Posted in My Space, My Story

Feedback Mahasiswa

Entah kenapa memeriksa tugas pertama mahasiswa semester ini benar-benar saya nikmati prosesnya. Ada kenikmatan saja membaca dengan detail setiap essai yang dikirimkan mahasiswa pekan lalu. Padahal ini baru tugas pertama dan persis sama dengan tugas yang saya berikan pada mahasiswa semester kemarin. Semester ini rasanya bisa lebih fokus ketika cuma diberikan satu mata kuliah (maklum masih dosen luar biasa yang masih minim pengalaman, baru juga lepas kuliah awal tahun lalu). Alhamdulillah ada dua kelas yang diberikan. Yah meskipun harus memeriksa sekitar 70 essai mahasiswa dan belum dengan permasalahan copy paste serta tugas yang persis sama dari awal hingga akhir, tapi tetap saja nikmat rasanya bisa fokus sama mereka. Membaca setiap detail essainya dan memberi feedback mulai dari isi essay hingga cara penulisan dan referensi untuk setiap mahasiswa.

Hmm… saya sempat berpikir saat sedang memeriksa tugas mereka, sepertinya memang ada baiknya dosen tidak perlu mengambil/diberi banyak mata kuliah  atau banyak kelas agar bisa benar-benar fokus pada mahasiswanya. Fokus memberi materi, memberi dan memeriksa tugas, memberi bahan diskusi yang menarik. Apalagi,di luar sana kan dosen juga punya segudang tanggung jawab dan tugas yang mesti dipenuhi sebagai dosen (yang ini belum saya lewati karena masih anak baru, aktivitas lain saya hanya dapur dan les privat hehe..). Bukankah akan keren sekali rasanya ketika dosen benar-benar serius memberi dan memeriksa tugas mahasiswa. Memberi feedback di setiap tugas mereka untuk memberikan gambaran sebaik apa kualitas tugas yang mereka kerjakan.  Continue reading “Feedback Mahasiswa”

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Posted in My Space, My Story

Komunikasi Itu Penting di Keluarga

Saya belajar banyak dari beberapa peristiwa dan pengalaman keluarga yang ada di sekitar saya maupun yang pernah saya temui secara tidak sengaja. Entah kenapa sebagian besar masalah yang muncul diantara keluarga yang pernah saya temui, even keluarga saya sendiri adalah komunikasi dan keterbukaan antar anggota keluarga.

Diam seakan menjadi sebuah solusi terbaik dari setiap permasalahan dengan harapan diam akan membuat semuanya cepat kembali seperti semula. Diam tidak akan menambah masalah. Diam itu emas. Tapi dari apa yang saya lihat, justru diam bisa menjadi solusi yang tidak baik dan dapat menjadi bom waktu yang kapan saja bisa meledak ketika sudah dihadapkan pada masalah yang lebih besar lagi. Segala uneg-uneg dapat menjadi senjata ampuh di kemudian hari untuk menyerang lawan dengan alasan selama ini sudah menyimpannya terlalu lama. Padahal bukankah diam berarti memutus kesempatan komunikasi dan mencari solusi terbaiknya? Yah, walaupun diam memang bisa menjadikan suasana jauh lebih tentram. Tapi itu yang tampak kan? Continue reading “Komunikasi Itu Penting di Keluarga”

Posted in Discussion, Education, General Discussion, Math Education

The Sociomathematical Norms Should be adopted to Mathematical Classroom

Mathematics classroom is still bored and not interesting for many students. The success in mathematics classroom is determined by good collaboration among teacher and students. Good collaboration is more likely to be realized by creating a good classroom environment and implementing the suitable norms in specifically mathematical aspects, called sociomathematical norms. For over two decades, the research has been focused on the specific role of norms in students’ mathematical learning opportunities. This research has covered the investigating how norms negotiated among students and teacher and the power of norms in specific areas of mathematics (Van Zoest, Stockero, & Taylor, 2012).

