TABLE OF CONTENT

TITLE PAGE ...... i STEERING COMMITTEE ...... iii PREFACE ...... v TABLE OF CONTENT ...... vii

THE EFFECTIVENESS OF THE ROLE OF STATE SENIOR HIGH SCHOOL COMMITTEE IN JOMBANG Kustomo, Pahriyono ...... 1

THE EXISTENCE AND CHALLENGE OF MADRASAH (Identification Problem and Typology of Madrasah Aliyah in Kudus) Supa'at...... 13

IMPROVING STUDENTS’ WRITING COMPETENCE THROUGH GUIDED IMAGERY Rustiani Widiasih ...... 23

E-COMMERCE AS ACCOMODATE AND TOOL NAROTAMA UNIVERSITY STUDENTS BECOME ENTREPRENEUR Sri Wiwoho Mudjanarko, Arasy Alimudin, Eman Setiawan, Gede Arimbawa, Bustomi .... 30

A STEP AHEAD EDUCATION (Human Potential Development Oriented) Azis ...... 36

INTEGRATION OF SCHOOL AND FAMILY AS MAIN CHARACTER EDUCATION IN EARLY CHILDHOOD Isfauzi Hadi Nugroho ...... 45

CONTENT VALIDITY OF CHARACTER EDUCATION IN KINDERGARTEN Umi Faizah, Badrun Kartowagiran, Darmiyati Zuchdi ...... 52

THE IMPLEMENTATION MODEL OF CHARACTER BUILDING BASED ON HONESTY CANTEEN IN A BASIC EDUCATION INSTITUTIONS (A Review of Behaviouristics theory, on Islamic and West Perspective) Sri Susanti ...... 59 LECTURERS’ STRATEGIES IN GIVING FEEDBACK TOWARDS STUDENTS’ THESIS WRITING: A CASE STUDY IN STATE ISLAMIC COLLEGE OF PONOROGO Restu Mufanti ...... 67

INTEGRATING LOCAL CULTURE TO TEACH ENGLISH FOR EFL STUDENTS Nuri Ati Ningsih, Lulus Irawati, Dahlia Novarianing Asri ...... 74

VERBAL ABUSE IN ADOLESCENT (Speech Act Study on Dating Chat) Rosita Ambarwati, Dwi Rositasari ...... 79

THE EFFECT OF BLENDED LEARNING IN TEACHING LISTENING Rengganis Siwi Amumpuni ...... 86

DIDACTIC CONTRACTS IN REALISTIC MATHEMATICS EDUCATION TEACHING PRACTICE IN INDONESIA: A LESSON ON ADDITION Zetra Hainul Putra ...... 93

SCHOOL MANAGEMENT WITH SECSI PROGRAM TO IMPROVE THE QUALITY OF SCHOOL CULTURE Mulyani ...... 101

THE EDUCATION OF "SUFFERING" TO STUDENTS (The Study on Excellent Program in Madrasah Aliyah Plus “Nururrohmah” Pondok Pesantren Al - Kamal Tambaksari Kuwarasan Kebumen, ) Azam Syukur Rahmatullah ...... 107

ISLAM AND MULTICULTURAL EDUCATION Moh. Toriqul Chaer ...... 113

CONVERSATION ANALYSIS IN AN INTERPERSONAL COMMUNICATION (Case Study of Conversation Analysis Between Trainer And Trainee In BBPPKS Yogyakarta) Anis Rahmawati ...... 121

LEARNING GRAMMAR FROM SHAKESPEARE Basilius Himawan Setyo Wibowo ...... 128

NEW MEDIA AS A POLITICAL EDUCATION IN ESTABLISHING QUALIFIED DEMOCRACY Darwadi...... 132

THE CORRELATIONS BETWEEN PARENTS KNOWLEDGE AND THE STIMULATION DEVELOPMENT OF A HARD MOTORIC CHILDREN 1-5 YEARS OLD AT “MELATI” POSYANDU IN MBAOSAN LOR VILLAGE OF NGRAYUN SUB-DISTRICT PONOROGO Ani Rosita ...... 140

PRIVACY MANAGEMENT IN NEW MEDIA (A Case Study of Civil Servant Facebook Users in Sukoharjo) Danang Wisnu Anggoro ...... 148

