ThatQuiz for teachers

Children love to learn in a playway method. Why not try evaluating their knowledge using readymade quizzes ? Recently, I was exploring some recreational Math resources for teachers and I stumled upon ThatQuiz.

ThatQuiz for Teachers is a free testing service for teachers to use with their classes. Multiple choice tests and math tests can be administered to students using this website. All grades are immediately reported to the students. Teachers receive complete record keeping of test results, including all grades and wrong answers.

Here is the link.

Ken Robinson Answers

I've written about Ken Robinson a few times (One and Two). The idea of creativity in mathematics was a sub-theme for my summer calculus class. Students at the end felt that some of the open-ended assignments (projects of their choice), non-standard problems (like the mobiles) and emphasis on problem solving helped open them up to creativity in math. But they suggested more specific demonstrations of how to be creative. (Boy, is that insightful.)

TED occasionally has question and answer sessions with their speakers who really ignited something with their presentation, and Sir Ken recently did this. (Here's the article.) He addresses math specifically:

"If you want to promote creativity, you need, firstly, to stimulate kids minds with puzzles and questions which will intrigue them. Often that's best done by giving them problems, rather than just solutions. What often happens in classrooms is, kids sit there trying to learn in a drone-like way things of not much interest that have already been figured out.

The best math teachers I know, like the best English teachers, are always giving kids puzzles. They're given things to work on where math skills are required but may not be the focus of the activity. There giving them problems to solve. Or they're made to engage with age-old mathematical problems. For example, I'm thinking about the problem of latitude. How do you go about measuring the planet? I mean, somebody had to do that. How do you do it? Professional mathematicians have such a cornucopia of fascinating puzzles, questions, proposals and conundrums. A great math teacher really has endless opportunities to stimulate kids minds and get them engaged with things they'd probably never thought about before. Rather than just giving them techniques." -Ken Robinson

It's not hugely original, but it's nice to get confirmation of things we believe from outside sources. He touches on engagement several times in the Q&A, and I do believe that's the central issue in teaching, and I love to ponder what is the key for math. Going to more and more of these reading conferences, I am insanely jealous of the teachers who talk about the book that turned a student on to reading. Problems don't seem to have the same effect.

Math Teachers at Play 13

The new carnival is up at Blog, She Wrote. The Money Games are there, as well as the generally nice idea of runnign a store for money practice at the Pumpkin Patch. I like some of the puzzles at Critical Thinking Puzzles. The card trick that's linked really makes you think about how much information there is in arrangement.

Money Games

Here are my two favorite money games. Change for the Better is based on a James Ernest design. He's the genius behind Cheapass Games (don't be put off by the name), and the game this is based on, Fight, he used to have on his business card. It really has some non-trivial strategy and thinking to it. Later I made the connection - or one of my preservice teachers did - with Smart, the excellent poem by Shel Silverstein. The other game I think I invented, Make It Take It. The idea was from a group of teachers who wanted students to be forced to find non-standard combinations of coins, instead of always taking 27 pennies, for example. That suggested a dwindling resource game to me. It's poissible to combine both with some visual representations of money, which is a nice support for struggling students. The handout is here, if you like worksheets or some of the representation support.

Smart
by Shel Silverstein

My dad gave me one dollar bill
'Cause I'm his smartest son,
And I swapped it for two shiny quarters
'Cause two is more than one!

And then I took the quarters
And traded them to Lou
For three dimes -- I guess he don't know
That three is more than two!

Just then, along came old blind Bates
And just 'cause he can't see
He gave me four nickels for my three dimes,
And four is more than three!

And I took the nickels to Hiram Coombs
Down at the seed-feed store,
And the fool gave me five pennies for them,
And five is more than four!

And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head--
Too proud of me to speak!

Change for the Better

Materials: Each player needs 1 quarter, 2 dimes, 3 nickels, and 4 pennies.

Rules: Play in groups of 2 to 6. Each player takes a turn. On their turn they put in one coin. They can take out a combination of coins that is less than the value of what they put in. For example, if you put in a dime (10¢) you can take back up to 9¢ – if it is there. Play continues until only one person has money left.

Instruction: Beginning players should just concentrate on the moves of the game. After students have gained some experience with the game, they can try recording their games to translate to symbolic representation. The data collected can then be examined for patterns.

Make It, Take It
a money game for 2 players or teams

Materials: Play coins or coin pictures or cards, amount cards. Record sheet if desired.

