"Virtual Manipulative" to help learning mathematics

All about Virtual Manipulative Mathematics

W h a t   I s   a   v I r t u a l   m a n I p u l a t I v e ?

W

hat are Virtual Manipulatives?, Patricia Moyer, Johnna Bolyard, and Mark Spikell (2002) defined a virtual manipulative as "an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (p. 373).  Static and dynamic virtual models can be found on the Web, but static models are not true virtual manipulatives.  Static models look like physical concrete manipulatives that have traditionally been used in classrooms, but they are essentially pictures and learners cannot actually manipulate them.  "...[U]ser engagement distinguishes virtual manipulative sites from those sites where the act of pointing and clicking results in the computer's providing an answer in visual or symbolic form" (p. 373).  The key is for students to be able to construct meaning on their own by using the mouse to control physical actions of objects by sliding, flipping, turning, and rotating them.

Virtual manipulatives have a range of characteristics, such as pictorial images only, combined pictorial and numeric images, simulations, and concept tutorials, which include pictorial and numeric images with directions and feedback (Moyer-Packenham, Salkind, & Bolyard, 2008).  Currently, virtual manipulatives are modeled after concrete manipulatives such as base ten blocks, coins, pattern blocks, tangrams, spinners, rulers, fraction bars, algebra tiles, geoboards, and geometric plane and solid figures, and are usually in the form of Java or Flash applets.  Patricia Deubel of CT4ME developed the figure above to illustrate virtual manipulatives found on the Web, which are useful for mastery of basic skills and conceptual understanding of K-12 mathematics and calculus.

What role can virtual manipulatives play in the classroom?

Virtual manipulatives can be used to address standards, such as those in  Principles and Standards for School Mathematics (NCTM, 2000), which calls for study of both traditional basics, such as multiplication facts, and new basics, such as reasoning and problem solving.  Using manipulatives in the classroom assists with those goals and is in keeping with the progressive movement of discovery and inquiry-based learning. For example, in their investigation of 113 K-8 teachers' use of virtual manipulatives in the classroom, Moyer-Packenham, Salkind, and  Bolyard (2008) found that content in a majority of the 95 lessons examined focused on two NCTM standards:  Number & Operations and Geometry. "Virtual geoboards, pattern blocks, base-10 blocks, and tangrams were the applets used most often by teachers. The ways teachers used the virtual manipulatives most frequently focused on investigation and skill solidification. It was common for teachers to use the virtual manipulatives alone or to use physical manipulatives first, followed by virtual manipulatives" (p. 202).

Virtual manipulatives provide that additional tool for helping students at all levels of ability "to develop their relational thinking and to generalize mathematical ideas" (Moyer-Packenham, Salkind, & Bolyard, 2008, p. 204). All students learn in different ways. For some, mathematics is just too abstract. Most learn best when teachers use multiple instructional strategies that combine "see-hear-do" activities.  Most benefit from a combination of visual (i.e., pictures and 2D/3D moveable objects) and verbal representations (i.e., numbers, letters, words) of concepts, which is possible with virtual manipulatives and is in keeping with Paivio and Clark's Dual Coding Theory .  The ability to combine multiple representations in a virtual environment allows students to manipulate and change the representations, thus increasing exploration possibilities to develop concepts and test hypotheses.  Using tools, such as calculators, allows students to focus on strategies for problem solving, rather than the calculation itself.

According to Douglas H. Clements (1999) in  'Concrete' Manipulatives, Concrete Ideas there is pedagogical value of using computer manipulatives. He said, "Good manipulatives are those that are meaningful to the learner, provide control and flexibility to the learner, have characteristics that mirror, or are consistent with, cognitive and mathematics structures, and assist the learner in making connections between various pieces and types of knowledge—in a word, serving as a catalyst for the growth of integrated-concrete knowledge. Computer manipulatives can serve that function" (Section: The Nature of "Concrete" Manipulatives and the Issue of Computer Manipulatives, para. 2).

Christopher Matawa (1998, p. 1) suggested many Uses of Java Applets in Mathematics Education:

·         Applets to generate examples. Instead of a single image with a picture that gives an example of the concept being taught an applet allows us to have very many examples without the need for a lot of space.

·         Applets that give students simple exercises to make sure that they have understood a definition or concept.

·         Applets that generate data. The students can then analyze the data and try to make reasonable conjectures based on the data.

·         Applets that guide a student through a sequence of steps that the student performs while the applet is running.

·         Applets that present ''picture proofs''. With animation it is possible to present picture proofs that one could not do without a computer.

·         An applet can also be in the form of a mathematical puzzle. Students are then challenged to explain how the applet works and extract the mathematics from the puzzle. This also helps with developing problem solving skills.

