Table of contents

It is our pleasure to welcome you in the third International Conference on Mathematics and Mathematics Education (ICM2E 2019) in Padang, West Sumatera, Indonesia. The conference presents on behalf of challenges in industrial revolution 4.0 that makes educator, practitioners and expert in mathematics and mathematics education have to take part to this era. Therefore, this conference provides researchers the opportunity to exchange information about the latest research results as well as the latest findings of mathematics and mathematics education in the era of industrial revolution 4.0.

We hope you have a nice experience by meeting others researchers to share idea about reforming mathematics and mathematics education in facing this era. Do not miss the opportunity to explore and to take a sample of the many diverse attractions in Padang, West Sumatera, Indonesia.

The program consists of invited sessions and parallel sessions and discussion with eminent speakers covering a wide range of topics in mathematics and mathematics education. We hope you enjoy joining this conference.

We would like to thank the organization staff of Universitas Negeri Padang especially Mathematics and Sciences Faculty, the lecturers and staffs of mathematics department of Universitas Negeri Padang. All members of the committee and the reviewers who work very hard in reviewing papers and making valuable suggestions for authors to improve their work. We also would like to express our gratitude to the external reviewers for providing extra helps in the review process and the authors for contributing their research result to the conference. Last but not a least, our special thanks go to IOP publishing. We wish all participants on ICM2E 2019 have an enjoyable scientific gathering in Padang, West Sumatera, Indonesia. We look forward to seeing all of you next year at the next ICM2E conference.

Chair of ICM2E 2019

Dr. Dony Permana, M.Si

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The Ornstein-Uhlenbeck stochastic differential equation is a one of the most applied equation in financial mathematics. To find the analytical solution of the equation is very difficult, so the numerical solution is the choice. One of the numerical method that can be used is Euler-Maruyama method. In this paper, we analyze the convergence of Euler-Maruyama method using Lipschitz condition and other concepts. The analysis shows that numerical solution of Ornstein-Uhlenbeck equation that resulted by Euler-Maruyama method has strong convergence to the exact solution.

Currency rates are one of the important indicators in the context of an economics country. The value of a country's currency always increases and decreases in value against another country's currency at any time. In this research, we make a model of dynamical currency rates data among Riyals and Rupiah. The data are obtained from the official website of Bank Indonesia. The aim research is to predict the currency rate between Riyal to Rupiah in the future time with the Markov Chain Fuzzy-Time Series method. The results of this research are data processing in the form of error value of the forecast used AFER and MEA methods. Those are 0.827% and Rp32.96 rupiahs respectively. The forecast value for the next 10 days are Rp3,779; p3,774; Rp.3,774; Rp3,779; Rp3,764; Rp3,760; Rp3,763; Rp3,797; Rp3,777 and Rp3,784.

We describe a prey-predator model with infected prey. The model using Holling response function of type II is a nonlinear system of ordinary differential equations consisting of two distinct population. Critical points of the model was determined and stability of the system was analyzed by eigenvalues of Jacobian matrix. The behaviour of the dynamical system was analyzed through this stability. Furthermore, threshold number determining the system is free of disease or infected was computed. Numerical solutions are presented on phase plane to confirm the analytical solutions.

A prey predator model which consists of two distinct population is discussed. The model used Holling response function of type II without limiting on prey population growth. Equilibrium points of the model was determined and stability of the model was analyzed by phase plane analysis. Furthermore, the model is reformulated by adding a diffusive terms to understand the spatial effect of the dynamical system behaviour. Solutions of the diffusive model were numerically illustrated with Neumann boundary conditions. Numerical simulations are presented to confirm the analytical results.

In this paper, we examine numerically the existence and stability of onsite solitons in a driven discrete nonlinear nonlocal Schrödinger equation. The equation interpolates cubic and Ablowitz-Ladik nonlocal equations. We obtain that the solitons are always stable for small interpolation parameter. We also obtain that the driving parametric can destabilize the soliton solution.

Human Immunodeficiency Virus (HIV) is a virus that attacks and damages the immune system of the human body so that it is easily attacked by various diseases. A collection of diseases that attack the body is called AIDS. HIV-AIDS is very contagious and deadly. Until now, there is no medicine, serum, vaccine that can cure sufferers of the HIV. HIV-AIDS infection is transmitted through 3 ways: vertically (from mother to child), sexual relations (homosexual, heterosexual and transsexual), and horizontally through inter-blood contact (sharing of contaminated needles, transfusion of contaminated blood, etc.). Sexual intercourse is the biggest cause of transmission. This research discussed construction of mathematical model of HIV-AIDS and LGBT transmission based on the interaction between infected and susceptible individuals in a population.

This paper discusses about a simple mathematical model of the pollutant transfer in n-ponds with three assumptions. First, the amount of pollutant come to the ponds always in constant rate, second, the volume of each pond is the same and third, the water discharge is constant. Using mass conservation rule, the models is constructed for the single water source for single ponds and multiple ponds. After getting the models, the solutions of the model can be achieved analytically. Afterward the solution of the models is investigated in several cases. Firstly, the pollutant that comes to the ponds is not zero, from the solutions the amount of pollutant in a pond is accumulated in the rate of pollutant additions. Secondly, there is no additional pollutant, in this case the amount of pollutant in the first ponds always decreases, but for the next ponds it slightly increases first until a time it start to decrease. The last case if the pond is in pure condition at first then the amount of pollutant in each pond has a linear correlation that increases from the first pond until the last pond.

STEM education has become a trending topic to be discussed among educational experts. However, there is still limited data about preservice teachers' perception about it. Therefore, the aim of this study is to describe teachers' perception about Science, Technology, Engineering and Mathematics (STEM) education. This study is a descriptive research using survey method. The data were collected through questionnaire. The collected data was analyzed by using percentage technique. The result shows that there is positive perception among the preservice teachers about STEM education and they are agree of implementing it to educational curriculum in Indonesia.

Until now there are at least three alternative methods of constructing lemniscate of Bernoulli. In this paper six alternative methods will be given to construct Lemniscate of Bernoulli in a simple way. Furthermore, at the end of the session will be given how to construct the incircle of Lemniscate of Bernoulli.

The validity of learning materials made by the teachers is untested, so it is not valid yet to use in supporting the improvement of students' mathematical communication skills. This research is a part of RME based research on Mathematics learning materials development to improve mathematical communication skills for Grade X SMK students on construction and property engineering programme. This research is aimed to assess validities of learning materials through two phases. First, self-evaluation was conducted by involving a peer. The results showed that Mathematics learning materials could be extended to the expert review phase with minor revision. Second, expert review, the researcher asked five experts to assess its validity. Thus, the results show Mathematics learning materials have been valid.

Creativity is a combination of logical and divergent thinking that is used to bring up a new idea. The type of research was a descriptive research by using qualitative approach. An initial observation of learning devices development based on discovery learning aims to (1) to know an initial conditions of mathematical planning and learning that are developed by the teacher (2) to know and review how creativity of senior high school students in mathematics learning (3) whether it is necessary to continue research development based on discovery learning to improve creativity of senior high school students. The results of preliminary observations indicate that: (a) mathematics planning and learning that are developed by teachers is still general. (b) So that the creativity of high school students in mathematics learning is still low. (c) Based on this, follow-up action is needed in the form of research on development based on discovery learning to increase creativity of senior high school students (SMA N 5 Padang on 2018/2019).