Sociomathematical norms refer to the practices of participation and contribution of students as well as teacher in mathematics lesson. Sociomathematical norms are the normative aspects of mathematical discussion that are specific to the students’ mathematical activities (Yackel & Cobb, 1996). Wedege (2010) stated that sociomatematical norms combine mathematics, people and society. The implementation of these norms should be adopted in the mathematics classroom.  In this paper, the reasons why sociomathematicals norms are really important to adopt will be discussed.

In several countries many teachers do not concern about sociomathematical norms because sociomathematical norms have not been accepted as a part of classroom culture where a more traditional methodology is applied. Teachers do not really understand how to implement the sociomathematical norms in their classes. Teachers have little basis to anticipate other creative solutions from students. However, sociomathematical norms will help to revise the way teachers teach mathematics in class where they are used to use a more traditional methodology to teach mathematics. In implementing sociomathematical norms, teachers tend to be equal members of the mathematics class. Teacher is the center of learning discussion where students are hoped to have more contributions in discussion activities. In addition, teacher is a representative of the mathematics community in the class (Yackel & Cobb, 1996). This is because the teacher handles the discussion in mathematics classes and also is responsible for the development of mathematical classroom and students’ activities (McClain & Cobb, 2001). During the mathematics activities, teacher helps students in improving their abilities how to deliver their knowledge to solve mathematical problems.

Sociomathematical norms help students in developing their explanation and justification skill in learning process. Explanation and justification are related to the construction of individual aspects as well as social aspect. The sociomathematical norms make students focus on mathematical thinking rather than thinking about mathematics. They are not only expected to give answers but also they can explain their strategies to get the answer. Sociomathematical norms support high-level cognitive activity (Yackel & Cobb, 1996). In this case, teachers can give some interesting, well-discussed and problem-solving-based mathematical problems which can encourage students to give solutions, compare theirs to the other students’ solutions and even judge the similarities and differences leading to create high-level cognitive activity. Acceptable mathematical explanations and justifications also deal with the actual process of making a contribution and facilitating communication. Sociomathematical norms focus on developing the interaction among students and teachers. This is because while doing mathematics, teacher and students adhere to similar rules and norms (Tatsis & Koleza, 2008) which help them to achieve learning goals.

In conclusion, by implementing these norms, mathematical class is no longer a boring class to students. They will enjoy their mathematics when they can improve their mathematical skill by giving more contribution in classroom. Teacher plays an important role to develop the mathematical quality of classroom environment, to establish norms for mathematical aspects of students and also to make students more confident in participating in mathematical activity. Eventually, there will be more benefits to the successful of mathematical activities and students’ mathematical achievements.

Ummy Salmah

References

McClain, K., & Cobb, P. (2001). An analysis of development of sociomathematical norms in one first-grade classroom. Journal for Research in Mathematics Education, 32(3), 236.

Tatsis, K., & Koleza, E. (2008). Social and socio‐mathematical norms in collaborative problem‐solving. European Journal of Teacher Education, 31(1), 89-100. doi: 10.1080/02619760701845057

Van Zoest, L., Stockero, S., & Taylor, C. (2012). The durability of professional and sociomathematical norms intentionally fostered in an early pedagogy course. Journal of Mathematics Teacher Education, 15(4), 293-315. doi: 10.1007/s10857-011-9183-y

Wedege, T. (2010). Sociomathematics: A subject field and a research field. http://dspace.mah.se/bitstream/handle/2043/10027/MES6-WedegeT.pdf?sequence=1

Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. doi: 10.2307/749877

Posted in Discussion, Education

The Important of Prior Knowledge to Commence a New Topic in Science and Mathematics

 

Learning is the process of people explore and develop their way of thinking and also behaviour. Learning new things is also important for people. They need some things that support them to explore and support their process of learning. The process of building a new knowledge needs skills, belief, concept, and also prior knowledge that can help them to familiarize with their environment. Some people said that in learning a new topic or a new concept teacher has an important role to help students build their undertanding about this topic. However, prior knowledge also as important as teacher’s role in helping students deal with new topic. In this paper, I would like to consider the concept of student’s prior knowledge and the important of assessing student’s prior knowledge before studying.

