Building Students’ Hard and Soft Skills through Innovative Teaching Approaches to Mathematics

第 54 卷第 5 期

2019 年 10 月

JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY

Vol. 54 No.5 Oct. 2019

ISSN:0258-2724 DOI：10.35741/issn.0258-2724.54.5.48

Mathematics Education

B

UILDING

S

TUDENTS

’

H

ARD AND

S

OFT

S

KILLS THROUGH

I

NNOVATIVE

T

EACHING

A

PPROACHES TO

M

ATHEMATICS

Euis Eti Rohaetia,*

a

Institut Keguruan dan Ilmu Pendidikan (IKIP) Siliwangi Jl. Terusan Jendral Sudirman, Cimahi 40526, Indonesia

[email protected]

Abstract

The goals of this case study were to (1) analyze the role of innovative mathematics teaching approaches among middle and high school students regarding their hard and soft mathematical skills; (2) to examine students’ perceptions about the mathematical teaching approaches, used by their teachers during class sessions, (3) to analyze aspects of innovation in them. The descriptive case study approach was used to analyze the role of innovative teaching approaches in helping students to develop various mathematical hard and soft skills. A qualitative meta-analysis methodology was applied to ten student theses about mathematics teaching within the Department of Mathematics in the School of Postgraduate studies of IKIP Siliwangi in Cimahi. This paper presents the results based on ten graduate students’ theses research studies, selected purposively from 68 student theses. The selection of articles aimed to include a variety of theses discussing mathematics skills teaching and learning approaches. The results show that, in general, students who were trained with innovative teaching approaches attained higher grades than students taught by conventional teaching methods. It has been established that students’ grades on mathematical hard skills varied after intervention. On the contrary, regarding students mathematical soft skills, some theses reported no difference between students taught using both approaches, while some reported greater differences. Finally, students had good opinions regarding the innovative teaching-learning approaches, used by their teachers.

Keywords: Mathematical hard and soft skills, innovative teaching approaches, student’s opinion on innovative teaching approaches 摘要 : 本案例研究的目的是：（1）分析中学生和高中学生创新数学教学方法在其软硬数学技能方面的作 用；（2）检查学生对他们的老师在课堂上使用的数学教学方法的看法，（3）分析他们中创新的方面。描 述性案例研究方法用于分析创新教学方法在帮助学生发展各种数学软硬技能方面的作用。在 Cimahi 的 IKIP Siliwangi 研究生的数学系内，对 10 篇有关数学教学的学生论文应用了定性荟萃分析方法。本文根据十个研 究生的论文研究结果（从 68 篇学生论文中有针对性地选出）给出了结果。文章的选择旨在包括各种讨论数 学技能教学方法的论文。结果表明，总体而言，接受过创新教学方法培训的学生的成绩要比传统教学方法 更高。已经确定，学生在数学硬技能上的分数在干预后会有所不同。相反，关于学生的数学软技能，有些 论文报告说这两种方法所教的学生之间没有差异，而有些则报告了更大的差异。最后，学生对他们的老师 使用的创新性教学方法有很好的意见。 关键词:数学硬技能和软技能，创新教学方法，学生对创新教学方法的看法 I. INTRODUCTION

Mathematics as a compulsory elementary and junior high school subject is considered to be one of the hardest disciplines by most students [1]; this is reflected in the interpretation of a number of mathematical contents and concepts whose connection appears difficult to most learners to

understand [1]. Teaching mathematical sciences to students at both elementary and high school encourages and helps enhance knowledge, skills [2], attitude, connectedness and competences needed for the learners’ better living in society.

In this regard, schools in Indonesia are required to provide direct experiences which may

encourage the development of hard and soft skills [3] and students are expected to acquire both number concepts and social meanings [2] through learning mathematics. Developing students’ hard and soft skills requires better teaching methods and approaches. In other words, in the effort to develop such skills through teaching of mathematics, teachers should handle issues related to questions of meaning, obtaining sense and skilling students with the necessary communication skills, needed by learners to develop proficiencies and better application of mathematics [4].

Mathematics learning enables students to develop both hard and soft skills. For instance, according to [5], mathematics helps teachers and students to think critically and also helps them to develop abstract and analytical thinking skills, which are a requirement for developing necessary hard skills in life. It is through the “hardness” of mathematics and the fact that there is an exact answer, which makes it a better subject for hard skills development [5] among students. Moreover, there are also a lot of soft skills acquired during learning and practicing of hard mathematics by the students, this is evidenced from the revelation from tech companies such as Google, PayPal, Career at Square, etc., who revealed that most of the soft skills sought from an individual develop during the learning of mathematics [5] while at school. Because of the importance of mathematics learning and following the suggested mathematics curriculum improvements in Indonesia, mathematics teachers are expected to improve students’ hard and soft skills simultaneously, because these two skills are fundamental to the future life of the students, especially in the world of work which becomes complex by each day that passes.

Mathematics learning being categorized as a hard area of study, attaining mathematical hard skills calls for high order thinking, which may lead to hard skills development [6]. For mathematical sciences to appear appealing and easy to understand, it is recommended to use a challenge approach as an innovative way of teaching mathematical lessons [1]. In this study, it was revealed that the use of this approach contributes to the improvement of learner motivation [1], hence enhancing skills development among learners.

To build the exact and required hard skills, students must have better attitudes towards the learning of mathematics or mathematical logical thinking concepts [7]. Teachers are able to stimulate any skills through teaching hard mathematical concepts. This leads to improving

skills, such as reflective, critical, and creative thinking, that require effort and persistence on the part of the students [8]. Experts have defined mathematical soft skills in differing ways, using terms such as mathematical disposition, self-regulated learning, self-confidence, self-efficacy, and mathematical resiliency [7], [9], [10]. The experts may differ in definition and description; however, the descriptions are found to complement one another, therefore we consider them all under the category of soft skills for the purpose of this study.

The goal of this study was to examine the contribution of innovative teaching approaches towards the development of students’ skills both in middle and high school, by looking specifically at the development of both hard and soft skills attained through learning mathematical sciences as well as examined the students’ perceptions in relation to the teaching approaches used in teaching and learning of mathematics. To understand the role of innovative teaching in the development of students’ mathematical skills, a study was conducted by analyzing ten (10) research reports of the postgraduate students, with the intention of critically examining the findings on the contribution of innovative teaching and learning in shaping students’ soft and hard skills.

II. L

ITERATURE

R

EVIEW

Seeking to build the learners’ skills through mathematics learning needs better teaching strategies and approaches. To attain this goal, teachers must be ready to apply teaching strategies and approaches which are innovative and can help develop students’ capacity to solve mathematics tasks [9]. Mathematical sciences are a basis for any technology transfer [11]. According to [5], in one of their surveys conducted on tech companies, it was established that many of the soft qualities needed are developed during the process of mathematics learning.

In the theses studied, it was noted that most of the authors looked at the role of mathematical sciences in building both hard and soft skills [12]-[16]. Some of the authors also examined the aspect of innovative teaching and learning approach in enhancing students’ skills, they divided the students into two categories: the middle and high school students [14]-[16]. In our survey through the literature studied, we found that for the control group lessons were delivered using innovative teaching methods, while the other group received instruction using traditional methods and strategies.

