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Abstract
This study aimed at describing the mathematical connection profile of Junior High School students in solving mathematical problems based on gender difference. The subjects were two eighth grade students who had the same math ability. They were one male student and one female student. Subjects were selected by giving a math ability test, and based on the same scores at a middle level. The research type was exploration with a qualitative approach. Data were taken by interviewing the subject in depth on the basis of Task problem-solving. The problem-solving task contained narrative matter related to Geometry matter and Social Arithmetic. Data credibility used time triangulation. Data analysis was done by data categorization, data reduction, data display, data interpretation, and conclusion. The research results showed that male student connected and used mathematical ideas in the Abstrak : Penelitian ini bertujuan untuk men deskripsikan profil koneksi matematis siswa Sekolah Menengah Pertama dalam memecahkan masalah matematika berdasarkan perbedaan gender.form of facts, concepts/principles, and mathematical symbols in sufficient quantity, and they were linked appropriately and the mathematical ideas connection were used effectively so that it could solve problems correctly. The female student made a connection with mathematical ideas in excessive quantity and the connection was not appropriate, so the student could not solve the problem correctly. This indicated that mathematical connection profile of male student in solving mathematical problems was an efficient, strong, and effective category. On the other hand, the mathematical connection profile of female student in solving mathematical problems was in the category of inefficient, weak, and ineffective. From this result, it is suggested to the math teachers to create a learning process that is able to facilitate all students to practice improving their mathematical connection ability so they are able to succeed in solving mathematical problems.
Introduction
Istilah “ mathematical connection s ”The term "mathematical connections" mulai dikenalkan dalam pendidikan matematika, oleh Brownell sekitar tahun 193 5 [1], [2] , tetapi masih terbatas pada koneksi antar konsep dalam aritmetika. began to be introduced in mathematical education by Brownell circa 193 5 [1], [2], but it was still limited to the connection inter concepts in arithmetic. Istilah ini menjadi terkenal setelah [3] memasukkan komponen koneksi matematis pada point ke empat dari lima standar proses pembelajaran matematika di USA, yaitu problem solving , reasoning and proof , communication, connections , dan representation . This term becomes famous after [3] entering mathematical connection component to the fourth point of the five standards of mathematical learning process in USA, namely problem solving, reasoning and proof, communication, connections, and representation. Membuat koneksi antara ide-ide matematika merupakan sesuatu hal yang penting, karena mathematics is not a set of isolated topics but rather a web of closely connected ideas Making connections between mathematical ideas is important because mathematics is not a set of isolated topics but rather a web of closely connected ideas [3] . [3]. Dari pemikiran inilah, maka dunia Internasional memasukkan koneksi matematis ke dalam kurikulum matematika di berbagai negara, termasuk Indonesia. From this thought, the international world incorporates mathematical connections into the mathematical curriculum in various countries, including Indonesia. Pemerintah Indonesia , dalam hal ini [4], [5] The Government of Indonesia, in this case [4], [5] menjadikan koneksi matematis dan pemecahan masalah sebagai tujuan pembelajaran matematika di sekolah , yaitu ”agar siswa memahami konsep matematika, menjelaskan keterkaitan antar konsep dan menggunakan konsep serta algoritma secara luwes, akurat, efisien, dan tepat dalam aktivitas memecahkan masalah matematika” . makes mathematical connections and problem-solving as the objective of mathematics learning at school, that is to enable students to understand mathematical concepts, to explain the connection between concepts and to use concepts and algorithms flexibly, accurately, efficiently, and in an appropriate way to solve mathematical problems.
Gender is a factor that can affect students' ability in making mathematical connections to be used in solving mathematical problems. Research to find out how the process and the result of mathematical connections made by male and female students in solving mathematical problems is necessary and interesting to do.
Objectives
The aim of this study was to describe how mathematical connection profiles of two students who are as the subjects of this research, namely how the process of male and female students link and use mathematical ideas in solving mathematical problems, and how the results of the link of mathematical ideas, whether efficient, strong, and effective, or vice versa.