HOW TO USE 3H (HERE, HIDDEN, IN MY HEAD) IN TEACHING READING OF NARRATIVE TEXT Brigitta Septarini Rahmasari ...... 155

STUDIES OF SOCIAL EDUCATION THEORY THROUGH YOGA LEARNING (TOURIST LEARNING PHENOMENON IN BALI) I Wayan Suyanta, Muhadjir Effendy, S. Mundzir , Hardika ...... 159

THE EFFECT OF WEBQUEST ON EFL READING ABILITY Nanang Fitrianto, Mohammad Adnan Latief, Nur Mukminatien, Sri Rachmajanti ...... 169

THE RELATIONSHIP BETWEEN INDEPENDENCE LEARNING AND PARENTS’ ATTENTION WITH THE LEARNING ACHIEVEMENT OF KDPK SUBJECTS IN SEMESTER II STUDENTS IN THE HARAPAN MULYA ACADEMY OF MIDWIFERY PONOROGO. Dwi Nurjayanti ...... 178

ACHIEVING A CULTURE AND AFFECTIONATE IN ISLAMIC BOARDING SCHOOL (PESANTREN) Wiworo Retnadi Rias Hayu, Din Azwar Uswatun ...... 185

HUMAN RESOURCE MANAGEMENT BASED KNOWLEDGE: TOWARDS EDUCATION PROFESSIONAL ORGANIZATION I Gede Sedana Suci, H. Ahmad Sonhadji, K.H, Ali Imron, Imron Arifin ...... 190

DEVELOPING AUDIO VISUAL CD MATERIAL FOR BASIC TEACHING SKILL IN TEACHING MATHEMATICS Novi Andri Nurcahyono, Eka Novarina ...... 195

THE FORMULATION OF NATIONAL EDUCATION IN A VIEW OF PHILOSOPHY PANCASILA IN ASEAN ECONOMIC COMMUNITY (MEA) GLOBAL ERA Rohmat Widiyanto ...... 202

BREAK THE BOREDOM IN READING CLASS: INTEGRATING ONLINE GAME WITH ESA TEACHING METHOD (ENGAGE, STUDY, AND ACTIVATE) Dodi Erwin Prasetyo, Shohibul Muttaqien Al Mandury, Wildan Isna Ashar ...... 208

PGSD STUDENTS’ CRITICAL THINKING SKILS DEVELOPMENT THROUGH MEDIA LITERACY IN THE GLOBALIZATION ERA Iis Nurasiah ...... 214

USING HOT POTATOES PROGRAM FOR READING TEST INSTRUMENT IN ENGLISH TEACHING LEARNING PROCESS Syamsudin ...... 220

PLAYING SONGS MATERIAL FOR ELEMENTARY SCHOOL STUDENTS IN PONOROGO REGENCY Hartini1, Endang Sri Maruti ...... 229

3K: EASY KEYS TO DEVELOP AN AUTONOMOUS LEARNER Siti Zulaihah, Ratri Harida, Heru Setiawan ...... 239

DISCOVERING THE CONCEPT OF RELIGIOUS MORAL VALUES FOR YOUNG LEARNERS Badruli Martati, Wahyuni Suryaningtyas, Misrin Hariyadi ...... 246

THE EFFECT OF PAIR WORK AS PREWRITING ACTIVITY TOWARDS THE STUDENTS’ WRITING QUALITY Vita Vendityaningtyas1, Erlik Widiyani Styati ...... 250

ANTI-TERRORISM EDUCATION POLICIES (THEORETICAL UNDERSTANDING OF INDONESIA’S PERSPECTIVE AS A RELIGIOUS LEGAL STATE) M.Arham AB ...... 256

RELIGION-BASED INTEGRAL EDUCATION (Effort In Solving Misunderstanding In Law-Governed Country) Yogi Prasetyo, Nurul Iman ...... 261

USING JIGSAW TECHNIQUE TO IMPROVE THE WRITING ABILITY OF THE SECOND YEAR STUDENTS OF MTs AL-ISLAM NGANJUK Muhammad Lukman Syafii ...... 268

THE ESSENCE OF MULTILITERACY LEARNING AS A TREND OF THE 21st CENTURY Mohammad Iskak ...... 276

THE DEVELOPMENT OF BUSINESS AND PROFESSIONAL EDUCATION ETHICS THROUGH TRI HITA KARANA BASED LOCAL WISDOM IN BALINESE SOCIAL ORDER Sunitha Devi, Ni Kadek Yuliandari, Christy K Sanjaya, Ni Made Rianita , I Gusti Made Arya Wijaya ...... 283