Learning process is the process which personal ideas or meaning is constructed  and involve students’ prior knowledge and also experiences (Tytler, 2004). In learning process, conceptual learning related to the concept of developmental stages of children’s cognitive development (Tytler, 2004). It was developed by Jean Piaget. Many books and papers explaining about learning area have been written by him. He has an enormous contribution to educational research. There are four stages of cognitive development namely sensory-motor (birth to 2 years), preoperational (2 to 7 years), concrete operational (7 to 11 years) and formal operation (11 plus years) (Novak, 1978). In each step, Piaget was successful to describe the way children develop their cognitive domain. Although learners now can reveal different types of thinking in different context, Piaget’s ideas about the stages of cognitive domain of children thinking guide us to know that learners might be able to do some kinds of things that depend on their age rather than their skills (Goos, Stillman, & Vale, 2007).  During the late 1980s and 1990s, these views were introduced  as the constructivism.

Generally, constructivism is a practical idea which considers students as an active learners in the meaningful and essential process of learning and interpretation is important process to facilitate students in constructing their understanding (Cobern, 1993). In constructivism view the process of creating or inventing knowledge is an active process rather than a passively received process. (Booker, Bond, Sparrow, & Swan, 2014). In addition, to help students construct their individual knowledge, learning process may involved social processes such as discussion, argumentation, justification, and negotiation. Developing and constructing their ideas will not be able to be realized without good interaction with other students, teachers, and also their environment. In this way, teachers have very important and essential role because they can help students to improve their skills and build more powerful constructions as well as to develop their self motivation.

In the process of constructing a new knowledge, the successful learning outcomes also comes from the knowledge that learners or students have (Cobern, 1993; Curcio, 1981; McComas, 2014; Novak, 1978). They have this existing knowledge either from their experiences or learning environment. Existing knowledge or prior knowledge is not necessarily a product of formal education which means that it comes from the learning process in the classroom. However, it could be come from student’s experiences or individual exploration (Bransford & National Research, 2000). A case in point is some students have information or know something because they have visited some places or because they have experienced a traumatic condition or even their parents work in particular places. Using prior knowledge in introducing and explaining new topic to students is important part of learning process which teacher should be more concerned about. The important of prior knowledge will be described as follows.

Firstly, a lot of studies talk about that prior knowledge affects how the students perceive and organize new information (Curcio, 1981; Guo, Yang, & Ding, 2014; Matsuka & Sakamoto, 2007; McComas, 2014; Resnick, 1983). In learning process when teacher start the activity with terms and concepts, every students will have many various interpretations based on their existing knowledge either from their previous studies or experiences. Cobern (1993) states that prior knowledge can affect interpretation and interpretation is supported by discourse. As was pointed out in the cognitive development stages of Piaget, the different interpretations may occurs in every stages. Interpretation of new things depends on student’s mental schema. The existing knowledge that students have in their mental schema will help students to intrepret new terms and can build their understanding of the topic discussed. As the result, new information will organize well in their mental schema.

Secondly, prior knowledge also affects how easily students make connections for new information. In the process of learning, students will find lot of new information and therefore existing knowledge can help them to hook up with information that they achieve. They can connect every single information, which is of course appropriate, that already exists in their memory to the new information. The more connections, the easier it is to remember. For instance in studying the concept of fraction, students who have better basic knowledge in proportion, least common multiple, greater common divisor, multiplication, and some other concepts will be easier to undertstand fraction and any operation in fraction.  This is why the meaningful process will come when students can connect their previous knowledge to the new knowledge.

Furthermore, in particular subjects, for example mathematics and science, prior knowledge can also help students when they are working with examples (Rittle-Johnson, Star, & Durkin, 2009). Examples can improve students’ skills in problem solving. Appropriate prior knowledge can assist students to understand and compare some kinds of examples to solve mathematical problems in order to estabilish their critical aspects (Guo et al., 2014). In fact, students without existing knowledge will find difficulties in dealing with the tasks given because they must complete some new information before solving the task, whereas the students with appropriate prior kowledge can easily solving the task without overloading their working memory. Rittle-Johnson et al. (2009) in their study of investigating the influence of prior knowledge in using solution methods carry out the effectiveness of comparison in learning equation found that students with lower level of prior knowledge tent to understand examples step by step. By contrast, students with higher level of prior knowledge tend to understand and investigate the number of solving methods. Solving mathematical problems needs students’ skills in dealing with multiple ways to find the solutions. Therefore, students who bring their existing knowledge into the mathematical problems will easily understand and work with the possible solutions.