Play: Put the coins in the center. Shuffle the amount cards and make a stack. Players each turn over an amount card, and the player with the smaller amount goes first. On subsequent turns, players turn over an amount card, and see if they can make that amount with the coins. If they can, they take the coins. If they can not, it’s the other player’s turn. Play until all coins are gone, or both players in a row can’t make their amounts. The winner is the player with the biggest total value of coins they collected.

Variations:
Recommended starting amounts – 4 quarters, 6 dimes, 8 nickels, 10 pennies. Other amounts can be used. Teachers can add amount cards for more complicated amounts.
Players can roll two dice to determine the amount. (Note the dice variation requires more pennies.) Advanced play allows people to make change with the coins they’ve collected. For example, trading a dime from the center with two nickels they have taken before.
Players can use dollar value charts to keep a running total.

Example:
Bill and Keenya have been playing for a few turns.
Bill turns over 12 cents and takes two nickels and two pennies.
Keenya turns over 25 cents, but there are no quarters left. She takes five nickels.
Bill turns over 50 cents and can not make it.
Keenya turns over 6 cents and takes a nickel and a penny.
Bill turns over …

Instruction:
As with most games, it is recommended to play a game with teacher vs. the whole class to launch the game. Emphasize the variation in ways to make an amount by soliciting other possibilities from the students. Ask questions like “what card would be good to turn over next?” or “what card would leave me with no possibilities?” If someone is stuck, encourage good sportsmanship in helping them figure out a way to make the total. If that doesn’t seem to be working, or you are worried about their ability to make the amounts, students can play in a team of two vs. another team of two.

Many students will try a place value approach first, taking dimes and pennies. This will rapidly run them out of one or the other, forcing them to find other amounts. The amount cards concentrate on values that can be made with one, two or three coins, though several can be made with many more coins.

In summary, the teacher may wish to have students share their strategy for figuring their total at the end of the game. It is important to summarize by having students describe how they knew if they could make an amount or not. Another interesting discussion to start is if there is a strategy for better ways to play the game – is there an advantage to using fewer or more coins to make your moves?

Soal SNMPTN 2009

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Math Mama Writes...: Math Teachers at Play #11

Math Mama Writes...: Math Teachers at Play #11

The new Carnival is up, with Michigan Smith. I was interested in the Spirograph link. I've been trying to figure out a way to use spirograph to explore gear ratios for a cool fraction lesson.

Michigan Smith

This is a fun game that I've used 2nd-4th grade and at a family math night with some older kids. Also with my preservice teachers, of course. It practices measurement technique and familiarity with cm, as well as sneaking in some geometry about efficient paths and distances. There's not a lot of strategy, but there is some. The downside to the game is needing a new sheet each time you play - unless you laminate, of course.

The name Michigan Smith is my takeoff on Indiana Jones. This would be an easy game to dress up, or have kids make their own variation. The Gauntlet of Power picture is from the Magic the Gathering card of the same name, and is tm Wizards of the Coast.

The pdf is here at my faculty website. As an image it's below. Comments and feedback are always welcome.

Joke

From my brother:
A mathematician was confronted by his wife upon returning home at 3am.
'You said you'd be home at 11:45,' stated the wife.
'I said I would return at a quarter of twelve,' said the husband.

The funniest thing is that I'm always having these kind of conversations. Not from staying out too late, but from being too literal.

For your listening and viewing pleasure

One of the many interesting ceiling panels.

Goals of Math Ed

Arthur Benjamin, self-proclaimed mathemagician and a very popular mathematician among teaching mathematicians, at TED on why calculus is not an appropriate pinnacle for math education. To be replaced by: discrete mathematics (statistics and probability).

Teacher Props
Taylor Mali, teacher/slam poet on What Teachers Make. One of my calc students shared this. As Mike warned me, I'll warn you: profanity.

Interesting glass floor and 6 or 7 story dome of the main rotunda.

Planning
An audio link from the new teacher resource center: an audio interview with Suzanne Lieurance, a teacher trainer and children's author, about planning in threes. There's a lot here that's compatible with workshop teaching, emphasis on assessment and evaluation and teaching for engagement. A form for note taking is in the post here.

The graphics are from the beautifully restored Michigan State Capitol that we visited this weekend, which include a couple of nice mathematical designs . Lots of nice 4-, 8- and 16-fold rotational symmetry. And much nice frieze-type translational symmetry, too. The architect was Elijah Meyers, and this was his crowning work.

