This research aims to analyze the difference effectiveness of learning model Realistic Mathematics Education (RME) and model learning problem based learning (PBL) to students' mathematical reasoning skills. The design of this research is quasi experiment with pretest-posttest control group design. The population of this study is the students of grade VIII SMPN 1 Watubangga 2015/2016 year that studying about building a flat side space. The data of mathematical reasoning skills is obtained by using the instrument in the form of mathematical reasoning test. Data analysis technique used is descriptive statistical analysis, F test with t test (paired-samples t test and independent-samples t test), at α = 0,05 . Based on the result of analysis of research data obtained that: 1). Student's mathematical reasoning skills before being taught with RME, PBL, and Direct learning models are in the less category after being given learning with the learning model RME, PBL and Direct students' mathematical reasoning skills are in sufficient category. Increased students' mathematical reasoning skills are in the medium category; 2). There is an improvement in students' mathematical reasoning skills after being taught with RME, PBL and Direct learning models; 3). The mathematical reasoning skills of students taught using the RME learning model were not significantly different from those taught by the PBL learning model; 4). There is a difference in the effectiveness of the learning model on improving students' mathematical reasoning skills, which is taught using a learning model RME more effective than students taught by direct learning model; 5). The students' mathematical reasoning skills are taught using the PBL learning model more effective than students taught by direct learning model; 6). Student activity during learning process using RME learning model and PBL learning models, indicating that students are very active.

The purpose of this study was to review the sensitivity of the two methods, the Mantel-Haenszel (MH and the Standardization methods to detect differences in function items (DIF). Sensitivity was based on the number of DIF grains. The data used in this study were generation data using the Wingen3 program in the form of a response dichotomy of 3054. Sample size was (200 and 1000) responses for the reference group and (200 and 1000) responses for the focus group. Samples were taken randomly as many as 35 replications. The distribution of the ability of the two groups was normal with average and variance, 0 and 1 respectively. The results of the study indicated that MH method were more sensitive than standardization method in DIF detection for samples of 400 and 2000. The finding also assumed there were possibility that standardization method was supreme when using a small sample or the number of population members of the focus group and reference was not balanced, while the focus group was less than the reference group. Abstrak:Tujuan penelitian ini untuk meninjau sensitivitas dua metode yaitu metode Mantel-Haenszel (MH) dan metode Standarisasi dalam deteksi perbedaan fungsi butir atau Differential item functioning (DIF). Sensitivitas ditinjau dari banyaknya butir DIF. Data yang digunakan dalam penelitian ini adalah data generasi dengan menggunakan program Wingen3 yang berbentuk respons dikotomi sebanyak 3054. Ukuran sampel (200 and 1000) respons untuk kelompok referensi dan (200 and 1000) respons untuk kelompok fokus. Sampel diambil secara acak sebanyak 35 replikasi. Distribusi kemampuan kedua kelompok adalah distribusi normal dengan rata-rata dan varians yaitu 0 dan 1. Hasil penelitian menunjukkan bahwa metode MH lebih sensitif dari pada metode standarisasi dalam deteksi DIF untuk sampel 400 maupun sampel 2000. Dari hasil penelitian ini ditemukan bahwa ada kemungkinan metode standarisasi lebih unggul ketika menggunakan sampel yang kecil atau jumlah anggota populasi kelompok fokus dan referensi tidak seimbang, dimana kelompok fokus lebih sedikit dibandingkan kelompok referensi.

Detection of differential item functioning (DIF) is needed in the development of tests to obtain useful items. The Mantel-Haenszel method and standardization are tools for DIF detection based on classical theory assumptions. The study was conducted to highlight the sensitivity and accuracy between the Mantel-Haenszel method and the standardization method in DIF detection. Simulation design (a) test participants consisted of 1000 responses in both the reference and focus groups, (b) the size of the proportion of DIF (0.1; 0.25; 0.50; and 0.75), and (c) the length of the multiple choice test with 40 choices the answer. Research shows that the Mantel-Haenszel method has the same sensitivity as the standardization method in DIF proportions of 10% and 25%, however, when the ratio of DIF proportions above 25% the standardization method is less sensitive, and conversely the sensitivity of the Mantel-Haenszel method increases. The standardization method has higher accuracy than the Mantel-Haenszel method in the DIF proportion of 10%, however, when the size of the DIF proportion above 10% the accuracy of the standardization method decreases, the accuracy of the Mantel-Haenszel method is higher than the standardization method. Thus, if the ratio of DIF is detected by the standardization method of (≤0.10), then the results of the standardization method are preferred as a reference. Conversely, if the proportion of DIF detected by the standardization method is (≥0.10), then the result of the Mantel-Haenszel method is chosen as a reference.

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NCTM) (2000) states the five stressed process standards namely, problem solving, reasoning and proof, communication, connections, and representation. This is also supported by the learning objectives stated in the Education Unit Level Curriculum (KTSP), that the expected ability of students are able to: (1) understand the mathematical concepts explaining the interrelationship between concepts and apply the concept or algorithm, flexibly, accurately, efficiently, and right in troubleshooting; (2) using reasoning in patterns and traits, performing Mathematical manipulations in generalizing, compiling evidence, or explaining Mathematical ideas and statements; (3) solve problems that include the ability to understand problems, design mathematical models, solve models and interpret the solutions obtained; (4) communicate ideas with symbols, tables, diagrams, or other media to clarify circumstances or problems; (5) has an attitude of appreciating the usefulness of natural life mathematics, that is having curiosity, attention, and interest in learning Mathematics as well as resilience and confidence in problem solving (MoNE, 2006). One of the abilities must be developed in the students is the Mathematical Communication Skills (MCS), students are expected to communicate the idea either in the form of symbols, tables, diagrams, or other media to clarify the circumstances or problems around him. Weigand (1999), communication is an important part of Mathematics education as a means to exchange ideas and tools to clarify understanding. In addition, learning mathematics in the classroom should help students to communicate their ideas. The ability of mathematical communication should be developed as described by Baroody (1993) that there are at least two important reasons why communication in learning mathematics should be developed in students, namely: (1) mathematics is essentially a language; Mathematics is not just a thinking