The philosophy about individual capacity to learn emphasizes the importance of one’s mind to grasp concepts through encouraging cooperation with others during learning sessions[17]. Though the grasping of concepts depends on individual capacity to learn, a teacher’s role is fundamental in helping develop students’ learning. The teacher’s competence to teach and the process can help improve the students’ knowledge, skills, and practice [18]-[19]. It is with a good process that individual capacity can lead to the development of both hard and soft skills through mathematics teaching [20]. In this regard, the students’ reports studied assert that each mathematical hard skill aims to strengthen learner competences[21]-[25].The assessment and teaching methods used, such as tests, lesson plans, and student activity sheets, are all intended to contribute to building the students competencies in the form of hard and soft skills.

Though the process of developing hard skills is inert, the rules tend to be the same irrespective of the type of organization and working conditions, whereas soft skills depend on the situation, nature and scope of the company activities [26]. In the literature studied, it has been established that innovative teaching approaches are used considering the characteristics of hard mathematical science concepts which seek to improve the students’ skills. The hard and soft mathematical skills examined in this study are mathematical reflection; critical and creative thinking; mathematical reasoning; communication, connection, and problem solving; mathematical resiliency; self-regulated learning; self-confidence; self-efficacy; and mathematical disposition.

These skills are believed to improve the individual competences of the learners. They are found to be fundamental, particularly, by the tech companies [5]. Having this in mind, the supervisors instructed their students to select an innovative teaching–learning approach whose characteristics [27] enable them to help students in improving their mathematical hard and soft skills [28]. The mathematical teaching and learning approaches involved in their studies were problem posing, inductive-deductive reasoning, scientific approach, problem-based learning, contextual teaching, generative approach, and method eliciting activities [29]-[33]. It has been established that innovative teaching and learning when compared to conventional learning is a better choice for students. It influences students’ performance and

exerts better effect on the building of students’ skills [29].

Some studies have established that the following hard and soft mathematical skills are relevant to the goal of teaching mathematics: understanding mathematics concepts and connections among mathematical concepts [3], [27]; understanding mathematics as a systematic, structured, and supporting science; communicating ideas by using symbols, tables, diagrams, or other media for explaining a situation or a problem; developing logical, critical, creative, and innovative thinking, as well as self-learning abilities; demonstrating critical, creative, accurate, objective, and open thinking, as well as self-confidence, curiosity, interest, perseverance, and persistent attitudes; and appreciating the beauty and the usage of mathematics in daily life [3], [34].

Some students’ studies also explain the expert theories, hence leading to establishment of sufficient guidelines for their further activities. After each sub-study explaining the reasoning of the students regarding the improvement of certain mathematical hard skills for the simplicity and easier understanding of mathematical lessons has led to a desired need to clarify definitions and indicators in more details. Though this is important, we have noticed that for more experts’ opinions, students drew only upon the limited resources with which they were already familiar. Nevertheless, all students met the requirement for definition of mathematical hard skills and could thus proceed to further research activities. Indicators of particular mathematical hard skills depend on the school level and the mathematics content to be taught. For example, indicators of mathematical hard skills for senior high school students [21], [22], [23], [25] are broader and deeper than indicators for the same mathematical skills for junior high school students [12], [14], [15], [20], [24]. According to [35], mathematical soft skills are similar to values and character cannot be taught as mathematical content.

III. R

ESEARCH

M

ETHOD

The goal of this descriptive case study was to examine the role of innovative teaching approaches in building hard and soft skills of mathematics students both in the elementary and high schools across Indonesia. The study focused on examining ten (10) students’ theses in a Mathematics Study Program at the School of Postgraduate of the Institute of Teacher Training and Education (IKIP), Siliwangi located in Cimahi district in the West Java Province.

The ten theses studied employed pretest and post-test experimental designs with control groups. These studies were designed to analyze the contribution of innovative teaching approaches to the formation of students’ mathematical hard and soft skills. The instruments for each thesis study consisted of two tests of mathematical hard skills and mathematical soft skills scale, and a survey on student perceptions of the innovative mathematics teaching approach.

The study, basically, sought to discover whether innovative teaching as concluded by the ten students helped improve students’ hard and soft skills, especially, when they studied mathematics. Because mathematics is considered to be a necessary subject by the Indonesian government and it is examined by government starting from primary leaving examination for junior and also senior high schools. This is done due to the importance attached to students learning hard mathematical sciences and due to the importance of teaching sciences, technologies and other subjects in the area of engineering [36]. Teaching such fields requires better teaching methods, particularly, in this rapidly changing world.

IV. F

INDINGS

A

ND

D

ISCUSSION

The findings are presented in the way that helps approve the need for the use of innovative teaching approaches in teaching mathematical sciences in the effort to build students’ hard and soft skills. The study was conducted to examine the empirical evidences presented by the ten students and hence, establish one voice combining the conclusions from the ten theses. Upon this, this paper discusses the reasoning used to select students’ theses which looked at mathematical hard and soft skills as well as the teaching approaches used during the study.

In the analysis and on examination of the theses, it was observed that the students conducted theoretical analysis of relevant resources to select and define variables which were of relevance to their studies. Next, they compiled operational definitions of each variable suitable for the subject of mathematics and content of their thesis studies. By assessing researchers’ arguments about the selected mathematical skills, they were able to identify the meaning of each research variable, and then formulated operational definitions.

Below are research extracts and summary which were derived from the observatory analyses made on the selected students’ theses:

The research of Carli [21]; Eriska [22]; Johanto [23]; Koswara [24]; Krismayanti [20]; and Mulyani [25] describe the preparation of activities in detail and with reference to many relevant experts’ views of the research variables related to mathematics, skills and teaching methods. Ruhiyat [12]; Suharyati [14] and Sumarni [15] described their activities with less detailed explanation, but their arguments were sufficient for further activities. However, it was found that all the students’ studies, based on their expertise arguments, derived relevant and clear operational definitions of each research variable, as well as a guide for compiling good research instruments and teaching materials (which include lesson plan and student work sheets).

In the reports analyzed it was also found that the instruments were well developed, and relevant statistical procedures were used, resulting in strong research instruments, as illustrated in Table 1 (See Appendix 1).

Based on Table 1 and the analysis of the teaching material (lesson plan and student work sheets), it is concluded that the teaching materials were satisfactory, with step-by-step descriptions of the teaching approaches applied. Besides, it was found that in each thesis student’s teaching materials included student activities allowing them to improve their mathematical abilities and attitudes (i.e.; hard and soft skills) during the classroom activities.

Based on the analysis of [3] and [34] it became true that understanding mathematics as a systematic, structured, and supporting science; and communication of ideas through the use of symbols, tables, diagrams, or other media for explaining a situation or a problem, help improve students’ abilities if involved in most of these activities. The students’ ability to learn and develop both hard and soft skills is an inert process; however, at times soft skills depend on the situation, nature and scope of the company activities [26].

In the analysis and review of the studied reports, it was also revealed that after the students had designed their research activities, they had to empirically implement the proposed learning activities to their respondents to demonstrate how innovative teaching approaches can be used in the real teaching and learning of mathematics in a classroom environment.