As have to be remembered that prior knowledge is not only neccessary for helping students exploring new topic but also it can be problematic as well. This is because, the prior knowledge which students bring into classroom cannot be guaranteed whether it can make learning meaningful or not. For example when students learn about how to measure length of objects using ruler, students consider that the lenght of this object can be representated by looking at the numbers in the ruler. The problem is that when they have to use the broken ruler, which the number is not started from 0, some students still use the same way and look at the number in the ruler. They do not recognize that their concept of lenght is  incorrect. Owing to this, teachers as the facilitator in learning activities should guide students with their various prior knowledge by giving some instructions. The role of teacher is to help students construct their ideas by solving the problem using their existing knowledge and make the classroom as the best place for them to explore new information, negotiate path to find the solutions, reflect on what has happened (Booker et al., 2014). Teachers will need to ask questions that challenge inappropriate ideas and generalisasiton, and create new problems that may help students to revise their previous constructions or ways of thinking. As have mentioned above, they are a guide as well as motivator to students. However, this is not an easy task to do because they have to deal with the students’ different condition in the classroom. “The challenge will then be to lead children to come to understand and accept this as a method of their own, rather than simply practising and acquiring by rote another person’s way of doing something” (Booker et al., 2014). Therefore, competence teacher needs to be a good guidance for students.

Another example of learning activities that show the important of using prior knowledge to help students successful in learning activies as well as teachers in improving their teaching quality is in topic of measuring angles. Teachers can guide students to understand how to measure angles using nonstandard units before using the standard units. They can start using something from students’ daily lives because it can make students more interested in doing the learning activities. Moreover, their prior knowledge also can come from their daily experiences. In teaching measuring angles teachers can use context of pizza (pizza pictures) as the starting point. Slices of pizza can be used as the nonstandard units to guide and introduce students about how to use standard units for example protractor. An angle measure constructed from a circle of pizza is helpful. Teachers can create some angles shape from pizza for example 900, 300, 450 and other angles and use them as nonstandard units. Students should have prior knowledge about kinds of angles and use it to build their understanding of measuring angles using protrator. By doing some meaningful activities using the context of pizza supported by their existing knowledge about angles, they will have a deep understanding of how to measure an angle using protractor as standard unit. In addition, teacher’s role is very important to facilitate students when they discuss and build their undertanding of this concept.

In conclusion, meaningful learning process can be started from constructing students knowledge. The idea of constructing knowledge that generally known as constructivism is developed based on the Piaget concept of developmental stages of children’s cognitive development. Constructivism looks learning process as the active process of creating knowledge. Constructing a new knowledge can be developed from knowledge which students have and bring to the classroom prior to commencing a new topic. Prior knowledge or existing knowledge might be coming from student’s experiences or their environment conditions. It enable to help students to accept, organize and connect the new information during the learning process. In adddition, prior knowledge can help students in comparing examples. However, the role of teacher is still important to guide and facilitate students develop their new knowledge. In the future, teacher should be more concerned about the prior knowledge of students and be more active to guide students in constructing and dealing with the new information. Teacher will be the main facilitator and also motivator for students in learning process.

Posted in Discussion, Education

History of the Field of Learning Environment

In the development of learning environments, there are some peoneers who have focused on the field of learning environment. Kurt Lewin and Murray are the first people who are concerned about classroom environment (Fraser, 1986). Their ideas used to work on educational research environment. Lewin (1936) admitted that dominant determinants of human behaviour is environment and the interaction with personal charactersitics. It was introduced in the formula B = f (P,E) which is emphasizes the need for research strategies in which behaviour is considered to be a function of the person and the environment (Fraser, 1986, 2012). Murray (1938) was the first person who followed Lewin’s approach. He introduced a needs-press model which created analogous representation of individual and her or his environment. Motivational personality characteristics describes personal needs (Fraser, 1986). On the other hand, enviromental press refers to external counterpart which determines the expression of internalized personality needs whether can be encouraged or discouraged (Fraser, 1986). Murray also proposed alpha press and beta press term as approach in educational environment. The environment as assessed by a detached observer was described by the term of alpha press, whereas the environment as perceived by milieu inhabitants was described by the term of beta press (Murray, 1938).

