Why use LaTEX?

The tool has always been as important as the technique. Once it was the slide rule, then the calculator, and now, computer is at the center stage.

LaTEX, a computer mark up language, is one of the tool that is still being used in scientific and academic community due to its precision, ease and portability. Unlike other commercial (although very popular solution), LaTEX is free and providing a simple introduction to the separation of content over style/formatting.

LaTEX might require some learning curve but the result is worth it. As an introduction, students might learn about LaTEX through editors like Codecogs before they can type it on their own.

My students use LaTEX to express trigonometry equations on their online assessment, below is the screen capture of one of my students’ work:

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Additional Mathematics – Pilihan Kelas Siswa Pintar (kah?)

imageHampir 18 tahun menjadi guru matematika sekolah menengah pertama dan atas, ini menjadi tahun pertama saya menjalani tugas mengajar di kelas “Additional Mathematics”, sebuah kelas dari program Cambridge Curriculum. Dengan silabus yang telah disiapkan secara detil oleh mereka, kami para guru seperti biasa menjadi lebih mudah dengan mengikuti silabus dan skema kerja yang sudah rapi, dan kami hanya melakukan penjadwalan pembelajaran ulang mengikuti jadwal sekolah, yang dikenal dengan “lesson plan”.

Cambridge International Exam, menyediakan exam di kelas 10 (upper Secondary), dengan pilihan banyak mata pelajaran, salah satunya adalah Additional Mathematics (A-Math), yang konon diminati karena menunjukkan “kebanggaan” sekaligus “kemudahan”. Additional berarti tambahan, maka banyak materi yang ditambahkan dan lebih mendalam dibanding kelas matematika normal. Kebanggaan, karena dengan mengambil kelas ini, sudah menunjukkan punya dasar hitung matematika yang baik, konon pintar matematika cenderung pintar akan hal-hal yang lain. Kemudahan, karena konon jika ingin melanjutkan pendidikan di universitas unggulan yang berhubungan dengan jurusan teknik maka makin dipermudah dan memiliki peluang lebih besar.

Apakah benar? Menurut saya? Bisa jadi benar, tapi sangat tidak mutlak 100 persen.

Jika seorang siswa memiliki pengetahuan dasar hitung matematika yang baik, plus dia tetap rajin belajar dan mempertahankan ketekunannya tersebut, sudah pasti tidak akan mengalami kesulitan yang berarti pada saat mengambil kelas ini.

Sebaliknya, jika siswa masuk dalam kategori pengetahuan dasar hitung matematika yang  biasa-biasa saja tetapi punya niat dan semangat yang kuat dalam belajarnya, dia juga memiliki peluang berhasil lulus di mata pelajaran ini yang hampir sama dengan yang disebut duluan  di atas.

Namun yang perlu diingat, siswa tidak perlu berkecil hati jika tidak memiliki kemampuan luar biasa di dalam problem matematika. Ingatlah bahwa problem dalam kehidupan nyata memiliki banyak jenis dan variabel. Kecerdasan bernalar siswa bukan hanya dinilai dari kemampuan berhitungnya saja.

Terlepas dari masalah penalaran tadi, dengan keragaman variasi berhitung yang jauh lebih banyak, siswa yang masuk kategori tidak cerdas secara matematis tidak perlu memaksakan diri untuk mengikuti pembelajaran dan ujian di kelas ini. Ada kelas matematika dasar untuk level usia kelas 10 normal, yang juga sudah menyesuaikan tingkat kemampuan siswa, dengan dibagi lagi sebagai “core” (basic) dan “extended” (advance).