This led to an examination of the students’ perception regarding the innovations in teaching and learning. The perceptions were obtained through surveying the students’ opinion and by use of interviews. The Figures from 1 to 9 illustrate the students empirical activities and the

setting of the classroom environment during the learning sessions:

The figures above, obtained from the analysis of nine theses, show that the teachers (or researchers) conducted their lessons seriously and conformed to the principles and steps of the innovative teaching approaches they had selected for their experimental studies. In addition, to evaluate students’ perception regarding the teaching approaches, two researchers [20], [22] carried out interviews with students’ representative from the categories of high group, the medium group, and the lower group.

In relation to thesis findings regarding students’ perception, it was established that students had positive opinions regarding the

innovative teaching and learning methods. On this point, it is confirmed that though the grasping of concepts depends on individual capacity to learn, a teacher’s role is important in shaping students attitudes [18]-[19]. This was evident in the beginning of the experimental lessons, students expressed that the new teaching approaches were confusing, and they also had problems with the worksheets, but with time the learners were able to meet the challenges and felt comfortable after thorough guide from their teachers. The students working as teachers during the field study reported at the end of their study

that the teaching methods helped students to learn the mathematics materials quicker and with ease. Tables 2-8 (see Appendix 1) present brief summaries and description of each thesis report examined during the study. The results are categorized as either mathematical hard or soft skills, or students’ perception towards the innovative teaching and learning approaches.

Based on data given in Tables 2-8, in all pretests regarding mathematical hard skills, there was no difference in students’ grades between those trained by means of innovative teaching and learning and those going through the usual conventional ways of learning; all students’ grades were at a low performance level due to the fact that they had not learned mathematic concepts and tasks. These findings were, therefore, not surprising, since students had not yet been taught the areas covered. This means that the innovative approaches succeeded in areas where students had prior knowledge or had been taught before they came in the experiments. This still points out the importance of teachers, just as Bishara [1] recommends using a challenge approach as an innovative way of teaching mathematical lessons. This means the teacher must be at the center of the teaching and learning process for better understanding of the mathematical content by the learners. It is the best way to help students and any other learners to understand mathematics as a systematic, structured, and supporting science, as well as self-learning subject which may lead to a demonstration of critical, creative, accurate, objective, and open thinking, as well as self-confidence, curiosity, interest, perseverance, and persistent attitudes; and appreciating the beauty and the usage of mathematics in daily life [3], [34].

Upon this it was further revealed that after the students were trained with various innovative teaching approaches, on all mathematical tasks, their hard skills improved, hence leading to the normalized gain (N-G) in students’ grades, meaning thing were becoming better compared to those students who had been taught using the usual conventional teaching and learning methods. In relation to this establishment, it is stated in [36] that teaching fields such as mathematics require better teaching methods in this rapidly changing world, in particular. With creative and innovative teaching learning activities turn to be of relevancy, of meaning and can easily help student to connect with others [36]. By contrast, in many mathematical hard skills, students taught with conventional teaching

remained at low grade levels (less than 60% of the ideal score).

In other words, mathematical hard skills improved greatly, leading to better mathematical connection and understanding ability of learners especially those of junior high students [12] and also there was tremendous improvement in mathematical communication and reasoning of senior high students [23], while those who were taught using conventional approaches obtained grades of medium level whereas there are those who remained at low performance level. Hence, such findings illustrate that innovative teaching approaches were effective in improving students’ mathematical hard skills. This is in line with the views that each mathematical hard skill aims at strengthening learner competences [20]-[25]. Similarly, students’ grades in post-tests for certain mathematical soft skills remained at low level under traditional teaching methods. Junior high students received low grades for mathematical critical thinking and mathematical creative thinking [20], as did senior high students in terms of mathematical critical thinking [25]. Through the learning of mathematical tasks, students who were trained with innovative teaching approaches obtained medium to good grades. Teachers’ views are very important on this aspect. As argued in [18] and [19], the teachers’ competence to teach and their techniques can improve the students’ knowledge, skills, and practice.

However, it was also revealed that mathematical critical thinking was somehow difficult for students. This might have happened because critical thinking involves high-level mathematical processes, such as giving reasons or explanations, or applying rules and principles toward each problem-solving step [17]. Some students were able to solve problems well, but they had difficulties in explaining the reasons for the solutions they provided.

The reasons for the development of hard skills depend on the students’ capacity to learn. First, where learning goals are hard to achieve, the students could have lacked mathematical communication skills or face difficulties in expressing their ideas. Second, students who only imitated teachers’ procedures in solving problems may lack the capacity to follow the necessary rules and procedures required for better performance. In such a situation, teachers must examine students’ difficulties more deeply using relevant scaffolding steps to help students in solving mathematical problems and tasks well. Third, the students’ low grades might have arisen due to the incompetence of the students to

comprehend the prerequisites of the basic mathematics content.

Upon this, it is suggested that before teachers or researchers discuss new mathematics content, they should examine students’ abilities to learn new content or material. It is only when students have already mastered the basic concepts and procedures that teachers can proceed with the teaching of the new content. However, if students have not mastered the basic content, teachers are required to provide lessons before continuation to the next topics.

Building hard and soft skills through innovative teaching of mathematics is in line with the idea that mathematics is a systematic and structured discipline, however, complex if not well taught or learned. It was revealed from [28], [30]-[33], [38]-[40] that students’ prior mathematical abilities play a big role in improving mathematical skills.

This statement was supported by their findings that the higher a student’s grade on the pretest, the higher the student’s gain was in the targeted skills. However, these studies also showed that the innovative teaching approaches were more important than students’ prior mathematical ability in determining skill gain. Those findings supported the statement that, even if a teacher’s effort is not yet optimal, the teacher can help improve students’ mathematical abilities, irrespective of student variables.

It was revealed that the students’ theses also reported different findings on hard skills compared to soft skills. For instance, with regard to mathematical hard skills, students who were trained with innovative teaching approaches obtained various grades at the differing levels, from low to high. By contrast, students’ grades concerning mathematical soft skills tended to be similar, at a medium grade level. These findings can be explained because all students had experience with mathematical soft skills from prior mathematics teachers, therefore, students were already capable of attaining a medium grade level in those skills, even before the intervention took place. However, after two months of the trial lessons, students’ mathematical soft skills did not improve dramatically. This supports [35] stating that mathematical soft skills, similar to values and character, cannot be taught as mathematics content.

As presented in the tables and figures, the students conducted further analysis of the associations between mathematical hard and soft skills (see Tables 2 to 8). All studies reported medium to high associations among mathematical hard skills. Additionally, some

studies reported associations between hard and soft skills [12], [14], [22], [23], [25] whereas, other studies [15], [20], [21], [24] did not report such associations. These inconsistent findings are similar to the findings of other studies [31], [34], [37]-[39] which reported associations between various mathematical hard and soft skills, whereas other studies[13], [30], [35], [40] did not report such associations.

As shown in Tables 2 to 8, there are studies which reported that students had many difficulties in solving mathematical problems, especially those who were trained by conventional teaching [12], [20], [21], [24]. By contrast, in other studies [14], [15], students had few difficulties in solving problems, and, in two of the studies.

V. C

ONCLUSION

Based on the analysis of the selected theses for this study, it is concluded that all studies explained in detail the reasons for choosing mathematical skills and teaching approaches in improving or building students’ competences for the future careers. Mathematics is one of the subjects required in this modern are due to its counting and arithmetic aspect required by almost all modern companies which are using modern technologies in most of the transactions.