This research is motivated by the low interest and motivation of students to learn mathematics in the third grade of SDN 19 Nan Sabaris. The purpose of this study was to see the effect of Ludo media to increase the interest and motivation of mathematics learning in third grade students of SDN 19 Nan Sabaris. This type of research is quasi-experimental with a sample of all third grade students of SDN 19 Nan Sabaris registered in the 2018/2019 school year. The research instrument used was in the form of a questionnaire to see motivation and student learning interest in mathematics in grade III of SDN 19 Nan Sabaris. The data analysis technique used is paired-sample t-test. The results of data analysis showed that there were significant differences in the results of interest in and motivation to learn mathematics in third grade students at SDN 19 Nan Sabaris. This means that the use of ludo game media can significantly increase students' interest and motivation in learning about Mathematics.

This research discusses the development of mathematics learning media based on problem-based instruction (PBI) to enhance students' critical thinking skill in grade X. The developed learning media are lesson plan and students' worksheets. The research was conducted until preliminary research phase including need analysis, student analysis, curriculum analysis and concept analysis by using Plomp model (Preliminary Research, Prototyping Phase, and Assessment Phase). Data collected through observation, questionnaire, and interview. The sample is Grade X students of SMAN 15 Padang. The results shown that the learning media used are not facilitating students' critical thinking skill in teaching-learning process.

This research discusses about the development of mathematics learning device based on cognitive conflict to improve critical thinking skills of class X students. Learning device was developed in the form of Learning Implementation Plans (in the form of RPP) and Student Worksheets (SW). The model of development research that has been used in this study is the Plomp model (Preliminary Research, Prototyping Phase, and Assessment Phase). However, this research only reached to the preliminary research stage. The subject of this study was the 1st grade students of SMAN 3 Painan. Based on the results of interviews to several teachers of SMAN 2 Painan and SMAN 3 Painan concluded that the learning device used by teachers have not been able to stimulate students to think critically optimally.

This article discussed the development of hypothetical learning trajectory for integral topic which based on realistic mathematics education for class XI Senior High School (SMA). The study focused on the phase of one to one evaluation by using observation. In this phase, we try it out to three students which divided into low, medium and high mathematics ability. Based on the observation, it can be concluded that the designed Hypothetical Learning Trajectory (HLT) can guide the students to achieve the expected purpose, that is the students can construct and discover the concept of integral by themselves based on their experience. Students use their reasoning ability to solve the given real problem so that their mathematical reasoning ability is improved.

This study aims to develop mathematical learning devices The aim is for students to be able to communicate ideas with symbols, tables, diagrams, or other media to clarify the state of a mathematical learning problem called mathematical communication skills. it is necessary to develop a device with an approach to improve the student's mathematical communication skill. The CTL approach can help students to create mathematical communication skills. Because with CTL, students can find the subject learned by linking it to real-life situations so that they can apply it in everyday life. The indicators of communication capabilities developed are Illustrating mathematical ideas, using symbols/notations and mathematical operations, selecting and writing relevant mathematical strategies and giving conclusions at the end of the answer. The development model used is the Plomp model, which consists of three phases. First is the initial investigation phase, the second is the development or prototype development phase, and the third is the evaluation phase.

The research is aimed to describe data of preliminary analysis on development of mathematics learning tools based on indicators of mathematical communication skills. Mathematical communication skills of senior high school students are still low. Therefore, the research intends to develop learning tools with RME approach by concentrating on redesigning students' worksheet. This research is a qualitative research because the main data signifies the result of tests of mathematical communication skills. The result of research indicate that the students' mathematical communication skills based on indicators were still weak and the mathematics learning tools that will be developed contains teaching-learning approach that will help students improving their mathematical communication skills.

The purpose of this research is to analyse the mathematical communication skill of student by using essay test. The method of this research is a quantitative approach with descriptive. We assess the communication skill from the students who take calculus course. The results showed the percentage of achievement of mathematical communication skill indicators of students were: 1) 45.7% students can express mathematical ideas in oral or written form into images, algebraic expressions, and graphics; 2) 34.3% students can state mathematics problem in daily life into a symbol or model in mathematics; and 3) 51.4% students can interpret figures into mathematical ideas. Based on the percentage, the mathematical communication skills of students in calculus course is still low and need to be improved for further research.

This paper discusses the validity of mathematical learning material based on MEAS approach in improving mathematical creative thinking skills of high school students. This learning material was validated by experts from mathematics, language and educational technology backgrounds. The conclusion that the learning material was categorized valid and can improve students' creative thinking skills.

West Sumatra has 2 peak of rainy seasons, October-November and March to May. The high intensity of rainfall causes West Sumatra has potential to floods. Precise forecasting is needed to be a reference for the government. One of the method can be used is SSA. This method is flexible because it does not require specific form of time series data, as well as parametric assumptions. Thus, accurate forecasting results is expected to be provided from the SSA method. From the forecasting process that has been done, obtained MAPE of 17% with the tracking signal value within the tolerance range.

Indonesian's data are obtained from BPS from census, but census are designed for large area. Now, local goverments need to have reliable and detailed information in small area. Direct estimation are unreliable to be applied in small area because produced high mean square error (MSE). To overcome this problem, we use the indirect estimation Small Area Estimation Hierarchical Bayesian (SAE HB) with Logit Normal as the model. From this study founded that HB produced a smaller MSE than direct estimation

West Pasaman Regency is one of the 50 largest disadvantaged regions in Indonesia. One indicator of disadvantaged areas is there are still many poor people in the area. The level of poverty in an area is estimated to be influenced by the poverty of the surrounding area. Relationships between these regions can be known by calculating spatial autocorrelation. This research aims to determine spatial autocorrelation in the poverty level in West Pasaman using the MoranIndex. The results of this study indicate thatthe poverty level in West Pasamanhave positive spatial autocorrelation, but the correlation is weak because the Moran Index value is close to 0, which is 0.0765.

Student can obtain the high learning achievement because some factors. Those factors can appear from themselves or out of themselves. One of them is learning attitude of student. Learning attitude could be observed by some indicators. There were four indicators of learning attitudes, which were honesty, responsibility, discipline, and tolerance. The good learning attitude will give effect to learning achievement. Learning achievement is result of the learning process. There are several indicators to find out about students learning achievement. They are GPA, understanding of the concept, application and analysis. Learning achievement and learning attitude are unobserved variable, called latent variables. The method was used to analysis the latent variable in this research that was Structural Equation Modelling (SEM). It is combination from factor analysis, path analysis and regression. The aim of this research was to known affecting indicators from learning attitudes to learning achievement. The result showed that indicators of learning attitude had t-value more than 1.96 and that mean all of indicators in learning attitudes gave effect to the learning achievements.