Permasalahan selalu terjadi pada pola pikir. Pola pikir orang tua yang ingin anaknya diterima di universitas ternama yang memberikan standar harus memiliki nilai dari A-Math. Lingkungan anak sendiri yang sesama teman saling gengsi, anak pintar matematika lebih favorit dan banyak teman. Dan yang paling menyedihkan mungkin datang dari sekolah sendiri yang  memiliki program jika siswa mengambil kelas pelajaran fisika dan kimia berarti sudah harus sepaket dengan A-Math. Kelas nomor satu 🙂

Sayapun mengamati,  banyak rekan guru yang mengajar matematika sering terpaku pada pola “soal susah harus membuat anak menjadi susah”. Dalam definisi saya, soal susah bukan berharap siswa akan kesusahan dan tidak dapat menjawab, tetapi berapapun susahnya soal itu justru memacu siswa untuk mencari solusinya dan mereka tetap bisa jawab.  Justru dengan soal susah itulah, siswa belajar mencari solusi dan tugas kitalah yang membantu membukakan solusinya, memberikan konsepnya, sehingga mereka dapat merekam pola jawabannya, mencampurnya dan menuangkan kembali jika dihadapkan pada soal lain.

Di perjalanan semester pertama ini, saya menerima satu siswa pindahan dari kelas mata pelajaran lain. Dia memiliki alasan bahwa dia menyukai tantangan dan senang berhadapan dengan angka dan walaupun telat akhirnya memutuskan bahwa mata pelajaran A-Math ini lebih cocok baginya dibanding bidang bisnis. Singkat cerita bergabunglah siswa ini di kelas saya dan saya setuju, siswa ini memiliki kecocokan bergabung di A-Math. Siswa yang cerdas, cerdas memilih yang tepat bagi dirinya dan yang terpenting anak ini bahagia dengan pilihannya.

Sementara di sisi sebaliknya, dua siswa di kelas saya, mengundurkan diri, dengan alasan yang kurang lebih sama, tidak mampu terus menerus berhadapan dengan angka, hitungan, rumus, aplikasi, dan semua kombinasinya. Satu dari dua siswa itu harus berhadapan dengan orang tuanya yang masih menaruh harapan agar tetap mengambil A-Math demi kemudahan memasuki universitas yang akan dituju nanti. Lambat laun, orang tua pun mengerti dan sangat mendukung sang anak. Sayapun bangga dengan anak ini, dia bisa menceritakan kesusahannya bergelut dalam belajar, berusaha mencari solusi, tiap hari sampai rumah jam 7 malam untuk pelajaran tambahan, tetapi yang terjadi, otaknya tidak sanggup menerima sebanyak itu, A-Math tetap “struggle”, pelajaran lain keteteran, merasa tertekan. Usia 14 tahun harus hidup setertekan itu? Tidak ada kegembiraan belajar lagi. Jadi saya sangat mendukung keputusannya dan percaya bahwa anak ini akan berhasil suatu hari nanti.

Sebagai siswa, jangan jadikan belajar sebagai beban apalagi jika siswa berada pada posisi diuntungkan dalam arti siswa mendapat kesempatan memilih mata pelajaran yang ingin diambilnya. Ambillah yang cocok dan memberikan lebih banyak peluang untuk bisa dikembangkan di kemudian hari.

Lebih ideal lagi, jika sebagai siswa bisa memahami apapun mata pelajarannya, kalau dijalankan dengan sebaik-baiknya, maka kemungkinan merasa terbeban bisa dihindari. Keuntungan bukan hanya diraih saat ini, tetapi bisa di kemudian hari. Belajar dan bahagia, dua kata bertolak belakang bagi siswa, benar bukan? 🙂

Percayakah sebagai siswa bahwa jika bahagia dengan apa yang kita pelajari maka apapun pelajarannya akan lebih mudah dipahami dan hasilnyapun (semoga) akan lebih baik. Seperti dalam hidup, kurang lebih sama, kita menjalani dan bersyukur, hidup kita senantiasa lebih bahagia.

Siswa juga kadang dihadapkan pada dua sisi, jika percaya diri mengatakan dirinya pintar, kesan pertama adalah sombong, lalu bagi orang tua atau teman beranggapan hal itu bukan disebut pintar tapi curang atau biasa saja. Tetapi jika selalu mengatakan dirinya tidak pintar, secara psikologis makin menghambat dirinya untuk percaya diri bahwa dirinya sanggup.