Using online tools-Prime number calculator

Web is expanding with information and creative tools for explorations. It has become easier for teachers to integrate readily available tools with classroom teaching. There are so many interesting tools which may be clubbed with teaching of Mathematics for creating not only interest in the subject but also extending a scope for further exploration. Say, for example when we are talking about Prime numbers in a classroom. Prime numbers are positive, non-zero numbers that have exactly two factors .Children normally see them upto 200 or a maximum of upto 500 as it is not expected from them to create a list by manual division process. And sometime they are not sure of correctness of what they have obtained.

I used Prime number calculator for checking whether a given number is Prime or not . This tool helped in finding next largest and next smallest prime numbers of a number. Prime number charts are created for displaying in classroom.

Other interesting links on Prime numbers

History

Eratosthenes of Cyrene

Prime number game using 100chart

Prime pages

Lesson

Eratosthene Sieve Interactive

Interactive prime number game

Soal UMB 2009

Tahun ini beberapa universitas negri seperti tahun sebelumnya mengadakan Ujian Masuk Bersama. Universitas yang tergabung dalam Ujian Masuk Bersama ini adalah Universitas Indonesia, Univesitas Negri Jakarta, Univesitas Islam Negri Jakarta, Univesitas Sumatera Utara, Univesitas Jambi, Univesitas Syiah Kuala, dan Univesitas Islam Negri Makasar. Pelaksanaan Ujian telah diadakan pada tanggal 6 - 7

Article on Interest in "Maths"

The same student that made the Problem Solving/Leadership connection sent me a cool link to a Guardian article. It's about adding interest to a dry subject (heyyy!) by adding content like art or emphasizing big ideas like infinity.

See the article by Marcus Du Sautoy

Metode Horizontal Perbarui Cara Vertikal

MATEMATIKA
Metode Horizontal Perbarui Cara Vertikal
Rabu, 17 Juni 2009 | 04:17 WIB

Oleh STEPHANUS IVAN GOENAWAN

Pengajaran berhitung dasar yang diajarkan di sekolah selama ini, meliputi penjumlahan, pengurangan, perkalian, dan pembagian, jika dilihat dari proses hitungnya, semua dilakukan secara vertikal.

Metode berhitung secara terstruktur ini disebut juga sebagai metode hitung tradisional. Sesuai dengan namanya, proses hitungnya dimulai dari atas menuju ke bawah. Karena metode hitung ini telah digunakan dalam dunia pendidikan selama berabad- abad, maka dapat disebut sebagai cara tradisional.

Pengajaran berhitung terstruktur secara horizontal merupakan cara berhitung baru, sebagai penyempurnaan cara hitung vertikal atau tradisional. Mengapa disebut sebagai penyempurnaan proses hitung tradisional?



Ada tiga alasan yang mendasari pernyataan tersebut berdasarkan proses hitung penjumlahan, pengurangan, perkalian, dan pembagian.

Pertama, konsep asosiasi tempat satuan, puluhan, ratusan, ribuan, dan seterusnya dalam metode tradisional untuk menyelesaikan proses hitung penjumlahan atau pengurangan tentu saja sudah ada, tetapi penekanannya kurang karena pemisahan nilai antara satuan, puluhan, ratusan, dan seterusnya tidak ditandai secara tegas dengan suatu notasi pemisah. Sedangkan pada metode horisontal konsep asosiasi nilai secara tegas dipisah dengan notasi pagar. Dengan adanya notasi pagar maka nilai tempat satuan, puluhan (|), ratusan (||) dan seterusnya menjadi lebih mudah dipahami dan dibayangkan.

Kedua, proses hitung perkalian melalui cara horizontal ternyata dapat menciptakan pola-pola khusus yang disebut sebagai portal atau pola horizontal. Melalui portal, proses perkalian menjadi lebih cepat dibandingkan dengan cara tradisional. Misal kuadrat bilangan 85 bila dikerjakan dengan metode horisontal adalah sebagai berikut; 8x(8+1)||25>72||25, atau hasilnya adalah tujuh ribu dua ratus dua puluh lima.

Selain itu, perhitungan cara horizontal merupakan pengajaran perantara yang baik dari belajar berhitung dasar secara tradisional masuk ke bidang aljabar. Aljabar merupakan cabang matematika dengan tanda-tanda dan huruf-huruf untuk menggambarkan atau mewakili angka-angka (KBBI). Dengan cara horizontal, khususnya penyelesaian perkalian menggunakan portal, siswa dituntun mengenal dari nilai variabel. Pengetahuan ini adalah fondasi dasar memahami sebuah persamaan atau fungsi dalam ilmu aljabar. Misalkan portal kuadrat a5 adalah ax(a+1)||25, di mana contoh soalnya seperti nampak di atas.