One of the students' academic achievement can be seen GPA, the higher the index value, the better student achievement success rate of students who obtained. Many factors affect student achievement index both internal factors and external factors. This paper described at factors that affect student achievement index of Department of Mathematics UNP who enrolled 2016 by using probit regression analysis. The results of this study are students SBMPTN, does not work while in college, and was not active in organizations on campus have the opportunity to get a better grade.

The purpose of this study is to produce a learning tools based on Realistic Mathematics Education that is valid, practical, and effective against the problem solving abilities of students in class VII. Learning Tools are developed Lesson Plan (LP) and Student Worksheets (SW). This research is a development research with Plomp model of the which consists of three stages items, namely preliminary research, development, and improvement. At the development stage, the learning tools design and evaluation is carried out through formative evaluations.

Critical thinking is one of the higher order thinking ability that needs to be developed in the 21st century. In fact, that the students' critical thinking ability are still low. In learning geometry students are still dependent on the teacher in receiving information, the media are inadequate in learning geometry so that students have not been trained to solve geometry problems with critical thinking. Thus a geometrical learning devices was made based on the van hiele theory. Before using the geometry learning devices, it is validated first with the experts, asking the teacher's response, and student responses through questionnaires and interviews. The subjects of this study were class VIII students of SMP 13 Padang. The results showed that the response of teachers and students showed the geometry learning devices is practical criteria.

Student engagement is important in every learning because learning activities are not just a transfer of knowledge but also as a potential development that is owned by students. This study aims to determine the increase student's engagement of MTs grade VIII learn based contextual teaching and learning (CTL) learning device in the form of lesson plans and student worksheets. The research design used One Group Design. The sample of this study involved students of class VIII in the 2018/2019 school year were 25 students of class VIII.1 as an experimental class. The instrument used was a student engagement questionnaire and field notes. Data were analyzed quantitatively using means and n-gain and described descriptively. The results showed that the n-gain was 0.215, which means that there was an increase in the student's engagement learning by using CTL-based mathematics learning in the low category.

This study discussed on the effectiveness of the use of mathematical learning tools based on guided inquiry models to improve mathematical communication skills (CS) for students of grade VIII SMP. The type of development research used is the Plomp model. The study was conducted on 30 students in one class to use learning tools, then given a final test to see how many students completed the test. The results showed that 86.6% had completely exceeded the minimum completeness criteria that had been set at 70. It could be concluded that the learning tools developed in the form of RPP and SW were effective in improving students' mathematical communication abilities so that they were suitable for use. Start your abstract here...

Geometry is one of the important subject in mathematics. One of the objectives of learning geometry is the students can gain confidence about their mathematical abilities and be able to communicate mathematically. However, in their practices students are still having difficulty understanding geometric material and students' mathematical communication skills are also still low. Considering the importance of geometry learning, the students' mathematical communication ability need to be improved to achieve geometry leaning goals. In this study, geometry learning devices were developed based on the Van Hiele Theory with the purpose to produce a product consisting of lesson plan and students worksheet to develop students' mathematical communication ability. The development model used is Model Plomp. Based on the results obtained in small group stage, there is increase in students' mathematical communication ability seen from the result of working the questions every meeting. Then, an analysis the questionnaire of students who obtained practical category. So that, it can be conclude that geometry learning sets based don Van Hiele Theory practical can be used to increase Students Mathematical Communication Ability in Class VII Junior High School.

This study aims to develop mathematics learning tools based on contextual teaching and learning approaches in the form of lesson plan and student worksheets for high school students grade VII. This research is a development research. Model used is Plomp model which consists of three stages, namely the initial investigation phase, the prototype development stage, and the assessment stage. This research is limited to the prototype development stage to see the practicality of learning devices that has been designed. Based on the test results of the practicality of learning tools through three assessment data, namely, the observation sheet data of the implementation of learning with an average of 89.38% - the category is very practical, the teacher questionnaire data with an average of 88% - the category is very practical, and the questionnaire data of students' responses with an average of 86.93% - the category is very practical. The results shows that the mathematics learning tool based on contextual teaching and learning approach is valid and practical.

Vocational students are prepared to work and have expertise in the vocational field, therefore learning in vocational schools should pay attention to the professional competencies of the students themselves. Learning mathematics in vocational schools in learning mathematics does not relate the relationship of mathematics to the subject matter so that made students bored in learning mathematics and think mathematics is a difficult, unattractive and less useful lesson. Learners prefer productive subjects according to their professional competence. This will affect the purpose of learning mathematics in Vocational Schools in improving students' mathematical problem solving skills. The development of professional competency-based learning tools is expected to overcome the problem of increasing problem-solving skills of vocational students in the audio video engineering program. This study aims to develop learning tools in the form of Learning Implementation Plans (RPP) and Student Worksheets (LKPD) using the Plomp model which consists of three stages: preliminary research, stage prototype, and assessment phase. This article is a preliminary research phase, which is needs analysis, curriculum analysis, and concept analysis, analysis of students and teachers of vocational mathematics. Audio video techniques. The results in the Preliminary Research stage become a reference in designing products in the form of mathematics-based professional learning devices in the audio video engineering expertise program.

This research is motivated by the low interest of students in the training in mathematics learning in the fourth grade of SDN 19 Nan Sabaris, Padang Pariaman Regency. The purpose of this study was to look at the contribution of snowball throwing-based teaching materials to increase the interest in working on mathematics training for fourth grade students of SDN 19 Nan Sabaris. This type of research is descriptive, with a sample of all fourth grade students of SDN 19 Nan Sabaris registered in the 2018/2019 school year. The sampling technique used was purposive sampling because the available sample classes were limited. The instrument used was the observation sheet, and the results of the instrument analysis showed an increase in students' interest in doing mathematics training after the use of Snowball Throwing-based teaching materials in grade IV SDN 19 Nan Sabaris.

Mathematics is not directly given to the students in the form of formulation, however students have to construct the knowledge by themselves through contextual problem interactively, both in formal and informal, so that students can discover the truth of the concept by themselves. One of the important components in mathematics learning is mathematical connection; however, students' ability of mathematical connection is far from the expectation. Therefore, the development of learning device with an approach and strategy to allow mathematics as the activity of the students is of vital importance. The designed learning device by using RME approach and by adding strategy of relating, experiencing, applying, cooperating, and transferring (REACT) based on constructivism which places the students as the center of the learning. The purpose of this research is to develop RME based learning device which is valid, practical and effective to improve students' mathematical connection of class IX Junior High School (SMP). This is a development research model by employing Plomp model which consists of three phases, namely, preliminary research phase, development and prototyping phase, and assessment phase. Preliminary research reveals that students are less interesting to learn mathematics since they have only few chances to find concept through relevant practice with their individual experience and that are suitable with students' cognitive level.