·         An applet can set a theme for a whole course. Different versions of an applet can appear at different stages of a course to illustrate aspects of the problem being studied.

While the research is scarce on mathematics achievement resulting from using virtual manipulatives, Moyer-Packenham, Salkind, and Bolyard (2008) found, overall, results from classroom studies and dissertations "have indicated that students using virtual manipulatives, either alone or in combination with physical manipulatives, demonstrate gains in mathematics achievement and understanding" (p. 205).  Generalizability might be a concern, however, as found in Kelly Reimer's and Patricia Moyer's action research study (2005), Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study.  The study provides a look into the potential benefits of using these tools for learning.  Interviews with learners revealed that virtual manipulatives were helping them to learn about fractions, students liked the immediate feedback they received from the applets, the virtual manipulatives were easier and faster to use than paper-and-pencil, and they provided enjoyment for learning mathematics.  Their use enabled all students, from those with lesser ability to those of greatest ability, to remain engaged with the content, thus providing for differentiated instruction.  But did the manipulatives lead to achievement gains?  The authors do admit to a problem with generalizability of results because the study was conducted with only one classroom, took place only during a two-week unit, and there was bias going into the study.  However, results from their pretest/posttest design indicated a statistically significant improvement in students' posttest scores on a test of conceptual knowledge, and a significant relationship between students' scores on the posttests of conceptual knowledge and procedural knowledge.  Applets were selected from the National Library of Virtual Manipulatives.

Boston Public Schools has a professional development initiative to provide teachers and students access to virtual manipulatives and technology equipment that directly support the district's math and technology curricula.   Partially funded by a NCLB state grant, SELECT Math contains alignments for Grades 6-8, Algebra I and II, and Geometry with a Scope and Sequence calendar describing which book or chapter is being used in math classes during each month of the school year.  Click on the individual book/chapter to see the related SELECT Math alignments, worksheets, and links to supporting virtual manipulatives. The project began in 2002 as a collaboration between the Boston Public Schools' Secondary Math and Instructional Technology departments, in conjunction with their partner, the Education Development Center, Inc.  CT4ME believes this initiative to be valuable for middle and high school math educators throughout the country.  Visit Teacher2Teacher for more on the role of manipulatives.

 Here is bellowed some link that we can use to practice virtual manipulative at the classroom:

http://www.mathplayground.com/math_manipulatives.html

http://nlvm.usu.edu/en/nav/vlibrary.html                               

References:

http://www.ct4me.net/math_manipulatives.htm

Perempuan Punya Banyak Cerita....

Oleh: Siti Fatimah Azzahra    (Math. Sec. B-2009110019)

Apa yang anda pikirkan ketika mendengar kata ‘perempuan’?. Mungkin tidak sedikit orang berpikir seperti ini: perempuan itu lemah, harus modis, kurang berani, terlihat pasrah, dan lain sebagainya. Sekali  lagi, apakah anda pernah mendengar, jika seorang perempuan itu tidak harus mengecap pendidikan yang tinggi, karena pada akhirnya juga tugas perempuan itu hanya mengurus anak dan patuh terhadap suami. Maaf, saya tidak termasuk ke dalam golongan tersebut.

Berbicara mengenai gender, tentunya tidak akan ada habis-habisnya dan erat kaitannya dengan perempuan. Hal ini terjadi karena masalah gender merupakan masalah yang kompleks, dalam artian dapat mempengaruhi berbagai aspek kehidupan. Di antarnya, keharmonisan sebuah keluarga, budaya, juga lingkungan sosial.

 Gender pertama kali diperkenalkan oleh Robert Stoller (1968), yang memilki makna dan tujuan untuk memisahkan pencirian manusia, berdasarkan sifat sosial budaya dan kondisi fisik maupun biologis. Namun, hal yang harus digaris bawahi dari makna gender yang membuat orang salah kaprah adalah, gender sama dengan seks, padahal berbeda. Perbedaanya dapat dilihat pada tabel berikut ini (berdasrakan hasil musyawarah PGRI, 2006):

Perbedaan Sex dan Gender

Seks	Gender
Ciptaan Tuhan	“Buatan” manusia
Bersifat kodrat	Tidak bersifat kodrat
Tidak dapat berubah	Dapat berubah
Berlaku sepanjang zaman & di mana saja	Tergantung  waktu dan budaya setempat

Gender di mata khalayak sangat erat kaitannya dengan seorang perempuan.  Pada paragrap pertama telah diulas berbagai perspektif tentang  perempuan dan perannya. Meskipun saya tidak termasuk dalam orang yang berpikiran seprti paragrap awal tentang peran perempuan, namun saya termasuk orang yang beraada di dalamnya.