Kemampuan siswa mengenal keteraturan pola angka juga dapat dikembangkan melalui portal-portal metode horizontal. Melalui kemampuan ini metode horizontal mampu menciptakan creative human calculator—siswa mampu lakukan perhitungan perkalian melebihi kemampuan kalkulator 12 digit. Kemampuan ini bukan lagi merupakan bakat sejak lahir (gifted), tetapi dapat dipelajari melalui metris sehingga potensi kreativitas siswa dalam berhitung semakin terasah. Kita bisa menyaksikan kemampuan mereka dalam Olimpiade Kreativitas Angka (OKA) II pada 14 November 2009 di Universitas Atma Jaya, Jakarta.

Dalam proses perhitungan pembagian dengan cara tradisional, mencari hasil akhir dilakukan dengan serial mencari hasil sementara secara bertahap. Hasil sementara itu bila dikalikan dengan bilangan pembagi harus lebih kecil atau sama dengan pembilangnya. Bila perhitungan dilakukan dengan cara horizontal, aturannya lebih umum sehingga bisa lebih cepat mencapai hasil akhir.

Ketiga-alasan ini menjelaskan mengapa pembagian cara horizontal adalah penyempurnaan cara tradisional. Hasil sementara proses penghitungan pembagian metris bila dikalikan dengan bilangan pembagi boleh lebih kecil, lebih besar, atau sama dengan pembilangnya karena dasar pemilihan hasil sementara adalah selisih terkecil-pembilang dikurangi perkalian antara hasil sementara dengan bilangan pembagi. Selisih itu bisa bernilai positif atau negatif. Karena konsepnya menggunakan selisih terkecil, cara horizontal mampu memperoleh hasil akhir lebih cepat karena lebih cepat konvergen (Metris: pembagian ajaib, Grassindo).

Kita sepakat, berhitung merupakan ilmu dasar dan pintu gerbang mempelajari ilmu pengetahuan lain. Oleh karena itu, agar pendidikan di Indonesia dapat mengejar ketertinggalan bahkan menjadi lebih unggul dari pada bangsa lain, Indonesia mesti mengembangkan metode pengajaran yang kreatif dan inovatif secara mandiri.

STEPHANUS IVAN GOENAWAN Penemu Metris, Dosen FT Universitas Atma Jaya

Cerita tentang "Monster Matematika"

Setelah sekian lama tidak aktif menulis di blog, khususnya setelah perjalanan dari Timor Leste dan Australia. Pagi ini saya membuka rumah matematika. Dan sungguh surprise banget, saya menemukan komentar yang ditulis oleh Penulis artikel "monster matematika" di Kompas yang saat itu masih duduk di bangku SD. Terima kasih Non Nandiasa. Senang mendengar kisahmu kembali. Sungguh inspiratif. Tulisan itu paling tidak membuat dan memaksa aku berefleksi sebagai guru matematika. Dan refleksi atas tulisan itu aku share ke banyak kolega guru matematika, paling tidak yang membaca KOMPAS. Nah, berikut adalah kisah yang ditulis Non Nandiasa tentang matematika dan menurutku sekali lagi sangat inspiratif. Bukankah tak ada pelajaran yang lebih berharga selain sharing hidup itu sendiri?

halo bapak yang menulis komentar ini...
Kenalkan pak, saya anak SD yang dulu pernah menulis artikel "Monster Matematika" di kompas tersebut. Sampai sekarang saya
masih menyimpan artikelnya ^^Saya sangat terkesan dengan sikap bapak terhadap realitas proses belajar ilmu pasti (khususnya matematika ya hehe) di Indonesia. Alhamdulilah setelah tujuh tahun lalu saya 'bermusuhan' dengan matematika, saya sempat menemukan saat dimana saya menyukai matematika hahahaa...


Saat2 itu dimulai dari kelas 2 smp...kelas 1 smp memang masih ada guru yg seperti itu haha..tapi sejak kelas 2 smp, saya privat dengn salah satu tetangga. Dan menurut saya guru saya tersebut sangat menyenangkan. Cara mengajarnya juga aplikatif. Dimulai dengan memberi saya soal yg cukup mudah, terus ia memberi saya tiga lagi soal dengan tingkat setipe..lalu saya mengerjakannya dengan benar. Ia lalu
bertanya, mau mengerjakan soal seperti ini lagi atau lanjut? Karena saya senang mengerjakannya, saya mau lagi dan lagi mengerjakan soal dengan tipe sprti tadi.

