Windy adalah salah satu siswa yang terkenal di kelas matematika selama duduk di bangku SMA. Di kelas sewaktu sekolah, memang ada beberapa siswa yang sangat terkenal dan dikenal oleh guru dan teman-temannya. Biasanya siswa tersebut pinter, jagoan di kelas atau sebaliknya- siswa yang ekstrem satunya, “ngga bisa apa-apa” atau “katrok” bangetlah pinjam istilahnya Tukul Arwana. Dan sayangnya, Windy masuk kategori yang ekstrem kedua, seringkali dianggap ‘nothing’ dalam pelajaran matematika. Setiap habis ulangan bisa dipastikan dia salah satu siswa yang harus mengikuti kelas remedial. Sehingga julukan “Mr. Remidi” melekat padanya.
Apakah Windy, diam dan menyerah begitu saja? Bagi kebanyakan siswa ketika dirinya dianggap “nothing” oleh kebanyakan teman dan gurunya dia biasanya akan menyerah, diam dan tidak melakukan apa-apa, cenderung memandang rendah dirinya sendiri, nggak percaya diri dan lebih percaya kalau dirinya memang nggak bisa apa-apa. Tapi hal itu ternyata tidak untuk Windy! Dia mengakui memang dirinya lemah dalam pelajaran matematika. Dia menyadari dia kurang dalam pelajaran ini. Tapi dia masih punya dua hal, pertama, keyakinan bahwa matematika bisa dipelajarinya, kedua dia memiliki ketekunan. Mungkin dua hal itu, yang tidak dimiliki oleh banyak orang yang menyerah terhadap matematika. Dengan dua hal itu Windy bertahan untuk terus belajar matematika.
Windy yang SD dan SMPnya ditempuh di Papua dan ketika menginjak SMA melanjutkan studi di Yogyakarta itu, memang menyadari benar kemampuannya. Dia tidak malu mengakui bahwa dirinya butuh lebih banyak waktu untuk memahami suatu materi matematika dibanding teman-temannya yang lain. Mungkin sekali dijelaskan, teman-temannya sudah paham. Tapi windy butuh dua atau tiga kali penjelasan untuk materi yang sama. Untunglah, guru matematikanya seorang pastor yang memiliki kesabaran dua atau tiga kali lebih banyak daripada guru matematika biasa dan mau membuka kelas matrikulasi untuk siswa-siswa yang tertinggal dalam pelajaran matematika.
Untuk mengejar ketertinggalannya Windy selalu mengikuti kelas matrikulasi matematika yang diadakan sore hari di sekolahnya. Selain itu, dia juga menyediakan waktu khusus untuk belajar matematika sendiri, entah untuk mengulangi materi atau mengerjakan PR. Jadi bisa dipastikan, Windy adalah salah satu siswa di kelas dan mungkin di sekolahnya yang selalu mengerjakan PR matematika. Meski juga bisa dipastikan dari pekerjaan itu banyak yang salah juga. Tapi dari mengerjakan PR itu, dia sedikit-sedikit tahu kesalahan yang dibuatnya, bisa belajar dari kesalahan-kesalahan yang dibuatnya tersebut dan memperbaiki kesalahan itu lewat mengerjakan ulang PR yang salah itu.
Windy memang “Mr Remidi”, setiap kali ulangan dia memang boleh dikata nilainya hampir selalu dibawah standar ketuntasan belajar. Tapi nilai hasil remidi yang diikutinya pasti selalu diatas tujuh puluh, tak jarang mendekati nilai sempurna. Dan jangan heran, meski jagoan “remidi”, Windy lulus SMA dari jurusan IPA. Kini ia sedang menyelesaikan tugas akhirnya di jurusan Teknik Informatika di salah satu PTS cukup terkenal di Yogyakarta. “Jangan pernah menyerah dengan matematika, meski sesulit apapun. Dia akan memberikan pada kita sesuatu yang memang pantas untuk diperjuangkan. Cara berpikir, bernalar yang benar, berpikir secara logis dan sistematis.” Ungkapnya penuh keyakinan. “Kamu boleh tidak percaya, tapi saya sudah membuktikannya!” Percaya deh…
Minggu, 08 November 2009
Berbagi Matematika
Pak Yanto, begitu dia sering disapa, mengakui suka dengan matematika sejak kecil. Dan jika ditanya “mengapa suka matematika?” hingga sekarang dia selalu mengatakan tidak tahu alasannya. “Suka saja!”, begitu ia selalu menjawab. Sewaktu SD matematika adalah pelajaran favoritnya. PR yang selalu dikerjakannya adalah PR matematika. Bahkan ketika tidak ada PR pun dia selalu memaksa ibunya untuk membuatkan soal PR matematika.
