Mathematics – Page 9 – Hedy's Place

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.

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

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

How to make pyramid (rectangle base)?

1. First make a rectangle.

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

3. Then take another line on the other diagonal.

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

How to make a cone?

1. Make a circle using this button

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

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

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

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

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 🙂

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:

Planning: refers to the appropriate selection of strategies and the correct allocation of resources that affect task performance.
Monitoring: refers to one’s awareness of comprehension and task performance.
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.

(Seni)nya Belajar

“In teaching our pupil’s school subjects, we fail lamentably on the whole in teaching them how to think. They learn everything except the art of learning”

Membaca kutipan dari Dorothy Sayers di atas, membuat saya merasa tergelitik dan merefleksikan bahwa mungkin sekali sebagai guru lupa menekankan betapa belajar itu bukan hanya belajar sebagai bisa atau tidak, benar atau salah, tetapi lebih dalam lagi sebagai sebuah seni.

Dengan memberikan kerangka untuk kualitas bagi anak-anak pelajar itu, kita turut membantu mereka untuk mengembangkan kreatif, semangat tangguh untuk belajar dan peningkatan kinerja yang akan menjadi katalisator seumur hidupnya untuk sukses.

Tetapi pertanyaannya, apa saja yang masuk dalam kerangka kualitas tersebut? Setiap orang merasa akan memiliki kerangka sesuai pola pikir masing-masing. Mungkin tidak ada benar atau salah di sini, melainkan kombinasi ide dan situasi kondisi yang dihadapi di lingkungan kita sebagai pendidik dengan para siswa sebagai yang dididik.

Berikut ini mungkin contoh yang bisa atau pernah terjadi. Siswa mendapatkan nilai tes yang baik di mata pelajaran yang diampu seorang guru. Banggakah siswa dan guru? Jelas. Bagaimana respon guru menanggapi hasil memuaskan si siswa? “Wah nak, kamu pandai sekali ya”, atau bercanda sesama guru “siapa dulu dong gurunya”, atau “saya bangga lho dengan usaha dan kerja kerasmu”. Kualitas respon mana yang lebih baik menurut anda?

“Bangga dengan usaha dan kerja keras” menunjukkan jika si guru sangat menguasai proses belajar siswanya. Jauh lebih bangga bagi kita jika mendapati siswa yang menjadi lebih suka belajar atau lebih mau belajar dalam proses bersama gurunya. Banyak sekolah dan guru terjebak dengan keuntungan memiliki siswa sebagai sumber daya yang sudah memiliki kemampuan / bakat menonjol baik akademis maupun bukan. Bangga dengan berbagai kejuaraan yang disandang walau kadang miris juga melihat kebanggaan guru yang sebenarnya “wong anaknya sudah pintar dari sananya”. Atau guru yang sudah terlihat apriori bahkan membuat label jika anak yang bersangkutan sudah pasti nilainya kurang. “Pasti remedial”… hmm, sadar tidak ya guru dan sekolah, bagi sebagian siswa, mereka mampu memanfaatkan remedial sebagai jalan keluar. “Ulangan? Pasti gagallah, tunggu saja nanti juga remedial”. Katalisator guru seperti itu jelas-jelas beda dengan katalisator yang dimiliki sebagian siswa. Siswa dari berbagai kalangan seringkali bertanya untuk apa saya belajar pelajaran ini? Belajar topik ini? Kaitannya di masa depan saya apa?

Belajar adalah seni. Seni apa? Ya itu dia, salah satu seninya belajar adalah menghargai proses. Setiap kali di kelas waktunya belajar, itulah proses. Dalam proses belajarnya, siswa dibimbing, dibantu oleh gurunya. Tapi jangan lupakan dalam proses itu juga, siswa menunjukkan kinerjanya dan secara formatif hal tersebut dapat dites-kan. Yang sering saya amati sebagai “gap” nya adalah si guru merasa tes yang harus formal dong, guru kan dituntut professional, harus dalam format tes rapi, sekolah akan menentukan jumlah soal, soal-soal didokumentasikan dengan rapi, nanti diperiksa pengawas sekolah, nanti untuk diperiksa dinas, supaya akreditasi baik…..yaaaa panjang deh urusan pendidikan di negeri ini. Kalau saya berkomentar, memang dalam proses tadi tes tidak dapat diformalkan? Dengan rubric score yang baik, sangat bisa. Jangan-jangan si guru dan sekolah yang merasa “rugi” karena siswa lagi sedang paham-pahamnya terhadap pelajaran lalu diambil nilainya. Kalau lewat 1-2 minggu kan siswa belajar ulang, usaha dong supaya harus bisa…. (moga-moga bukan yang terakhir itu X_X).