Literature Review
Mathematical Connections
Ada beberapa indikator kemampuan koneksi matematis yang perlu diajarkan guru kepada siswa, yaitu ” mathematics instru ction should enable students to : recognize and use connections among mathematical ideas,….and recognize and apply mathematics in contexts outside of mathematics”There are several indicators of mathematical connection capabilities that teachers need to teach to students, namely "mathematics instruction should enable students to recognize and use connections between mathematical ideas, ... .and recognize and apply mathematics in contexts outside of mathematics" [3] . [3]. Kemudian ditambahkan lagi oleh Then it is added again by [6] bahwa ” Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences”. [6] that "Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences". Dari kedua pendapat tersebut jelas bahwa From these opinions, it is clear that guru matematika di sekolah perlu megajarkan kepada siswa agar memiliki kemampuan untuk mengenali dan menggunakan k oneksi ide-ide matematika dalam matematika itu sendiri, meng gunakan keterkaitan ide-ide matematika tersebut untuk memecahkan masalah pada mata pelajaran lain maupun masalah dalam kehidupan sehari-hari. teachers of mathematics at schools need to teach students to have the ability to recognize and use mathematical ideas in mathematics itself, apply the connection of mathematical ideas to solve problems in other subjects as well as problems in everyday life.
Proses mental dalam fikiran siswa untuk mengoneksikan ide-ide matematika dapat digambarkan sebagai jaringan (network).The mental process in students’ minds to connect mathematical ideas can be described as a network. This is said by [1], and [7] that "mathematical connection is a part of a network structured like a spider's web; where the junctures, or nodes, can be thought of as pieces of representation information, and threads between them as the connections or relationships”. Mathematical connections can also be described as components of a schema or connected groups of schemas within a mental network. [8] posits that a defining feature of a schema is the presence of connections. The strength and cohesiveness of a schema are dependent on the connectivity of components within the schema or between groups of schemata. From the opinion, it can be concluded that the term "mathematical connections" can be viewed as a mental process linking mathematical ideas and can be described as a structured network in students’ minds, formed from the link of various mathematical ideas to be used in solving problems, both in mathematics itself, other subjects, as well as problems in everyday life. From here, the mathematical connections made by students in solving mathematical problems can be called efficient if the connection of mathematical ideas made by the students is sufficient, not less and not excessive; it is called strong if the connection of mathematical ideas is logical, and the use of connections made by students is effective when it can solve problems correctly. If mathematical connections made by students do not meet the category, it is called inefficient, not strong (weak), and ineffective.
Solving Mathematical Problems
Berbicara tentang koneksi matematis, maka tidak lepas dari aktivitas memecahkan masalah matematika.talking Talking about mathematical connection, it cannot be separated from the activity of solving mathematical problems. [9] argues that problem-solving is a complex mental process that requires visualization, imagination, manipulation, analysis, abstraction and the unification of mathematical ideas. To train students' ability in solving math problems, then we can provide narrative matters that contain various topics. In this study the problem given to students is a matter of mathematical narrative matters that relate to the context of everyday life, containing the matter of Geometry, and Social Arithmetic. [3] states that "... mathematical connections are" tools "for problems Solving ...". This means that mathematical connections have a close relationship with "problem-solving", in which the ability of students to connect mathematical ideas will determine the success of students in solving mathematical problems. [10] adds that in order to solve mathematical problems, students should understand the problem and make mathematical connections between ideas in mathematics. Ideas that need to be linked include facts, concepts/ principles, procedures, representations of verbal, images, numerical, symbols, formulas, and mathematical equations.
Gender
Istilah gender sering dikaitkan juga dengan proses siswa membuat koneksi matematis dalam memecahkan masalah matematika.The term gender is often associated also with the process of students in making mathematical connections in solving math problems. [11] defines gender as the difference in roles between men and women influenced by social and cultural concepts. Man is a male gender that has masculine behavior and woman is a female gender that behaves feminine. From various research results, for example [12], [13], [14], it is stated that mathematical achievement including mathematics solving problems achievement of male students is better than that of female students.
Research Methodoly Subject
Subject
Subjek dalam penelitian ini adalah dua orang siswa kelas delapan Sekolah Menengah Pertama yang memiliki kemampuan matematika sama pada level sedang dan dapat berkomunikasi dengan baik.Subjects in this case study were two eighth graders of Junior High School who had the same math ability and could communicate well. Subjects were selected by giving a Mathematics Ability Test (TKM) to all eighth grade students at SMPN 1 Jember in 2016/2017. Then one male student (initial AFP) and one female student (initial FZ) with the same score of 71.43 were chosen.