Namun, kesukaannya terhadap matematika sempat meredup ketika SMP. Nilai matematikanya tidak cukup memuaskan buat dirinya, meskipun jika dibanding teman-temannya yang lain sebenarnya lebih dari cukup. “Waktu di SMP, guru matematikanya tidak menyenangkan.” kilahnya. Namun demikian, dia tetap belajar matematika meski standar seperti teman-teman lainnya, tidak seperti waktu di SD dulu.
Sewaktu SMA minatnya pada matematika kembali tumbuh. Di sekolah dia dikenal sebagai jago matematika oleh teman-temannya. Setiap pagi, dia selalu menjadi orang yang paling ditunggu di kelasnya. Teman-temannya sudah banyak yang antri untuk melihat dan mencontoh PR atau tugas matematikanya. Kadang malah ada yang pagi-pagi sudah nyamperi kerumahnya. Resikonya, karena “digilir” banyak temannya, kertas pekerjaannya jadi lecek dan tak jarang sobek. Untuk itu kadang dia harus buat tugas yang dikumpul rangkap dua. Maka jangan heran, kalau dia sering terpilih mewakili sekolah untuk mengikuti lomba matematika meski selama SMA itu tak satupun kejuaraan yang dimenanginya. Tapi itu tidak membuatnya surut menyukai matematika. Sebaliknya, hal itu membawanya pada kesadaran bahwa dia belajar matematika untuk tahu, mengerti dan paham tentang konsep matematika dan kalau bisa membagi apa yang diketahuinya itu pada teman-teman lain yang mau belajar matematika, bukan untuk menjadi juara lomba matematika, apalagi sekedar mendapatkan nilai matematika yang baik. Kesadaran baru itu semakin membawanya pada rasa suka yang lebih besar terhadap matematika.
Pada waktu SMA itulah, ia juga berinisiatif mengajari teman-temannya belajar matematika seminggu dua kali untuk persiapan ujian nasional di sekolahnya. Dan hasilnya, semua teman satu kelasnya lulus, meski dia sendiri hanya memperoleh nilai 6,25 untuk pelajaran matematika.
Kecintaannya terhadap matematika membuatnya memilih jurusan pendidikan matematika di salah satu PTS terkemuka di Yogyakarta, sebagai pintu masuknya menjadi guru untuk berbagi matematika dengan banyak orang. Kini ia pun menjadi guru matematika dan berbagi matematika dengan murid-muridnya.
Namun, kesukaannya terhadap matematika sempat meredup ketika SMP. Nilai matematikanya tidak cukup memuaskan buat dirinya, meskipun jika dibanding teman-temannya yang lain sebenarnya lebih dari cukup. “Waktu di SMP, guru matematikanya tidak menyenangkan.” kilahnya. Namun demikian, dia tetap belajar matematika meski standar seperti teman-teman lainnya, tidak seperti waktu di SD dulu.
Sewaktu SMA minatnya pada matematika kembali tumbuh. Di sekolah dia dikenal sebagai jago matematika oleh teman-temannya. Setiap pagi, dia selalu menjadi orang yang paling ditunggu di kelasnya. Teman-temannya sudah banyak yang antri untuk melihat dan mencontoh PR atau tugas matematikanya. Kadang malah ada yang pagi-pagi sudah nyamperi kerumahnya. Resikonya, karena “digilir” banyak temannya, kertas pekerjaannya jadi lecek dan tak jarang sobek. Untuk itu kadang dia harus buat tugas yang dikumpul rangkap dua. Maka jangan heran, kalau dia sering terpilih mewakili sekolah untuk mengikuti lomba matematika meski selama SMA itu tak satupun kejuaraan yang dimenanginya. Tapi itu tidak membuatnya surut menyukai matematika. Sebaliknya, hal itu membawanya pada kesadaran bahwa dia belajar matematika untuk tahu, mengerti dan paham tentang konsep matematika dan kalau bisa membagi apa yang diketahuinya itu pada teman-teman lain yang mau belajar matematika, bukan untuk menjadi juara lomba matematika, apalagi sekedar mendapatkan nilai matematika yang baik. Kesadaran baru itu semakin membawanya pada rasa suka yang lebih besar terhadap matematika.
Pada waktu SMA itulah, ia juga berinisiatif mengajari teman-temannya belajar matematika seminggu dua kali untuk persiapan ujian nasional di sekolahnya. Dan hasilnya, semua teman satu kelasnya lulus, meski dia sendiri hanya memperoleh nilai 6,25 untuk pelajaran matematika.
