The Development of Reasoning Ability and Self Efficacy of Students

through Problem-based Learning Model

Muhammad Daut Sia

ian, Rosliana Sire

and Metrilitna Br. Sembirin

Universitas Islam Sumatera Utara, Jl. Sisingamangaraja. Teladan-Medan. Medan. Indonesia

Keywords: Reasoning ability, Self-Efficacy, Problem Based Learning.

Abstract: This study aims to determine the development of reasoning ability and self-efficacy of students through

Problem Based Learning model. The population in this study is all students of grade XI Prayatna High

School Medan and sampling is done by purposive sampling so that selected class XI IPA-1 as the

experimental class and class XI IPA-2 as the control class. This type of research is a quasi-experiment.

From the test data obtained, the sample comes from a population that has a homogeneous variance and

normal distribution. This research was analyzed by using two way ANAVA test. The results showed that the

development of: (1) the students' reasoning ability using Problem Based Learning model is better than the

conventional model with the value of F arithmetic for learning equal to 119,653 with significance 0,000 <

0,05, (2) self-efficacy of student by using model Problem Based Learning is better than the conventional

model with the value of F arithmetic for learning of 11.392 with significance 0.001 < 0.05.

1 INTRODUCTION

Mathematics is a knowledge learned by students

from Elementary School level to University level.

This is because mathematics has a very large role in

other knowledge, especially for the exact and social

knowledge, such as economics in the matter of

production, marketing and others. It requires to do

solving based on mathematical rules. Some people

consider mathematics as the most difficult field of

study. Nevertheless, everyone needs to learn

mathematics because it is a means to solve the

problems of everyday life. (Siagian, 2016) explains

that mathematics is one branch of science that has an

important role in the development of science and

technology as a tool in the application of other fields

of science as well as in the development of

mathematics itself. Mastery of mathematical

material by students becomes an indispensable

necessity in the arena of reasoning and decision

making in an increasingly competitive era in this

modern time.

Reasoning ability is one thing that should be

owned by the students in learning mathematics.

Beside mathematics being a knowledge that

obtained by reasoning it also because one of the

goals in learning mathematics is that students are

able to use reasoning in patterns and character,

performing mathematical manipulations in making

the generalizations, compiling evidence or

explaining the mathematical ideas and statements.

Mathematical reasoning ability, is a component that

must be governable by the student. Ayal, Kusuma,

Sabandar & Dahlan (2016) explain that

mathematical reasoning plays an important role,

both in solving problems and in conveying ideas

when learning mathematics. Russell states that

mathematical reasoning is essentially about the

development, justification and use of mathematical

generalizations. The generalizations create an

interconnected web of mathematical knowledge–

conceptual understanding. Seeing mathematics as a

web of interrelated ideas is both a result of an

emphasis on mathematical reasoning and a

foundation for reasoning further (Brodie, 2010). In

an effort to improve students' mathematical

reasoning there are two things that are associated

with reasoning, namely inductive and deductive

reasonings. Inductive reasoning is a process of

thinking that seeks to relate known facts or special

events to a general conclusion. Deductive reasoning

is a thinking process that draws conclusions about a

particular thing that stands from general thing or the

things that have previously been proved (assumed)

are true (Bani, 2013).

Siagian, M., Siregar, R. and Sembiring, M.

The Development of Reasoning Ability and Self Efﬁcacy of Students through Problem-based Learning Model.

DOI: 10.5220/0008889404830487

In Proceedings of the 7th International Conference on Multidisciplinary Research (ICMR 2018) - , pages 483-487

ISBN: 978-989-758-437-4

483

In an effort to improve students' mathematical

reasoning there are Permana and Sumarmo (2007)

stating that reasoning is a process of thinking in the

process of drawing conclusions. Broadly speaking

there are two types of reasoning, namely the

inductive reasoning also called induction and

deductive reasoning also called deduction. The

similarity between deduction and induction is that

both are structured arguments, composed of several

premises and one conclusion. The difference

between deduction and induction on the basis of the

inference conclusion and also the characteristics of

the conclusions it derives.

