and it is an approach in

which individuals are confronted with simulated

situations like the ones they are probable to face in

their daily lives and encouraged to learn

individually through self-study and research. This

method being used in mathematics classes has an

importance for the permanent storage of knowledge.

One other factor which affects the students’ learning

is their efficient and proper way of study”

(Karaduman, 2013). “Problem Based Learning can

also develop important capabilities such as problem

solving, flexibility, adaptability, and critical

thinking” (Savin, 2000). The key components in

Problem Based Learning are (a) students working in

small groups; (b) student-centered learning; (c) the

educator acts as a facilitator; and (d) the use of real-

life issues as a focus in learning (MacMath, 2009).

Based on interviews to teachers of SMP Negeri 3

Surakarta obtained information that the factor of a

success in learning apart from the learning model

used is the basic ability of learners. The basic skills

that learners have as a basis for understanding new

things that teachers give are often called initial

abilities. This is in accordance with the opinion

which states that the capabilities that have been

mastered before the learning process of a particular

subject begins (Dick & Carey, 1990). “Early ability

of learners into three groups, namely high, medium

and low” (Rahman & Maarif, 2014). The process

how to categorize high, medium and low group is

with how to sort the score of mathematics learning

outcomes before (daily tests and middle

exams semester), and classification done by

classroom teachers. When we are dealing with a

number of learners who are not specifically chosen

for their intelligence, among them are children who

are highly capable, moderate and weak.

In connection with the background that has been

described, the proposed research statement is: How

the learning achievement of learners who have high

initial ability in learning mathematics model

Problem Based Learning.

2 METHOD

This type of research is qualitative descriptive

research. This research was conducted at SMP

Negeri 3 Surakarta learners VIII C. Determination of

sample using purposive sampling technique. This

study begins by measuring the initial ability of

learners using written tests and interviews

determining the level of initial ability of learners.

This research begins with taking the initial ability

score from previous research. After that, learners are

categorized into three high, medium, and low levels.

Subjects in this study are two students who are

categorized to have high early ability. In addition,

the teacher gives problem/test to solve the

learners/subject after given the model of Problem

Based Learning. It is intended for the

implementation of this research.

The data in this study was collected directly by

the researchers, so that the main instrument of this

study is the researcher himself who assisted with the

aids instruments in the form of a written test and

interview guidelines. This means that the main data

sources in this study are worksheets of learners,

words, and additional data such as documents and

Proﬁle of Learners Who Have High Early Ability in Algebra Subject with Problem Based Learning

411

others in algebra material. The data obtained will be

described by students who have high initial ability in

learning mathematics using Problem Based

Learning model.

Data collection techniques in this study using test

and non-test techniques. Non-test techniques use

interview methods to obtain valid results. After the

teacher gives the written test the initial ability of the

learners, then the teacher provides the learning

process with Problem Based Learning model and

provide questions to solve, then continued the

interview to confirm the test conducted in writing

with the subject of research. Validity of data is

required in qualitative research. “Examination of the

validity of data include credibility, transparency,

dependence, and certainty” (Sugiyono, 2010). Data

credibility will be more valid if we use data

triangulation techniques. Triangulation techniques

was done by using a test and interview

techniques. Data Dependence is reached by taking

two subjects who already have high starting

capabilities.

Collecting data in an objective way through the

creation of interview guides, written

test guides initial capability, and presenting data in

accordance with reality is done to obtain data

certainty. Data analysis was done by 2 stages, is at

the stage before and in the field of analysis during

the field. The analysis before the field is done by

validation of instrument research in the form of test

written questions. The analysis during the field is the

process of searching and systematically compiling

data obtained from the results of initial skills

testing and interviews. Data analysis is done by data

reduction, data presentation, and conclusion

drawing. Data reduction is an activity that refers to

the selection process, concentration of attention,

simplification, extracting and transforming raw data

in the field. Presentation of data is done by

classification and identification of data, that is to

write organized and categorized data collection so

that it will enable to draw conclusions from the

data. Drawing conclusions is the concluding activity

of data that has been collected and verify the

conclusion.

3 RESEARCH RESULT AND

DISCUSSION

The determination of the research subjects

based on initial ability test results using the initial

ability test instrument. Gafur stated that there are

two steps to determine the characteristics of the

learner's early abilities: first, using the available

records such as the Graduation Letter of Learning

(STTB) and the entrance test score; second, using

prerequisite initial test and pre-test (Slameto, 2010).

Based on the description of Gafur, it can be

concluded that the initial ability can be measured by

a specific initial test and the result can be used by

the teacher to determine the learning model to be

used.

3.1 Classification of Capability

Data on the classification of learners based on initial

ability test of the learner will be presented in Table 1

below.

Table 1: Classification Capability Early Learners Class

VIII C

Category

Number of Students

High

1 7

Medium

Low

Table 1 shows that out of 32 students of

class VIII in SMP Negeri 3 Surakarta, 17 students

have early ability high, 10 students entered in initial

ability medium, and 5 students classified as

having low initial ability. Results of initial

capability classification. These learners are used as a

reference for choosing a research subject. Early

ability data of learners derived from the initial

ability tests subjects L and B are subjects that fall

into the category of learners who have the initial

ability. The data obtained is used to determine the

sample in this study.