Kecintaannya terhadap matematika membuatnya memilih jurusan pendidikan matematika di salah satu PTS terkemuka di Yogyakarta, sebagai pintu masuknya menjadi guru untuk berbagi matematika dengan banyak orang. Kini ia pun menjadi guru matematika dan berbagi matematika dengan murid-muridnya.
Jumat, 06 November 2009
Golden Math Cartoon & Math Teachers at Play 19
I had to post this. I'm trying to help edit a collection of extension activities for Geometry being put together by teams of students under Char Beckmann for the Michigan Council of Teachers of Mathematics. (The Sum More books - more as they become available.) One of the activities involves cutting up a cartoon and then trying to arrange it in order to make the idea of arranging arguments in order in a proof. Long ramble, here's the cartoon: (Click for full size)
Their take on a pi joke. Pretty good for 9 and 10, eh? I inked it, and was told I boffed Fiddlestick's mouth in the last frame. They did a great job putting in clues as to what comes next.
Math Teachers at Play 19 (back on numbering) came out last Friday. My contribution was Area Block. The carnival is moving to a monthly schedule, which I think will be good. What was most fascinating to me:
Math Teachers at Play 19 (back on numbering) came out last Friday. My contribution was Area Block. The carnival is moving to a monthly schedule, which I think will be good. What was most fascinating to me:
- Maria Anderson, just up the road in Muskegon, is doing amazing work with technology in a math for elementary teachers class. I've got to meet her sometime!
- Jason Dyer's post on a reading experiment was interesting. (I wonder if it has to do with this cognitive miser issue. (Not a MTAP link.)
- Kendra at the Pumpkin Patch had a cute, quick sum game.
Selasa, 03 November 2009
Mencari beda dalam deret aritmetika
Salah satu bentuk soal matematika yang sering muncul dalam materi deret adalah mencari beda dalam deret aritmetika. Sebagaimana telah diketahui sebuah beda dalam deret aritmetika dapat dicari dengan aturan mencari selisih antara sebuah suku dengan suku sebelumnya, selain itu beda dalam deret aritmetika ( yang berhubungan denga Sn ) juga bisa dicari menggunakan aturan Un = Sn - Sn-1.Berikut adalah
Kamis, 29 Oktober 2009
An Ad?
While Math Hombre is traditionally ad free, I do owe a link to my daughter Ysabela. In exchange for her review of Babymouse: Dragonslayer, the excellent math/fantasy graphic novel by Jennifer Holm, I promised to plug her market craft.
Yzzy's Sticky Silverware has recycled silverware affixed with two powerful magnets and artistic embellishments to make a beautiful and practical refrigerator decoration. A steal at $1.25 decorated ($1 plain), you might pay up to $5 for a similar product at a craft show. Check it out! Mailing is at cost.
Some of the math involved was: figuring out the unit cost from the total materials cost, and also balances, profit margin, the length of the total wire based on the wire per silverware, (which was a pretty good upper el measurement problem). What is her break even point? That's the next calculation!
Yzzy's Sticky Silverware has recycled silverware affixed with two powerful magnets and artistic embellishments to make a beautiful and practical refrigerator decoration. A steal at $1.25 decorated ($1 plain), you might pay up to $5 for a similar product at a craft show. Check it out! Mailing is at cost.
Some of the math involved was: figuring out the unit cost from the total materials cost, and also balances, profit margin, the length of the total wire based on the wire per silverware, (which was a pretty good upper el measurement problem). What is her break even point? That's the next calculation!
Minggu, 25 Oktober 2009
Area Block
New game! Blokus meets Nim, this game works on area and strategy. Tested with fourth and fifth graders, but flexible upwards with sophistication in area computation techniques. Get it as a pdf here: AreaBlock.pdf
Materials: Game Board, 2 different color pens, pencils, crayons or markers.
How to play: Players take turns making a single shape on the board that has an area of 10 or less. The game is done when the board is filled, and the player with the most squares covered wins. The table is for recording how many squares you cover each turn.
The first player to go can only color up to 8 squares on their first shape. (Otherwise it would always be best to go first.) After that the limit is always 10.
The squares colored in to make your shape need to share a side, not just touch at a corner. (The shape you make has to be a polygon.) A player can even use slanted lines – as long as they can figure out the area for their shape! When you are making a new shape, it does not have to touch your old – you can put it anywhere there’s room.
After you make or shade in your shape, record the area of your block – you don’t want to miss any points. The next player then colors a polygon of up to 10 squares of area in a different color.
When the board is completely filled, the game is done. Total up your squares and see who won!
Notice you can check if all the squares are counted by adding both scores – you should get 100.
Whoever lost gets to choose the next time if they want to go first or second.