THE ADOLESCENTS’ DISCLOSURE PROCESS COMMUNICATE THEIR PERSONAL PROBLEMS WITH PARENTS AT SMAN 3 SURAKARTA Muhammad Aulia Waliulu ...... 293

THE DEVELOPMENT OF COMIC LEARNING MEDIA AS INNOVATION IN IMPROVING LANGUAGE SKILL FOR EARLY CHILDHOOD EDUCATION Ida Yeni Rahmawati ...... 300

STRATEGIES FOR IMPROVING MUSICAL ABILITY OF TEACHERS FOR VERY YOUNG LEARNER IN YOGYAKARTA: A CASE STUDY AT SEKOLAH CIPTA LAGU ANAK (S.C.L.A) STPI BINA INSAN MULIA YOGYAKARTA Setyoadi Purwanto, Umi Faizah ...... 306

THE INFLUENCE OF COMMUNICATION COMPETENCE AND COMMUNICATOR CREDIBILITY OF SUPREME AUDIT BOARD TOWARD THE EFFECTIVITY OF AUDIT (STUDY AT DEPARTMENT OF EDUCATION, YOUTH AND SPORT DENPASAR) Nugroho Agus Rianto ...... 312

THE INFLUENCE OF RELIGIOSITY TOWARDS DECISION MAKING TO SELECT COURSE STUDY IN THE ISLAMIC-BASED UNIVERSITY (STUDY IN THE FACULTY OF SHARIAH AND LAW OF SUNAN KALIJAGA ISLAMIC STATE UNIVERSITY, YOGYAKARTA) Yusuf Safingi ...... 325

EDUCATION COMMUNICATION OF FAMILY PLANNING CADRE Laili Hikmawati Azizah, Prahastiwi Utari, Mahendra Wijaya ...... 336

AN ANALYSIS OF A RELATION BETWEEN PERSONAL FACTORS AND BALANCE NUTRITION PERCEPTIONS AMONG FAMILIES LIVING IN DOWN SYNDROME ENDEMIC AREA (A Study of The Role of Nurse As A Health EducatoR) Sugeng Mashudi ...... 348

ANALYSIS OF SUSCEPTIBLE MENTAL DISORDER WOMEN (Study of Anxiety Reviewed from Education Level) Eky Okviana Armyati ...... 351 THE POLICY OF TEACHER’S CONDEMNATION BASED ON CHILD PROTECTION LAW Arief Budiono ...... 356

CHILDREN'S RIGHT TO EDUCATION BASED ON CHILD PROTECTION LAW IN INDONESIA Wafda Vivid Izziyana...... 361

SEX EDUCATION IN EARLY CHILDHOOD BY HYPNOTHERAPY METHOD Betty Yulia Wulansari ...... 366

STRATEGY IMPLEMENTATION OF SCHOOL LITERACY MOVEMENT Moh. Safii ...... 372

IMPLICATIONS OF DIDACTIC PHENOMENOLOGY AND PROGRESSIVE MATHEMATICIAN IN MATHEMATICS LEARNING Warsito, Sukirwan ...... 379

EMOTIONAL INTELLIGENCE AND SPIRITUAL EDUCATIONAL PSYCHOLOGY IN ISLAMIC PERSPECTIVE Muh Tajab ...... 389

THE EFFECT OF HUMAN RESOURCES COMPETENCE AND ORGANIZATION OF LEARNING TO PERFORMANCE AND ITS IMPACT ON COMPETITIVENESS (Studies in the School of Economic in the Environment of Kopertis VII Area, East Java) Fariz ...... 395

MANAGEMENT ACTIVITIES OF STUDENTS LEARNING PACKAGE B KBM IN GORONTALO Abdul Rahmat, Aisa Hasan ...... 404

ENVIRONMENTALISM-BASED E-LEARNING FOR CHILDREN Eliyyil Akbar ...... 409

THE EFFECTIVENESS OF A PLAY MODEL FOR DEVELOPING READING, WRITING, AND NUMERACY IN EARLY CHILDHOOD Sugiono, Kuntjojo ...... 416

