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Journal of Mathematics and Mathematics Education (JMME)
Published by Universitas Sebelas Maret
ISSN : 20898878     EISSN : 27158276     DOI : https://dx.doi.org/10.20961/jmme
Core Subject : Education,
Education Mathematics
Journal Mathematics and Mathematics Education (JMME) is a peer-refereed open-access journal which has been established for the dissemination of state-of-the-art knowledge in the field of mathematics and mathematics education. This journal was founded by the Magister of Mathematics Education, Universitas Sebelas Maret. It is published twice in a year (June and December). The JMME welcomes high-quality manuscripts resulted by researchers, scholars, teachers, and professionals from a research project in the scope of Pure Mathematics, Computing Mathematics, Statistics, Mathematics Learning, Evaluation and Assessment in Mathematics Learning, STEAM, Ethnomathematics, ICT in Mathematics Education, Design / Development Research in Mathematics Education
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 131 Documents
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DIMENSI METRIK LOKAL PADA GRAF ANTIPRISMA DAN GRAF SUN Silfiatul Khoiriah; Tri Atmojo Kusmayadi
Journal of Mathematics and Mathematics Education Vol 8, No 1 (2018): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v8i1.25816

Abstract

Abstract: For example G is a connected and nontrivial graph. The distance between two vertices u and v in G is the shortest path length between vertex u and v which is denoted by d (u, v). For an ordered set of of n vertex and v is a vertex in G, then the representation of vertex v to W is an ordered pair Set W is called as local distinguishing if for each pair of vertex u and v is adjacent to G. Local distinguishing set W with minimum cardinality is called as local metric base and the number of vertex on the local metric base of graph G is called as local metric dimension which is denoted by . In this study, the local metric dimension is determined on antiprism An graph and sun Sn graph. The results reveal that local metric dimension of antiprism graph is  for . Local metric dimension of sun graph is  for even n and  for odd n.Keywords: local metric dimension, antiprism graph, sun graph, local distinguishing set.
EKSPERIMENTASI MODEL PEMBELAJARAN PBL, JIGSAW DAN STAD TERHADAP PEMAHAMAN KONSEP DAN PEMECAHAN MASALAH MATEMATIKA DITINJAU DARI ADVERSITY QUOTIENT (AQ) SISWA Lia Ariati; Budiyono Budiyono; Dewi Retno Sari Saputro
Journal of Mathematics and Mathematics Education Vol 6, No 2 (2016): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v6i2.10052

Abstract

Abstract: The aim of this research was to know the effect of the Problem Based Learning (PBL), Jigsaw, and Students Teams Achievement Divisions (STAD) to the mathematics conceptual understanding and problem solving viewed from students Adversity Quotient (AQ). The type of this research was quasi-experimental with factorial design 3x3. The population was all the students of grade XI IPS SMA/MA in Wonogiri on the second semester of 2014/2015 academic year. The sample of this research consisted of 224 students. The instruments that used to collect the data were early ability test, conceptual understanding test, problem solving test, and questionnaires Adversity Quotient of students. Data were analyzed using unbalanced two ways multivariate analysis of variance with a significance level α = 5%. The results of the research were as follows. (1)Students who were subjected to the PBL learning model have a better conceptual understanding than with the learning model of Jigsaw and STAD while students were subjected to the learning model of Jigsaw have a better conceptual understanding than with the learning model of STAD. (b) Students who were subjected to the PBL learning model have the same problem solving as students with the learning model of Jigsaw but it have better than with the learning model of STAD while students with Jigsaw learning models have the same problem solving as students with learning model of STAD (2)Students with high AQ have better conceptual understanding and problem solving than students with medium and low AQ, and the students with medium AQ were better than low AQ. (3)(a) In learning model of PBL and Jigsaw, students with high AQ have the same conceptual understanding as medium AQ but better than low AQ, and students with medium AQ have a better conceptual understanding than low AQ while in learning model of STAD, students with high AQ have a better conceptual understanding than students with medium and low AQ, and the students with medium AQ were better than low AQ. (b) In learning model of PBL, Jigsaw and STAD, students who have high AQ have better problem solving than students who have students with medium and low AQ, and students with medium AQ have a better problem solving than students with low AQ. (4)(a) For high and low AQ, students were subjected to the PBL learning model have the same conceptual understanding as students who were subjected to the learning model of Jigsaw and STAD while for medium AQ, students who were subjected to the learning model of PBL have the same conceptual understanding as students who were subjected to the learning model Jigsaw but better than STAD and students who were subjected to the learning model of Jigsaw have a better conceptual understanding than students who were subjected to the learning model of STAD. (b) In each AQ, students with the PBL learning model have the same problem solving as students with Jigsaw learning model but better than STAD learning model, and students with Jigsaw learning model have a better problem solving than students of  STAD learning model.Keywords : PBL, Jigsaw, STAD, AQ, conceptual understanding, problem solving. 
EKSPERIMENTASI MODEL PEMBELAJARAN KOOPERATIF TIPE TEAMS GAMES TOURNAMENT DENGAN PETA KONSEP PADA POKOK BAHASAN TRIGONOMETRI DITINJAU DARI EMOTIONAL SPIRITUAL QUOTIENT DAN KONSEP DIRI SISWA SMA/MA KELAS XI IPA SE-KABUPATEN BANYUMAS Nastiti Rahayu; Budi Usodo; Mardiyana Mardiyana
Journal of Mathematics and Mathematics Education Vol 4, No 1 (2014): Journal of Mathematics and Mathematics Education
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v4i1.9998