Instrument
Instrum ent utama penelitian ini adalah peneliti sendiri .The instruments were (a) Mathematics Ability Test (TKM) to select the subject and (b) Problem Solving Task (TPM) for collecting data. TKM memuat 10 soal uraian yang diambil dari soal Ujian Nasional terstandar untuk siswa kelas enam dan kelas tujuh. TKM contained 10 questions that were drawn from the question of standardized National Examination for sixth and seventh-grade students.Adapun TPM memuat satu soal cerita yang berkaitan dengan konteks kehidupan sehari-hari, dan memuat materi bangun datar, teorema Pythagoras, dan Aritmetika Sosial. TPM contained one narrative matter related to the everyday life context and contained Geometry matter and Social Arithmetic. TPM dibuat dua set (TPM 1 dan TPM 2) dan memiliki tingkat kesulitan yang sama . TPM was made of two sets (TPM 1 and TPM 2) and had the same difficulty level. TKM dan TPM tersebut divalidasi oleh tiga pakar dan telah dinyatakan valid dan layak digunakan untuk mengambil data penelitian. TKM and TPM were validated by three experts and had been declared valid and fit to be used to retrieve research data.
Contoh soal uraian pada TKM dan TPM diberikan di bawah ini.Examples of descriptions on TKM and TPM are given in Table 1.
Example of Mathematical Ability Test | Problem Solving Task |
Determine the result of 132 + 62. | Mr. Amir had a square plot of land with a size of 21 meters x 8 meters. Setahun kemudian tanah ini terkena proyek pelebaran jalan, sehingga Pak Amir menjual sebagian tanahnya yang terletak di pojok dengan bentuk segitiga siku-siku yang sisi-sisi siku-sikunya berukuran 6 meter, dan 8 meter dengan harga Rp.100.000,00 per m 2 . A year later this land was hit by a road widening project, so Mr. Amir sold a part of this land in a corner with a right triangle shape with 6-meter and 8-meter sides with a price of QUOTE _x0001_ per m 2. Hasil penjualan tanah tersebut digunakan Pak Amir untuk membuat pagar di sekeliling tanahnya yang sekarang. The income from the sale of the land was used by Mr. Amir to create a fence around his present land. Biaya pembuatan pagar Rp.50.000 ,00 per meter, sedangkan untuk pintu dibuat pintu besi sepanjang 4 meter, dengan biaya Rp.1.000.000,00. The cost of making a fence of QUOTE _x0001_ per meter, while for the iron gate along the 4 meters, the cost was QUOTE _x0001_ Berapakah dana yang masih perlu ditambah Pak Amir? How much money did Mr. Amir need? |
The ratio of the length and width of the rectangle 3: 1. If the circumference of the rectangle is 72 cm, then specify the area. |
Example of Mathematical Ability Test, and Problem Solving Task
Procedure
Penelitian ini merupakan penelitian eksplorasi dengan menggunakan pendekatan deskriptif kualitatif.This research was an exploratory research using a qualitative approach. Peneliti sendiri yang mengumpulkan dan menganalisis data sehingga tidak bisa digantikan oleh orang lain [14] . The researcher himself collected and analyzed data so that it could not be replaced by others. Data dikumpulkan dengan melakukan wawancara mendalam kepada subjek penelitian ber basis Tugas Pemecahan Masalah (TPM) . Subjek mengerjakan TPM dengan kemampuan nya sendiri, kemudian peneliti mewawancarai untuk mengeksplor aktivitas koneksi matematis yang sudah dilakukan siswa dalam me njawab TPM tersebut.Selama siswa mengerjakan TPM dan wawancara berlangsung direkam menggunakan audio video sehingga tidak ada data yang hilang.The data collection procedure to explore students’ mathematical connection activities in solving mathematical problems, started by giving problem-solving task (TPM) to the subject, subject solved the TPM based on his or her ability and wrote down the answer. Next, the researcher interviewed the subject related to aspects of mathematical connection activities. Time triangulation of data was used to have a credible data. This procedure was applied to the two subjects (a male student and a female student in respectively). Then, the collected data (task analysis, interviews) were analyzed by the following steps: 1) data categorization, 2) data reduction, 3) data display, 4) data interpretation, and 5) conclusion [15][16]. At the stage of data categorization, grouping data of mathematical connection is done according to indicators. In the data reduction stage, data mining is done and removing unnecessary data. Next, in stage of data display is done descriptively, that is in the form of description/text, and chart/scan result of students answers. Next in the data interpretation stage, it is interpreted that the meaning of data in accordance with the mathematical connections indicators. The final stage in data analysis is the conclusion to determine how mathematical connections profiles the subjects in solving mathematical problems.