Researchers reported positive opinions of innovative teaching approaches. However, students’ positive opinions did not affect their skill development. Other variables more strongly affected students’ learning outcomes. Based on the findings of some thesis studies, students’ prior mathematical ability or their mastery of prerequisite mathematics content might have played a role in skill development.

This study provided evidence that innovative teaching approaches could be more effective than conventional teaching in improving mathematical hard skills. However, this was not the case for some mathematical hard skills studied, as evidenced by students’ grades. As explained earlier, we suggest that teachers examine students’ prior mathematical abilities before teaching a new mathematics topic. Furthermore, to help students to develop higher and more meaningful hard skills, we suggest that teachers explain the rules or principles used in each step of solving mathematical problems. This strategy is expected to support mastery of mathematics conceptsby students.

A

CKNOWLEDGMENT

I take this opportune moment to thank Institut Keguruan dan Ilmu Pendidikan for the support

provided through its publication initiative project, where I was advised on how to write for publication and searching for reputable Journals. I also thank the Journal of Southwest Jiaotong University for the thorough description and guideline offered to me as an author, simplifying my work in writing and typesetting the manuscript. Lastly, I am grateful to the fellow staff from the department of Mathematics of IKIP Siliwangi for the support provided during the writing of this paper. I pray it is published soon.

R

EFERENCES

[1]

BISHARA, S. (2016) Creativity in

unique problem-solving in mathematics

and its influence on motivation for

learning.

Cogent

Education,

3:

1202604,

pp.

1-14.

http://dx.doi.org/10.1080/2331186X.20

16.1202604.

[2]

MOSER, E.H., KINNEY, L., and

PURDY, C. (1948) Aims and Purposes

in the Teaching of Mathematics.

Review of Educational Research, 18(4),

The Natural Sciences and Mathematics

(Oct. 1948), pp. 315-322.

[3]

Kurikulum. (2013). Peraturan Menteri

Pendidikan Nasional No. 81a Tahun

2013 tanggal 27 Juni 2013 tentang

Implementasi Kurikulum Standar Isi.

[4]

JAWORSKI, B., MALI, A. and

PETROPOULOU,

G.

(2015)

Approaches to teaching mathematics

and

their

relation

to

students'

mathematical

meaning

making.

Presented at the 39

th

Meeting of the

Psychology of Mathematics Education

(PME39), 13th-18thJuly 2015, Hobart,

Australia.

[5]

Cox, F. (2018) Hard and soft skills for

career preparation. Available from

https://www.canr.msu.edu/news/hard_a

nd_soft_skills_for_career_preparation.

[6]

PUTNAM, R.T., HEATON, R.M.,

PRAWAT, R.S. and REMILLARD, J.

(1992) Teaching mathematics for

understanding: Discussing case studies

of four fifth-grade teachers. Elementary

School Journal, 93,pp. 213–228.

[7]

HENDRIANA, H. (2017). Teachers’

hard and soft skills in innovative

teaching

of

mathematics.

World

Transactions on Engineering and

Technology

Education

(WIETE),

15(2), pp. 145-150.

[8]

NATHAN, M.J., and KOEDINGER,

K.R. (2000) An investigation of

teachers’ beliefs of students’ algebra

development.

Cognition

and

Instruction,18, pp. 209–237.

[9]

IULIANA,

M.

(2011).

How

Mathematics Teachers Develop Their

Pupils' Self-Regulated Learning Skills.

Acta Didactica Napocensia, 4(2-3), pp.

9-14.

[10] GANDHI, H., and VARMA,M. (2009)

Strategic Content Learning Approach

to Promote self-Regulated Learning in

Mathematics,

Proceedings

of

epiSTEME 3, pp. 119-124.

[11] National Research Council. (1991)

Mathematical Sciences, Technology,

and

Economic

Competitiveness.

Washington,

DC:

The

National

Academies

Press.

https://doi.org/10.17226/1786.

[12] RUHIYAT, A. (2017) Meningkatkan

Kemampuan

Komunikasi,

Berpikir

Kreatif dan Disposisi Matematik Siswa

SMP dengan Menggunakan Pendekatan

Kontekstual. Theses at School of

Postgraduate

Studies

of

STKIP

Siliwangi, Bandung.

[13] SUMARMO,

U.,

HIDAYAT,

W.,

ZULKARNAEN,

R.,

HAMIDAH,

SARININGSIH, R. (2012) Kemampuan

dan disposisi berpikir logis, kritis, dan

kreatif matematis: Eksperimen terhadap

Siswa SMA menggunakan Pembelajaran

Berbasis Masalah dan strategi

Think-Talk-Write. Makalah dimuat dalam

Jurnal Pengajaran MIPA, 17(1), pp.

17-33.

[14] SUHARYATI.

(2017)Meningkatkan

Kemampuan

Komunikasi

dan

Penalaran

Matematik

serta

Kemandirian

Belajar Siswa SMP

melalui Pendekatan Model Eliciting

Activities. Unpublished Thesis at Post

Graduate Study STKIP Siliwangi.

Bandung.

[15] SUMARNI,C. (2017) Meningkatkan

Kemampuan Pemahaman, Penalaran,

dan Kemandirian Belajar Siswa SMP

melalui Pembelajaran Generatif. Thesis

at Postgraduate Study of STKIP

Siliwangi.

[16] SUMARNI, C., and SUMARMO,U.

(2017)Penalaran

Matematik

dan

Kemandirian

Belajar:Eksperimen

terhadap

Siswa

SMP

melalui

Pembelajaran Generatif. Edusentris:

Jurnal

Ilmu

Pendidikan

dan

Pengajaran, 3(1), pp. 290-299.

[17] MCCONNELL, C. (2002) Community

Learning and Development the Making

of an Empowering Profession, Revised

Third Edition, Scotland.

[18] EVANS, L. (2002) What is Teacher

Development?

Available

from

http://leeds.academia.edu/LEvans/Pape

rs/120585/ on 1st April, 2012.

[19] FILIPATALI, T. (2013) Learning

Theories: Their Influence on Teaching

Methods, Seminar Paper. Available

from

https://www.grin.com/document/29349

8.

[20] KRISMAYANTI,

R.

(2017)

Meningkatkan

Kemampuan

Komunikasi

dan

Berpikir

Kreatif

Matematik serta Self Efficacy Siswa

SMP melalui Pembelajaran Berbasis

Masalah. Unpublished Thesis at Post

Graduate Study of STKIP Siliwangi.

Bandung.

[21] CARLI.

(2017)

Meningkatkan

Kemampuan Berpikir Reflektif dan

Berpikir

Kreatif

Serta

Resiliensi

Matematik

Siswa

SMA

dengan

Menggunakan Pendekatan

Problem-Posing. Unpublished Thesis at School

of Postgraduate Studies of STKIP

Siliwangi. Bandung.

[22] ERISKA, K. (2017) Meningkatkan

Kemampuan

Komunikasi

dan

Penalaran Serta Disposisi Matematik

Siswa

Madrasah

Alyah

dengan

Menggunakan Pendekatan

Induktif-Deduktif.

Unpublished

Thesis

at

Postgraduate

STKIP

Siliwangi.

Bandung.