3.2 The Steps of the Problem Based

Learning Model

Learners will get learning with Problem Based

Learning model, then after the completion of

learning can be obtained data from learning results

of written tests. The steps of the Problem Based

Learning model include: first, the orientation of

students to problem (teacher explains learning

objectives, outlining the need for logistics (materials

and equipment) required for solving the problem,

encourage students to engage in problem-solving

activities that have been students and teachers, as

well as self-selected by learners); second, defining

the problem and organizing students to

learn (teacher helps students define and organize the

tasks learners in learning to solve problems, to

ICMIs 2018 - International Conference on Mathematics and Islam

412

determine the theme, schedules, tasks, and

etc); third, to guide self and group investigation

(teacher encourages learners to hypothesize, collect

information, data relevant to problem-solving tasks,

conduct experiments to obtain information and solve

problems); fourth, to develop and present their work

(teachers assist students in planning and preparing a

work that is relevant for example reports, help share

the task with friends in his group and others, then

students presented works as the proof of

troubleshooting); and fifth, reflection and assessment

(teacher guides students to reflect, understand the

strengths and weaknesses of their reports, notes in

memory of important points or concepts related to

problem solving, analyzes and assesses the processes

and outcomes of problem investigations)(Warsono

& Hariyanto, 2012).

Table 2: Initial Ability of Learners

Steps of

Early

Problem

Based

Learning

Capabilities

Subject L

Subject B

Student

Orientation

to Problems

The subjects choose to

work on algebraic

issues from the easiest

one

Subjects choose

to work on

algebraic issues

from the most

difficult one

Defining

Problems

and

Organizing

Students to

Learn

Subjects have been able

to organize problems

and some solutions

from algebra problem

Subjects have

been able to

organize

problems and

solutions of

algebraic

material

Guiding

Independent

Investigation

as well as

Group

Investigation

The subject is easy in

solving complex algebra

problems

Subject takes a

little time to

solve the

complicated

problem itself

Developing

and

Presenting

Works

The subject can work on

the problem in some

way of completion, but

it is little difficult to

present in front of the

class

Subjects can

work on and

present algebra

material

smoothly in

front of the class

Reflection

and

Assessment

Subjects can work on

issues that are given,

but it is difficult to

convey to other friends

Subjects are

less efficient at

times in solving

algebra

problems, but

can solve the

problems given

Subjects L and B solve algebra problems using

Problem Based Learning model well. Subject L can

solve algebraic problems from problems he finds

easy in several ways. In contrast to the subject B

who worked on algebraic issues from which he

considered the most difficult. This causes subject B

to spend more time than subject L in solving the

problems. Subject B can present the questions done

in front of the class well and smoothly, while the

subject L is difficult to convey/explain how to do the

questions in front of the class.

Based on the results of this study the subject of L

and B has a high initial ability to complete learning

using Problem Based Learning model well.

Ruseffendi said that “from a group of children who

are not specifically selected there are a number of

gifted children who are above moderate-minded

learners, who are the same number as low-ability

children” (Herdian, 2010).

4 CONCLUSIONS AND

SUGGESTIONS

Early ability of the students/subjects L and B are

high and can meet some of the steps of

learning Problem Based Learning model. The steps

of the Problem Based Learning model are: first, the

student orientation to the problem (teacher explains

the learning objectives, outlines the logistical needs

(materials and tools) needed for problem

solving, encourages learners to engage in problem-

solving activities that students have selected together

with teachers, as well as those chosen by the learners

themselves); second, defining the problem and

organizing students to learn (teacher helps students

define and organize the tasks learners in learning to

solve problems, to determine the theme, schedules,

tasks, and others); third, to guide self and group

investigations (teacher encourages learners to

hypothesize, collect information, data relevant to

problem-solving tasks, conduct experiments to

obtain information and solve problems); fourth,

developing and presenting their work (teacher assists

students in planning and preparing a work that is

relevant for example reports, help share the task with

friends in his group and others, then students

presented works as a proof of troubleshooting); and

fifth, reflection and assessment (teacher guides

students to reflect, understand the strengths and

weaknesses of their reports, notes in memory of

Proﬁle of Learners Who Have High Early Ability in Algebra Subject with Problem Based Learning

413

important points or concepts related to problem

solving, analyzes and assesses the processes and

outcomes of problem investigations). Subjects L and

B solve algebra problems using Problem Based

Learning model well. Subject L can solve algebraic

problems from problems he finds easy in several

ways. In contrast to the subject B who worked on

algebraic issues from which he considered the most

difficult. This causes subject B to spend more time

than subject L in solving the problems. Subject B

can present the questions done in front of the class

well and smoothly, while the subject L is difficult to

convey/explain how to do the questions in front of

the class. Teachers should be able to design learning

activities tailored to the level of each child's initial

ability. For learners who have a low and moderate

initial ability, it is best to apply a learning model that

can improve the initial ability to better understand

the material to be taught.

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