Results and Discussion
Mathematical Connection Profile of Profil Koneksi Matematis Siswa Laki-Laki dalam M emecahkanMale Student in Solving Mathematical Problems
Dari pengamatan selama siswa laki-laki (AFP) memecahkan masalah matematika yang ada dalam Tugas Pemecahan Masalah (TPM), maka kegiatan yang dilakukan siswa adalah sebagai berikut.Based on the observation of the male student (AFP) solved mathematical problems in TPM, the activities done by the student was as follows.
First, the student read the problem to understand the meaning of each sentence in the problem. After that, he drew a rectangular image, a right triangle, and wrote the length and width of the rectangle, as well as the base and the height of the right triangle on the image. Next, he wrote "what is known" containing the data or information that he understood from the problem by using verbal sentences and mathematical symbols. The data/information were: rectangle length ( QUOTE _x0001_ rectangle width QUOTE _x0001_ , right triangle base QUOTE _x0001_ , and right triangle height QUOTE _x0001_ . He also wrote information about the sale price of land QUOTE _x0001_ 2, the cost of making a fence of QUOTE _x0001_ , and the cost of making iron gate QUOTE _x0001_ for 4 meters. Next, he wrote "Asked", or what the student should count, namely how much money still needed by Mr. Amir to make the fence and the gate?
Kegiatan berikutnya yang dilakukan siswa adalah menjawab pertanyaan dengan menulis kata “jawab” dalam lembar jawaban, yang artinya solution.The next activity the student did was answering the question by writing the word "answer" in the answer sheet, which meant solution. Untuk mengetahui aktivitas mental dan pemahaman siswa dalam membuat koneksi matematis sehingga menghasilkan jawaban pada lembar jawaban, maka berikut disajikan sebagian cuplikan wawancara antara peneliti (R) dengan Subjek (AFP). To know the mental activity and understanding of student in making mathematical connections so as to generate answers on the answer sheet, the following presented some interview snippets between the researcher (R) and Subject (AFP).
R R | :: | Baiklah, waktu kamu menjawab soal, apa yang pertama kamu lakukan?Well, when you answer the question, what did you do first? |
AFPAFP | :: | Pertama, mencari sisi miring segitiga siku-sikuFirst, find the hypotenuse of the right triangle |
R R | :: | Rumus apa ini yang kamu gunakan untuk mencari sisi miring?What formula do you use to find the hypotenuse? |
AFPAFP | :: | Rumus PythagorasPythagorean formula |
RR | :: | Lalu langkah ke-2 mana?Then which is the second step? |
AFPAFP | :: | Ini (siswa menunjuk lembar jawaban) , m enghitung luas segitiga siku-sikuThis (the student points the answer sheet), calculate the area of the right triangle |
R R | :: | Apa rumusnya?What is the formula? |
AFPAFP | :: | Rumusnya setengah kali alas kali tinggi (1/2xaxt)The formula is half-time base time height QUOTE _x0001_ QUOTE _x0001_ |
R R | :: | Selanjutnya apa yang kamu kerjakan?What do you do next? |
AFPAFP | :: | Mencari hasil penjualan tanah.Find the sale income of land. Dari luas tanah yang dijual, 24 meter persegi dikali dengan harga penjualan tanah Rp.100.000 Of the land area sold, 24 square meters multiplied by the sale price of land QUOTE _x0001_ per meter persegi , hasilnya Rp.2.400.000 . per square meter, the result is QUOTE _x0001_ |
R R | :: | Please,Coba jelaskan bagaimana cara kamu menghitung panjang pagar ini (peneliti menunjuk lembar jawaban) ? explain how do you calculate the length of the fence (the researcher points the answer sheet)? |
AFPAFP | :: | QUOTE _x0001_ 15 m + 10 m + 21 m + 8 m = 54 m – 4 m = 50 m |