[23] JOHANTO T. (2017) Meningkatkan

Kemampuan

Komunikasi

dan

Pemecahan Masalah Matematik serta

Kepercayaan

Diri

Siswa

SMA

melaluiPendekatan

Problem

Based

Learning.

Unpublished

Thesis

at

Postgraduate

STKIP

Siliwangi.

Bandung.

[24] KOSWARA, D. (2017) Meningkatkan

Kemampuan

Berpikir

Kritis

dan

Kreatif serta Resiliensi Matematik

Siswa

SMP

melalui

Pendekatan

Saintifik. Unpublished Thesis at School

of Postgraduate Studies of STKIP

Siliwangi. Bandung.

[25] MULYANI, E. (2017) Meningkatkan

Kemampuan Komunikasi dan berpikir

Kreatif

Matematik

serta

Self

Confidence

Siswa

SMK

melalui

Pembelajaran Saintifik. Unpublished

Thesis at Post Graduate Study of

STKIP Siliwangi. Bandung.

[26] PATTERSON, R. (2019) Hard Skills

Vs. Soft Skills: Why You Need Both to

Succeed.

Available

from

https://collegeinfogeek.com/hard-vs-soft-skills/.

[27] NCTM.

(2000).

Principles

and

Standards

for

School

Mathematics.United States: National

Council of Teachers of Mathematics.

[28] ROHANA. (2015). The enhancement

of student’s teacher mathematical

reasoning ability through reflective

learning. Journal of Education and

Practice, 6(20), pp 108-114. Available

from

https://eric.ed.gov/?id=EJ1079064.

[29] AMINAH, M., KUSUMAH, Y.S.,

SURYADI, D., and SUMARMO, U.

(2018) The Effect of Metacognitive

Teaching and Mathematical Prior

Knowledge on Mathematical Logical

Thinking Ability and Self-Regulated

Learning. International Journal of

Instruction,

11(3),

pp.

45-62.

https://doi.org/10.12973/iji.2018.1134a.

[30] AMINAH, M. (2016) Mengembangkan

Kemampuan

Berpikir

Logis,

Komunikasi dan Kemandirian Belajar

Matematis

Siswa

SMA

Melalui

PembelajaranMetakognitif.

Unpublished Dissertation at School of

Postgraduate Studies of Indonesia

University of Education. Part of the

dissertation

was

submitted

for

publication in the International Journal

of Instruction (in press).

[31] KURNIAWATI, L., KUSUMAH, S.Y.,

SUMARMO, U. and SABANDAR, J.

(2014)

Enhancing

Students’

mathematical

intuitive-reflective

thinking ability through problem based

learning with hypnoteaching method.

Journal of Education and Practice,

6(36), pp. 130-135. Available from

https://www.iiste.org/Journals/index.ph

p/JEP/article/view/17480.

[32] ISMAIMUZA, D. (2010). Kemampuan

Berpikir Kritis dan Kreatif Matematik

SiswaSMP

Melalui

Pembelajaran

Berbasis Masalah dengan Strategi

KonflikKognitif.

Unpublished

Dissertation at School of Postgraduate

Studies

of

Indonesia

University

Education: Bandung.

[33] MAYA, R. and SUMARMO, U.

(2011) Mathematical understanding

and Proving Abilities: Experiment with

Undergraduate

Student

by

Using

Modified Moore Learning Approach.

Journal on Mathematics Education,

2(2), pp. 231-250.

[34] QOHAR, A. and SUMARMO, U.

(2014)

Improving

mathematical

communication

ability

and

self-regulated learning of junior high

students by using reciprocal teaching.

Journal on Mathematics Education,

4(01), pp. 59-74.

[35] SINURATI, R. (2014)Meningkatkan

Kemampuan

Berpikir

Kritis

dan

Kreatif serta Disposisi Matematik

Siswa SMA melalui Pembelajaran

Kontekstual. Unpublished Thesis at

School of Postgraduate Studies of

STKIP Siliwangi. Bandung.

[36] HOWE,

R.E. (2018) Let’s teach

students why math matters in the real

world.

Available

from

http://theconversation.com/lets-teach-

students-why-math-matters-in-the-real-world-102316.

[37] MUIN, A. (2016). Meningkatkan

Kemampuan dan Disposisi Berpikir

Reflektif Matematis Mahasiswa dengan

Pendekatan Metakognitif. Unpublished

Dissertation at School of Postgraduate

Studies of Indonesia University of

Education. Bandung.

[38] PUJIASTUTI, H., KUSUMAH, Y. S.,

SUMARMO, U., and DAHLAN, J. A.

(2014) Inquiry co-operation model for

enhancing junior high school students'

mathematical problem solving ability.

International Journal of Contemporary

Educational Research, 1(1), pp. 51-60.

[39] WARDANI, S., SUMARMO, U., and

NISHITANI,I. (2011). Mathematical

creativity and disposition: Experiment

with grade-10 students using Silver

Inquiry Approach. Journal of Science

and Mathematics Teaching, 59, pp.

1-16.

[40] SETIAWATI,

E.

(2014)

Mengembangkan kemampuan berpikir

logis, kreatif, dan disposisi matematis,

melalui

Pembelajaran

Berbasis

Masalah. Unpublished Dissertation at

School of Postgraduate Studies of

Indonesia University of Education.

参考文:

[1] BISHARA，S.（2016）数学中独特问题解 决 的 创 造 力 及 其 对 学 习 动 机 的 影 响 。 Cogent Education，3：1202604，第 1-14 页。 http://dx.doi.org/10.1080/2331186X.2016.120 2604。 [2] MOSER，E.H.，KINNEY，L。和 PURDY， C。（1948），《数学教学的目的与目的》。 教育研究评论，第 18（4）页，自然科学 和数学（1948 年 10 月），第 315-322 页。 [3] 课程。 （2013）。国家教育部长令日期为 2013 年 6 月 27 日的 2013 年第 81a 条，涉 及内容标准课程的实施。。 [4] JAWORSKI ， B. ， MALI ， A. 和 PETROPOULOU，G.（2015）数学教学方 法及其与学生数学意义的建立。在 2015 年 7 月 13 日至 18 日在澳大利亚霍巴特举行的 第 39 届数学教育心理学会议（PME39）上 发表。 [5] Cox，F.（2018）职业准备的软硬技能。可 从

https://www.canr.msu.edu/news/hard_and

_soft_skills_for_career_preparation

[6] PUTNAM ， R.T. ， HEATON ， R.M. ， PRAWAT，R.S.和 REMILLARD，J.（1992） 理解数学的教学：讨论四位五年级老师的 案例研究。小学学报， 93, 第 213–228 页。

