This study aims to describe enhancement and achievement of mathematical critical thinking skills of students who received the 5E Learning Cycle with Metacognitive technique, the 5E Learning Cycle, and conventional learning. This study use experimental method with pretest-posttest control group design. Population are junior high school students in Indramayu city, Indonesia. Sample are three classes of eighth grade students from high level school and three classes from medium level school. The study reveal that in terms of overall, mathematical critical thinking skills enhancement and achievement of students who received the 5E Learning Cycle with Metacognitive technique is better than students who received the 5E Learning Cycle and conventional learning. Mathematical critical thinking skills of students who received the 5E Learning Cycle is better than students who received conventional learning. There is no interaction effect between learning model and school level toward enhancement and achievement of students’ mathematical critical thinking skills.

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Using the 5E Learning Cycle with Metacognitive Technique to Enhance Students’ Mathematical Critical Thinking Skills

This study aims to describe the enhancement and achievement of students’ critical thinking skills in mathematics (CTSM) as a result of 5E Learning Cycle with Metacognitive Techniques (LCM), Learning Cycle (LC) and Conventional Learning (CL) implementation is measured entirely and based on student’s Mathematical Prior Ability (MPA). This research used a quasi-experimental design with pretest-posttest control group. The population of the research is Junior High School students in Indramayu City, West Java Province, Indonesia. The sample is eighth grade students from two school levels classified as high and medium levels, amounted to 173 students. Three classes were randomly selected from each school, one class received LCM, one class received LC, and the other class received CL. The instruments consisted of CTSM tests, MPA test, and observation sheet. The study revealed that in terms of overall, the enhancement and achievement of students’ CTSM who received LCM is better than those who received LC and CL. Likewise the achievement of students’ CTSM who received LC is better than those who received CL. The enhancement and the achievement of LCM group students’ critical thinking skills is 0.62 and 27.30 while the LC group is 0.49 and 22.84, and the CL group is 0.34 and 17.80. There is an interaction effect between learning model and MPA towards enhancement of students’ CTSM. However descriptively, there is no interaction effect between learning model and MPA towards achievement of students’ CTSM. Keywords—critical thinking skills in mathematics; 5E Learning Cycle model; Metacognitive techniques

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The Enhancement of Students' Critical Thinking Skills in Mathematics through The 5E Learning Cycle with Metacognitive Technique

Symbol sense is crucial in the understanding of mathematical problems comprising various symbols. The misuses of symbols happen due to misinterpretation, which is considered the constraint to learn algebra more comprehensively, including in linear programming. The term ‘metaphor’ is defined as a means to carry over symbol sense, and is used to improve mathematical understanding. This present research was aimed at analyzing errors on mathematical symbol as a metaphor in linear programming. This research was conducted by means of descriptive qualitative design, with a test and interview as the instruments. The test was made essay, and its results were analyzed qualitatively. The test, further, was administered to five eleventh graders selected according to highest rates of errors committed. This research has shown that the students committed a number of errors in some cases, such as representing symbols as variables, representing numbers, and interpreting symbols as relational operators. In addition, errors which the students committed in constructing mathematical models covered defining the final value, representing numbers, applying inequality system, and interpreting symbols as operation counts. This present research has provided some ways for symbol sense, and thus the errors on mathematical symbol as a metaphor could be lessened. Next, this research can be further followed up by reviewing the effectiveness of remedial instruction according to the committed errors on mathematical symbols.

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An Analysis of Errors on Mathematical Symbol as a Metaphor in Linear Programming