DEVELOPING AND LEARNING HOW TO OPTIMIZE EARLY CHILDHOOD ACTIVITY THROUGH PLAYING Rosa Imani Khan ...... 422

VILLAGE LIBRARY AS A MEANS OF NON-FORMAL EDUCATION BASED ON THE LOCAL WISDOM Johan Bhimo Sukoco ...... 427

STUDENT PARTICIPATION IN RELATION WITH PAKEM AND LEARNING AUTONOMY, COMPLETENESS OF SOCIAL SCIENCE LEARNING Muhamad Chamdani ...... 434

OPTIMIZATION OF COOPERATIVE LEARNING FOR DEVELOPMENT OF CHARACTER IN EARLY CHILDHOOD Anwardiani Iftaqul Janah ...... 443

CHARACTER EDUCATION IN THE REYOG ART OF PONOROGO AND A TEACHING STRATEGY OF ETHNOLINGUISTIC Alip Sugianto ...... 447

THE USE OF SOCIAL MEDIA AS A TOOL OF EDUCATING PEOPLE Roso Prajoko ...... 453 TEACHING MATERIALS DEVELOPMENT BASED ON PROJECT OF MATHEMATICS INSTRUCTIONAL MEDIA Eka Novarina, Novi Andri Nurcahyono ...... 458

THE USE OF COMIC MEDIA TO IDENTIFY THE INTRINSIC ELEMENTS OF DRAMA TEXTS FOR EIGHTH GRADERS STUDENTS OF SMPN 1 MANTINGAN Asri Musandi Waraulia ...... 467

COMMUNICATION PROCESS IN EDUCATION Media Gustriani ...... 473

THE SPIRITUAL EDUCATION TOWARD INSAN KAMIL IN THE EDUCATION OF MODERN HUMANKIND Wahyudi Setiawan ...... 479

THE ROLE PROFESSIONALISM ROLE OF AL ISLAM AND LECTURER IN FORMING ISLAMIC CHARACTER Dyah Lyesmaya, Leonita Siwiyanti ...... 485

EFFECTIVE LEADERSHIP IN BUILDING THE STUDENTS’ CHARACTER Rokhmaniyah ...... 490

INCLUSIVE EDUCATION CURRICULUM FOR EXCEPTIONAL CHILDREN IN THE ELEMENTARY SCHOOL Astri Sutisnawati ...... 496

THE EFFECT OF PARENTS’ ATTENTION ON STUDENTS’ WILLINGNESS TO LEARN AT MADRASAH IBTIDAIYAH MUHAMMADIYAH PK SUBDISTRICT KARTOSURO SUKOHARJO IN 2016 Eti Kurniasih...... 502

THE DEVELOPMENT OF HUMAN POTENTIAL THROUGH EDUCATION ACCORDING TO IBNU SINA Katni ...... 508

SOURCES OF LECTURER ASSISTANTS’ TEACHING ANXIETY IN TEACHING INSTRUCTIONAL TECHNOLOGY COURSE: A QUALITATIVE INTERVIEW STUDY Nenden Octavarulia Shanty ...... 513

COMMUNICATION ETHICS IN AN ORGANIZATION (A Case Study: Communication Ethics in Improving Public Services at Education Official of Sukoharjo) Heri Prasetyo ...... 526

EDUCATION IN THE USE OF TECHNOLOGICAL INNOVATION DIFFUSION E - PROCUREMENT IN SUKOHARJO DISTRICT Danang Indra Sumardi ...... 535

IMPLEMENTATION OF DEMOCRATIC NURTURE IN UPHOLDING LEARNERS’ LEARNING AUTONOMY Prihma Sinta Utami ...... 541

THE IMPLEMENTATION OF COOPERATIVE LEARNING IN TRANSLATION 2 COURSE (A Case Study at English Education Study program in IKIP ) Yuli Kuswardani1, Ermi Adriani Meikayanti ...... 548

INTEGRATION OF LOCAL WISDOM IN EDUCATION Rido Kurnianto, Niken Lestarini...... 558