Besides cognitive, there are things that are also

very important to note by a teacher with regard to

the development of their students’ attitude to

mathematics itself. Attitude is the part that also

determines the success of students in the learning

process. According to the authors thing important to

note is the self-efficacy of students. Research during

the past 30 years has revealed a positive relationship

between self-efficacy beliefs and academic

performance and persistence (Martin & Marsh,

2006; Multon, Brown, & Lent, 1991; Skaalvik &

Skaalvik, 2004). Self-efficacy is in practice

synonymous with "self-belief", although "self-

belief" is a non-descriptive term (Bandura, 1997),

which refers to the power of belief, for example one

can be very confident, but ultimately fail. Self-

efficacy is defined as a person's judgment about his

or her ability to attain desired or determined

performance levels that will influence the

subsequent action (Bandura, 1997). Mathematics

self-efficacy positively impacts academic

achievement by allowing one to use cognitive

strategies, enhancing the belief in successful

completion of tasks, and encouraging one to come

up with alternative solutions for the problem in hand

(Stevens, Olivarez, Lan, & Runnels, 2004). Studies

shows that students with high-perceived self-

efficacy make more effort to accomplish a task and

are more persistent in the face of difficulties (Aşkar

& Umay, 2001). Hackett & Betz (1989) report that

students with higher mathematics self-efficacy have

lower mathematics anxiety and place more value on

mathematics.

Pintrich and De Groot (Rahmi, Nadia, Hasibah,

& Hidayat, 2017) found that students who believed

they could perform academic tasks using cognitive

and meta-cognitive strategies are more and still

doing better than unbelieving students. Self-efficacy

makes a difference in the way people act, as a

follow-up of feelings and thoughts. People who

believe they can do something that has the potential

to transform environmental events are more likely to

act and more likely to succeed than those with low

self-efficacy. Behavior is influenced by the extent to

which a person believes to perform the actions

required by the particular situation.

Based on observations made at SMA Prayatna

Medan, it is known that the ability of reasoning and

self-efficacy owned by students in this high school is

still low. This can be seen from the only few

students who are able to make allegations, perform

mathematical manipulations, give reasons for the

answers, present the results of group work and draw

conclusions from a given mathematical problem.

According to the results of interviews conducted by

the authors to several mathematics teachers and

some students at Prayatna High School Medan, it is

found that the factors that cause the low of reasoning

ability and self-efficacy of students are students are

deficient in understanding the mathematical

concepts such as not precisely solving a problem

provided by teachers, also less using the reasoning

on patterns and characteristic as explaining the

mathematical ideas and statements, lacking the

ability to design mathematical models and

interpreting the solutions obtained. The lacks of

interest in students' learning mathematics are caused

by the lessons and motivations provided by teachers,

difficulty to accept, their absence of interest in

mathematics, lack of facilities and infrastructure,

fear of the math teacher and all of this cause the

students not to be active to ask if there is a lesson

that students do not understand.

Based on the above problems a solution is

needed to improve students’ reasoning and self-

efficacy by providing treatment using a problem-

based model. Borrow (Huda, 2014) defines that

problem-based learning (PBL) is the lessons learned

through the process towards understanding the

resolution of a problem. The problem is found first

in the learning process. Hudojo (in Gunantara, et al,

2014) state that Problem Based Learning (PBL) is a

process taken by a person to solve the problem they

face until the problem is no longer a problem for

them. Also, Sudarman (2014) says the PBL is an

approach to learning that uses real-world problems

as a context for students to learn about critical

thinking and problem-solving skills, as well as to

acquire knowledge and essential concept of the

subject matter.

So based on the explanation above an attempt to

develop students' reasoning and self-efficacy skills,

is done so the formulation of problems in this study

are: (1) Is the reasoning ability of students using

Problem Based Learning model is better than the

ICMR 2018 - International Conference on Multidisciplinary Research

484

conventional model? (2) Is the student's self-efficacy

using Problem Based Learning model better than

conventional model?

2 METHODS

The type of research in this study is quasi-

experimental research. Quasi-experimental research

is a study intended to determine the existence or

effect of a subject imposed on students. In other

word quasi-experimental research tries to examine

the presence or absence of causal relationships.

Technique used to test the research hypothesis is

Analysis of Variance (ANAVA) a two-way at

significant level α = 0.05. To test the requirements

analysis is done by normality test and homogeneity

test. The design of data analysis is using the two-

way ANAVA. Instruments used to collect the data

are questionnaires and tests of learning outcomes.

Questionnaires are for seeing students' self-efficacy

and tests to measure students' reasoning abilities of

the given material and also seeing students' learning

mastery.