Berikut ini merupakan beberapa isu dan kenyataan yang erat hubungannya dengan gender.

Hidup di tengah keluarga yang konservatif tidaklah mudah, karena terdapat beberapa larangan yang harus dipatuhi, terutama oleh perempuan. Keluarga saya yang notabanenya termasuk orang-orang yang berpikir ke depan, juga tidak mempersilahkan para anak-anak perempuan mereka untuk mengecap pendidikan ke jenjang yang lebih tinggi, cukup hingga tingkat dasar saja atau menengah. Sayangnya,  mereka, para perempuan hanya bisa menundukkan kepala, karena percuma jika mereka bicarapun tidak akan di dengar.

Tidak hanya di pedasaan, keadaan sejenis cerita tersebut pun terjadi di masyarakat perkotaan. Sebut saja kota bunga. Terdapat seorang ibu dengan satu anak. Ibu tersebut tidak bisa berbuat apa-apa selain pasrah hingga hidupnya hancur dan anaknya terlantarkan. Peristiwa ini terjadi, karena sang almarhum suaminya. Dahulu suaminya tidak mengizinkan istrinya untuk membantunya mencari  nafkah, juga lebih menyerahkan semua urusan rumah tangga ke tangan pembantu daripda istrinya. Hingga akhirnya, ketika sumaninya meninggal istrinya tidak bisa hidup berdiri sendiri.

Hanung Bramantyo pun menyumbangkan karyanya dalam sebuah film layar lebar yang berjudul “Perempuan Berkalung Sorban”, yang diambil dari novel  karya Abidah El Khalieqy. Dari film tersebut, Annisa (peran utama) digambarkan sebagai perempuan yang penuh dengan larangan.  Annisa merasa tidak sependapat dengan penjelasa gurunya, yang mengatakan bahwa perempuan sejatinya harus tunduk kepada laki-laki, ini berarti perempuan berada pada posisi yang lemah dan tidak seimbang.

Tiga isu di atas, menggambarkan bahwa perempuan itu tidak lebih hanyalah seorang pembantu rumah tangga dan sebagai penurut. Pendidikan perempuan tidak boleh lebih tinggi dari laki-laki atau suaminya, merupakan masalah klasik yang cukup rumit. Suara perempuan seringkali diabaikan begitu saja, bagaikan hembusan angin belaka. Padahal tidak sedikit dari hasil pemikiran seorang perempuan mampu membawa suasana ke arah yang lebih baik lagi.

Contohnya Raden Adjeng Kartini, seorang putri dari bupati Jepara pada tahun 1980-an, menjadi promotor emansipasi perempuan. Beliau sangat menginginkan para perempuan Indonesia bisa mengecap pendidikan yang lebih tinggi dan suara para perempuan bisa lebih didengar. Berkat kegigihan beliau, kini peran perempuan lebih bisa dihargai daripada masa sebelumnya, meskipun  penyetaraan tersebut belum bisa dirasakan secara menyeluruh oleh semua perempuan, khusnya perempuan di Indonesia.beliau, kini peran perempuan lebih bisa dihargai daripada masa sebelumnya, meskipun  penyetaraan tersebut belum bisa dirasakan secara menyeluruh oleh semua perempuan, khusnya perempuan di Indonesia.

Di era globaslisai saat ini, tentunya tidak etis jika kita semua masih berada pada kelompok orang yang menganggap, bahwa perempuan itu tidak boleh melakukan hal yang dilakukan oleh lawan jenis pada umumnya, contohnya saja bekerja. Kebebasan untuk mendapatkan pekerjaan telah diatur dalam UUD RI 1945 pasal 27 ayat 2: “Tiap-tiap warga negara berhak atas pekerjaan dan penghidupan yang layak bagi kemanusiaan”. Pasal tersebut jelas mengindikasikan bahwa tidak ada batasan yang menghalangi seseorang untuk bekerja, termasuk perempuan. Karena pada hakikatnya laki-laki dan perempuan itu sama, yang membedakan hanya dari segi biologisnya saja.

Indonesia merupakan Negara hukum, yang memiliki aturan sendiri dalam menyampaiakan pendapat.  Dalam UUD RI 1945 pasal 28 yang mengatur hak asasi manusia mengatakan bahwa “Kemerdekaan berserikat dan berkumpul mengeluarkan pikiran dengan lisan dan tulisan dan sebagainya ditetapkan dengan undang-undang”. Pasal ini mendukung keras  kepada setiap warga Negara, untuk tidak segan-segan dalam menyalurkan aspirasi atau pendapat mereka, karena telah dilindungi oleh UU.