Tujuan penelitian ini adalah (1) menguji kualitas Inductive Discovery Learning terhadap kemampuan representasi matematis peserta didik, (2) menganalisis kemampuan representasi matematis ditinjau dari self efficacy peserta didik pada Inductive Discovery Learning. Penelitian ini merupakan penelitian kombinasi (mixed method) tipe concurrent embedded, dimana metode penelitian kualitatif lebih ditekankan. Populasi dalam penelitian ini adalah seluruh peserta didik kelas VII SMP Islam Sultan Agung 4 Semarang. Sampel penelitian adalah dua dari lima kelas yang ada pada kelas VII (dipilih kelas eksperimen dan kelas kontrol). Pada kelas eksperimen dilakukan pengkategorian ditinjau dari self efficacy masing-masing peserta didik (self efficacy tinggi, sedang, dan rendah). Setiap kategori self efficacy diambil dua peserta didik untuk dijadikan subjek penelitian kualitatif. Pengumpulan data dilakukan melalui (1) pengumpulan data kuantitatif dengan tes dan kuesioner, (2) pengumpulan data kualitatif dengan wawancara dan dokumentasi. Hasil penelitian menunjukkan: (1) tahap perencanaan pembelajaran dinyatakan dalam kategori baik dari perolehan skor penilaian perangkat pembelajaran 3,954; tahap pelaksanaan pembelajaran dinyatakan dalam kategori baik dari perolehan rata-rata penilaian aktivitas guru 4,108; dan tahap penilaian menggunakan uji ketuntasan klasikal (lebih dari 75% dari seluruh peserta didik kelas eksperimen tuntas secara klasikal) dan uji beda rata-rata (t hitung > t tabel  dinyatakan rata-rata kemampuan kelas ekspeimen lebih dari rata-rata kemampuan representasi matematis kelas kontrol). Dari ketiga tahap tersebut dapat diperoleh kesimpulan kualitas pembelajaran melalui IDL terhadap kemampuan representasi peserta didik termasuk kategori baik, (2) Peserta didik dengan self efficacy tinggi dapat menggunakan semua indikator representasi matematis dengan maksimal dibandingkan dengan peserta didik dengan self efficacy sedang dan rendah.
The purpose of this study are (1) Inductive Discovery Learning quality of voice to the ability of mathematical representation of learners, (2) the ability to represent themselves from self-learning. This research is a combination research (mixed method) type of concurent embedded, where qualitative research method is more emphasized. The population in this research is all students of class VII Islamic Junior High School Sultan Agung 4 Semarang. The study sample is two of the five classes that exist in class VII (selected experimental class and control class). In the experimental class, categorization is done in terms of self efficacy of each learner (self efficacy is high, medium, and low). Each category of self-efficacy is taken by two students to be the subject of qualitative research. Data collection was conducted by (1) completion of quantitative data with tests and questionnaires, (2) completion of qualitative data with interviews and documentation. The results showed: (1) learning planning stage in good category of score assessment appraisal tool 3.954; Stage of learning implementation in the category of both average work average 4,108; And the assessment stage uses classical exhaustiveness test (more than 75% of all classical experiments class experiments are classical) and average difference test (t count = 15.92> t table = 1.675 average ability of expeimen class higher than average The ability of the mathematical representation of the control class). From the three stages can be obtained through the quality of learning through IDL to the ability of student representation including good category, (2) learners with high self efficacy can use all indicators of mathematical representation with the maximum compared with learners with moderate and low self efficacy.

Analisis Kemampuan Representasi Matematis Ditinjau dari Self Efficacy Peserta Didik melalui Inductive Discovery Learning

This research aims to: (1) knowing the positive influence of ethnomathematics-contained PBL model towards mathematical representation skill, (2) knowing the positive influence of mathematical disposition towards mathematical representation skill, and (3) knowing the positive influence of ethnomathematics-contained PBL model and mathematical disposition skill towards mathematical representation. This is a quantitative research. Four classes in fifth semester from Educational of Elementary School students of 2016/2017 became the population of this research. The sample in this research was Education of Elementary School 2 (two) as the experiment class, and class of Educational of Elementary School 1 (one) as the control class. As for data collection, the used of documentation, test, questionnaire, and observation technique was done to complete this research. The research analysis data was using SPSS 16, which is homogeneity test, normality test, simple regression test, and double regression test. The result showed that (1) there is positive influence of ethnomathematics-contained Problem Based Learning (PBI) model and mathematical disposition skill toward mathematical representation, (2) there is positive influence of mathematical disposition towards mathematical representation skill, (3) there is positive influence of Problem Based Learning (PBL) model and mathematical disposition skill toward mathematical representation.

https://ejournal.umm.ac.id/index.php/MEJ/article/download/4624/4778

The influence of ethnomathematics-contained problem based learning model and mathematical disposition skill toward mathematical representation