Dengan hal ini, guru saya telah memunculkan rasa percaya diri kepada saya untuk AKHIRNYA ^^ bisa mengerjakan matematika tanpa stres hehehe...setelah itu guru saya menyuruh saya mengajarkan langakh2nya kepada ibu saya. Saya tahu mungkin saat itu ibu saya sudah tahu, tapi ketika saya jelaskan "gini lho caranya!!" lalu mendengar ibu saya ilang "Oo..! Jadi..." saya merasa orang paling pintar matematika sedunia hahaha...

Besok paginya dikelas, guru saya memberikan soal yang persisss setipe dengan yang saya pelajari sebelumnya itu. Kontan sy berdiri dan memberanikan diri maju. Saya mengerjakannya dengan benar semua...setelah itu saya sering maju kedepan kelas untuk mengerjakan soal dan kadang mengajari teman saya...guru saya pun mengakui adanya kemajuan ini, apalagi temen2 saya hehehehe...

lalu yang paling absurd, saat saya pindah ke daerah serpong saat kelas 3 smp. Kepala sekolah di sekolah tersebut memang terkenal sangat perhatian terhadap muridnya karena sekolahnya juga baru, dan muridnya sedikit...

Disitu alergi saya terhadap matematika muncul lagi karena sudah terlalu lama liburannya hehehe...tapi setelah beberapa lama, tiba2 kepala sekolah meminta saya ikut olimpiade MIPA di salah satu sekolah (tepatnya madrasah) yang terkenal dengan siswa/i nya yang pintar, cerdas, dan bermoral tinggi. Saya langsung kaget dong! Bisa apa saya ko tiba2 diminta ikut olimpiade MIPA??

Gila apa, mau kalah!
Setelah dikarantina beberapa hari, memang tim saya kalah. Dari 51 sekolah, saya berada pada urutan 49 ahahahahhaa...tapi setelah itu ibu saya senang melihat wajah saya. Ternyata kepala sekolah memang sengaja meletakkan saya di olimpiade tersebut agar kepercayaan diri saya terhadap matematika bisa tumbuh.

Terharu...
Besoknya saya berniat aktif dikelas matematika, karena sekarang ternyata kepala sekolahnya yang mengajar. Dan hati saya jumpalitan bukan main ketika suatu hari saya mendapat nilai 100 untuk ulangan mtk T.T...bener2 ga nyangka!! Saya yang bego matematika dulu gini...hahaha...

dan alhamdulilah sekarang saya sudah berkuliah di ITB, Bandung, di fakultas paling keren se ITB (hehehhehee), menjelang semester ke 3. Saya tahu fakultas ini bukan fakultas yang mengandalkan matematika atau MIPA sebagai pegangan utama akademiknya. Tapi saya sangat bahagia berkuliah dsini karena dsinilah saya menemukan orang2 yang setipe...hahahaha

Saya sangat berterimakasih kepada keluarga saya, terutama ibu yang selama ini selalu yakin terhadap kemampuan saya, lalu semua guru2, dan guru seperti bapak :))

Carnival

Trig Rummy is up in this edition of Math Teachers at Play, a nice way to experience some of the variety of math ed blogs that are out there. It's hosted this time by Homeschool Bytes.

Here's a quick game for young kids up to 1st or 2nd grade. I think I invented it, but it's basic enough that many people have done something similar, I'm sure.

Give Away - It’s better to give than to receive!

Players: 2 to as many as you can stand.

Rules: All players start with five blocks (coins, beads, etc.) For one player they should all be the same, but different from the other players. The goal is to give all your pieces away.

Turn: Player says how many pieces they have. Then they roll a die. Players give away as many as they rolled – except on a 6 they give away nothing. Choose one other player you are going to give your blocks to. The first player to give all their pieces away wins!

Questions: Good questions to ask include “How many will you have left? How many will I have? If you have 4, how many have you given away? I can give back 4 blue, how many red do I need to put in?” Work on counting on and subitizing. Subitizing is recognizing an amount by looking – for example, asking: “Can you tell how many blue beads you have just by looking?” Try arranging the pieces in common patterns, such as on dice or dominoes. For counting on, if the player knows how many of one color (like 3) count on the others (4, 5, 6, …) instead of counting them all from 1. Ask about strategy and try to get players to think about giving to those with least.