R R | :: | Ini dari mana angka 15 m?Where can you get the number 15 QUOTE _x0001_ from? |
AFPAFP | :: | QUOTE _x0001_ 21 m - 6 m = 15 m |
R R | :: | Lalu angka 10 m dari mana?Then, where can you get the number 10 QUOTE _x0001_ from? |
AFPAFP | :: | Panjang sisi miring segitiga siku-sikuThe length of the hypotenuse of the right triangle |
R R | :: | Lalu setelah ini kamu mencari apa?Then after this, what will you find? |
AFPAFP | :: | Mencari biaya pembuatan pagar dan pintu besiFinding the cost of making fence and iron gate. |
R R | :: | Lalu yang berikutnya apa?Then what is next? |
AFPAFP | :: | Menghitung jumlah biaya yang masih diperlukan pak AmirCalculate the cost that is still needed by Mr. Amir |
R R | :: | Bagaimana cara kamu menghitung nya ?How do you calculate it? |
AFPAFP | :: | Ini biaya pembuatan pagar Rp.2.500.000, dijumlahkan dengan biaya pembuatan pintu besi Rp.1.000.000, hasilnya Rp.3.500.000.The cost of making a fence is QUOTE _x0001_ , summed with the cost of making iron gate QUOTE _x0001_ . the result is QUOTE _x0001_ . Setelah itu dikurangi hasil penjualan tanah Rp.2.400.000, hasilnya Rp.1.100.000. After that reduced with the sale of the land QUOTE _x0001_ , the result is QUOTE _x0001_ . |
Based on the observation, answer sheet, and also interview, we can see that the male student (AFP) took some steps in answering the problem The first step was to find the length of the hypotenuse of the right triangle by using the Pythagorean theorem, namely QUOTE _x0001_ Here, he used the formula and mathematical symbols, data/facts which were obtained from the problem, as well as addition arithmetic operation, power, and root squaring Symbol x for the hypotenuse of the right triangle , a for the base, and t for the height After being substituted, a = 6, and t = 8, then x = 10 The second step, he calculated the area of the triangle and the income from the land sale Here, he linked and used the triangle area formula, namely QUOTE _x0001_ , the concept of social arithmetic (buying and selling), data/facts, symbols, and some counting operations The mathematical data and symbols used were L for the Area, QUOTE _x0001_ for the base, QUOTE _x0001_ for the height, the sale price of the land = QUOTE _x0001_ The counting operations used here were multiplication, and division After the calculation, the area of the triangle was 24 QUOTE _x0001_ , and the sale of the land was QUOTE _x0001_ In the third step, he created a right trapezoid image to search for trapezoid circumference Here, he added up all the trapezoid sides, namely k=15 m+10 m+21 m+8 m where 21 m=-6 m=15 m21 m The result was 54 QUOTE _x0001_ To find out the length of the fence built on the land of Mr Amir, then the trapezoid circumference was subtracted by the length of the gate, so obtained QUOTE _x0001_ =54m-4m=50mThe fourth step, he searched the cost of making a fence: the length of the fence multiplied by the price of making a fence every meter, namely QUOTE _x0001_ , Rp50,000/ m so that the cost of making the fence was QUOTE _x0001_ Rp2500,000 The last step, he calculated the cost that was still needed by Mr Amir Thus, he calculated the entire cost required to make the fence and gate, namely
Rp.2500,000+Rp.1,000,000=Rp.3,5000,000 after that, it was subtracted from the money from the land sale, which was QUOTE _x0001_ . Rp.2,400,000 So, the cost that was still needed by Mr. Amir to make a fence and gate was Rp.3,500,000-Rp.2,400,000=Rp.1,100,000 After he finished answering the problem, he checked the correctness of the data, the formula, and the counting operation used. After feeling sure that everything was correct, then he submitted the answer sheet to the researcher.