3 RESULTS AND DISCUSSION

3.1 Results

To see whether there is a development in reasoning

ability and self-efficacy of students, problem based

learning model ANAVA two-way test is done:

Statistical hypothesis:

𝐻



∶ 𝜇



𝜇



(1)

𝐻



∶ 𝜇



𝜇



(2)

Criteria: If significance 0,000  0,05, then

𝐻



accepted.

Table 1: ANAVA 2 Way Test Results of Student

Reasoning Ability.

Tests of Between-Subjects Effects

Dependent Variable: N_Gain_PM

Source

Type III

Sum of

Squares df

Mean

Square F Sig.

Corrected

Model

1.032

5 .206 32.101 .000

Intercept 11.903 1 11.903 1852.057 .000

KAM .311 2 .156 24.196 .000

Pemb .769 1 .769 119.653 .000

KAM *

Pemb

.044 2 .022 3.430 .038

Error .463 72 .006

Total 15.066 78

Corrected

Total

1.494 77

a. R Squared = .690 (Adjusted R Squared = .669)

From table 1 above it is obtained of F count for

learning equal to 119,653 with significance

0,000<0,05. Then H

rejected or H

accepted,

meaning there is an increase in reasoning ability

between experimental class students and control

class students. Besides, it is also concluded that the

improvement of students' reasoning ability by using

learning model of problem based learning is better

than students by using conventional learning.

Furthermore, by using ANAVA two-way test it

will be seen whether the development of self-

efficacy of students using learning model problem

based learning is better than students who are given

learning by using conventional learning.

Research hypothesis:

: Increased self-efficacy of students using learning

model problem-based learning is no better or

equal to the students who use conventional

learning.

: Increased self-efficacy of students using learning

model problem-based learning is better than

students who use conventional learning.

Criteria: If significance 0,000  0,05, then

𝐻



accepted.

The Development of Reasoning Ability and Self Efﬁcacy of Students through Problem-based Learning Model

485

Table 2: ANAVA 2 Way Test Results of Students’ Self-

Efficacy.

Tests of Between-Subjects Effects

Dependent Variable:N_Gain_SE

Source

Type III

Sum of

Squares df

Mean

Square F Sig.

Corrected

Model

.266

5 .053 6.419 .000

Intercept 6.268 1 6.268 757.013 .000

KAM .059 2 .029 3.547 .034

Pemb .094 1 .094 11.392 .001

KAM *

Pemb

.169 2 .084 10.177 .000

Erro

.596 72 .008

Total 7.808 78

Corrected

Total

.862 77

a. R S

uared = .308

(

usted R S

uared = .260

)

From the table above it is obtained that F count

for learning of 11.392 with significance 0.001 <0.05.

Then H

is rejected or H

accepted, meaning there is

an increase of self-efficacy between experiment

class students and control class students. So it can be

concluded that the increase of self-efficacy of

students by using learning model problem based

learning better than students who use conventional

learning.

3.2 Discussion

Based on the discussion of the results of the

students' reasoning abilities test above it is obtained

that the value of F count for learning is 119.653 with

significance 0,000<0,05. This means that there is an

increase in mathematical reasoning ability between

experimental class and control class students.

Likewise, with students’ self-efficacy it is obtained

F count for learning is 11.392 with significance

0.001 <0.05. This is also in line with the results of

research that has been done by Mulyana and

Sumarmo (2017) that the achievement and

improvement of mathematical reasoning ability of

students who received problem based learning better

than students who receive conventional learning.

The students 'mathematical reasoning abilities using

problem based learning as the model are still

moderate, and the students' mathematical reasoning

using conventional learning is still low. Students on

problem-based learning class still have difficulty in

solving problems in terms of giving reasons for the

truth of a statement. Similarly, the results of research

conducted by Sariningsih and Purwasih (2017) that

the results of the calculation show that the self-

efficacy of the experimental class is better than the

self-efficacy of the control class, meaning that the

experimental class students have the ability to

complete the task of mathematical problem solving

abilities provided well. This can be seen from the

result of mean score percentage of self-efficacy

score in experiment class is greater 3,91 from

control class. Ekinci & Gökler (2017) find that

learned helplessness decreases with increasing

academic self-efficacy as well. Our finding is

consistent with that of (Ekinci & Gökler, 2017).

4 CONCLUSION

Based on the results of the research findings,

hypothesis testing and discussion, the conclusions

are: (1) The development of students' reasoning

ability by using problem based learning model is

better than conventional learning model. (2) The

development of self-efficacy of students by using

problem based learning model is better than

conventional learning model.