[7] HENDRIANA，H.（2017 年）。教师在数 学创新教学中的软硬技能。 《工程技术教 育世界交易》，15（2），第 145-150 页。 [8] NATHAN，M.J。和 KOEDINGER，K.R。 （2000 年）对教师对学生代数发展的信念 的调查。 《认知与指导》，18，第 209-237 页。 [9] IULIANA，M.（2011）。数学教师如何发 展学生的自我调节学习技能。拿破仑行动 学报，4（2-3），第 9-14 页。 [10] GANDHI，H.和 VARMA，M。 （2009） 战略内容学习方法，以促进数学中的自我 调节学习，epiSTEME 3 的论文集，第 119-124 页。 [11] 国家研究委员会。 （1991）数学科学， 技术和经济竞争力。华盛顿特区：国家科 学院出版社。 https://doi.org/10.17226/1786。 [12] RUHIYAT，A.（2017）通过情境方法提 高中学生的沟通技巧，创造性思维和数学 素养。万隆 STKIP Siliwangi 研究生院论文。 [13] SUMARMO ， U. ， HIDAYAT ， W. ， ZULKARNAEN ， R. ， HAMIDAH ， SARININGSIH，R.（2012）逻辑，批判和 数学创造性思维的能力和处置：使用基于 问题的学习和思维策略的高中生实验-讲话 写。论文发表在《教学与数学杂志》，第 17 期（1），第 17-33 页。 [14] SUHARYATI。 （2017）通过选拔活动模 型方法提高初中学生的沟通和数学推理能 力以及学习独立性。 STKIP Siliwangi 研究 生研究中未发表的论文。万隆 [15] SUMARNI，C。 （2017）通过创生学习 提高初中生的理解，推理和学习独立能力。 STKIP Siliwangi 研究生研究论文。 [16] SUMARNI ， C 。 和 SUMARMO ， U 。 （2017）数学推理和学习独立性：通过生 成学习对中学生进行的实验。以教育为中 心：《教育与教学 杂志》，3（1），第 290-299 页。 [17] MCCONNELL，C。（2002）社区学习和 发展，以建立赋权的职业，第三版，苏格 兰修订版。 [18] EVANS，L。（2002）什么是教师发展？ 可 在 2012 年 4 月 1 日 从

http://leeds.academia.edu/LEvans/Papers/

120585/ on 1st April, 2012

。 [19] FILIPATALI，T。（2013）学习理论：它 们对教学方法的影响，研讨会论文。可从

https://www.grin.com/document/293498

。 [20] KRISMAYANTI，R.（2017）通过基于问 题的学习提高中学生的沟通技巧和数学创 新思维以及自我效能。 STKIP Siliwangi 研 究生研究中未发表的论文。万隆 [21] CARLI。 （2017）通过使用问题定位法 提高高中学生的反思性思维能力和创造性 思维以及数学适应能力。 STKIP Siliwangi 研究生院未发表的论文。万隆 [22] ERISKA，K.（2017）通过归纳演绎法提 高伊斯兰学校伊斯兰学生的沟通和推理能 力以及数学处理能力。 STKIP Siliwangi 研 究生未发表的论文。万隆 [23] JOHANTO T.（2017）通过基于问题的学 习方法提高沟通技巧和数学问题解决能力 以及高中生的自信心。 STKIP Siliwangi 研 究生未发表的论文。万隆 [24] KOSWARA，D.（2017）通过科学方法提 高中学生的批判性和创造性思维能力和数 学弹性。 STKIP Siliwangi 研究生院未发表 的论文。万隆 [25] MULYANI，E。（2017）通过科学学习 提高职业学生的沟通技巧和数学创新思维 及自信心。 STKIP Siliwangi 研究生研究中 未发表的论文。万隆 [26] PATTERSON，R.（2019）Hard Skills Vs. 软 技能： 为什么需 要两者 都成功 。可 从

https://collegeinfogeek.com/hard-vs-soft-skills/

。 [27] NCTM。 （2000）。学校数学原理和标 准，美国：国家数学教师委员会。 [28]精神。 （2015）。通过反思性学习提高学 生老师的数学推理能力。教育与实践杂志， 6 （ 20 ） ， 第 108-114 页 。 可 从 https://eric.ed.gov/?id=EJ1079064 获得。 [29] AMINAH ， M. ， KUSUMAH ， Y.S. ，

SURYADI，D.和 SUMARMO，U.（2018） 元认知教学和数学先验知识对数学逻辑思 维能力和自我调节学习的影响。国际教学 杂 志 ， 11 （ 3 ） ， 第 45-62 页 。 https://doi.org/10.12973/iji.2018.1134a。 [30] AMINAH，M.（2016）通过认知学习发 展逻辑思维能力，交流和独立性的数学学 习高中学生。印度尼西亚教育大学研究生 院未发表的论文。论文的一部分已提交发 表在国际教学杂志上（印刷中）。 [31] KURNIAWATI，L.，KUSUMAH，S.Y.， SUMARMO ， U 。 和 SABANDAR ， J 。 （ 2014 年 ） 通 过 基 于 问 题 的 学 习 和 hypnoteaching

方法来增强学生的数学直观-反 思性思维 能力。 教育与 实践杂志 ， 6 （ 36 ） ， 第 130-135 页 。 可 从 https://www.iiste.org/Journals/index.php/JEP/ article/view/17480 获得。 [32] ISMAIMUZA，D。（2010 年）。通过基 于问题的学习和认知冲突策略，批判性思 维能力和 SMP 的数学创新学生。印度尼西 亚大学研究生院未发表的学位论文教育： 万隆。 [33] MAYA，R.和 SUMARMO，U.（2011） 数学理解和证明能力：使用改良的摩尔学 习方法对大学生进行实验。数学教育杂志， 2（2），第 231-250 页。 [34] QOHAR，A.和 SUMARMO，U.（2014） 通过运用对等教学，提高初中学生的数学 交流能力和自我调节学习能力。数学教育 学报， 4（01）,第 59-74 页。 [35] SINURATI，R.（2014）通过情境学习增 强高中学生的批判性和创造性思维能力和 数学素养。 STKIP Siliwangi 研究生院未发 表的论文。万隆 [36] HOWE，R.E。 （2018 年）让我们教学生 数 学在现 实世界中 为何如 此重要 。可 从 http://theconversation.com/lets-teach- students-why-math-matters-in-the-real-world-102316 获取。 [37] MUIN，A。（2016）。 通过元认知方法 提高学生的数学反思性思维能力和性格。 印 度尼西亚教育大学研究生院未发表的论文。 万隆 [38] PUJIASTUTI，H.，KUSUMAH，Y. S.， SUMARMO，U.和 DAHLAN，J. A.（2014） 咨询合作模型，旨在增强初中学生的数学问 题 解 决 能 力 。 国 际 当 代 教 育 研 究 杂 志 ， 1 （1），第 51-60 页。 [39] WARDANI S. ， SUMARMO U. 和 NISHITANII。 （2011）。 数学创造力和性 格：使用 Silver Inquiry 方法对 10 年级的学生 进行实验。 科学与数学教学杂志，59, 第 1-16 页。 [40] SETIAWATI，E.（2014）通过基于问题 的学习发展逻辑，创造性和数学倾向的思考 能力。 印度尼西亚教育大学研究生院未发表 的论文。

第 54 卷第 5 期

2019 年 10 月

JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY

Vol. 54 No.5 Oct. 2019

A

PPENDIX

1

Tables

Table 1. Mathematical Skill Development through Innovative Teaching: Realistic Mathematics and Contextual Teaching