 

Stern has revived and explicated the theory of needs-press in his comprehensive book and widely cited articles (Fraser, 1986). Moreover, based on Murray’s work, Stern (1970) developed personal-environment congruence theory. In this theory, “complimentary combinations of personal needs and environment press could improve student outcomes” (Fraser, 1986).

 

The other pioneers in the development of learning environment who focused on research which involve assessment of perceptions of classroom environment (Fraser, 1986) are Herbert Walberg and Rudolf Moos. It was more than 40 years ago since Walberg evolved earlier versions of the widely used Learning Environment Inventory (LEI) in research. He was also involved in evaluation activities of Harvard Project Physics (Walberg & Anderson 1968). Moos, collaborated with Edison Trickett, developed the first of his social climate scales in which psychiatric hospital and correctional institutions used, which conclusively caused the development of the Classroom Environment Scale (CES) (Moos & Trickett, 1974). Moos’s scheme for classifying human environments is used as in classification of scales for learning environment instruments. There are three basic dimensions namely Relationship Dimensions, Personal Development Dimensions, and System Maintenance and System Change Dimensions (Fraser, 2012). Relationship Dimensions identify the nature and tension of personal relationship within the environment and assess people’s contributions to help the other one in their environment, while Personal Development Dimensions assess basic directions where personal growth and self-improvement appear. On the other hand, System Maintenance and System Change Dimensions involve the term how the environment is orderly, clear in expectations, is under control, and is responsive to change. In addition, all the learning environment instruments can be classify at least in one of the Moos’s scheme.

Posted in Discussion

Pembelajaran Tematik Kurikulum 2013: Perubahan Energi dan Konsep KPK

Kurikulum 2013 yang baru mulai diterapkan di tahun ini, 2013. Penerapan memang belum dilaksanakan di semua kelas di setiap jenjang pendidikan. Penerapan Kurikulum 2013 baru dilaksanakan di kelas I dan IV Sekolah Dasar (SD), kelas VII Sekolah Menengah Pertama (SMP), dan kelas X Sekolah Menengah Atas (SMA). Di tingkat SD, kompetensi pembelajaran dikembangkan melalui pembelajaran tematik integratif yang dilaksanakan dengan pendekatan sains. Pembelajaran tematik meliputi berbagai mata pelajaran yang disajikan secara terpadu dengan tema sebagai pemersatu.

Berikut salah satu contoh penerapan pembelajaran tematik integratif yang diterapkan di kelas IV Sekolah Dasar. Pembelajaran ini dilaksanakan dengan mengintegrasikan pelajaran Matematika, IPA dan Bahasa Indonesia dengan Tema Selalu Berhemat Energi dan subtema Pemanfaatan Energi. Pada materi ini siswa mempelajari tentangenergi dan perubahannya serta dikaitkan pula dengan konsep Kelipatan Persekutuan Terkecil (KPK). Video pembelajaran berikut salah satu bentuk pembelajaran yang berlangsung di kelas.

Berikut pula disajikan contoh Rencana Pelaksanaan Pembelajaran (RPP) dan Lembar Aktivitas Siswa (LAS) untuk memberikan gambaran secara garis besar pelaksanaan pembelajaran yang berlangsung di kelas. Untuk mendownload contoh RPP dan LKS dapat didownload di bawah ini:

RPP Pembelajaran KPK: download

LAS Pembelajaran KPK: download

Posted in Discussion

Realistic Mathematics Education (RME), Solusi Pembelajaran Matematika yang Bermakna bagi Siswa

Dewasa ini, matematika masih dianggap sebagai momok bagi siswa. “Matematika itu sulit.” Kata sebagian besar siswa. Banyaknya rumus dan konsep matematika mungkin menjadi hal yang tidak menarik bagi siswa, yang pada akhirnya membuat matematika lagi-lagi tidak menjadi pelajaran favorit bagi mereka. Bukan hanya itu, penyampaian materi oleh guru masih dianggap terlalu monoton dan bukannya menjadikan matematika menarik bagi siswa tetapi menjadi membosankan.