Variations:
• The board can be changed to have holes or blocks or be a different shape. As long as there are 100 squares. After trying these boards, make your own.
• The game can be played with dice. Roll 2 dice, and you can fill in the total rolled.
• Advanced players could try where their score is not the area – but the perimeter. (You might want to try that with no slanted sides.)
Board 0:
Board 1:
Board 2:
Board 3:
Board 4:
It's pretty fun! I haven't been able to spot a degenerate strategy yet. Give it a try, and let me know what you think.
Materials: Game Board, 2 different color pens, pencils, crayons or markers.
How to play: Players take turns making a single shape on the board that has an area of 10 or less. The game is done when the board is filled, and the player with the most squares covered wins. The table is for recording how many squares you cover each turn.
The first player to go can only color up to 8 squares on their first shape. (Otherwise it would always be best to go first.) After that the limit is always 10.
The squares colored in to make your shape need to share a side, not just touch at a corner. (The shape you make has to be a polygon.) A player can even use slanted lines – as long as they can figure out the area for their shape! When you are making a new shape, it does not have to touch your old – you can put it anywhere there’s room.
When the board is completely filled, the game is done. Total up your squares and see who won!
Notice you can check if all the squares are counted by adding both scores – you should get 100.
Whoever lost gets to choose the next time if they want to go first or second.
Variations:
• The board can be changed to have holes or blocks or be a different shape. As long as there are 100 squares. After trying these boards, make your own.
• The game can be played with dice. Roll 2 dice, and you can fill in the total rolled.
• Advanced players could try where their score is not the area – but the perimeter. (You might want to try that with no slanted sides.)
Board 0:
Board 1:
Board 2:
Board 3:
Board 4:
It's pretty fun! I haven't been able to spot a degenerate strategy yet. Give it a try, and let me know what you think.
Sabtu, 24 Oktober 2009
Group Matematika SMA
Mungkin sebagian besar kita sudah memiliki akun di salah satu jejaring sosial paling banyak anggotanya di seluruh dunia, Facebook. Ya, sebagian besar kita sepertiya lebih betah untuk berlama - lama duduk di depan PC kita hanya untuk sekedar mengupdate status ataupun membalas di wall teman kita. Nah ngga ada salahnya kan kalau sebagian waktu anda ketika mengutak - atik fb anda mampir ke group
Selasa, 13 Oktober 2009
GeoGebra: Triangle Tuning
What can we deduce from the side lengths of a triangle?
This is a preservice teacher activity, easily adaptable to middle or high school use. GeoGebra is a free dynamic geometry program available as an online applet or downloadable program, from geogebra.org.
Objective: TLW explore triangle properties relating type and side length.
Schema Activation: What are the 7 triangle types? Fill them in in the ‘Type’ column below. You'll fill in the other columns as you go through the activity.
.....Type ....................... Examples [Like (3,5,5) ] .......................What do you notice?
1.
2.
3.
4.
5.
6.
7.
Focus: One of the reasons dynamic geometry is so powerful is the support it allows the teacher (or curriculum designer) to give students for finding examples. Lots of examples. As we’ve discussed in class, the natural way we reason is to go from lots of specific examples to the general.
Activity:
1) Open the sketch TriangleBySide.ggb. (Online at faculty.gvsu.edu/goldenj/TriangleBySide.html)
a. Collect at least 2 examples of each type of triangle. Where possible, try not to have the triangles be similar, where all the sides are multiples of another triangle.
b. Which were hardest to find? Was it something to do with the type or how you were looking?
2) Open the sketch PythagoreanData.ggb. (Online at faculty.gvsu.edu/goldenj/PythagoreanData.html)
a. Look at your right triangle examples on this triangle. How do you think ancient mathematicians noticed this cool pattern with the squares
b. Check your other examples on this sketch. For each, record whether the sum of the areas of the smaller squares is <, =, or > the area of the large square.
c. What pattern(s) do you notice?
d. Why do you think your pattern(s) might be true?
3) Go to http://teachers.henrico.k12.va.us/math/GeoGebra_Site/pythagoras/pythaPrblm1.html (link on Blackboard) for the Ladder sketch. Answer the questions there.
a. How high will he get if he places the ladder 3 m off the wall? Drag the ladder point and find a solution. Sketch the solution with all its lengths (s, r, h) on paper.
b. Now, calculate the solution of task (a) on paper. Which lengths are given, which are sought? Do you get the same solution?
c. At what distance of the wall should Pythagoras place his ladder in order to reach the window 4.50 m above the ground? Sketch the solution with all its lengths (s, r, h) on paper.
d. Now, calculate the solution of task (c) on paper. Compare your solution to your sketch?
e. As a teacher, what do you notice about the difference between doing the tasks in sketch and on the paper?