Abstract

Abstract: This research was conducted to find out: (1) which produces better mathematics achievement: students who were given TGT cooperative learning with mind mapping, TGT cooperative learning, or conventional learning; students who have high emotional spiritual intelligence or low one; students who have a positive or negative self-concept. and (2) which is better, the mathematics achievement of students in each category of spiritual emotional intelligence (high or low) and the category of self-concept (positive or negative) on the TGT with mind mapping, TGT cooperative learning, and conventional learning. This study used a quasi-experimental study with a factorial design 3x2x2. The population in this study were all students of Science Second Grade Students of senior high schools in Banyumas Regency in the Academic Year of 2012/2013. The hypothesis test used three-way analysis of variance with unbalanced cell. Based on the analysis, we concluded as follows. (1) The mathematics achievement of students given TGT learning model with mind mapping was better than students given TGT learning model and the conventional model of learning. However, there was no difference in achievement between students given TGT learning models with conventional learning model; there was no difference in mathematics achievement of students with high emotional spiritual intelligence with students with low emotional spiritual intelligence; the mathematics achievement of students with positive self-concepts better than students with a negative self-concept. (2) In every model of learning, students with high emotional spiritual intelligence always provide a better learning achievement than students with low emotional spiritual intelligence. In the learning model TGT with mind mapping, students with a positive self-concept provided better mathematics achievement than students with a negative self-concept, while in the TGT and conventional learning model, there was no difference in achievement between students with a positive self-concept and students with negative self-concept.Key words: Mathematics Learning Achievement, TGT, Mind Mapping, ESQ, Self Concept
EKSPERIMENTASI MODEL PEMBELAJARAN MISSOURI MATHEMATICS PROJECT (MMP) TERMODIFIKASI DITINJAU DARI KEMAMPUAN SPASIAL SISWA KELAS X SMA NEGERI KOTA SURAKARTA Santosa Santosa
Journal of Mathematics and Mathematics Education Vol 2, No 2 (2012): Journal of Mathematics and Mathematics Education
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v2i2.9966