REFERENCES

Aşkar, P. & Umay, A. 2001. İlköğretim matematik

öğretmenliği öğrencilerinin bilgisayarla ilgili öz-

yeterlik algısı. Hacettepe Üniversitesi Eğitim Fakültesi

Dergisi, 21, 1–8.

Ayal, C. S., Kusuma, Y. S., Sabandar, J., & Dahlan. J. A.

2016. The Enhancement of Mathematical Reasoning

Ability of Junior High School Students by Applying

Mind Mapping Strategy. Journal of Education and

Practice. 7(25), 50-58.

Bandura, A. 1997. Self- Efficacy: The Exercise of Control.

New York: W.H. Freeman and Company.

Bani, A. 2011. Meningkatkan Kemampuan Pemahaman

Dan Penalaran Matematik Siswa SMP Melalui

Pembelajaran Penemuan Terbimbing. Universitas

Pendidikan Indonesia.

Brodie, K. 2010. Teaching Mathematical Reasoning in

Secondary School Classrooms. (New York: Springer

Science+Business Media).

Gunantara. dkk, 2014. Penerapan Model Pembelajaran

Problem Based Learning Untuk Meningkatkan

Kemampuan Pemecahan Masalah Matematika Siswa

Kelas V. Jurnal Mimbar PGSD, 2(1).

Hackett, G. & Betz, N. E. 1989. An exploration of the

mathematics self-efficacy, mathematics performance

correspondence. Journal for Research in Mathematics

Education, 20, 261-273. doi: 10.2307/749515.

ICMR 2018 - International Conference on Multidisciplinary Research

486

Huda, M. 2014. Model-Model Pembelajaran dan

Pengajaran. Yogyakarta: Pustaka Pelajar.

Martin, A. J., & Marsh, H. W. 2006. Academic resilience

and its psychological and educational correlates: A

construct validity approach. Psychology in the

Schools, 43, 267–281.

Multon, K. D., Brown, S. D., & Lent, R. W. 1991.

Relation of selfefficacy beliefs to academic outcomes:

A meta-analytic investigation. Journal of Counseling

Psychology, 38, 30–38.

Mulyana, A., Sumarmo, U. 2017. Meningkatkan

Kemampuan Penalaran Matematik dan Kemandirian

Belajar Siswa SMP Melalui Pembelajaran Berbasis

Masalah. DIDAKTIK (Jurnal Ilmiah STKIP Siliwangi

Bandung, 9(1), 40-51.

Permana, Y dan Sumarmo, U. 2007. Mengembanngkan

Kemampuan Penalaran dan Koneksi Matematik Siswa

SMA Melalui Pembelajaran Berbasis Masalah. Jurnal

Educationist, I(2), 116-123.

Rahmi, S., Nadia, R., Hasibah, B., & Hidayat, W. 2017.

The Relation between Self-Efficacy toward Math with

the Math Communication Competence. Infinity, 6 (2),

177-182. doi:10.22460/infinity.v6i2.p177-182.

Sariningsih, R., Purwasih, R. 2017. Pembelajaran Problem

Based Learning untuk Meningkatkan Kemampuan

Pemecahan Masalah Matematis dan Self Efficacy

Mahasiswa Calon Guru. JNPM (Jurnal Nasional

Pendidikan Matematika, 1(1), 163-177

Siagian, M. D. 2016. Kemampuan Koneksi Matematik

dalam Pembelajaran Matematika. MES (Journal of

Mathematics Education and Science), 2(1), 58-67.

Skaalvik, E. M., & Skaalvik, S. 2004. Self-concept and

self-efficacy: A test of the internal/external frame of

reference model and predictions of subsequent

motivation and achievement. Psychological Reports,

95, 1187–1202.

Stevens, T., Olivarez, A., Lan, W. & Runnels, M. K. 2004.

Role of mathematics self-efficacy and motivation ın

mathematics performance across ethnicity. The

Journal of Educational Research, 97(4), 208-221. doi:

10.3200/JOER.97.4.208-222.

Sudarman. 2007. Problem Based Learning: Suatu Model

Pembelajaran Untuk Mengembangkan dan

Meningkatkan Kemampuan Memecahkan Masalah.

Jurnal Pendidikan Inovatif, 2 (2).

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