4) Open the sketch AdjustableLadder.ggb (Online at faculty.gvsu.edu/goldenj/AdjustableLadder.html)
a. What young Pythagoras might not have known is that a safe ladder ratio is 4:1 for the height to distance from the wall. What length ladder does he need to reach the window safely? Is there one solution or more?
b. How would you solve this problem on paper?
Reflection:
a. What confirmed, new or deepened understanding did you develop regarding triangles through these activities?
b. How did the dynamic environment affect your understanding?
EDIT:
Be sure to look at the comments. Scott Farrar has some notes on using this with 9th grade geometry, and has added a complimentary activity.
This is a preservice teacher activity, easily adaptable to middle or high school use. GeoGebra is a free dynamic geometry program available as an online applet or downloadable program, from geogebra.org.
Objective: TLW explore triangle properties relating type and side length.
Schema Activation: What are the 7 triangle types? Fill them in in the ‘Type’ column below. You'll fill in the other columns as you go through the activity.
.....Type ....................... Examples [Like (3,5,5) ] .......................What do you notice?
1.
2.
3.
4.
5.
6.
7.
Focus: One of the reasons dynamic geometry is so powerful is the support it allows the teacher (or curriculum designer) to give students for finding examples. Lots of examples. As we’ve discussed in class, the natural way we reason is to go from lots of specific examples to the general.
Activity:
1) Open the sketch TriangleBySide.ggb. (Online at faculty.gvsu.edu/goldenj/TriangleBySide.html)
b. Which were hardest to find? Was it something to do with the type or how you were looking?
2) Open the sketch PythagoreanData.ggb. (Online at faculty.gvsu.edu/goldenj/PythagoreanData.html)
b. Check your other examples on this sketch. For each, record whether the sum of the areas of the smaller squares is <, =, or > the area of the large square.
c. What pattern(s) do you notice?
d. Why do you think your pattern(s) might be true?
3) Go to http://teachers.henrico.k12.va.us/math/GeoGebra_Site/pythagoras/pythaPrblm1.html (link on Blackboard) for the Ladder sketch. Answer the questions there.
a. How high will he get if he places the ladder 3 m off the wall? Drag the ladder point and find a solution. Sketch the solution with all its lengths (s, r, h) on paper.
b. Now, calculate the solution of task (a) on paper. Which lengths are given, which are sought? Do you get the same solution?
c. At what distance of the wall should Pythagoras place his ladder in order to reach the window 4.50 m above the ground? Sketch the solution with all its lengths (s, r, h) on paper.
d. Now, calculate the solution of task (c) on paper. Compare your solution to your sketch?
e. As a teacher, what do you notice about the difference between doing the tasks in sketch and on the paper?
4) Open the sketch AdjustableLadder.ggb (Online at faculty.gvsu.edu/goldenj/AdjustableLadder.html)
a. What young Pythagoras might not have known is that a safe ladder ratio is 4:1 for the height to distance from the wall. What length ladder does he need to reach the window safely? Is there one solution or more?
b. How would you solve this problem on paper?
Reflection:
a. What confirmed, new or deepened understanding did you develop regarding triangles through these activities?
b. How did the dynamic environment affect your understanding?
EDIT:
Be sure to look at the comments. Scott Farrar has some notes on using this with 9th grade geometry, and has added a complimentary activity.
Math Resources
Moodle
Moodle Math documentation
http://docs.moodle.org/en/Mathematics
Pretty technical information, but accurate and detailed.
Book about teaching math with Moodle
http://www.packtpub.com/moodle-1-9-math/book
Content
http://illuminations.nctm.org/
NCTM’s free lesson and resource center, with many online applets. Note the Calculation Nation link leads to some excellent 1 and 2 player games, but require a free login account. (Guest access to try it.)
http://ohiorc.org/for/math/
An Ohio Resource Center with links to many topics by grade and content. Some high quality resources.
http://nrich.maths.org
From the British equivalent of the NCTM. Once you get past how they say ‘maths,’ there’s an excellent supply of interesting problems, some clever student solutions, and open challenges. Also features some interactive applets.
Internet Resources for in class use
http://math.hippocampus.org/
An extensive collection of online exposition of topics from algebra and calculus. (As well as Bio, Chemistry, Physics, etc. Some support for Spanish.) Includes a voice delivering reading of the text (with a skip forward feature), and assessment along the way. Not clear what the purchase of a license adds, but everything I’ve seen was free.
http://www.imagination3.com/
GE’s interactive whiteboard, open to collaboration, optional graph paper background. Colors and some shapes are possible. You can save files.
http://www.wolframalpha.com/
Wolfram|Alpha, a free computational engine online. Amazing and worth exploring. Also some encyclopedia function. Supercedes some of the older online utilities.
http://geogebra.org
GeoGebra, a free dynamic geometry program that can be used as a web app or by downloading and installing. Some powerful algebraic applications, too.
http://www.plu.edu/~heathdj/java/
A collection of java applets, from many different mathematical content areas.
http://www.univie.ac.at/future.media/moe/onlinewerkzeuge.html
Powerful collection of online tools. One of the best online function plotters (graphing calculator) is here.