This research is development research using Plomp development model. This research aimed to analyze the curriculum between mathematics and productive subjects of design and creative product craft expertise program. Analysis curriculum aims to obtain information in developing the mathematics learning devices in the form of Learning Plans and Student Worksheet based on Realistic Mathematics Education (RME) approach

Our preliminary research conducted on students grade VII of junior high school showed that the students' mathematical problem-solving ability was still low. We suspected that learning tools used so far have not been able to facilitate students to develop mathematical problem-solving abilities. The low ability to solve mathematical problems of students can be overcome by developing learning tools based on Problem Based Learning. The purpose of this study was to analyse the results of the development of learning tools based on Problem Based Learning to improve the mathematical problem-solving ability of students in grade VII. This type of research is development research where the subjects were students grade VII of junior high school. We used the Plomp model which consists of three stages; investigation, development or prototype, and the assessment. The instruments used to find out the practicality of the learning tools developed were interview guidelines, student questionnaire responses, teacher questionnaire responses, and observation sheets for the implementation of lesson plans. The results showed that our newly developed learning tools have been practical for use in the learning process.

Mathematical critical thinking ability of junior high school students in Indonesia is still low. Previous studies indicate that critical thinking ability of junior high school students is ≤ 50%. The inavailability of a helpful learning tool turns out to be the ground of lack of development on the students' critical thinking ability at junior high schools. This condition is the foundation of conducting development research on learning tool using Model Eliciting Activities (MEAs) to improve the mathematical critical thinking of junior high school students. This research is part of the phases of plomp model development that is the premilinary research. The research is investigation study in which the activities in this introductory research are analyzing prerequisite and context (analysis of curriculum, concept and students) and review of related literature. The data are collected through questionnaires, interviews, documentation, and test of critical thinking ability. The data gained are examined descriptively. The subjects of the study are the students of SMP Negeri 8 Padang Grade VIII and the math teacher. Conclusion of this preliminary research is that it is imperative to develop MEAs based learning tool in math learning to advance critical thinking ability of junior high school students.

The study aim to analyze the curriculum to see and find out the linkages between Basic Competence mathematics and Basic Competence productive subjects in the art expertise program. This research was part of Plomp's model development research. Curriculum analysis is carried out to obtain information in developing mathematics learning devices in the form of Learning Implementation Plans and Student Worksheets based on the Realistic Mathematics Education (RME) approach. From the results of curriculum analysis that has been done, it was obtained data that not all Mathematical Basic Competencies have anything to do with productive subjects in the fine arts expertise program. From a number of mathematics material in grade one 1st semester, there are four materials that have relevance to the context studied in students' productive subjects, including the absolute value of one variable, the system of three-variable linear equations, functions, and the composition of functions. This means that the context studied in productive subjects can be used as an initial problem in the process of learning mathematics in the material

Based on the results of observation and experience of researchers as mathematics teachers in one of the vocational high schools in Indonesia, information are obtained that the average mathematics scores of students are still below the Minimum Mastery Criteria. This is caused by: the mind-set of students who think mathematics is not important compared to the subject of vocational specialization, the learning process is less engrossed and interesting because of the teacher's monotonous teaching style. As a result, students' interest in learning mathematics is low. To overcome this problem, the teacher must design a mathematics learning strategy in the form of a mathematics learning tool in the form of a learning implementation plan and a student worksheet based on Realistic Mathematics Education (RME). Because the RME-based learning approach starts from 'real' things for students. This type of research is development research with the Plump model consisting of the preliminary research phase, the prototype phase and the assessment phase. In this study researchers were only at the initial investigation stage, namely at the student analysis stage. The purpose of this study was to increase students' interest in learning mathematics. The instrument collection for initial investigation data was observation sheets, questionnaires and interviews with data analysis techniques namely descriptive techniques. The results of the initial investigation of the analysis of learners found that the interest in learning mathematics in vocational secondary school students is very low.

This study aims to discuss a draft RME-based math learning tool for the students of tenth grade vocational high school of hospitality and tourism services program skill. This study is part of a research model development Plomp. This research only to the preliminary stage of research is the analysis of needs and learners. Data analysis in this study uses an interactive analysis model that consists of data collection, data reduction, data presentation, and drawing data conclusions. The instruments used in this study were interview and questionnaire guidelines. The analysis shows that devices made by teachers are universal to all membership programs and not pay attention to the character of each program skill.

Students' ability in solving mathematical problem has optimal yet. This is due to mathematics learning provide less opportunity for the students to get involved in a challenging problem during learning process. The purpose of this research is to develop learning devices in the form of lesson plan and worksheet based on Problem Based Learning (PBL). This is a development research. The development model employed in this research is Plomp Model. This model consists of 3 phases, namely, preliminary research, development or prototyping phase, and assessment phase. In this part, the reported one is the preliminary research. The result of data analysis on preliminary research shows that: 1) Teacher is not able yet to develop learning device in order to improve students' ability in problem solving. 2) Students' inability to solve story problem. 3) Students are not capable to work on different question from the sample given. 4) Students are expecting to have a real life context problem on worksheet in relation with their daily life. 5) Students prefer to work on group. 6) Students who live in a rural coastal area tend to be less motivated and less active in the learning process.

The aim of this research is to develop the math learning devices with RME-based in mechanical engineering and automotive engineering programs for students of grade 10. The devices designed are adjusted to the students' major. The students of mechanical engineering learn about design, construction and operation of machinery, while automotive engineering students focus on the design and construction of cars. Learning devices were designed in the form of lesson plans and students' worksheets. The development model used in this research was Plomp model. This paper focuses on the preliminary research. The preliminary research covers needs analysis, curriculum analysis, concept analysis and students analysis. The instruments used were questionnaire sheets, interview sheets, and observations. Data analysis technique is a qualitative data analysis technique. The result of the preliminary research shows the learning devices made by the teachers were universal for all major and ignore the character of each major, neither mechanical engineering nor automotive engineering. The curriculum analysis done toward the syllabus and KD of math and the productive subjects related. The result of this preliminary research will be a guidance in prototype of learning devices that will plan.

This research has aimed to develop a math learning device based on Quantum Teaching and Learning model for seventh-grade students. The learning device which is developed involves learning implement plan and student's worksheet. The development model which was used in this research is Plomp model. This research only until prototype development, which discuses character analysis of students during the learning process occurs. In learning with Quantum Teaching and learning device, learners study in a group and discuss to understand the concept, so this activity could facilitate the characteristic of learners whose like to have a group and have a discussion. The finding of this research is expected to increase learners to study mathematics and become more active in the learning process.

Problem solving ability is one of the mathematical abilities that is very important so that students are able to apply the concepts they have learned. The purpose of this study was to analyze the initial ability of mathematical problem solving in mathematics learning of eighth grade students of junior high school. this is seen from the indicators as follows; 1) Identifying the elements that are known, asked, and the adequacy of the elements needed, 2) Formulating problems or compiling mathematical models, 3) Implementing strategies to solve various problems inside or outside mathematics, and 4) Summing up the results. The instrument used in this study was a preliminary test of students' mathematical problem-solving abilities with questions as many as 3 items and a research sample of 32 people in the first school and 30 people in the second school. Assessment of students' mathematical problem solving ability tests is based on a scoring rubric of mathematical problem solving abilities. Based on the results of this study, the percentage of students' mathematical problem solving abilities was 18.95% and 14.57. The results of this study indicate the low ability of students to solve mathematical problems and the need for further action to improve them.