Di samping menghargai proses, membimbing dengan contoh juga merupakan satu bentuk lain dari seni belajar. Membimbing dengan contoh saya yakini sebagai bagian dari “meta cognition” (berpikir untuk berpikir, belajar cara belajar).

Pada saat memberikan tugas kepada siswa, “memberikan contoh tugas” diyakini banyak pihak sebagai menutup peluang siswa berpikir dan berkembang atau dengan melontarkan pernyataan bahwa siswa harus kreatif dong. Itu dia, meminta siswa menjadi kreatif tetapi tidak dibimbing bagaimana mencari “kreatif” itu sendiri, tidak adil dong bagi siswanya. Kreatif kan bukan tujuan, bukan pula menunjukkan diri jadi guru yang kreatif, tetapi justru bagaimana si guru menciptakan peluang mencari cara menjangkau siswa dengan metode dan bahasa yang mereka mengerti, baru mudah-mudahan dari situlah metode kreatif akan muncul dengan sendirinya.

Percayalah, contoh yang kita berikan, tidak ada apa-apanya dibanding kemampuan mereka mengeksplor sendiri. Pancingan contoh kita membuat mereka berusaha menjangkau level kemampuan seperti itu bahkan tidak jarang bertekad mengalahkan level kemampuan itu (tergantung juga dengan kemampuan si siswa sendiri).

Contoh lain, guru tidak asing kan dengan kata kisi-kisi atau notifikasi untuk evaluasinya? Maukah guru memberikan kisi-kisi? Pasti beragam juga cara guru menjawab 🙂 “wahh muridnya nanti keenakan, mereka kan harus tahu belajar sendiri”, “sudah SMP, sudah SMA, sudah besar, bukan SD lagi, nanti keenakan”, “UN kan ada kisi-kisi, kita juga harus ada dong”, “tidak boleh sama sekolah, sekolah memiliki kebijakan tidak boleh kasih kisi-kisi”, “ah percuma, sudah capek-capek dibantu dengan kisi-kisi, belajar juga tidak, malah fotokopinya dibuang”… Atau sebaliknya justru ada sekolah yang mewajibkan buat kisi-kisi untuk formal tes nya, tetapi si guru yang sungkan memberikan lalu cukup dengan “outcomes” seperti “siswa dapat menyelesaikan soal aljabar” 😉 aljabar itu luassssss, yang mana? Berharap anak usia 12-16 tahun jadi jenius tahu aljabar semua?

Pernahkah guru mengajarkan pada siswanya bagaimana membaca kisi-kisi / notifikasi tadi? Bisa dicoba dengan mengajarkan kalimat-kalimat “outcomes” tersebut menjadi rangkaian kalimat soal dalam evaluasi yang akan dilakukan. Ajak mereka membuat soal-soal sendiri atau diawali dengan mencari kembali pada referensi buku teks atau catatan mereka soal-soal yang mencerminkan outcomes tersebut. Ajar mereka untuk melakukan prediksi, mencari alur dan koneksi dalam belajarnya akan kemungkinan soal-soal yang akan muncul dalam evaluasi nanti.

Untuk mengatasi ekspektasi yang tinggi dari anak-anak yang berkemampuan di atas rata-rata, guru juga dituntut sanggup memberikan materi lebih berarti juga perhatian lebih serta mengakomodasi sesuai dengan kebutuhan individual siswa. Jadi saat evaluasi berlangsung, siswa yang berkemampuan seperti ini juga layak mendapatkan ekstra bobot soal yang lebih mengundangnya untuk berpikir.

Jadi, belajar adalah sebuah seni yang akan terus menerus mengalir, tidak akan mati. Selamat belajar! Selamat mencoba berbagai metode / teknik pembelajaran baru / mengkombinasikannya! Semoga bermanfaat!

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