Abstract

Abstract This research is aimed: (1) To know which model among the MMP modified model, MMP model and the conventional model that produces a better student achievement. (2). To know which students who have better learning achievement among those who have high spatial ability, medium and low. (3). To know which model that produces better student achievement, the MMP modified modeI, MMP model or conventional model at each level of students’s spatial abilities.This is a quasi-experimental research design with a factorial 3 x 3. The research population is students of Grade X Senior High School Students Surakarta of the academic year 2010/2011. The sampling technique is a combination of studies stratified random sampling and cluster random sampling. The selected samples of this research are: (1). First experimental group consist of 99 student’s (34 students of X1 class of SMA Negeri 2 Surakarta, 33 students of X1 class of SMA Negeri 3 Surakarta and 32 students of X5 class of SMA Negeri 8 Surakarta; (2). Second experimental group consist of 100 student’s (34 students of X2 class of SMA Negeri 2 Surakarta, 34 students of X2 class of SMA Negeri 3 Surakarta and 32 students of X6 class of SMA Negeri 8 Surakarta; (3). Control group consist of 100 student’s (34 students of X3 class of SMA Negeri 2 Surakarta, 34 students of X3 class of SMA Negeri 3 Surakarta and 32 students of X7 class of SMA Negeri 8 Surakarta.The instrument used for data collection is the preliminary ability tests, achievement tests and ability tests of spatial learning of students in the form of multiple choice. Before the test instruments are used, they are being tried out first. For preliminary ability and achievement test, the validity, reliability (used KR-20 test) and difference and difficulty level tests are tried out. While the instruments of spatial ability tests are taken from standardized tests so they do not need any try out. Before conducting the research first tested using a one-way Analysis of Variants with an unequal cell. Hypothesis of the research were tested by using a two-way Analysis of Variants with an unequal cell at the significance level of 5%. Previously, it is prerequisites tested, namely: normality test using the test Lilliefors and homogeneity test using Bartlett's test.The conclusion of this research are: (1) The MMP modified learning model produce student achievement better than the MMP learning model and the conventional learning model, and the MMP learning model produces a better student achievement  than conventional model; (2) The students who have high spatial ability are having better academic achievement than students who have medium and low spatial abilities, and students who have medium spatial abilities are having better academic achievement than students of low spatial ability; (3) On the students who have high spatial ability, the MMP modified learning model, the MMP learning model and conventional learning model produce similar student achievement. While the students who have medium and low spatial ability, the MMP learning modified model produce student achievement better than the MMP learning model and conventional learning model, and the MMP learning model produces student achievement better than the conventional learning model. Keywords: Learning Model, Missouri Mathematics Project, Spatial Ability. 
Mathematics Learning Practice Training with the "MiKIR" Approach to Improve Analysis and Algebra Reasoning Abilities in Mathematics MGMP SMP Sragen Ikrar Pramudya; Mardiyana Mardiyana; Sutrima Sutrima; Ponco Sujatmiko; Dyah Ratri Aryuna
Journal of Mathematics and Mathematics Education Vol 10, No 2 (2020): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v10i2.47076

Abstract

The curriculum currently applied at the junior high school level is Curriculum 2013. This curriculum focuses on student learning activities. In a sense, knowledge must be actively built by students themselves. This paradigm has been known for a long time. At least since the introduction of the concept of active student learning in 1984 by Professor Dr. Conny R. Semiawan. However, in reality the teaching and learning process that occurs is that the teacher remains the center of attention when the teaching and learning process takes place in the classroom. In other words, those who are active in learning are still teachers and students sitting quietly listening to the teacher's explanation. The challenge is whether mathematics teachers are willing and brave to change the mindset from "teacher as a learning center" to "students as a learning center". To create a teaching and learning process with "students as the learning center", of course, it must be started from the making of the learning design to the practice of its application in the learning process in the classroom. In line with these wishes and intentions, this service activity answered by providing "Training and Assistance in Mathematics Learning Practices with the" MiKIR "Approach to Improve Analytical and Algebraic Reasoning Ability for mathematics teachers who are members of the Mathematics MGMP SMP Sragen Regency. In this case, the "MiKIR" approach is interpreted as a learning approach which, when applied in a teaching and learning process, occurs in students’ situations and conditions: experiencing, interaction, communication, and reflection both between students and students and students and teachers and that means "Students as a learning center". 
MODUL τ[M]-INJEKTIVE Suprapto Suprapto; Sri Wahyuni; Indah Emilia Wijayanti; Irawati Irawati
Journal of Mathematics and Mathematics Education Vol 1, No 2 (2011): Journal of Mathematics and Mathematics Education
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v1i2.9934

Abstract

Abstract Let  R be a ring with unit and let  N be a left R-module. Then N is said linearly independent to  R (or N is R-linearly independent) if there is monomorphisma  By the definition of R-linearly independent, we may be able to generalize linearly independent relative to the R-module M. Module N is said M-linearly independent if there is monomorphisma .The module Q is said M-sublinearly independent if Q is a factor module of modules which is  M-linearly independent. The set of modules M-sublinearly independent denoted by  Can be shown easily that  is a subcategory of the category R-Mod. Also it can be shown that the submodules, factor modules and external direct sum of modules in  is also in the .The module Q is called P-injective if for any morphisma Q defined on L submodules of P can be extended to morphisma Q with , where  is the natural inclusion mapping. The module Q is called -injective if Q is P-injective, for all modules P in .In this paper, we studiet the properties and characterization of -injective. Trait among others that the direct summand of a module that is -injective also -injective. A module is -injective if and only if the direct product of these modules also are -injective. Key words : Q ()-projective, P ()-injective.
PEMODELAN KADAR AIR PADA SIFAT FISIK STABILISASI TANAH GAMBUT Mohammad Syaiful Pradana; Awawin Mustana Rohmah
Journal of Mathematics and Mathematics Education Vol 8, No 1 (2018): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v8i1.25826