Based on the preliminary research stage conducted in Public Junior High School (SMPN) 3 Muara Bungo, it is obtained that students' reasoning ability is low and has yet achieved optimum result. This is due to inappropriate learning device available in which it is yet facilitating the students in improving their mathematics reasoning. Therefore, it is of vital importance to develop learning devices in the form of lesson plan (RPP) and student worksheet (LKPD) based on Realistic Mathematics Education (RME). RME provides more opportunities for the students to be more active in comprehending mathematics concept, think logically, and are able to draw a problem fine conclusion. The purpose of this research is to obtain valid, practical, and effective learning device based on RME for class VII of Junior High School. Research data were collected through observation, interview, document, questionnaire, and mathematical reasoning ability. The research participants are students of class VII SMPN 3 Muaro Bungo. This is a model development research. Plomp model was employed as the development model in this research. There are 3 phases on this model, namely, preliminary research phase, development or prototyping phase, and assessment phase. However, this research focuses only on preliminary research phase. It is including things required to design the expected learning device. The result of preliminary research is 1) students' mathematical reasoning ability has optimum yet; 2) class VII students are in their transition from elementary school to junior high school level; hence mathematics learning requires concrete learning object or mathematics learning should be linked with their daily life; 3) RPP used provides less support to improve students ability in mathematical reasoning and it provides less opportunities for the students to be more active; 4) students expected that LKPD has to be detail, attractive, fun, and easy to comprehend.

Students need critical, systematic, logical, innovative thinking skills and effective collaboration in the learning process. Students want math learning that is fun, relaxed, easy to understand and the material displayed in a colorful book so it is fun to read and it can be presented in comic form. The classroom action research conducted aims to see the use of comic worksheets. Mathematics learning using comic worksheets can improve learning activities, understanding concepts and can improve students' mathematical problem solving. Students feel happy if the mathematics material can be presented in comic form because it is easier to understand, presented in the form of pictures and series of stories that can lead in the discovery of concepts so that it is clearer and easier to understand, adds enthusiasm in learning and does not create a tense atmosphere of learning.

The issue of students' difficulties in Mathematical problem solving should be resolved. One of the ways to overcome that problem is developing an appropriate learning tools. This case is expected to increase students' ability in solving Mathematical problem. The type of this research was development research and used plom model in it. This research was consisted of three stages. They were prelimenary, development, and evaluation analysis. The result of this research was practical and effecctive Mathematics learning device. The analysis validation of lesson plan and students' worksheet stated that they were valid. Besides, learning device was practical based on the result of analysis. The result was proven at interview guidelines, teacher's response questionnaire, students' response questionnaire and observation sheet in implementation of learning. The result of average percentage of practical score, teacher's response got 88.99 %. Meanwhile, students' response was 85.12 %. The result of practicality of learning device was strongly practical categories. Besides, learning device was effective to increase the ability of students in solving problem, especially at grade one of senior high school in Indonesia. Learning device that was developed had effective criteria. The result of students' competency who are able to solve the Mathematic problem was 63.63 %. Theirscore were above Minimum Criteria of Mastery Learning.

One of the efforts to create Accelerated learning revolution of XXI century is the importance of innovation in mathematics learning by developing learning device based on Coaching Technique. The learning devices are in the form of lesson plan (LP) and student worksheet (SW) designed as the substitute coach for both teacher and student, hence the purpose and the target of learning can be achieved. Coaching provides steps that are systematic, practical, and in line with the learning purpose. Coaching technique can be implemented in the classroom by providing opportunity for teacher to conduct improvisation in teaching, to facilitate teacher to uncover students characteristics, as to provide opportunity for students to develop their own learning style based on their individual ability. The development model employed in this research is plomp model. This model consist of three phases, first, preliminary research, second development or prototyping phase and third assessment phase.

The research problem in is the students' mathematical reasoning ability is low, it is caused by learning device designed by the teacher does not yet support how to construct student's mathematical reasoning ability. Through the development of this learning instrument, it is expected that students' abilities in mathematical reasoning can increase. Learning tools are developed in the form of Lesson Plan and Student's Worksheets. We use research Plomp's model: initial research, prototype phase, and assessment phase. The results of preliminary analysis research, mathematical reasoning ability and student learning outcomes are still low. Teachers and students need learning tools based on Learning Cycle 5E with simple language and guide students to understand mathematics well. This study produced a valid mathematics learning device.

The goal of this research is to determine the influence of the realistics mathematics education (RME) approach by oriented higher order thinking skills (HOTS) on the results of students' mathematics learning on the subject of the calculus in SMAN 10 and SMAN 12 Padang. The method used is the experimental research with pre and post-test design randomized control group. The data analysis technique used is the test for normality and homogeneity test followed by using a t-test. The results revealed that there were an increase in student mathematic learning outcomes approach realistic mathematics education oriented higher order thinking skills in class XI MIPA SMAN 10 and SMAN 12 Padang. There is impact-oriented approach to realistics mathematics education approach by oriented higher order thinking skills to understanding student learning in class XI SMAN 10 and 12 MIPA Padang.

This study aimed to know the difference of geometry learning outcome between students studying with problem-based learning model and students studying with scientific learning approach after controlling mathematics initial ability. The design of this study was non-equivalent control group design. Random sampling technique was used to take the research sample which amounted to 18 students. Technique of collecting data was the tests mathematics initial ability and geometry learning outcome. Data was analysed by using analysis of covariate. The results showed that geometry learning outcomes between students studying with problem-based learning model were higher than that studying with scientific learning approach after controlling mathematics initial ability.

The objectives of hierarchical learning in hierarchical learning start from understanding mathematical concepts to a higher level. Understanding mathematical concepts is the initial foundation for students to be able to achieve other mathematical goals. This shows that the ability to understand mathematical concepts is a basic ability that students must have in learning mathematics. One mathematical learning model that can help understanding mathematical concepts is to apply the STAD type cooperative learning model. The STAD cooperative learning model is a model that is able to improve students 'understanding of mathematical concepts because each stage of the learning model is able to support in improving students' understanding of mathematical concepts. To find out and describe the development of students' understanding of mathematical concepts with the STAD type cooperative learning model through student worksheets, a study was conducted in class VIII 3 of SMP Negeri 18 Padang. The quiz was conducted 6 quizzes and the results of the study showed that there had been an increase in understanding of students' mathematical concepts during the application of the STAD type cooperative learning model.

This research aims to develop a learning devices based on guided discovery methods that have valid, practical, and effective characteristics in order to improve the problem solving ability of grade VII SMP/MTs. The learning devices developed include lesson plan and student worksheet. The subject of this research was students of grade VII MTsN 1 Kerinci. The type of this research is development research using a PLOMP model that has three phases, namely, preliminary research, development or prototyping and assessment. The preliminary phase of research consists of needs analysis, curriculum analysis, student analysis, and concept analysis. Based on the results of preliminary research obtained the information that student problem-solving ability are not optimal, one of the factors that cause this is the unavailability of learning devices that can facilitate Students to improve their problem solving abilities. In the development or prototyping phase of the activities conducted is designing products such as lesson plan and student based Discovery guided, which then conducted a formative evaluation to determine the validity and practicality of the product. At the last stage, the assessment phase is conducted assessment of practicality test and effectiveness test.