Abstrak Tujuan penelitian ini adalah untuk menghasilkan perangkat pembelajaran matema-tika yang valid, praktis dan pembelajaran yang efektif. Model pengembangan pemb-elajaran mengacu pada model Plomp. Hasil pengembangan perangkat pembelajaransebagaiberikut: (1)perangkat pembelajaranyangdikembangkan valid;silabus adalah4,32 (sangatbaik); RPPadalah 4,42 (sangatbaik); LKSadalah4,28 (sangat baik);bukusiswaadalah 4,32 (sangatbaik)); danTKBKadalah4,40 (sangatbaik);(2)perangkat pembelajaran dinyatakanpraktis,yaitu:a)kemampuangurumengelolakelas rata-ratanya4,10 (baik);danb)responsiswapositif denganrata-rata85,5%; (3) pembelajaran matematika dinyatakan efektif  yaitu: a) KBK siswa secaraindividu minimal mencapai kriteria 75, serta  proporsi siswa mendapatkan nilaiminimal KBKsama dengan 75 melebihi 75%; b) adanya pengaruh positif  disposisimatematis dan keterampilan berpikir kritis terhadap KBKsebesar 95,5%; c) berdasarkanuji banding KBK kelas LearningCycle5E dengan pendekatan Scientific lebihbaikdari pada kelas ekspositori;dan d) adanyapeningkatan disposisimatematissebesar0,47,keterampilanberpikirkritissebesar0,35dankemampuan berpikir kritis sebesar 0,47. Hasilpenelitianperangkat pembelajaran dengan LearningCycle 5Edengan pendekatan Scientifictelah valid dan terbukti praktis dan efektif. Abstract The purpose of  this study was to produce a valid mathematics learning equipment, practical,and to determine the effectiveness of  learning. The research that used is instructional developmentmodelwhichrefersto a Plomp’smodel. Theresultof learning equipment development asfollows: (1) learning equipment developed is valid: syllabus 4,32 (very good); RPP4,42 (verygood); LKS4, 28(very good); student books 4,32(very good); and TKBK 4,40 (very good);(2) learning tool use specified practice: a) ability to manage classroom teacheris an average4,10 (verygood), b) the positive student response to learning has an average 85,5%;(3) learningmathematicseffective:a) the proportionof students who learn a minimum value criticalthinking  abilities  equal by 75 by 75%; b) the existence of  a positive influence of  dispositionmathematics  and skill softhe critical thinking ability as large as 95,5%; c) class that learn use5E Learning Cycle Model with a Scientific Approach better than expository; and d) an increasinginthedisposition mathematics as 0,47,theskills of the critical thinking as 0,35 and theKBK formation proccess of  experimental class as 0,604. The results have a valid and provenpractical and effective.

Model learning cycle 5e dengan pendekatan scientific untuk meningkatkan disposisi matematis dan berpikir kritis

Abstrak Penelitian ini bertujuan untuk menghasilkan perangkat pembelajaran Penelitianini bertujuan menghasilkan perangkat pembelajaran matematika Model IKRARberpendekatan RME yang valid, praktis dan efektif. Model pengembangan mengacupada model Plomp. Hasil penelitian ini adalah: (1)perangkatpembelajaran yangdikembangkan valid: Silabus 3,99 (baik); RPP3,93 (baik); bukusiswa 3,86 (baik);LKS 3,84 (baik); dan TKRM 4,03 (sangat baik) untuk rentang 1-5; (2) Perangkatpembelajaran dinyatakan praktis: a) rata-rata kemampuan guru mengelola kelas4,27 (sangat baik) untuk rentang 1-5; danb)rata-rata respon siswa positif  83,64%;(3) Pembelajaran matematika dinyatakan efektif: a) rata-rata KRM kelas uji cobaperangkat lebih besar dari 70, proporsi siswa dengan nilai minimal 70 melebihi75%; b) KRM siswa kelas IKRAR dengan rata-rata sebesar 81,95 lebih baik daripada kelas ekspositori sebesar 68,91; c) KRM siswa dipengaruhi secara bersamasamaoleh kemandiriandanketerampilansebesar73,2%;d)peningkatan KRM kelasIKRARsebesar 0,62 (sedang).Dalam pembelajaan matematika, hendaknya gurumemperhatikankemampuanrepresentasimatematikasiswa,khususnya dalammerepresentasikansoaldari bentuk teksmenjadibentuksimbolmatematika. Abstract The purposeof  this studywas toproduce amathematics learning equipment is valid, practice,and effectiven. The research that used is instructional development model which refers toa Plomp’s model.Theresult of  learning equipment development as follows: (1) learningequipment developed isvalid: syllabusis 3,99 (good); RPPis3,93(good); student book is3,86 (good); LKSis3,84 (good); and testthe KRM is 4,03 (very good) for 1 to 5 scale; (2)learningtooluse specified practice, namely: a) abilityto manage classroom teacher is very goodhas an average 4,27, b) the positive student response to learning hasan average 83,64%;(3)learningmathematicseffective: a) KRM average grade test device is greater than 73, aswell as the proportion of  students who learn a minimum value equal by 70 by 75 %; b)the existence of  a positive influence of  independent learning and skill of  the matematicalrepresentationabilityas large as 81,95; c) class that learn use IKRAR Models better thanexpoxitory; and d) an increasing intheKRM formation proccess ofIKRAR class is 0,62(medium). In mathematics learning, teacher should pay attention to student’s mathematicalrepresentation ability, specialy to representate text form to mathematics symbol.

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Model learning cycle 5e dengan pendekatan scientific untuk meningkatkan disposisi matematis dan berpikir kritis

Pembelajaran matematika model ikrar berpendekatan rme untuk meningkatkan kemampuan representasi matematika