Abstract

Abstract: Peat soil is an organic soil with very low carrying capacity and high compressibility. The condition is less profitable for civil engineers in building a civil foundation foundation. One method of peat soil improvement can be done with astabilization method that more environment-friendly and cheaper than other methods. Laboratory based peat stabilization studies to increase carrying capacity, reduce compression and improve peat soil physical properties have been conducted in Indonesia. The results of laboratory studies shown in the graph are still limited by time and content of the mixture. Therefore, further research is needed on the mathematical model toward the physical properties of peat soil stabilization. In this research will be formulated mathematical model of water content on the physical properties of peat soil stabilization. The model is derived from the fluid equation through porous media based on the principle of continum and controlvolume. The model is then resolved numerically by different method until MacCormack scheme with two steps are predictor step using forward difference and correctorstep using backward difference. The MacCormack scheme has the advantage of solving fluid flow equations and continuity. The model is then simulated and validated by comparing the simulation results with the real system. From the simulation results obtained the water content gradually decreased, the decrease is almost close to zero. In addition, it can be seen the difference in decrease in moisture content at each test point although in small quantities.Keywords:Moisture Content, MacCormack, Peat Soil Stabilization.
EKSPERIMENTASI MODEL PEMBELAJARAN TEAM ASSISTED INDIVIDUALIZATION (TAI), PROBLEM BASED LEARNING (PBL) DAN PEMBELAJARAN KLASIKAL DENGAN PENDEKATAN SAINTIFIK PADA MATERI BENTUK ALJABAR DITINJAU DARI AKTIVITAS BELAJAR SISWA Suprapto Suprapto; Mardiyana Mardiyana; Dewi Retno Sari Saputro
Journal of Mathematics and Mathematics Education Vol 6, No 2 (2016): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v6i2.10062

Abstract

Abstract: The aim of the research was to determine the effect of learning models on mathematics achievement viewed from student’s leraning activity. The learning models compared were TAI with scientific approach, PBL with scientific approach, and classical with scientific approach.This experiment was quasi-experimental. It uses 3 x 3 factorial planning. The population was the entire 8th grade students of State Junior high School in Grobogan regency in the academic year 2014/2015. The sampling technique used was stratified cluster random sampling. The sample consisted of students of SMP N 2 Tegowanu, SMP N 3 Godong and SMP N 5 Purwodadi. Data collection instruments used were learning achievement test and student learning activity questionnaire. Hypothesis examination used was variance analysis (anava) with unequal cell.Conclusions acquired from this thesis are as follows: 1) PBL using scientific approach gives better mathematics learning achievement compared to TAI and classical Learning, TAI using scientific approach gives better mathematics learning achievement compared to classical learning. 2) student’s mathematics achievement with high learning activity is better than those with intermediate and poor learning activity, intermediate learning activity is better than those with poor learning activity. 3) on TAI using scientific approach, student’s mathematics achievement with high learning activity is as good as those with intermediate learning activity, high learning activity is better than those with poor learning activity, and intermediate learning activity is good as those with poor learning activity. Students which is given PBL using scientific approach, students with high learning activity have mathematics learning achievement as good as those with intermediate learning activity, high learning activity is better than those with poor learning activity, and intermediate learning activity is good as those with poor learning activity. 4) for students with high learning activity, PBL gives learning achievement as good as TAI, PBL gives learning achievement better than classical learning, and TAI gives learning achievement better than classical learning. For students with intermediate learning activity; TAI, PBL and classical learning gives the same good result. For students with poor learning activity; TAI, PBL and classical learning gives the same good result on student’s learning achievement. And student’s learning achievement on algebra which is given PBL is as good as those which is given classical learning.Keywords: TAI using scientific approach, PBL using scientific approach, classical learning, learning activity, learning achievement 
EKSPERIMENTASI MODEL PEMBELAJARAN KOOPERATIF TIPE TEAM ASSISTED INDIVIDUALIZATION DENGAN SCAFFOLDING BERBASIS MODUL PADA MATERI GEOMETRIDIMENSI TIGA DITINJAUDARI KEMANDIRIAN BELAJAR SISWA SMK KELAS XI DI KABUPATEN SRAGEN Hartono Hartono; Riyadi Riyadi; Imam Sujadi
Journal of Mathematics and Mathematics Education Vol 5, No 2 (2015): Journal of Mathematics and Mathematics Education
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v5i2.10030