The purpose of this study is to identify student errors in solving the matter of circular material and spherical analytic geometry. The subject of this research is the 2nd semester students of the Mathematics Department at Universitas Negeri Padang. The type of this research is descriptive research. The type in this study is a qualitative approach. The data collection were obtained through documentation, tests and interviews. Data analysis was carried out in a qualitative descriptive. The results showed that the learning difficulties of students in the circle and sphere materials in terms of concepts, principles, and algorithms were: (a) Inability to remember, (b) Misclassification, (c) Error strategy, (d) Error calculation, (e) Difficulties in using algorithms. Teachers' efforts to overcome student learning difficulties, namely: (a) provide training in varied questions (b) make a personal approach to students (c) repeat the questions that have been learned (d) provide direction to students to remember the formula learned (e) guiding and directing students to use the algorithm correctly. So that the teacher needs to use the right strategies and methods in teaching mathematical concepts.

Real analysis is required for mathematicians. The competency is that students are able to analyze and think critically in solving a problem, and write their solutions in a logical statement. Students must have the definitions and theorems to solve the problems and perform a process which is often called the preliminary analysis. After that, students construct the proof based on the preliminary analysis. Based on the characteristics of the problem in real analysis, the solution given to the problem is using flow proof in composing preliminary analysis. Before the learning materials are prepared, it is important to know the characteristics of learners in following the learning of mathematics that affect the learning outcomes. There are five factors that influence the learning outcomes, namely background, interest, attitude, motivation and learning styles. The purpose of research is to determine the factors that influence learning outcomes. This research is a descriptive. The instruments are assessment sheets for students' characteristics and test. Results are the factors that influence the learning outcomes of students directly are background and learning style.

The purpose of this research is to examine the effectiveness of student worksheet (LKPD) based on realistic mathematics educations (RME) of class VIII of Junior High School. This is a development research with Plomp Model. The research design employs quasi experiments with Only-Posttest Control Group Design. This research took place in Public Junior High School (SMPN) Padang of class VIII. The sample is determined by purposive sampling. The treatment toward experiment group is learning by using LKPD based on RME. Meanwhile, control group is using student book according to curriculum 2013. The research instruments are test items, learning observation sheet, and learning device which had been tested for validity and practicality in the development research stage. Data analysis is conducted through t test for the mean difference test and the Scheffe test for the effectiveness of the LKPD test. The research result showed that students' mathematical communication ability of class VIII of Junior High School (SMP) by using LKPD based on RME is better than student who uses student book. Finally, it can be concluded that LKPD based on RME is effective in improving students' mathematical communication ability.

This study aims to design student learning trajectories in learning the concept of the importance of hypothesis testing in inferential statistics. This study used design research. Design research consists of three stages, i.e. (1) preparing for the experiment; (2) teaching experiment; and (3) retrospective analysis. This study focused on the first stage, because the main purpose of this research was to develop a series of learning activities to learn the importance of hypothesis testing in inferential statistics. The result of this study is an hypothetical learning trajectory (HLT) to find the concept of the importance of hypothesis testing in inferential statistics. HLT was designed using a realistic mathematics education (RME) approach. The context used in designing HLT is to tossed a coin to determine which football team will kick off. Using iceberg, a series of learning trajectories are designed so that students are able to find out by themselves that testing hypotheses is an important concept in proving the assumption that coin is used in balance.

Research on teacher professionalism in the learning process experiences exponential growth. One form of teacher professionalism is how teachers can use media that can make learning interesting. Geogebra is an application that can be used by teachers in learning on certain material. This research was a survey research that sees teacher interest in the use of geogebra software. Sixteen teachers from 10 junior high schools in one sub-district in one of city at Indonesia were chosen as research subjects. The training was held for five hours. When the teacher training was videotaped, observed, and interviewed. Obtained 84.76% percent of teachers gave good attention and 73. 18 % give good participation to this training.

Media tools are always been believed can increase students' learning outcomes. This study is to describe mathematics teachers' perspective of media tools in mathematics learning. Instrument is a questionnaire about media tools in Likert scale. Questionnaire was delivered to 35 mathematics teachers in Padang Pariaman. The result shows that mathematics teachers have good perspective of media tools in mathematics learning at senor high school but the frequency of using it is still low.

Many factor influence mathematics learning outcomes, such as students' attitude, interest and motivation. The aim of this research was to describe students' characteristics, learning outcomes and geometry media tools that was been used in Junior High School at Padang. Type of study was descriptive research with qualitative approach. Instruments were questionnaire, test, observation and interview. The result shows that students' attitude, interest and motivation to learn are in well category.

Self-efficacy has important role in determining the success and adjustment of first-year college students, including college students in study programs of mathematics education. The purpose of this study is to analyze the source of self-efficacy of first-year college students based on gender and prior knowledge. The research method used is descriptive. The study sample consisted of 68 students enrolled in calculus lectures and 58 students enrolled in algebra lectures. Other researchers have tested instrument of self-efficacy for there students. This study finds that a source of self-efficacy of first-year college students, namely vicarious experience and mastery experience affects more male and female students. Vicarious experience is the most dominant source of self-efficacy for each category of prior knowledge.

The purpose of this research was to increase student's understanding about place value at elementary school. This research was conducted at second grade of an elementary public school no 13 in Kecamatan Padang Barat. There were three phases of the development: preliminary research, development/prototype phase, and assessment phase. The model of development was adapted from Plomp model. This research was focused until development/prototyping and implementation. The first step was discuss with teacher to get some information about the problems in mathematics instruction at the second grade. The teacher still have the difficulty how to show the real process in addition and subtraction operation at natural number. The second step was preparing the Base Ten Blocks and creating the booklet about how to use it. In this prototyping phase the booklet was corrected by teacher and expert. This phase had micro-cycle until the teacher and the students find the booklet useful. In first prototype, validation was conducted by self-evaluation and expert review. After the revision of the first prototype, the second prototype was created, and then it was used to know about its practicality by implementation in small group evaluation and student in class.

The low learning outcomes of students in solving story questions was indicate the occurrence of problems in students. That problem is caused one of them by the mistakes of students in working on story problems. This study will see an increase in student learning outcomes and the types and causes of student errors. This type of research is a mixed method with the research design is sequential mixed method. The results of this study indicate that the probability value is 0,000 so that How is rejected or in other words there is a significant increase after learning is given using the M-APOS approach. The results of the error analysis based on the Newman procedure consist of understanding errors, transformation errors, process errors and writing error answers. Then found another error in this study is an error in writing the unit.