Dari uraian di atas, maka dapat diungkap bahwa profil koneksi matematis siswa SMP laki-laki (subjek AFP) dalam memecahkan masalah matematika, dapat digambarkan sebagai berikut.From the description above, it can be revealed that the mathematical connection profile of male junior high school student (AFP) in solving math problems can be described as follows. The student linked and used connections mathematical ideas to solve problems. The connections of mathematical ideas include the concept of a rectangle linked with the concept of a right triangle and the concept of a trapezoid. Next, he linked these ideas with the concept of triangle area, trapezoidal circumference, and social arithmetic concepts related to the calculation of the cost of fence, gate, and funds still needed by Mr. Amir. He also linked each concept with data/facts, mathematical symbols and counting operations correctly. From the relevance of mathematical ideas that student recognized and used, the connection of mathematical ideas in solving mathematical problems had sufficient numbers and were all required to solve math problems. In addition, the attribution of ideas that were made was correct and logical and used effectively to obtain the correct answer. So, it could be concluded that mathematical connection profile of male junior high school student in solving mathematical problems had included an efficient, strong, and effective category.
Profil Koneksi Matematis Siswa Perempuan dalam MemecahkanMathematical Connection Profile of Female Student in Solving Masalah Matematika Mathematical Problems
Kegiatan yang dilakukan siswa perempuan (FZ) dalam proses memecahkan masalah matematika berdasarkan pengamatan adalah sebagai berikut.The activities done by the female student (FZ) in the process of solving mathematical problems based on the observations are as follows.
Pertama, siswa membaca soal dalam hati untuk memahami arti setiap kalimat dalam soal.First, she read the problem to understand the meaning of every sentence in the matter. Setelah itu ia membuat gambar persegi panjang, segitiga siku-siku, beserta ukuran sisi-sisinya. After that, she made a rectangular image, a right triangle, along with the measurement of the sides. Berikutnya, siswa menuliskan “ D iketahui” yang memuat data atau informasi yang difahaminya dari dalam soal dengan menggunakan kalimat verbal dan simbol matematika. Next, she wrote "known" which contained the data or information she understood from the problem by using verbal sentences, images, and mathematical symbols. Data/informasi tersebut adalah : ukuran awal 21m x 8m, ukuran jual 8 x 6m, harga jual 100.000/m 2 , harga pagar 50.000/m, dan pintu besi 4 meter 1.000.000. Data/information were: the initial size: QUOTE _x0001_ , 21m*8m sale size: QUOTE _x0001_ , 8*6m the selling price: QUOTE _x0001_ , 100,000/m2the price of making fence: QUOTE _x0001_ , 50,000/m and the iron gate 4 meters QUOTE _x0001_ . Selanjutnya, siswa menulis “Ditanya”, atau apa yang harus dicari siswa, yaitu dana yang masih perlu ditambah pak Amir. 1,000,000 Next, she wrote "Asked", or what she should find, namely fund which was still needed by Mr. Amir.
Kegiatan berikutnya yang dilakukan siswa adalah menjawab pertanyaan dengan menulis kata “jawab” dalam lembar jawaban, yang artinya solution.The next activity that the student did was answering the question by writing the word "answer" in the answer sheet, which meant solution. Untuk mengetahui aktivitas mental dan pemahaman siswa dalam membuat koneksi matematis sehingga menghasilkan jawaban pada lembar jawaban, maka berikut disajikan sebagian cuplikan wawancara antara peneliti (R) dengan Subjek ( FZ ). To find out the mental activity and understanding of students in making mathematical connections so as to generate answers on the answer sheet, the following presented some interview snippets between the researcher (R) and Subject (FZ).