Games
http://www.funbrain.com/brain/MathBrain/MathBrain.html
K-8 math games. Not very challenging, but there are students for wom this will be just right. Connected with Poptropica, which my kids love, and features some decent problem solving.
http://gprime.net/game/
Huge collection of flash games – not all kid appropriate. Some excellent math and reasoning games, though. Try 3D logic, a maze game on 3 cube faces (http://gprime.net/game.php/3dlogic), gridlock, the classic game (http://gprime.net/game.php/gridlock) or grow island, a deductive reasoning game (http://gprime.net/game.php/growisland), and one of a family of grow games (http://www.eyezmaze.com/grow/v3/index.html).
http://www.logicmazes.com/
Very challenging puzzles by a very interesting man, Robert Abbott. Also links to some games of his creation.
Utility
http://incompetech.com/graphpaper/lined/
Free graph paper pdf generator. Very handy.
Teacher
http://www.learner.org/resources/browse.html?discipline=5
Annenberg Teacher Resource Center. Extensive collection of lessons, videos of students and teachers, and professional development materials. All free. Sortable by grade level.
Moodle Math documentation
http://docs.moodle.org/en/Mathematics
Pretty technical information, but accurate and detailed.
Book about teaching math with Moodle
http://www.packtpub.com/moodle-1-9-math/book
Content
http://illuminations.nctm.org/
NCTM’s free lesson and resource center, with many online applets. Note the Calculation Nation link leads to some excellent 1 and 2 player games, but require a free login account. (Guest access to try it.)
http://ohiorc.org/for/math/
An Ohio Resource Center with links to many topics by grade and content. Some high quality resources.
http://nrich.maths.org
From the British equivalent of the NCTM. Once you get past how they say ‘maths,’ there’s an excellent supply of interesting problems, some clever student solutions, and open challenges. Also features some interactive applets.
Internet Resources for in class use
http://math.hippocampus.org/
An extensive collection of online exposition of topics from algebra and calculus. (As well as Bio, Chemistry, Physics, etc. Some support for Spanish.) Includes a voice delivering reading of the text (with a skip forward feature), and assessment along the way. Not clear what the purchase of a license adds, but everything I’ve seen was free.
http://www.imagination3.com/
GE’s interactive whiteboard, open to collaboration, optional graph paper background. Colors and some shapes are possible. You can save files.
http://www.wolframalpha.com/
Wolfram|Alpha, a free computational engine online. Amazing and worth exploring. Also some encyclopedia function. Supercedes some of the older online utilities.
http://geogebra.org
GeoGebra, a free dynamic geometry program that can be used as a web app or by downloading and installing. Some powerful algebraic applications, too.
http://www.plu.edu/~heathdj/java/
A collection of java applets, from many different mathematical content areas.
http://www.univie.ac.at/future.media/moe/onlinewerkzeuge.html
Powerful collection of online tools. One of the best online function plotters (graphing calculator) is here.
Games
http://www.funbrain.com/brain/MathBrain/MathBrain.html
K-8 math games. Not very challenging, but there are students for wom this will be just right. Connected with Poptropica, which my kids love, and features some decent problem solving.
http://gprime.net/game/
Huge collection of flash games – not all kid appropriate. Some excellent math and reasoning games, though. Try 3D logic, a maze game on 3 cube faces (http://gprime.net/game.php/3dlogic), gridlock, the classic game (http://gprime.net/game.php/gridlock) or grow island, a deductive reasoning game (http://gprime.net/game.php/growisland), and one of a family of grow games (http://www.eyezmaze.com/grow/v3/index.html).
http://www.logicmazes.com/
Very challenging puzzles by a very interesting man, Robert Abbott. Also links to some games of his creation.
Utility
http://incompetech.com/graphpaper/lined/
Free graph paper pdf generator. Very handy.
Teacher
http://www.learner.org/resources/browse.html?discipline=5
Annenberg Teacher Resource Center. Extensive collection of lessons, videos of students and teachers, and professional development materials. All free. Sortable by grade level.