Terlepas dari isu-isu yang erat kaitannya dengan gender maupun diskriminasi, sebagai warga Negara Indonesia yang tahu adat istiadatnya, tentu tidak akan membiarkan segala permasalahan larut dalam waktu yang cukup lama. Emansipasi wanita sudah lebih dari 60 tahun di gebrakkan. Hal terpenting bagi adalah kita mampu memberikan dan melakukan yang terbaik untuk Indonesia. Dan untuk para perempuan Indonesia, jangan merasa kecil untuk hal yang lebih besar, karena Josiah G. Holland dalam Chicken Soup for the Woman’s Soul (2010), mengatakan bahwa “Harta milik paling berharga yang pernah muncul bagi manusia di bumi ini adalah hati seorang perempuan.”

REFERENSI

Canfield, J., dkk. 2010. Chicken Soup for the Woman’s Soul. Jakarta: Gramedia Pustaka Utama.

Majelis Permusyawartan Rakyat Republik Indonesia. 2000. Undang-Undang Dasar Negara Republik Indonesia Tahun 1945, Amandemen II. Jakarta. Diambil pada 11 November 2010, dari http://id.wikisource.org/wiki/Undang-Undang_Dasar_Negara_Republik_Indonesia_Tahun_1945/Perubahan_II#Pasal_28,

NN. 2010. Kartini. Diambil pada 16 November 2010, dari http://id.wikipedia.org/wiki/Kartini#Pemikiran

NN. 2009. Perempuan Berkalung Sorban. Diambil pada 15 November 2010, dari http://www.21cineplex.com/perempuan-berkalung-sorban,movie,2004.htm

 Persatuan Guru Republik Indonesia. 2006. Apa itu Gender?. Diambil pada 15 November 2010, dari http://www.scribd.com/doc/2591144/-Konsep-Gender

Toer, P., A. 2003. Panggil Aku Kartini Saja. Jakarta: Lentera Dipantara.

Gambar: dari http://www.google.co.id/imglanding?q=perempuan+-+gender&um=1&hl=id&sa=G&rlz=1C1_____enID399ID399&tbs=isch:1&tbnid=N7c1UaNYITyBgM:&imgrefurl=http://www.satuportal.net/content/ketidakadilan-gender-sebabkan-perempuan-rentan-hivaids&imgurl=http://www.satuportal.net/system/files/galeri/gender-adis-satu02.jpg&zoom=1&w=200&h=164&iact=hc&ei=pending&oei=LC7mTPKmL8P78Abx153VDA&esq=10&page=3&tbnh=131&tbnw=141&start=49&ndsp=18&ved=1t:429,r:0,s:49&biw=1366&bih=665Gender

Teaching Assistance will help Learning Process

Begins with a story, a story is about teaching assistance to develop education. 

There are so many lesson and value from teaching assistance and teaching experience that SSE's students who have done for their third semester project. At that time, some of them doing teaching assistance at SMAIT Nurul Fikri which  located at Jl. H. Sairi no. 145, Tugu-Cimanggis, Depok.  In this season, they have so many activities that are invaluable and unforgettable.

Actually, the team teaching have to teach at the second week, nevertheless in fact it doesn’t appropriate with campus’s plan. The school where students attend, ask to them for helping to teach. Thus, some of them have to teach at the first week, detail at the second day. They have to teach for X-B-Girl Class. In SMAIT Nurul Fikri the class are divided into two whole big class, girl-class and boy-class. Before they teach, they have to make a lesson plan. What a wonderful acrivity!

First day, they observed the class X-C boys and searching school data of SMAIT Nurul Fikri for completing administration. Based on their observation, the learning process is less effective, because I see that some of students don’t pay attention to the lesson and there exist students who still understand not ye about the course, quadratic equation. We konw with this situation, teaching whole  students and make them understand is not easy, and therefore being an effective teacher is not easy, although we have been a teacher or professional teacher.

For the next day, they have taught. They teach more than time that their campus has predetermined. They teach for the second until fifth day, but the way of teaching methods are different. At the second and third they teach at X-B-Girl class. The students are curiosity of the lesson, even though they are a little bit annoying. However, they try to be patient and know about them.  For the third fourth and fifth day, the class is made be small class. It means the class are divided into small group and we as a tutor of them.

Fortunately  , the small class  makes class be more effective than big class, because the student’s understanding and their attention will be easier to be controlled and students said that they more brave to ask what they o not understand not yet.

That’s all the story about teaching assistance. Hopefully, we as teacher candidate or whoever you are will do the best for education of Indonesia.