R R | :: | Baiklah, sekarang yang pertama ini apa yang kamu lakukan ?Well, first what did you do? |
FZ FZ | :: | Mencari ukuran awalSearched for initial size |
R R | :: | A pa yang kamu cari i tu ?What did you search for? |
FZ FZ | :: | Luas persegi panjangRectangular area |
R R | :: | Kalau di dalam soal apa artinya luas persegi panjang ini?In the problem/matter, what does this rectangular area mean? |
FZ FZ | :: | Tanah pak Amir yang belum dijualLand of Mr. Amir that has not been sold. |
R R | :: | Lalu yang berikutnya apa ini?Then what's next? |
FZ FZ | :: | Ukuran jualFind the sale size |
R R | :: | Apa maksudnya ukuran jual?What does it mean? |
FZ FZ | :: | Luas tanah yang dijual pak AmirLand area sold by Mr. Amir |
R R | :: | Nah, langkah ketiga ini apa maksudnyaWell, in this step, what is the meaning of Ukuran awal dikurang ukuran jual? initial size subtracted from sale size? |
FZ FZ | :: | Mencari luas trapesium , yaitu luas tanah pak Amir yang sekarangCalculating trapezoidal area, namely Mr. Amir’s present land area |
R R | :: | Lalu berikutya apa ini (menunjuk langkah keempat) ?Then what's this (pointing at step four)? |
FZ FZ | :: | Mencari harga jual, yaitu uang hasil penjualan tanahFinding the sale price, namely income from the sale of land |
R R | :: | Then, wSelanjutnya apa yang kamu cari?hat’s next? |
FZ FZ | :: | Sisi miring segitiga siku-sikuFind hypotenuse of the right triangle |
R R | :: | Dengan menggunakan rumus apa ini?What formula did you use? |
FZ FZ | :: | Rumus PythagorasPythagorean formula |
R R | :: | Berikutnya mencari harga pagar apa maksudnya?Next, you find the price of the fence. What does it mean? |
FZ FZ | :: | Maksudnya mencari biaya pembuatan pagarThe point is to find the cost of making a fence |
R R | :: | PleaseCoba jelaskan bagaimana kamu mencari nya ? explain how you count it? |
FZ FZ | :: | (21+15+8+10) = (54-4) = 50 x 50,000 = Rp.2,500,000 QUOTE _x0001_ . QUOTE _x0001_ |
R R | :: | Langkah terakhir ini kamu mencari apa?In this last step, what did you do? |
FZ FZ | :: | Mencari dana yang masih perlu ditambah pak Amir.Calculated the fund that is still needed by Mr. Amir. |
R R | :: | Bagaimana caranya?How? |
FZ FZ | :: | Caranya adalah harga pagar + harga pintu besi – harga jual, h asilnya 2.500.000 + 100.000 – 2.400.000 = 200.000 .The price of fence plus the price of the iron gate minus the selling price, the result is QUOTE _x0001_ |
Dari hasil pengamatan, lembar jawaban tertulis, dan wawancara , kita dapat melihat bahwa s iswa melakukan beberapa langkah dalam menjawab masalah.Based on the observation, the answer sheet, and also interview, we can see that the student took several steps in answering the problem. In the first step, the female student (FZ) searched for "initial size", which meant the land area of Mr. Amir before sale and purchase happened. Here, she used the formula of rectangle area, namely length multiplied by width, so that obtained QUOTE _x0001_ . In the second step, she searched for "sale size", namely searched for land area sold by Mr. Amir. Here, she used the triangle area formula, namely QUOTE _x0001_ QUOTE _x0001_ , and the result was QUOTE _x0001_ . In the third step, she searched for a trapezoidal area, namely the land area which was not sold by Mr. Amir. Here, she used the rectangular area data, and the area of the right triangle already obtained in the first step, and the second step, and used subtraction operation, so as to obtain the trapezoidal area QUOTE _x0001_ . In the fourth step, she searched for the income from the sale of Mr. Amir’s land by linking and using the data area of a right triangle, and the concept of social arithmetic. The result was QUOTE _x0001_ . In the fifth step, she searched for the hypotenuse of the right triangle by using the Pythagorean formula, namely, QUOTE _x0001_ the data of the right triangle base QUOTE _x0001_ , and the right triangle height QUOTE _x0001_ , obtained c QUOTE _x0001_ . In the sixth step, she searched for the cost of making a fence, by linking and using the concept of the trapezoidal circumference, and the concept of social arithmetic. From the calculation result, it was obtained (21+15+8+10) = (54-4) = 50 x 50,000 = Rp.2,500,000 QUOTE _x0001_ . In the last step, she searched for the fund that was still needed to be added by Mr. Amir, by summing up the cost of making fence and gate, then subtracting it by the money from the land sale. From the answer sheet, it could be seen that the student was less precise in writing the cost of making the iron gate, which should be Rp.1,000,000, she wrote 100,000, so the final answer was wrong, that was Rp.2,500,000 + 100,000 – 2,400,000 = Rp. 200,000 QUOTE _x0001_ but it should be Rp.2,500,000 + Rp.100,000 – Rp.2,400,000 = Rp. 1,100,000 QUOTE _x0001_ . After the student finished answering the problem, the student did not check carefully the correctness of the data, and the counting operation she used so that there were some symbols, such as QUOTE _x0001_ and QUOTE _x0001_ . In addition, there was the use of wrong data, namely the cost of the iron gate that should be QUOTE _x0001_ she wrote QUOTE _x0001_ , so the result of calculation was wrong.