Padahal jika ditilik dari fungsi matematika, pelajaran ini bukan tidak ada gunanya sama sekali. Matematika sangat memegang peranan penting  karena dapat meningkatkan pengetahuan siswa dalam berfikir secara logis, rasional, kritis, cermat, efektif, dan efisien. Oleh karena itu matematika harus dikuasai sejak dini oleh para siswa.

matematika-stkip-pgri-nganjuk

Banyak metode dan cara-cara kreatif untuk memperkenalkan matematika kepada siswa. Sekarang ini, bermunculan berbagai macam metode yang berusaha membantu siswa memahami dan menyelesaikan permasalahan matematika. Bermunculan pula cara-cara praktis dan cara-cara singkat menghafal rumus matematika. Namun ternyata, tidak semua metode dan cara-cara itu mampu menjadikan matematika bermakna bagi siswa. Menghafal rumus hingga mengetahui cara-cara singkat penyelesaian soal matematika tidak menjamin siswa memahami secara mendalam konsep yang diberikan. Padahal yang terpenting sebenarnya adalah makna dari konsep tersebut yang harus tertanam di benak mereka. Bukankah akan lebih mudah menyelesaikan permasalahan matematika, jika memahami secara mendalam tentang konsepnya terlebih dahulu? Adakah metode yang mampu menghantarkan siswa memahami konsep tersebut?

1

Di negeri Kincir Angin, Belanda, ada sebuah pembelajaran yang dikembangkan sejak tahun 1970 yang dikenal dengan Realistic Mathematics Education (RME). RME merupakan buah pemikiran penulis, pendidik, dan matematikawan Belanda berkebangsaan Jerman, Hans Freudenthal. Pemikiran menarik dari pendiri Freudenthal Institute ini salah satunya adalah ”mathematics as a human activity, mathematics must be connected to reality, stay close to children’s experience and be relevant to society, in order to be of human value”. Matematika harus relevan dengan kehidupan sehari-hari dan dekat dengan siswa.

Dalam pembelajaran RME, siswa dikenalkan dengan konsep dan abstraksi matematika melalui hal-hal konkret dan diawali dari pengalaman dan lingkungan sekitar siswa (use of context). Untuk mengantarkan siswa ke bentuk abstrak dari matematika, digunakanlah model berupa benda manipulatif yang tentunya juga harus menarik dan dapat meningkatkna minat siswa (use of model). Peran siswa dalam pembelajaran pun sangat diperlukan (student contribution), juga bagaimana mereka mampu berinteraksi dengan siswa lainnya maupun dengan guru (interactivity). Selain itu keterkaitan antara konsep dalam matematika juga penting perannya dalam pembelajaran RME ini (intertwining).

soal-matematika1

Perkembangan RME saat ini sudah cukup luas, tidak hanya di tanah kelahirannya, Belanda. Di Indonesia sendiri, RME sudah mulai ramai diperbincangkan dan diterapkan di beberapa sekolah. Di Indonesia sendiri, RME telah diadopsi dan dikembangkan sesuai dengan karakteristik pembelajaran di Indonesia. RME di Indonesia dikenal dengan Pendididikan Matematika Realistik Indonesia (PMRI). Dalam kurun waktu empat tahun terakhir ini pula beberapa calon dosen yang tergabung dalam International Master Program on Mathematics Education (IMPoME), mendapatkan kesempatan untuk belajar langsung tentang RME di Utrecht University. Apa yang mereka dapatkan di sana, nantinya akan diterapkan dan dikembangkan di Indonesia. Harapannya adalah, semoga pembelajaran RME mampu merubah image matematika menjadi pelajaran yang menyenangkan.

Sumber:

Yuwono, Ipung. 2007. Pembelajaran Matematika Realistik. Malang: UM Press.

Marja van den Heuvel. 2000. Mathematics Education in the Netherlands: A guided tour. Utrecht University.