FEARLESS FEEDBACK FOR EFL LEARNERS Ana Maghfiroh ...... 565

OPTIMIZATION OF CHARACTER VALUES IN EARLY CHILDHOOD THROUGH BUJANG GANONG FIGURE Dian Kristiana ...... 570

THE ANALYSIS OF COLLEGE STUDENTS’ DIFFICULTIES IN PRODUCING PROOFS Arta Ekayanti ...... 576

THE ISLAMIC EDUCATIONAL VALUES IN ABOGE TRADITION IN THE CIKAKAK VILLAGE BANYUMAS CENTRAL JAVA Happy Susanto, Suryati ...... 581

THE EDUCATIONAL AND SOCIO-CULTURAL ANALYSIS TOWARD COMMUNITY AROUND SOUTHERN CROSSROAD OF Maryono, Mukodi, dan Sugiyono ...... 589

VALUE EDUCATION IN SÊRAT MANEKA CARITA AS LITERATURE LEARNING MATERIALS IN THE EFFORTS TO BUILD CHILDREN CHARACTER Istanti Fatkhul Janah ...... 597

THE SCHOOL ASPECTS CAUSED CHILDREN STRESS Rina Wijayanti, Mochammad Ramli Akbar ...... 602

INTERPERSONAL RELATIONSHIPS BETWEEN PARENTS AND CHILDREN IN FAMILY Sarah Emmanuel Haryono ...... 616

GENDER EDUCATION BASED ON FAMILY MANAGEMENT FOR INDONESIAN WORKERS IN PONOROGO Ekapti Wahjuni Djuwitaningsih...... 620

THE THINKING PROCESS OF JUNIOR HIGH SCHOOL STUDENTS’ IN SOLVING MATHEMATIC PROBLEM BASED ON GENDER Dwi Avita Nurhidayah ...... 626

THE ANALYSIS OF STUDENTS’ AUTONOMY BASED ON THE ACHIEVEMENT IN LEARNING MATHEMATICS (A CASE STUDY) Senja Putri Merona ...... 631

THE USE OF THE EUPHEMISM FORM AS MADIUN’S CULTURAL SOCIETIES AND EFFECT IN LANGUAGE TEACHING Nanang Cendriono ...... 636

THE IMPLEMENTATION OF SCIENTIFIC APPROACH IN ENGLISH LEARNING Niken Reti Idriastuti ...... 640

ORGANIZATION OF GENERIC STRUCTURE IN RECOUNT TEXTS WRITTEN BY THE UNDERGRADUATE STUDENTS Adip Arifin, Syamsudin Rois ...... 646

ENCOURAGING THE STUDENTS’ PARTICIPATION IN SCIENTIFIC LEARNING Intan Sari Rufiana ...... 653

FROM INDRA TO MELVINO: A STUDY ON LANGUAGE SHIFT IN NAMING JAVANESSE CHILDREN Diyah Atiek Mustikawati ...... 658

THE INFLUENCE OF HEALTH EDUCATION ON KNOWLEDGE OF SUPERVISOR OF SWALLOWING DRUGS ABOUT LUNG TUBERCULOSIS IN PONOROGO Sulistyo Andarmoyo ...... 665

LANGUAGE AND PERSONALITY Harmawan Wardani...... 671

THE EFFECTIVENESS OF INSTAGRAM AS THE MEDIA OF LITERACY EDUCATION FOR ADOLESCENTS Muh. Zainuri Iskandar ...... 675

CHILDREN'S FAITH EDUCATION IN AN INTERFAITH MARRIAGE FAMILY (A Case Study of Moslem and Catholic Couples in the Special Region of Yogyakarta) Waharjani ...... 679

THE AUTONOMY OF PONDOK PESANTREN WALI SONGO NGABAR PONOROGO GRADUATES IN SELF- DETERMINATION THEORY PERSPECTIVE Darmani ...... 692

THE EDUCATIONAL VALUES IN THE LIFE OF WONG SIKEP BLORA Mukodi, Afid Burhanuddin ...... 704

INCREASING SCIENCE CAPACITY THROUGH NATURE CENTER SETTING (ACTION RESEARCH IN TK B AL HIKAM OF 2016) Siti Muntomimah ...... 710

THE COMBINATION OF REWARD AND PUNISHMENT IN INCREASING STUDENTS’ LISTENING ABILITY Risqi Ekanti Ayuningtyas Palupi ...... 714

ISLAMIC TEACHER ROLE IN IMPLEMENTING THE VALUE OF DEMOCRACY FOR THE EARLY VOTERS IN MADRASAH ALIYAH NEGERI KEMBANGSAWIT MADIUN Nuraini, Wahyudi ...... 720