Karena pintar itu beragam dan setiap orang berhak mendefinisikan kepintarannya jika dibarengi dengan tindakan nyata dan hasil. Pintar berbahasa, pintar mengeluarkan pendapat, pintar mengatur keuangan, pintar menganalisa fakta sejarah, pintar mendisain / menggambar, pintar mengelola tangga nada, pintar dalam berolahraga, pintar  dalam kemampuan interpersonal, pintar memasak, dan segala pintar-pintar positif yang lain.

Maths Project Presentation

This is one of the examples from Matthew’s class projects. His Math Teacher required him to present this topic. Same thing with his friends with different topics. They did peer teaching in class. Good idea! (as long as the teacher still gives summary and correction after that).

After learning “factorisation” by himself (which was very hard for him in the beginning), he came up with the idea to use Power Point Presentation as his media when explaining in front of class.

With given help in video, his presentation looks like “a real video” 🙂 but unfortunately, he didn’t want to use his own voice 🙂 it’s okay 🙂

Hopefully, this video can help other students who need it.

Using Google SketchUp “3D for everyone”

Students in Primary and Junior high level, usually get introduced to 3D basic shapes through topics of finding the surface area and its volume. I’m not sure how deep they get into the idea and concept about it. Sometimes it can be so  hard for the children to see things in 3D or perspective.

Basic 3D shapes are prisms, cylinder, pyramid, cone and sphere. There are many prisms based on its bases. Rectangular prism means a prism with rectangle form base. Hexagonal prism means a prism with hexagon form base. Prisms and pyramid have flat faces, while cylinder, cone and sphere have curved surfaces.

They also focus on learning of rectangular prism or sometimes called cuboid (“balok” in Indonesian), there are some terms used to represent part of it.

1. Face Diagonal: is a diagonal on one of the faces. Since there are 6 faces in rectangular prism then the total is 12 face diagonals.

2. Body Diagonal / Space Diagonal: is a diagonal passing through the interior of the polyhedron, so there are 4 body / space diagonals.

3. Plane Diagonal: When two opposite face diagonals connected, a plane diagonal is formed. There are 6 plane diagonals.

Beside 3D basic shapes, there are composite 3D, such as capsules, combination between cube and pyramid, pendulum.

There are many 3D modeling softwares, and teachers can choose one that is more suitable for their students. For me, to help my students develop their three dimensional visualization ability, I found that Google SketchUp is a very useful software tools. A little bit of SketchUp, SketchUp is a 3D modelling program for a broad range of applications such as architectural, civil, mechanical, film as well as video game design — and available in free as well as ‘professional’ versions.

The concept of using Google SketchUp, is the basic knowledge of mathematics when students need to study how they find the volume. You just find the base area and measure how height it will be. That is volume. SketchUp tells you after drawing 2D shape as its base, “pull up” as height as you want then booommm 3D shape has been made. Easy to connect with Primary or Junior High level, isn’t it?

When I said about diagonals in a cube above, pictures below are the result when it’s drawn in Google SketchUp:

From left to right: cube 1, 2 and 3 describe plane diagonals (plane diagonal is in 2D shape), cube 4 describes face diagonals and cube 5 describes body / space diagonals.

diagonals' types

Below are some basic steps how to use Google SketchUp to create 3D shapes (my student Chika helped me with the tutorial)

How to make prism (4 sides)?

1.  First make a rectangle using this button tool rectangle

on layer rectangle

2. Press  pushpull tool  button then select the rectangle and pull the rectangle into a prism 4 sides.

rectangular prism

How to make pyramid (rectangle base)?

1.  First make a rectangle.

on layer rectangle

2.  Press line tool  button then make one line on the first diagonal of the rectangle.

face diagonal

3. Then take another line on the other diagonal.

two face diagonals

4. Then use button move tool , put on the intersection point of two face diagonals, move up, to make it into pyramid.

pyramid

How to make a cone?