Student Name Teaching Approach Subject Mathematics skills Stat. Desc

Innovative Teaching Approach Conventional Teaching n Pre-test Post-test N (Gain) n Pre-test Post-test N (Gain) Endang Rahmat Realistic Mathemati cs n = 76 9th- Grade Students (Junior High School) Mathematical Connection X 38 _{14.11 34.13 0.54} 38 _{12.55 31.26 0.48} % _{27.13 65.64} 24.14 60.12 SD _{7.95 11.65 .12 7.80 12.30 .12} Mathematical Understanding X _{13.24 33.61 .57 13.11 30.08 .46} % 26.47 67.21 26.21 60.16 SD _{10.12 12.76 .12 8.58 11.22 .13} Mathematical Disposition X 91.16 86.74 % _{75.96 72.28} SD _{7.61 7.16} Adang Ruhiyat Contextual Teaching n = 92 9th- Grade Students (Junior High School) Mathematical Communicati on X 46 5.07 42.20 .58 46 4.41 17.70 .21 % 7.45 62.05 6.49 26.02 SD 3.71 4.93 .07 3.09 3.97 .05 Mathematical Creative Thinking X 2.67 41.03 _.55 2.63 18.30 .23 % 3.92 60.33 3.87 26.02 SD 1.78 7.81 .12 1.94 4.13 .05 Mathematical Disposition X 87.87 74.70 % 73.22 62.25 SD 7.85 5.86 Perception of Contextual T.

Students enjoyed contextual teaching, they were able to overcome their difficulty in solving

problems and learning concepts

Table 2. Findings on Mathematical Skills’ Development through Innovative Teaching: Generative Approach and Method Eliciting Activities

Thesis student

Teaching Approach

Subject Math skills Stat. Desc

Innovative Teaching Approach Conventional Teaching N Pre-test Post-test N (Gain) n Pre-test Post-test N (Gain) Cicih Sumarni Generative Approach n = 56 8th -Grade Students (Junior High School) Mathematical Understanding X 2 8 8.18 27.7 0.62 28 7.21 22.1 0.45 % 21.3 70.7 18.6 57.2 SD 3.09 4.21 0.12 1.91 4.76 0.14 Mathematical Reasoning X 6.71 18.1 0.49 6.11 14.4 0.35 % 23.8 62.9 17.5 51.6 SD 2.80 359 0.15 2.35 4.22 0.16 Mathematical Self-Regulated Learning X 83.9 78.1 % 69.9 65.1 SD 8.20 5.45 Perception on Generative Appr.

Students expressed positive opinions on the generative approach; the learning environment

was enjoyable, students discussed inventing learned concept by themselves and solving

exercise tasks. Suharyati Method Eliciting Activities (MEAs) n = 72 8th-Grade Students (Junior High School) Mathematical Communication X 3 6 8.56 27.92 .66 36 8.53 22.19 .29 % 2.67 73.46 2.38 3.51 SD 22.51 3.77 .11 22.44 58.41 .03 Mathematical Reasoning Ability X 6.53 23.33 .72 7.19 12.94 .25 % 21. 76 77.78 23.98 43.15 SD 2.78 2.66 .10 2.41 3.31 .12 Mathematical Self-Regulated Learning X 106 98.39 % 63.10 58.56 SD 8.14 8.20 Perception on MEAs Appr.

Student expressed positive opinions of the MEAs learning process, which challenged them to participate in solving real problems; students were unafraid to pose questions and tries to comprehend learning material before the lesson

Table 3. Findings on Mathematical Skills’ Development through Innovative Teaching: Scientific Approach and Problem Posing Approach Thesis student Teaching Approach

Subject Math skills Stat. Desc

Innovative Teaching Approach Conventional Teaching N Pre-test Post-test N (Gain) n Pre-test Post-test N (Gain) Dadang Koswara Scientific Approach n = 66 7th_- Grade Students (Junior High School) Mathematical Critical Thinking X 32 2.47 21.03 _.59 34 2.44 13.74 .37 % 7.26 61.85 7.18 40.41 SD 2.17 7.83 .24 1.67 8.87 .27 Mathematical Creative Thinking X .41 32.63 .77 .38 13.76 .32 % 7.26 62.75 7.18 26.46 SD .76 15.62 .37 .70 12.45 .30 Mathematical Resiliency X 132 133 % 66 66.50 SD 10.00 9.79 Perception on Scientific App

Student expressed high perception under the scientific teaching approach; they performed more active learning in all four phases of the scientific approach

Carli Problem Posing Approach n = 66 11th- Grade Students (Senior High School) Mathematical Reflective Thinking X 33 11.37 33.51 .46 33 10.66 24.51 .28 % 19.61 57.78 18.37 42.27 SD 2.02 7.93 .16 _{3.61 9.03 .17} Mathematical Creative thinking X 12.77 37.06 0.52 13.40 27.31 0.30 % 21.29 61.76 22.33 45.52 SD 3.87 8.69 0.17 3.59 7.74 0.14 Mathematical Resiliency X 86.74 85.91 % 64.73 64.12 SD 9.58 7.69 Perception on Problem Posing Approach

Students tend to be comfortable with the problem posing approach, they actively learn; problems are difficult but challenge students to think

Table 4. Findings on Mathematical Skills’ Development through Innovative Teaching: Inductive-Deductive Approach and Scientific Approach

Thesis student

Teaching Approach

Subject Math skills Stat. Desc

Innovative Teaching Approach Conventional Teaching N Pre-test Post-test N (Gain) n Pre-test Post-test N (Gain) Kiki Eriska Inductive-

Deductive Approach n = 71 11th-Grade Students (Senior MA) Mathematical Communication X 35 _{12.07 32.03} .73 36 _{11.90 27.26} .42 % _{4.02 80.07 4.58 68.16} SD _{30.18 5.20} .15 _{29.76 5.37} .22 Mathematical Reasoning X 17.59 43.66 .64 16.43 36.78 .47 % 29.32 72.76 27.39 61.30 SD 6.37 8.38 .16 4.78 8.69 .18 Mathematical Disposition X 90.40 5.20 81.36 % 67.97 61.17 SD 9.41 9.28 Perception on Induct-Deduct Approach

Students expressed positive opinions of the inductive-deductive approach: the learning process challenged students to solve mathematical problems, and students were unafraid to pose question and explain in front of the class Elis Mulyani Scientific Approach n = 56 11th Grade Students (Vocatio nal High School) Mathematical Communication X 28 6.18 27.68 .54 28 6.11 23.00 .42 % 13.4 3 60.17 13.28 50.00 SD 2.52 6.50 .16 2.25 4.06 .10 Mathematical Critical Thinking X 4.25 35.61 .53 4.39 29.21 .42 % 6.64 55.64 6.86 45.65 SD 2.12 7.41 .12 2.31 6.09 .10 Mathematical Self Confidence X 88.43 78.93 % 78.95 70.47 SD 11.72 8.28 Perception on Scientific Appr

Positive opinions; they performed more active learning in all four phases of the scientific approach.