THE FULFILLMENT OF THE BASIC EDUCATION MINIMUM SERVICE STANDARDS (SPM) OF JUNIOR HIGH SCHOOL IN PONOROGO 2015 Subangun, Diyah Atiek Mustikawati ...... 726

MATHEMATICAL MODELLING COMPETENCIES FOR HIGH SCHOOL STUDENTS Erika Eka Santi ...... 734 International Seminar on Education “Education Trends for Future Society” Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo, August 30, 2016

THE ANALYSIS OF COLLEGE STUDENTS’ DIFFICULTIES IN PRODUCING PROOFS

Arta Ekayanti Universitas Muhammadiyah Ponorogo [email protected]

Abstract Learning difficultness is a condition which the student can’t learn as usual because of the threat and disturbances in learning. Learning difficultness faced by students happened when they followed the lessons from the teacher. Based on result observation of real analysis course work known that many students got the difficultness when prove the proposition given by the teacher. The research results showed that the students got contents understanding difficulties, such as misunderstanding of definitions, not enough word and lack of understanding. It means that they got difficulties with mathematics processes. There are many student identified proving using examples to be invalid. They use specific examples to prove general statements. Keywords: learning difficultness,mathematical proof, students error

INTRODUCTION Mathematics is as such an essential discipline because of the important role it plays in the individual’s personal life. It is considered as symbolic and universal language that enables human beings to thinks, record and communicates ideas concerning the elements and relationship of quantity. Mathematical skills are abstract skills that involve mapping of language into symbols. The basic purpose of learning mathematics should be problem solving, which involves presenting a problem and developing the skills needed to solve that problem. Every individual is required to make effective use of the quantitative information available in his/her environment in problems of day-to-day life (Jena, 2013: 68). Luce and Suppes in Jena (2013) suggest that future mathematical research should address to the content of mathematics, concentrating particularly on the character of mathematical thinking rather than on nature of mathematical objects. Yin Ko and Eric (2009) say that proving and refuting are crucial abilities in advanced mathematical thinking because they help demonstrate whether and why propositions are true or false. In the mathematics community, proving and refuting are inextricably linked given the role each plays in establishing mathematical knowledge. A mathematical proof requires that definitions, statements or procedures are used to deduce the truth of one statement from another, helping people understand the logic behind a statement and insight into how and why it works. Mathematical proofs can provide students with insight into meanings behind statements and also help them see why statements are true or false. Accordingly, undergraduate mathematics students are expected to learn and to use proofs throughout the undergraduate mathematics curriculum. Looking at the processes involved in proving and how students understand proofs are thoroughly addresses topics. Of particular interest to us is how students verify and validate proofs and the misconceptions in proving. Stylianides in Stavrou (2014) reports students’ misconception that empirical arguments constitute valid proofs. That is, students use specific examples to prove general statements. Pfeiffer in Stavrou (2014) conducted a study in which she presented mathematical proofs containing errors to first year mathematics undergraduates and asked them to evaluate and criticize the statements. Pfeiffer notes that many students identified proving using examples to be invalid. (Stavrou, 2014: 1-2) This paper considers undergraduate educations students who are take real analysis course. We examine common errors that these students make when proving statements in their course work.

575 International Seminar on Education “Education Trends for Future Society” Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo, August 30, 2016