Abstract

Abstract: The purposes of this research were to investigate: (1) which learning models of  Team Assisted Individualization learning model  with scaffolding based on  module (TAI-S), Team Assisted Individualization learning model (TAI), or direct learning model (DL) results in a better learning achievement in the material of three-dimensional geometry; (2) which independence category of student learning, high, medium or low results in a better learning achievement on the material of three-dimensional geometry;  (3) in each category of student learning independence, which  learning models of the TAI-S, TAI, or DL model results in better  learning achievement  on the material of  three-dimensional geometry. This research used the quasi experimental method with the factorial design of 3x3. Its population was all the students in Grade XI of Vocational High Schools in Sragen regency. The samples of the research were taken by using the stratified random sampling technique. The data of the research were gathered through documentation, questionnaire, and test. The documentation was employed to investigate the scores of semester test in Mathematics of the students in Semester 1, Academic Year 2012/2013, and was used for balance test among the classes exposed to the TAI-S, TAI, and DL models. The questionnaire was used to find out the independence category of student learning. The test was used to know the students learning achievement in Mathematics with material of three-dimensional geometry. The data of the research were analyzed by using the unbalanced two-way analysis of variance at the significance level of 5%. The results of the research are as follows: (1) the TAI-S learning model result in a better learning achievement than both the TAI and DL models. There are no any differences in the learning achievement of the students with the TAI learning  model and DL model. (2) the students with the high independence category result in better learning achievement than students with medium and low independence category. The students with medium independence category result in better learning achievement than students in low independence category (3) in each category of student learning independence, based on  the material of  three-dimensional geometry, the TAI-S learning model, TAI learning  model and DL  model do not have correlation between one and another.Keywords : TAI-S learning model, TAI learning model,     DL    learning.   Three Dimensional Geometry, Learning  Independence.
PROSES BERPIKIR REFLEKTIF SISWA KELAS X MAN NGAWI DALAM PEMECAHAN MASALAH BERDASARKAN LANGKAH KRULIK DAN RUDNICK DITINJAU DARI KEMAMPUAN AWAL MATEMATIKA Ulfa Masamah; Imam Sujadi; Riyadi Riyadi
Journal of Mathematics and Mathematics Education Vol 5, No 1 (2015): Journal of Mathematics and Mathematics Education
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v5i1.10008

Abstract

 Abstract: The aim of this research was to describe reflective thinking process of 10th grade MAN Ngawi students with different initial mathematics capability (high, normal, low) in solving problems based on Krulik and Rudnick steps. This research was a kind of qualitative research on a case study. The collecting data in this study used task-based on interview method. The analyzed of the data in this study did with reducing the data, presenting the data, and conclusing the data. The results of this research were: 1) on reading and thinking step, students with normal and low initial mathematics capability convince what they read and thought correctly by reading repeatedly. Students with high initial mathematics capability did it by reading and understanding each question sentences repeatedly; 2) on exploring and planing step, selecting and considering information, both students with high and normal initial mathematics capability did these steps by information identification and analysis of main problems and conditions; to convince that initial problem solving planning was right, they did it by organizing problem and deciding the initial steps planned; 3) on selecting a strategy step, to consider confidently the problem solving step based on information obtained, students with high initial mathematics capability did the step by exploring initial problem solving strategy and using representation result by trial-error and guessing test, concerning problem solving pattern, and recheck every step done. Students with normal initial capability did it by exploring initial problem solving strategy and using representation result by trial-error step, making proper initial plan by question stimulation. 4) on finding an answer step, to understand each steps based on selected problem solving strategy, both students with high and normal initial mathematics capability did it by (a) ascertain formula that used for the area of that shapes, triangle area if known two sides which flank an angle, and comparing trigonometry on special angle correctly (students with normal capability used question stimuly); (b) trying repeatedly using selected patterns and recheck every step and calculation done; and (c) aware of each mistakes (computation, formula, way, and writing) and fixed them (students with normal capability needed question stimuly and wrong answering strategy). Student with high initial capability combined the process by paying attention and rechecking every steps and calculation by step back process. 5) on reflecting and extending step, to considering results and problems, students with high initial mathematics capability did it by reflection to get solution and rechecking by verification process. Students with normal capability did it by rechecking and looking back the problem and result obtained. In every steps, students with high initial mathematics capability always used intuition and self-questioning to convince the step done. 10th grade MAN Ngawi students with low initial mathematics capability did not use reflective thinking in problem solving based on Krulik and Rudnick.Keywords: Process, reflective thinking, problem solving, and initial mathematics capability.

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