Dari uraian di atas, maka dapat diungkap bahwa profil koneksi matematis siswa SMP perempuan (subjek FZ) dalam memecahkan masalah matematika, dapat digambarkan sebagai berikut.From the description above, it can be revealed that the mathematical connection profile of female junior high school student (FZ) in solving mathematical problems can be described as follows. The student linked and used connections between mathematical ideas to solve problems. The connections of mathematical ideas included the concept of a rectangle linked with the concept of a right triangle and the concept of a trapezoid. Next, she linked the ideas with the concept of rectangular area, triangle area, and trapezoidal area, trapezoidal circumference, as well as social arithmetic concepts related to the calculation of the cost that was still needed by Mr. Amir to make a fence and iron gate. She also linked each concept with data/facts, mathematical symbols and counting operations. Although she had linked and used mathematical ideas to solve problems, it is unfortunate that she linked and used the excessive number of mathematical ideas namely searching for a rectangular area and trapezoidal area, whereas both of these ideas were not needed to solve the problem. The linking of these two mathematical ideas with other mathematical ideas was clearly inappropriate. In addition the student several times did not write the symbols and use the wrong data in the work of counting operations. This error made a wrong final answer. Thus, it could be concluded that the mathematical connection profile of female junior high school student (FZ) in solving mathematical problems included in an inefficient, weak, and ineffective category.
Hasil penelitian tersebut sesuai dengan hasil penelitian yang menyatakan bahwa gender berhubungan dengan hasil belajar matematika, seperti hasil penelitian yang dikemukakan oleh [11], [12], [13], bahwa prestasi matematika termasuk prestasi pemecahan masalah matematika siswa laki-laki lebih baik daripada siswa perempuan.The result was consistent with the result of the study stating that gender-related to mathematical learning outcomes, such as the results of research presented by [12], [13], [14] that mathematical achievement including mathematical problems solving achievement of the male student was better than that of the female student. Based on these results, mathematics teachers need to create a learning process that is able to facilitate all students to practice improving their mathematical connection ability so they are able to succeed in solving mathematical problems.
CONCLUSION Conclusion
There were different responses between male and female students in this case study. The research results showed that male student connected and used mathematical ideas in the Penelitian ini bertujuan untuk men deskripsikan profil koneksi matematis siswa Sekolah Menengah Pertama dalam memecahkan masalah matematika berdasarkan perbedaan gender.form of facts, concepts/principles, and mathematical symbols in sufficient quantity, and they were linked appropriately and the mathematical ideas connection were used effectively so that it could solve problems correctly. On the other hand, the female student made a connection with mathematical ideas in excessive quantity and the connection was not appropriate, so the student could not solve the problem correctly. This indicated that mathematical connection profile of male junior high school student (subject AFP in this study) in solving mathematical problems includes an efficient, strong, effective category, while mathematical connection profile of female junior high school student (subject FZ in this study) is inefficient, weak, and ineffective. From this result, it is suggested to the math teachers to create a learning process that is able to facilitate all students to practice improving their mathematical connection ability so they are able to succeed in solving mathematical problems.
ACKNOWLEGMENT Acknowledgment
Penulis mengucapkan terima kasih kepada DRPM Kemenristekdikti , dan Universitas Jember atas supporting dana Penelitian Disertasi Doktor tahun 2018.The authors would like to thank DRPM Kemenristekdikti, and the University of Jember for supporting the Research Fund for a Doctoral dissertation in 2018.
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