This study focuses on the development of mathematical learning tools based on realistic mathematics instruction for the Class X Professional High School Nursing Education Program to improve students' mathematical communication skills. Learning tools designed in the form of Learning Implementation Plans and Student Worksheets. The development model used in this study is the Plomp model including the preliminary research phase, the prototype phase and the evaluation phase. However, this research only reached the preliminary stage of the research. The subjects in this study were students in the Nursing Science Competency Program Class X SMK Bukittinggi. The development of learning tools is done by linking the topics of nursing expertise programs with mathematics through a needs analysis and a concept analysis. The results of the curriculum analysis show that the students' mathematical communication skills are still weak. One of the factors behind the students' mathematical communication skills has not been optimally achieved, namely the lack of learning devices that facilitate the improvement of mathematical communication.

Financial Accounting is one of expertise programs in Indonesia Vocational High Schools. The prospective Vocational High School graduates are expected to be equipped with a great problem-solving skill which demanded in the field of working. Mathematics is the lesson that develop students' problem-solving skill. This paper discussed development in learning devices based on realistic mathematics education for financial accounting expertise program in Xth grade Vocational High School. The research was conducted until preliminary research phase by using Plomp model. Based on the interview results conducted on Mathematics teachers in SMK N 2 Padang and SMK N 3 Padang, the writer concludes that the mathhematis learning devices commonly used by teachers are general without giving differences in the characteristics of each expertise program, specifically in financial accounting programs. Lastly, students have low mathematics problem-solving skill.

This study aims of this research to describe the value of learning devices based on the realistic mathematics education that are developed, the improved student ability to solve problem mathematically which is taught through learning devices based on realistic mathematics education developed, and the student's response to a learning device based on realistic mathematics education developed on a pharmaceutical program for 10^th grade vocational high school students. Developed learning tools consisting of the learning implement plan and the student's worksheet. This study uses development research with the model used is Plomp (Preliminary Research, Prototyping Phase, dan Assessment Phase). The research only did until the preliminary research covered the student's analysis. Based on a student's observation that a student's mathematical problem solving ability is low because the learning tools have not supported the students in improving the problem-solving ability, the learning tools that teachers use are not in accordance with the student's skill program, only a few teachers present problems reading for practicing the mathematical skills of students. The instrument used in this research is the validity test sheet, practical test sheet, and problem solving ability test.

The aims from this study observe at the effect of using the RME approach with the TANDUR design on students' ability to understand concepts and solve problems in Mathematics in SMP Negeri 1 Pantai Cermin both to the students who had high previous knowledge and those who had low previous knowledge. This was a quasi-experimental research. Samples are choose using randomized sample. Data are analysed using t-test, Mann Whitney test and two Ways Anova using MINITAB software. The result of data analysis showed that: (1) the application of RME with TANDUR can improve students' MPS skills and still need to improve their ability to understand concepts, (4) there was no interaction between learning approaches and previous knowledge toward the eighth grade students.

This research is motivated by the low ability of students to communicate mathematical ideas, compile mathematical evidence using complete sentences, symbols, tables, and diagrams, to clarify the existing problems. This study aims to find out how the initial mathematical communication skills of students in learning mathematics, namely by giving mathematical problems related to the daily lives of students of grade VIII SMP. Problems are constructed based on indicators of communication ability and then assessed using the scoring rubric mathematical communication skills. The instrument used in the form of a preliminary test with 2 item and a sample of as many as 21 students. The results of the scoring rubric of students' mathematical communication skills obtained in indicator 1 were 23.81%, indicator 2 was 28.57%, indicator 3 was 38.11% and indicator 4 was 14.28%. If seen from the overall results of the initial test students only get 14.28% who is able to explain with the idea of dramatic communication. The results of this initial test study was 42.85%. It indicate the need for follow-up to improve students' communication skills.

This study aims to describe the errors of student in solving ordinary differential equation (ODE) problems based on SOLO taxonomy. In this case there are 5 kinds of errors, namely concept errors, using data, language interpretation, technical, and making conclusions. This descriptive study involved 10 ODE research subjects. The research results obtained are the subjects of research tends to make mistakes in the five SOLO taxonomy errors. The reason is because students are not skilled in using formulas, are not thorough, and the habit of not repeating lessons.

A good learning devices will deliver students to have good mathematical problem solving skills. This type of research was a descriptive research by qualitative approach. The initial observation was aimed at finding out, reviewing and explaining problem-solving ability of high school students in mathematics learning and condition of learning devices used and developed by teachers, then whether it was necessary to continue research development based on realistic mathematics education to improve the mathematical problem solving ability. The results of observations at SMAN 14 Padang and SMAN 15 Padang, can be concluded that the learning devices used do not link to real life problem that the instructional becomes meaningless. Learning devices used were still general and have not been able to facilitate the students to find their own concepts and did not help the students to improve problem solving ability. An approach that can accommodate it is a realistic mathematics education. The result needed to follow-up in form of research on development of realistic mathematics education based learning devices to improve the mathematical problem solving ability of senior high school students.

A problem-based mathematic learning model with high validity, practicality, and effectiveness is produced to improve students' competence. The stages on developing it consist of 1) preliminary stage, 2) proto-type stage including planning, evaluation, and revision, 3) product assessment stage. The mathematic learning model based on problem was tested to the college students of PGSD Department of FKIP, Bung Hatta University involving 30 students and 3 mathematic lecturers. The instrument used in this study consisted of 1) instrument of validity appraisal, component of learning model and toolkit, 2) instrument of practicality appraisal from students and lecturers, 3) effectiveness instrument covering test result and students' appreciation appraisal toward problem-based mathematic learning model. The result showed that problem-based mathematic learning model including syntax/learning steps, along with learning tools in term of semester learning plan and students' worksheet was considered valid, practical, and effective.

This research based on reality because it is found in the research fields that a study of the learning has already been worked optimally, but the results of learning are still gained some lower minimum achievement criteria In student's activities they do not want to ask and express their ideas or opinions, even though they often get some difficulties to solve their problems are about the expressing of learning. Teachers have low competencies in using their skill usages for learning methods, and the textbooks of the study which are not used to facilitate in the concept meanings from the materials are being learned. When they described it to their students, they will also feel the poor relation for the reality and also daily student lives. The products are gained from this research, such as, the HLT, the teachers' books and the students' books. That each of them They use the Plomp developed model which consists of the initial investigation phases, the prototype making and pointing phase, both of them make a discussion of the study development in this research. This is as an introduction phase. The purpose of this research wants to produce the design learning development as a set topic base on the problem based learning on the 7th at SMPN l VII Koto Sungai Sarik is validly, practically, and associatively. The data is obtained this initial stage and used to design the HLT, the teachers' and student's worksheet

This study is development of mathematical learning devices based on Realistic Mathematics Education (RME) in the chemical engineering expertise program in students in class XI senior vocational schools that supports valid, practical and effective problem-solving skills. This research is development research. The method used in the research is the method of developing Plomp with stages: (1) preliminary research (initial research), (2) prototyping phase (development stage), and (3) assessment phase (assessment phase). The product is a learning device. Learning tools developed include: (1) Lesson plan and (2) Student Worksheets. (1) analyzing the needs, (2) the draft development process, (3) drafting the development, (4) expert reviews and trials carried out in several stages namely (a) expert review and learning media experts, (b) analysis and revision I, (c) expert review of learning design, (d) analysis and revision II, (e) individual trials and small group trials, (f) analysis and revision III, (g) field trials: class and teacher, (h) analysis and revision IV, and (i) end product development results.