Thesis student

Teaching Approach

Subject Math skills Stat. Desc

Innovative Teaching Approach Conventional Teaching n Pre-test

Post-test

N (Gain) n Pre-test Post-test N (Gain) Tri Johanto Problem Based learning (PBL) n = 66 11th- Grade Student (Senior High School) Mathematical Communication X 33 12.24 29.91 0.64 33 11.94 26.15 .51 % 30.61 74.77 29.85 65.38 SD 0.16 5.73 0.16 4.96 5.95 .13 Mathematical Problem Solving X 14.48 35.52 .59 14.21 31.03 .47 % 28.97 71.03 28.42 62.05 SD 15 6.59 .15 4.48 4.95 .06 Mathematical Self Confidence X 102.40 95.30 % 76.42 71.12 SD 12.35 12.57 Perception on PBL

Positive opinion of PBL; they performed more active learning in all four phases of PBL. Rika Krismay anti Problem Based Learning (PBL) n = 51 8th Grade Students (Junior High School) Mathematical Creative Thinking X 26 _{12.08 25.65 12.08} 25 _{11.00 19.68 .18} % _{20.47 43.47 20.47 18.64 33.36} SD _{2.08 4.18 2.08 1.83 4.36 .09} Mathematical Problem Solving X _{13.15 31.77 .26 12.00 21.72 .18} % _{19.92 48.13 18.18 32.90} SD _{2.58 7.24 .13 3.25 8.02 .13} Mathematical Self Efficacy X _{74.62 75.96} % 61.16 62.26 SD 10.97 7.76 Perception on PBL

Positive opinion of PBL (72.56% of ideal score); they performed more active learning in all four phases of PBL; problems on student worksheet were challenging, related to daily life problems, and could be applied in other disciplines; learning material help students to learn quicker.

Table 6. Association between Variables and Student’s Difficulties in Solving Mathematical Problems

Thesis student

Teaching Approach

Subject Mathskills Assc among variables Interpre tation Students’ Difficulties Variables (2_), sig, 2 tailed Q % out of Id score Innv. Appr % out of Id score Conventional Endang Rahmat Realistic Mathematics n = 76 9th- Grade Students (Junior High School) Math Connect (MC) (MC, MU) 34.154a .000 .843 High assoc 65.64% (med.) Few difficulties 60.12% (med.) Fair difficulties Math Underst (MU) (MU,MD) 29.847a

.000 .813 High Assoc 67.64% (med.) Few difficulties 60.18% (med.) Fair difficulties Math Dispost (MD) (MC,MD) 27.236a

.000 .791 High Assoc Adang Ruhiyat Contextual Teaching n = 92 9th- Grade Students (Junior High School) Math Commc (MCm) (MCm,MCv) .011 .49 Medium Asscoc 62.05% (med) Few difficulties 26.02% (very low) Almost all items were very difficult Math Creatv (MCv) (MCm,MD) .000 .45 Medium

Assoc

60.33% (med) Few difficulties

26.02% (very low) Almost all items were very difficult Math Dispost (MD) (MCv, MD) .011 .49 Medium

Asscoc Cicih Sumarni Generative Approach n = 56 8th_-Grade Students (Junior High School) Math.Reasoning (MRs) (MRs,MUn) 9.927a .042 .63 Medium Assoc 62.90% (med) Few difficulties 51.60% (low) Many difficulties Math.Underst (MUn) (MRs,MSRL) 1,269a _.867 - No Assoc 70.74% (fair) No difficulty 57.23% (low) Few difficulties Math.Self Reg Learning (SRL) (MUn,MSRL) 8,196a .085 - No Assoc Suharyati Method Eliciting Activities (MEAs) n = 72 8th-Grade Students (Junior High School) Math. Comm (MCm) (MCm,MRs) 31,000a .000 .833 High Assoc 73.46% (fair) No difficulty 58.41% (low) Few difficulties Math.Reason (MRs) (MCm,MSRL) 32.000a .000 . . 840 High Assoc 77.78% (fair) No difficulty 43.15% (low) Many difficulties Math.Self Reg Learning (SRL) (MRs,MSRL) 36.000a _{.000 .707 High} Assoc

Table 7. Association between Variables and Students’ Difficulties in Solving Mathematical Problems

Thesis student

Teaching Approach

Subject Math skills Assc among variables Interpr etation Students’ Difficulties Variables (2), sig, 2 tailed Q % out of Id sc Innv. Appr % out of Id sc Conventional Dadang Koswara Scientific Approach n = 66 7th_- Grade Students (Junior High School) Math Critic Think (MCc) (MCc, MCv) 34,154a .000 .843 High assoc 65.64% (med.) Few difficulties 40.41 % (med.) Fair difficulties Math Creatv (MCv) (MCc,MR) 5.738a .220 . - No assoc 67.64% (med.) Few difficulties 26.46% (med.) Fair difficulties Math Resiliency (MR) (MCv,MR) 5.738a .220 - No assoc 40.41 26.46 Carli Problem Posing Approach n = 66 11th_- Grade Students (Senior High School) Math.Reflc Th (MRT) (MRl,MCv) 22,469a .000 .755 High assoc 57.78 % (med) Fairly difficult 42.27 % (low) Many difficulties Math Creatv (MCv) (MRl, MRc) _8,220a .084 - No Assoc 61.76% (med) Few difficulties 45.52 % (low) Many difficulties Math Resiliency (MRl) (MCv, MRc) 7,370a .118 - No Assoc Kiki Eriska Inductive- Deductive Approach n = 71 11th-Grade Students (Senior MA) Math. Comm (MCm) (MCm,MRs) 21,159 a .002 .752 High Assoc 80.07 % (good) No difficulty 68.16% (fair) No difficulty Math.Reason (MRs) (MCm,MD) 21,710 a _{.000 .759 High} Assoc 72.76 % (fair) No difficulty 61,30%(med) Few difficulties Math. Disp (MD) (MRs,MD) 13,982a .095 .654 Medium Assoc Elis Mulyani Scientific Approach n = 56 11th Grade Students (Vocational High School) Math. Comm (MCm) (MCm,MCT) 15.740 a .003 .735 High Assoc 60.17 % (fair) Few difficulties 50.00% (low) Many difficulties Math.Critic Th (MCT) (MCm,MSC) 16.369a .002 .743 High Assoc 55.64% (fair) Few difficulties 45.65% (very low) Much more difficulties Math. Self Conf

(MSC)

(MCT,MSC) 36.000a _{.000 .758. High}

Assoc

Table 8. Association between Variables and Students’ Difficulties in Solving Mathematical Problems

Thesis student

Teaching Approach

Subject Math skills Assc among variables Interpre tation Students’ Difficulties Variables (2_), sig, 2 tailed Q % out of Id sc Innv. Appr % out of Id sc Conventional Tri Johanto Problem

Based learning (PBL) n = 66 11th- Grade Student (Senior High School ) Math. Comm (MCm) (MCm, MPS) 41,186a .000 .913 High assoc 74.77% (fair) No difficulty 65.38% (med.) Few difficulties Math.Prob.S olv. (MPS) (MCM,MSC) 38,354a .000 .893 High assoc 71.03% (fair) No difficulty 62.05% (med.) Few difficulties Math. Self Conf (MSC) (MPS,MSC) 27,500a .000 .826 High assoc Rika Krismayanti Problem Based Learning (PBL) n = 51 8th Grade Students (Junior High School) Math Creat Th (MCv) (MCv,MPS) 26,000 .000 .866 High assoc 43.47% (low) Fairly difficulties 33.36 % (very low) Very much difficulties Math.Prob.S olv. (MPS) (MCv, MSE) 8,001a .092 - No Assoc 48.13% (low) Many difficulties 32.90 % (very low) Many difficulties Math. Self Effc (MSE) (MPS, MSE) 4.368a .113 - No Assoc