Blog guru
Sebelumnya saya pernah memberikan daftar guru - guru yang ikut ngeblog membahas matematika pada artikel blog matematika dan blog matematika part 2. Tentu saja masih banyak lagi guru yang ngeblog tetapi belum saya masukkan ke dalam daftar tersebut, sebab ternyata semakin hari semakin banya guru yang menyeburkan dirinya ke dunia maya untuk berbagi ilmunya dengan anda semua.BTW, setahun yang lalu
Kamis, 08 Oktober 2009
Money Problems
Excellent variation on the "how many ways to make change problem" at the New York Times today. The Freakonomics column is reporting the work of Patrick DeJarnette. I can see giving this problem from 4th grade to linear algebra!
Click on the money tag to see my previous money games. Click on the cartoon to go to the excellent Non Sequitur website.
Sabtu, 03 Oktober 2009
Math Teachers at Play #16
The new carnival is up.
A clock face activity for learning how to tell time supports students with a nice simple representation. The biographies reviewed here look like must buys. Very nice math teaching memoir from Math Mama. We should all write more of these. Denise, carnival originator, starts a good division discussion. Some interesting online math games are highlighted at the Innovative Educator.
The order of operations conversation reminded me of a student teacher I just saw who has picked up the nickname Aunt Sally. ("It's Not Funny," she said in response to my giggle.) I'm hugely in favor of a four step Order of Operations. It's also a great opportunity to discuss with students the difference between a result or theorem and a convention.
A clock face activity for learning how to tell time supports students with a nice simple representation. The biographies reviewed here look like must buys. Very nice math teaching memoir from Math Mama. We should all write more of these. Denise, carnival originator, starts a good division discussion. Some interesting online math games are highlighted at the Innovative Educator.
The order of operations conversation reminded me of a student teacher I just saw who has picked up the nickname Aunt Sally. ("It's Not Funny," she said in response to my giggle.) I'm hugely in favor of a four step Order of Operations. It's also a great opportunity to discuss with students the difference between a result or theorem and a convention.
Kamis, 01 Oktober 2009
Anchor Charts
While we did this as a teacher prep activity, I think it would be interesting with K-12 students as well. I first heard about anchor charts in Mosaic of Thought (I think), and like how they serve as both assessment and culture building. I've had students make charts about a particular concept, about what to do when you're stuck, and for what it means to do, learn and teach mathematics.
For this most recent lesson I had the students read "Mind mapping As a Tool in Mathematics Education", by Astrid Brinkman from Mathematics Teacher, Feb 2003. (They had previously expressed curiosity about and a lack of experience with concept maps.) One reason I love these is that they are frequently surprising. I expect one like this, that echoes the NCTM process standards we emphasize in the first unit: (Remember you can click images to see them full size.)
But then they go and make these completely original things like:
with different processes emphasized
and
Highlighting the difference and connection between
school mathematics and real mathematics.
Instructions to the students:
Activity: Anchor Charts
The following example comes from Ellin Keene’s (2008) To Understand: "Teachers generate anchor charts to capture and celebrate increasing sophistication in oral language use." (p. 278)
If you substitute ‘understanding learning in mathematics’ for ‘oral language use,’ you have the purpose of this activity. (Follow a link for a free pdf of the first chapter, under samples.)
Create an Anchor Chart for Learning in Mathematics
1. Identify the concepts and ideas that you want to remember as they relate to doing mathematics.
2. Develop an anchor chart that captures and celebrates your increasing sophistication in understanding “Doing Mathematics.” This might be a list, or a mind map, or a representation of your own creation. You decide – just be prepared to share your chart during our next class.
3. Be sure you leave 10 minutes to reflect.
Reflection: How well does your group’s anchor chart capture what you want your future students to think of hen you ask them “what does it mean to do mathematics?”
Home Extension: You might want to check out how math teachers use anchor charts at books.google.com - Integrating Literacy and Math. by Ellen Fogelberg, Carole Skalinder, Patti Satz, Barbara Hiller, and Lisa Bernstein.
Other interesting examples:
Send me yours or your students' and I would be happy to post that!
For this most recent lesson I had the students read "Mind mapping As a Tool in Mathematics Education", by Astrid Brinkman from Mathematics Teacher, Feb 2003. (They had previously expressed curiosity about and a lack of experience with concept maps.) One reason I love these is that they are frequently surprising. I expect one like this, that echoes the NCTM process standards we emphasize in the first unit: (Remember you can click images to see them full size.)
But then they go and make these completely original things like:
with different processes emphasizedand
Highlighting the difference and connection between
school mathematics and real mathematics.
Activity: Anchor Charts
The following example comes from Ellin Keene’s (2008) To Understand: "Teachers generate anchor charts to capture and celebrate increasing sophistication in oral language use." (p. 278)
If you substitute ‘understanding learning in mathematics’ for ‘oral language use,’ you have the purpose of this activity. (Follow a link for a free pdf of the first chapter, under samples.)