Our purpose then is to gathering and analyzing these common mistakes. This paper was guided by questions: What are the common errors that mathematics education students make when writing proofs. Accordingly, from this question we know the learning difficultness of mathematics undergraduate students in Muhammadiyah University of Ponorogo. LITERATURE REVIEW Learning difficultness is a condition which the student can’t learn as usual because of the threat and disturbances in learning. Learning difficultness faced by students happened when followed the lessons from the teachers. Trying to detect learning difficulties can also be done with different perspectives and there are several general questions to consider, for example: Are the measures proper, e.g. examinations and other tests? What are the common informal indications? Do we need special diagnostic tools than the ones that seem more common in primary school? Can students recognize and understand their own difficulties? (Lithner, 2011:290-291). Learning difficulties in mathematics can lead different meaning. Different things and the problem are not just makes misunderstand each other, but also that different meanings may lead to different conclusions and actions. The characteristics of learning difficulties can be related to educational goals that some students fail to reach to various degrees. These goals can, in a similar way as in for example the NCTM Standards (NCTM, 2000) for K-12 education, be seen as comprising both content and processes to master. 1. Content understanding difficulties Many learning and achievement difficulties are directly related to inherent mathematical difficulties within specified concepts. For example, concerning calculus the difficulties found in the research literature seem related to all of its fundamental notions, e.g. variable, function, limit, derivative, integral and differential equation. There are other literature examples related to linear algebra, abstract algebra and real analysis. It is clear that students’ concept images often differ substantially from the concept definitions, not only in the sense that they are incomplete but also in characteristics. These difficulties are at least partially explained by theory indicating the complexity of mental concept formations. It is also clear that a conceptual understanding is not sufficient for mathematical proficiency. 2. Difficulties with mathematical processes There are findings related to difficulties with what in the NTCM Principles and Standards (NCTM, 2000) are denoted processes, e.g. non-routine problem-solving, proof and proving, reasoning, representing and modeling. There are many studies on different aspects of learning, understanding and implementing proof. Students have difficulties in differing proofs from other less rigorous types of argumentation, understanding proof statements, making the transition from informal to formal reasoning and constructing proofs (Lithner, 2011:291-293). Stefanonowicz (2014) stated that a proof was a sequence of logical statement, one implying another, which given as explanation of why a statement is true. Previously established theorems may be used to deduce the new ones, one may also refer to axioms, which are the starting points, “rule” accepted by everyone. Mathematical proof is absolute, which means that once a theorem is proved, it is proved forever. Until proven though, the statement is never accepted as a true one. Writing proofs is the essence of mathematics study. Every word will be defined, notations clearly presented and each theorem proved. Students learn how to construct logical arguments and what a good proof looks like. It is not easy though and requires practice, there for it is always tempting for students to learn theorems and apply them, leaving proofs behind. Yin ko and Eric (2009) say that from a traditional perspective, “a mathematical proof is a formal and logical line of reasoning that begins with a set of axioms and moves through steps to a conclusion”. A mathematical proof requires some aspects, such as the essential components of sets of accepted statement, modes of argumentation and modes of argument representation. In this statement, proof serves as a means to communicate thoughts with learners in the

576 International Seminar on Education “Education Trends for Future Society” Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo, August 30, 2016 mathematics community. Common sense suggests that individuals who understand what constitutes a mathematical proof may be more successful at evaluating purported arguments or their written responses as a valid proof or not. In order to better characterize undergraduates’ proof productions for a true proposition, three proof classifications applied to the study reported here. The first proof category, the inductive proof scheme, describes how individuals convince themselves or persuade others by providing one or more particular examples, which corresponds to naive empiricism (verification by several randomly selected cases) and crucial experiment (verification by carefully selected cases). The second proof category, non-referential symbolic proof scheme, demonstrates that individuals employ symbolic manipulations with little or no coherent understandings of their meanings. In other words, students manipulate symbols with no “functional or quantitative reference[s]”. The third proof category, the structural proof scheme, suggests that individuals realize that “definitions and theorems belong in the structure created by a particular set of axioms”. According to Balacheff in Yin Ko (2009), calculations on statements mean students rely on definitions, theorems, or explicit properties related to the statement when producing a proof. Similarly, Weber and Alcock in Yon Ko (2009) described how an individual attempts to construct a proof by stating the mathematical definition or using related facts that he or she knows about the concepts of producing proofs as defined by syntactic proof productions (Yin ko, 2009: 69). METHOD This research is a qualitative research. This research was conducted in two classes at Mathematics Department, Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo. The course work of undergraduate students in mathematics department who take real analysis course was observed here. Real analysis course is proof-based and require that students be able to write and understand mathematical proofs. The data were collected by correcting the student works in doing real numbers system problems. As their assignments were being graded and compiled a list of errors made by the students. From this list, the most common errors were noted and described. The purpose of this is to answer the research question of what the common errors are that education students make when proving. Instruments validated by two lecturers who are experts in their fields. The instruments are used to identify the student error when proving. Instrument is taken from textbook that is used in real analysis course. DISCUSSION In introduction has been stated that the question of this research is “what is the common error that mathematics education students make when writing proofs?” Below are sample examples:

1. Show that, if , then * + ( | |).

A sample solution is: Let and , then on the left side we get * + * + On the right side, we get ( | |) ( | |) ( ) Therefore, we have

* + ( | |)

The above example is representative of some student work who was proving general statements using specific examples. A proof is a deductive argument for a mathematical statement. Based on student work above, it seemed that student do not understand that proving processes in mathematics can’t be done by specific case. They think if a proposition can be applied in a special case, it leads to general case.

