The purpose of this research was to reveal how the construction process of symbolic representation and verbal representation made by students in problem solving. The construction process in this study referred to the problem-solving stage by Polya covering; 1) understanding the problem, 2) devising a plan, 3) carrying outthe plan, and 4) looking back. This research was qualitative research by getting involved 4 students of Junior High School class VIII. This study obtained results that the construction process of symbolic representation made by students since in the process of understanding the problem. In understanding the problem, students were able to identify the problem well. Then students could make the symbol used as a variable that the value was not known. By using the symbol students could perform a series of calculation to obtain the value of the symbol. Symbols created by students were very helpful and facilitated students in solving problems. While in the construction process, verbal representation was done by students since the process of understanding the problem. The form of verbal representation was manifested by writing down all information known from a slightly changed problem because they used a language that they understood more. Based on the known information, students could plan and performed a series of calculations using written sentences so that the problems could be solved properly.

The ability to do translation from one form of representation to another representation form is a fundamental ability to build a conceptual and mathematical thinking. Related to the important of translation process, this study aimed to investigate the process of mathematical representation translation from verbal to graph. This research was a qualitative research. Collecting data was done through the assignment sheet and interviews after the subjects completed the task given. The result showed that the students were able to do the process of translation from verbal representation to graph well at every stage of the translation. The translation process was done in four stages: unpacking the source, preliminary coordination, constructing the targets, and determining equivalence. The translation process of verbal to graph representations required more than one translation process. This process through the intermediary of some other representations like symbolic, schematic, equations, numerical. In general, students do the same activity except at preliminary coordination activity. Preliminary coordination activity can be done in two ways, namely students determined the formula of the relationship between distance and time, and by connecting the distance between the two cars and the increasing time. The more the time increased, the distance the two cars decreased.

Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building relational understanding on concept of area and perimeter of a rectangle. This research is a case study. The research instrument is tests and interviews. The participants in this study were Grade seven students. Two students are selected based on the characterization of the mathematical representations that appear. The study results a visual and symbolic representation used by students in building relational understanding on the concept of area and perimeter of a rectangle. Visual and symbolic representation suggests students to build relational understanding.

Penelitian ini bertujuan untuk mendeskripsikan proses translasi representasi siswa dalam menyelesaikan masalah matematika berorientasi pada high order thinking skills (HOTS). Penelitian ini merupakan penelitian kualitatif. Subjek penelitian ini adalah 26 siswa kelas XI di Sekolah Menengah Pertama Negeri 4 Metro. Teknik pengumpulan data dilakukan melalui tes dan wawancara. Siswa menyelesaikan tes sambil mengungkapkan secara lisan apa yang mereka pikirkan (think aloud), kemudian dilakukan wawancara terkait dengan hasil pekerjaan siswa. Hasil penelitian menunjukkan bahwa siswa dalam menyelesaikan masalah matematika berorientasi pada HOTS dilakukan melalui dua proses translasi yaitu translasi representasi verbal ke grafik (gambar) kemudian ke simbolik. Proses translasi representasi tersebut dilakukan melalui tahap unpacking the source, preliminary coordination, constructing the target, dan determining equivalence. Hasil penelitian ini diharapkan dapat digunakan guru sebagai bahan pertimbangan untuk menyusun desain pembelajaran yang tepat khususnya pada soal pembelajaran yang mendorong siswa melakukan HOTS. Sehingga guru dapat mengoptimalkan berpikir siswa dan meminimalkan kesulitan siswa dalam proses translasi representasi. Penelitian selanjutnya dapat memeriksa lebih mendalam karakteristik tiap tahapan translasi representasi.

Intisari : Pendidikan anak usia dini adalah suatu upaya pembinaan yang ditujukan kepada anak sejak lahir sampai dengan usia enam tahun yang dilakukan melalui pemberian rangsangan pendidikan untuk membantu pertumbuhan dan perkembangan jasmani dan rohani agar anak memiliki kesiapan dalam memasuki pendidikan lebih lanjut. Hasil penelitian yang dilaksanakan menunjukkan bahwa subyek tidak mengalami kesulitan untuk menyelesaikan operasi perhitungan penjumlahan dalam bentuk gambar dan angka, sedangkan untuk pengurangan mengalami kesalahan perhitungan. Tetapi untuk penyelesaian soal penjumlahan dan pengurangan dalam bentuk soal cerita, subyek belum mampu menyelesaikannya. Hal tersebut dikarenakan subyek belum mampu memaknai isi dari soal yang diberikan. Untuk mengatasi permasalahan tersebut, alternatif yang diberikan pada saat penelitian adalah memberikan bimbingan untuk memaknai isi dari soal yang diberikan, setelah subyek dapat memaknai isi dari soal kemudian subyek diminta untuk menyelesaikan soal tersebut. Kata Kunci: Kesulitan Belajar Matematika, Anak Usia Dini. PENDAHULUANMatematika adalah suatu pengetahuan yang mampu mengembangkan kemampuan berpikir anak. Oleh sebab itu matematika dapat sebagai sarana untuk membangun kemampuan berpikir anak mulai dari usia dini, usia pendidikan kelas awal (pendidikan dasar), pendidikan menengah, pendidikan lajutan dan bahkan sampai mereka berada di bangku perkuliahan.Undang-Undang Sistem Pendidikan Nasional dalam pasal 1 menegaskan bahwa, pendidikan anak usia dini adalah suatu upaya pembinaan yang ditujukan kepada anak sejak lahir sampai dengan usia enam tahun yang dilakukan melalui pemberian rangsangan pendidikan untuk membantu pertumbuhan dan perkembangan jasmani dan rohani agar anak memiliki kesiapan dalam memasuki pendidikan lebih lanjut.

Mathematical learning to implant the concept of algebra operation using constructivism approach is very important. Students should be actively involved in the process of building their understanding, so meaningful learning experiences can be to gained. This research was an experimental research involving 91 students of grade 8. This research applied constructivism-based mathematics module used by the students during studying the concept of algebra operation. The result showed that the use of constructivism based mathematics module was very effective in improving students' mathematical understanding on algebra operation material. This result was obtained by performing the initial test (pre-test) before the use of modules and final test (post-test) after the use of module. In addition, the result of observation conducted during the learning activities showed that in the use of modules in learning mathematics, students with high academic ability tended to be more active in the discussion process.

The translation between mathematical representations was one of the indicators in understanding mathematical concepts. Understanding the things related to the process of student representation translation was very important in learning mathematics. One of the activities that plays a role in translation was unpacking the source. This study aimed to determine the characteristics of student activity in unpacking the source when doing the process of translational verbal representation to the graph. This research was using a qualitative research. The subject of this research were twenty mathematics education students. Selection of research subjects used purposive sampling. The data were collected by test and interview. The results showed that the characteristics of student activity in unpacking the source were two that are drawing scheme of verbal situation and interpreting verbal information with its own language. In addition, there were still many students failed in translation because of difficulties in unpacking the source. The results of this study were expected to add insight into learning to minimize student difficulties in unpacking the source.

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