Create an Anchor Chart for Learning in Mathematics
1. Identify the concepts and ideas that you want to remember as they relate to doing mathematics.
2. Develop an anchor chart that captures and celebrates your increasing sophistication in understanding “Doing Mathematics.” This might be a list, or a mind map, or a representation of your own creation. You decide – just be prepared to share your chart during our next class.
3. Be sure you leave 10 minutes to reflect.
Reflection: How well does your group’s anchor chart capture what you want your future students to think of hen you ask them “what does it mean to do mathematics?”
Home Extension: You might want to check out how math teachers use anchor charts at books.google.com - Integrating Literacy and Math. by Ellen Fogelberg, Carole Skalinder, Patti Satz, Barbara Hiller, and Lisa Bernstein.
Other interesting examples:
(OK, the last one's mine.
Fair's fair if I'm putting up my students.
No, I don't know what's up with that guy's hair.)
Fair's fair if I'm putting up my students.
No, I don't know what's up with that guy's hair.)
Send me yours or your students' and I would be happy to post that!
Minggu, 20 September 2009
Geogebra
I know I've gone post crazy. I will stop soon, really.
I'm trying Geogebra this semester with my Geometry K-8 class, first computer session tomorrow. It's a freeware java implementation of dynamic geometry quite similar to Geometer's Sketchpad, with an even stronger algebraic interface. In addition to playing with it to get a sense of what's going on, I've got two sketches to look at:
Square Not Square Where you adjust quadrilaterals by vertices
to check the 'real' type, as all 9 look like squares.
Links lead to webpages with the java sketches, as geogebra has a great export to webpage feature. They are java, so some browsers don't handle them as well as Firefox. If you prefer the actual geogebra sketches, it's SquareNotSquare.ggb and QuadByAngle.ggb. Most of the sketches I've seen so far have been for HS or university, so if you're interested in K-8 uses, please let me know!
EDIT: Followup - the students were mostly positive, and some extremely positive. Definitely a better reaction than to the old computer labs with sketchpad. There was more interest in the program because it is so accessible; many more of them saw themselves as potential users of this time. It also connected with people's desire for visual representation. Makes me wonder, have I been underusing manipulatives this semester?
I'm trying Geogebra this semester with my Geometry K-8 class, first computer session tomorrow. It's a freeware java implementation of dynamic geometry quite similar to Geometer's Sketchpad, with an even stronger algebraic interface. In addition to playing with it to get a sense of what's going on, I've got two sketches to look at:Square Not Square Where you adjust quadrilaterals by vertices
to check the 'real' type, as all 9 look like squares.
Quad By Angle Where you determine a quadrilateral
by the angles rather than by edges or diagonals.
Links lead to webpages with the java sketches, as geogebra has a great export to webpage feature. They are java, so some browsers don't handle them as well as Firefox. If you prefer the actual geogebra sketches, it's SquareNotSquare.ggb and QuadByAngle.ggb. Most of the sketches I've seen so far have been for HS or university, so if you're interested in K-8 uses, please let me know!
EDIT: Followup - the students were mostly positive, and some extremely positive. Definitely a better reaction than to the old computer labs with sketchpad. There was more interest in the program because it is so accessible; many more of them saw themselves as potential users of this time. It also connected with people's desire for visual representation. Makes me wonder, have I been underusing manipulatives this semester?
Sabtu, 19 September 2009
Book Review: Babymouse
Read a very cute book recently, Babymouse: Dragonslayer, by Jennifer Holm and her brother Matthew. I had never read Babymouse before, but it was recommended by Jen Robinson (who herself was recommended by Kathy Coffey, my guru in all things about teaching reading). Jen Robinson's blog is a great resource for anyone interested in kid's lit as a parent, teacher or reader.Babymouse is a math-hater, because she is bad at it. Her teacher, shockingly, starts her on her adventure by sending her to be a mathlete. While there is no math per se in the book, it is all about immersion and expectations by the Mathlete coach, and employment and approximation on Babymouse's part. And all with excellent connections and fantasies of our great fantasies, Narnia, Lord of the Rings and Potter. A homerun all around. My only unrequited wish - more actual math. All that for only $6 at Amazon.
The italicized terms here are from one of the best frameworks for teaching and learning I've ever seen. It's really the lens through which I evaluate and work on my teaching. Brian Cambourne's article "Toward an educationally relevant theory of literacy learning: Twenty years of inquiry" is available online here.
My daughter Ysabela's review is here. She says the title misspelling is intentional...
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