The aims of this research was to produce the learning devices based ona valid Problembased learning (PBL) to improve the students' problemsolving ability They are lesson plan and students' worksheet. for grade VII SMP. PBL aims to involve students in solving problems using real-world problems as a context for students to learn through problem solving ability. Learning devices using a PLOMP Model consist of three stages: the preliminary investigation phase, the development phase and the evaluation phase. Learning devices are said to be valid if they meet the validity of content and construction. The result of research known that instrument used is a validation sheet containing the presentation aspects, content worthiness and material, graphic and language. Expert validation results show that learning devices meet valid criteria.

Objective of this study is to increase students' critical thinking skills through geometry instructional device based on Van Hiele's theory. Instructional devices developed include lesson plans and student worksheet based on Van Hiele's theory. The stages of instructional are integrated with the stages of learning Van Hiele's theory which consists of five stages, namely information, direction orientation, explication, free orientation, and integration. The development model used is adapted from the Plomp model which consists of three phases, namely the initial investigation phase, the prototype development phase, and the assessment phase. The subjects of this study were grade VIII students of SMP 13 Padang. The results of the research obtained showed an increase in indicators of mathematical critical thinking abilities of students using geometry instructional devices based on Van Hiele's theory.

This study aims to produce cooperative learning tools based on blended learning that meets the validity criteria. The development research used Plomp model which consists of three phases namely the initial preliminary phase, the prototyping phase, and the assessment phase. The subjects of this study were 10th-grade Islamic senior high school student of KMM Kauman Padangpanjang. The validation sheet conducted by three mathematical education experts, one educational technologiest expert and one Indonesian language expert. Based on these results we conclud that instruments of the cooperative mathematics learning model based on blended learning is valid.

Mathematics is a subject that requires the students to gain reasoning abilities. Reasoning ability can be found when students learn geometry material. However, several studies concluded that geometry material is one of the difficult material for students. Difficulty of geometry is caused by the majority of mathematics teachers still use conventional media and teaching instruments in learning, especially in term of constructing the space. This is implemented on the AR-Geometry Interactive Book. This book is designed by using the principle of interactive 3D (three-dimensional) appearance by utilizing Augmented Reality (AR) based technology. This research uses a combination of qualitative and quantitative methods. The first qualitative data was taken by depth interviews to 4 informants selected with certain conditions using purposive sampling technique. The first phase of data collection aims to explore the information related to student interest in using the AR-Geometry Interactive Book. Furthermore, the second stage data was taken using a questionnaire to 21students in class VIII of SMPN 4 Ujung Batu. The second stage of data collection aims to support the results of the first phase of the research, all data in the second stage were then analyzed descriptively using quantitative analysis tools. Overall, the results of the second analysis indicate that the AR Geometry Book is appropriate to use in learning. To see students' mathematical reasoning abilities, tests were conducted by testing 3 essay questions. The results of the study prove that the use of AR-Geometry Interactive can improve students' mathematical reasoning abilities.

The research that has been overshadowed in which teaching materials used by students are not all of the material in accordance with the KD. So that the material presented elusive student and as a result students awaiting an explanation by the teacher. Therefore, to create students who are active in learning, students can build their own thoughts or develop his own knowledge is to improve students' reasoning skills learning concept. To improve reasoning skills students need learning tools that make the students can learn and be independent in constructing ideas. And with the development of mathematical learning prangkat based constructivist approach, students can become more active, independent and able to build the knowledge gained.

The goals of this study is to produce the learning tools of mathematics with a valid, practical and effective CTL approach. The developed learning tool consist of a lesson plan and a student worksheet. The development model used in this study is the Plomp model (preliminary research, prototyping phase, and assessment phase). The device created is used to improve understanding of concepts and mathematical problem solving for elementary school students. The instruments used were validation sheets, teacher, and student response questionnaires and mathematics learning achievement tests. Learning devices are said to be valid if they meet the content and construct validity. Practicality seen from the ease of use of the device. The effectiveness of the device seen from the percentage of students' completeness of the test at least 70%. The results of the experts' validation show that the learning device meets the valid criteria. Practicality reaches very practical criteria based on the questionnaire responses of teachers and students. The percentage of students' completeness tests is 75%.

A learning trajectory (LT) for teaching the least common multiple (LCM) and the greatest common factor (GCF) using realistic mathematics education (RME) approach was developed to improve the students' mathematical reasoning abilities. The cycle of design research namely preparing for the experiment, conducting the experiment, and retrospective analysis were applied in the development processes. The subjects of the research were 26 fifth grade students at a primary school in Padang, Indonesia. The method of data collection were videotaping, interviews, observations, and analysing the students' worksheets. The validity and practicality of the LT were evaluated trough expert judgements, one-to-one and small group try out, and field test. The results show that the LT reached the criteria of validity as it fulfilled the state of the art and characteristics of RME. The LT also worked as intended in which the students could reinvent the concepts of the LCM and the GCF by themselves after solving a series of the contextual problems provided in the LT. It indicated that the LT satisfied the criteria of practicality. Finally, we discovered that the LT effective in improving the reasoning abilities of the students.

The research aimed to develop learning trajectory (LT) to teach the topic of integer division based on Realistic Mathematics Education (RME) which is valid, practical and effective through research on the development of Gravemeijer & Cobb types. The trial subjects were the third-grade of elementary school students in Padang. The research was supported by data collection techniques in the form of document analysis, observation, interviews, questionnaires, and tests. Data analysis was performed using descriptive statistics and parametric statistics. The results showed that the LT developed to teach the topic of integer division using RME helped the teacher in learning. LT describes the characteristics of RME and facilitates students in a class. Besides, LT can help students to find integer division algorithms. Students are more confident in using their strategies for solving the contextual problems so that students' mathematical problem-solving abilities also develop.

The purpose of this study was to describe the process and results of the development of 21st century learning tools based math problem based learning to improve high-order mathematical thinking students' in senior high school Padang city and describe the quality of math learning tools of the 21st century based on problem based learning to improve the aspect of validity, practicality. The methods of study is a research development that is used to develop a software product math learning 21st century form of RPP and LKPD integrating 4 C which was adapted from the model Plomp. (Plomp and Nieveen, 2013: 30). Subjects tested in this study were class X SMA Padang. The data collection instrument were the sheet analysis, field notes, interview, questionnaire, and test results of learning. Data were analyzed using descriptive analysis that describes the validity and practicality of learning tools are developed. This research data analysis technique used is based on a questionnaire filled by experts then analyzed for the validity of the resulting product. Analysis of the validity of using a Likert scale. The results of the validation of the validator indicates that the device is a valid PBL based learning and practical with some characteristics such as learning devices produced have been adapted to the characteristics of Problem Based Learning (PBL). RPP and LKPD designed as a guideline for teachers in implementing the learning process is valid and practical.