1. Make a circle using this button circle tool

on layer circle

2. Then use line tool  button and put it on the center of the circle and drag it up, vertically on blue axis.

height of cone

3. Still use line tool button to draw a line from the top to one side of the circumference.

slant height

4. Still use line tool button and draw the third line connects the two end points, it becomes a right angle triangle.

before follow me

5. Press  tools  and press follow me lists in tools, then drag the triangle around the circle.

cone being followed

After creating 3D basic shapes, students explored and practiced themselves (under my supervision) to create many shapes and objects. Capsules and torus are combined as follow and students might end up with a very interesting cartoon character 🙂

Grisel's cartoon

This kind of active learning is one of the example of metacognition (The idea of controlling our thinking processes and becoming more conscious of our learning).  When higher-order thinking skills are what teachers are striving for in the classroom, then, teachers should make sure each student know their basic building blocks, and know how to combine it into more complex knowledge.

First, students installed the software. Second, they recognised and learned the tools. And finally, they created 3D shapes (started from the basic one – from simple composite 3D up to complex 3D object).

As their teacher, I also created one 3D object and use it to challenge them. This based on the metacognitive principles to include three essential skills:

  1. Planning: refers to the appropriate selection of strategies and the correct allocation of resources that affect task performance.
  2. Monitoring: refers to one’s awareness of comprehension and task performance.
  3. Evaluating: refers to appraising the final product of a task and the efficiency at which the task was performed. This can include re-evaluating strategies that were used.

Enjoy Learning! 🙂

After the lesson, then I received “A Gift” 🙂 love it…

A Gift

What is the most interesting present that you have ever received in your life?

When someone gives you a present, you must be very happy, don’t you? There are a lot of reasons why people buy presents for others. To celebrate graduation, having a baby, get marriage etc.  Or maybe, it is not only about buying the present but also creating or making product. Whether the gift was bought or created, it will surely be appreciated by the receiver.

Sometimes, the gift is a special creation by someone “gifted”, and it become a unique one-of-a-kind appreciation for the receiver, and it feels great to receive such gift.

Recently, I received a gift from my previous student. The gift is so special because he made “this project” after I introduced him to free software Google SketchUp during one lesson. The gift really shows his appreciation since he explored himself the technique needed to create a very futuristic 3D figure based on his imagination. From a simple lesson in Maths class become a marvelous design. The lessons also enabled him to nurture his hobby to create and share his own SketchUp based design. This is one of the best gift I have ever had 🙂

Hereby, I attach his email citation to me with the screen capture of his “Chrome Delta Space Ship”.

Hi, ma’am.

…….

Anyway, I never got a chance to properly say thank you
for introducing me to SketchUp, and a proper goodbye. The
file I have attached here is part of what basically is a
friendly competition between me and Nathan Hartanto. We sent
SKP files for Space ships designs. I have made two, one is
the one I sent in this mail, and one other I made for
practice. He made a highly detailed escape pod, and what
looks like a plain but somehow coordinated shape of the
ship. We’re done with that war when he started writing, and
he asked me to do revisions for him. That still continues
today. Shame about not being in the same class though.

The interior is not done, but you can either walk in
through the hangar door under the back thrusters, or just
X-Ray the whole ship. Underneath the front thrusters (To
make amends to what Star Wars did wrong, the lack of
opposing force to decelerate ships in space), is a landing
gear, and underneath both wings are two more landing gears.
There are a total of six thrusters, Two in the back, one in
each wing, and two in the front. Nathan commented on the
uneffective design on the hangar, saying that a ship should
not carry many fighters, and that the hangar should be able
to fit at least three on one drop. But, it was made
aesthetics first.

If you have never introduced me to SketchUp, this would
not have been possible. I never would’ve made a dozen more
projects, and this ship to satisfy my imagination. So for
that, I formally here in this e-mail would like to say thank
you, ma’am. Thank you.

Also,…… I’d like to also say good bye to you,
and hope that somewhere else, you may help other students
progress. Your teaching style is quite top notch ma’am, and
I am sure your son is grateful to have a mother like you.

One last thing, …… I wanted
something better to present. Something that would make
people kinda have a sense of disbelief that this project was
made from scratch by a then eight grader. I believe I’ve
done it, in my own honest opinion, and though it’s very
late, consider this a farewell gift. I want to create a
version 2,0 of the similar ship from scratch, but that needs
time. So, this’ll do.

Picture 9

Picture 3

Picture 6

Picture 7

Picture 8

Picture 4