577 International Seminar on Education “Education Trends for Future Society” Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo, August 30, 2016

2. If and irrational numbers, are irrational? A sample solution is: Let √ and √ then √ √ is irrational. Hence, if and irrational, then is irrational. 3. If and irrational numbers, are irrational number? A sample solution is: Let √ and √ then √ √ . Then, if irrational number then rational number. 4. If and irrational numbers, are irrational? A sample solution is:

√ Let √ and √ then √ irrational. The example given above is representative of the responses from some students who almost provided an example to make the answer of that question is false. These students seemed have assuming that the conclusion of the statement is true, so they provide an example that supported the truth value of the statement “if and irrational, then and irrational.” It showed that if the student did not master the topic mathematical proofs well, so the student found the difficult. It seemed they get problem in counter example concept understanding. 5. Use the definition of the limits of a sequence to establish the following limits.

( )

A sample solution is:

( ) ( ) ( )

Based on the student’s work, it showed that student provided an incorrect proof with inadequate understandings of limits of sequences to prove use formal definition. These students did not apply the definitions correctly. In Stavrou (2014) have mentioned that Edwards and Ward have mathematics education research about “Student (mis) use of mathematical definitions”, they got results that nothing that students did not understand the role formal definitions play in mathematics. Firstly, students do not understand that definitions are stipulated and context- dependent. Secondly, students that can correctly state definitions cannot necessarily apply them correctly, if at all, “even in the apparent absence of any other course of action”. 6. Use the definition of the limits of functions to establish the following limits.

| | A sample solution:

Let ( ) for all and . . If | | | |

| ( ) | | | | | | | | |

578 International Seminar on Education “Education Trends for Future Society” Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo, August 30, 2016

Based on student’s work above, the students can write down the definition of limit of functions. But, there are some missing steps on proving processes above, such as the determination of . Whereas, proving limits of functions case, the essence of proof lies on determination. Besides that, students did not justify the proofs, but they use symbols only. It seemed that they are trying to memorize the definition rather than understand them. CONCLUSIONS Writing proofs in mathematics course is different from what has been done during school, so it will take some time to get used to do this properly. The students get a type a difficultness that is content understanding difficultness and difficulties with mathematical processes. A common mistake that students make when trying to present a proof, for content understanding difficultness such as: 1. Misunderstanding of definitions. Students do not know where to start because they do not know the definitions of the objects they are working with. 2. Not enough word. Students don’t explain the step in their arguments, as if they think they are not allowed to use word, only symbols. 3. Lack of understanding. When a student gets to a point in a proof that they are cannot proceed from, often the conclusion of the result follow immediately and it is clear that the student does not understand the necessary missing arguments. University mathematics students is not only get context understanding difficultness but also mathematics processes difficultness, such as incorrect steps. For example they prove by using specific example. REFERENCES Darmawilis, Retni S Budiarti, Gardjito, “Analysis of Learning Difficultness in Xth Grade Social Science Class in Understand The Fungi Topic Concept SMA N 11 Jambi”. Darmawilis: AIC409070 Biologi PMIPA UNJA. Jena, S.P.K. 2013. Learning Disabilty Theory to Practice. SAGE Publications India Pvt Ltd. Mathura Road, New Delhi. Lithner, Johan. 2011. University Mathematics Students’ Learning Difficulties. Education Inquiry. Vol. 2, No. 2, May 2011, pp.289-303. Stavrou, Stavros Georgios. 2014. Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. IUMPST: The Journal. Vol 1 (Content Knowledge), March 2014 [www.k- 12prep.math.ttu.edu] ISSN 2165-7874. Stefanowich, Agata. 2014. Proofs and Mathematical Reasoning. University of Brimingham. Yin Ko Yi, Eric Knuth. 2009. Undergraduate mathematics majors’ writing performance producing proofs and counterexamples about continuous functions. The Journal of Mathematical Behavior 28 (2009) 08-77.

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