Trig Rummy

My calc students have really been struggling with trig substitution, mostly, i think, due to lack of fluency with trigonometric functions. I'm a big believer in games for skill practice, as they are an engaging context that encourages more practice and ideally offer a chance for forging new connections.

So today we played Trig Rummy. Many of my card games are based on concentration, rummy, or go fish. And occasionally Euchre. (I still think the partially ordered quadrilateral Euchre has a future.) Links for printables are after the rules. I think it would adapt to high school trig pretty easily. I'd replace the calculus relations with graphs and triangle identifications.

Trig Rummy

Objective: the player will practice and gain facility with trigonometric identities and calculus relations.

Players: 2-4

Goal: get the most cards in play.

Set up: randomize cards and deal 7 cards to each player. (You may want to introduce the game with only 4 cards as 7 is overwhelming.)

Play: On your turn you may do one of:
• take any card from the discard pile (not just the top card).
• draw a new card.
After that you may do either or both of:
• pick up any sets you have.
• play any new sets you have.
At the end of your turn, if you did not play a set, discard a card.

Special:
• if at any point the discard pile contains a complete set, the first player to otice can cal “Rummy!” and take the set out to play for themselves.
• you can not play matching operator cards, like a pair of d/dx cards.
• There is a wild card, which you can choose to be -1× (times -1), or d/dx, or ∫ ⋅ dx.

End: After the last card is drawn from the deck, each player gets one more turn from the discard pile. Then the cards are counted up and the player with the most cards played wins. No penalty for unplayed cards.

Variation: Play until one player is out.

Example plays:
• Play sin2(x) matching 1 − cos2(x).
• Play d/dx with sin(x) matching cos(x).
• Play ∫ ⋅ dx with sec(x)tan(x) matching d/dx with ln|sec(x) +tan(x)| (since both are equal to sec(x).)

If a player lays a mistaken combination and no one catches it before the next player’s turn, they stay in play but turned face down. If someone does catch it, that player has to pick up the pair.

Feel free to use a trig cheat sheet.

Rules PDF - includes a trig cheat sheet
Trig Cards PDF - for 54 2-sided cards of trig identities and calc relations. Could use for flash cards or other games also.

Another Math Blog

Which, come to think of it, would have been a good title for this blog.

I've been cosistently loving a lot of the links given by Y of X. It records the musings of Hendree Milward, a Connecticut math teacher (at Tunxis Community College?). Recently he's posted interesting links to the cool Institute of Figuring and an offbeat math poetry blog. If you read his blog, I won't have to bother putting up those links here.

Realising the presence...

Mathematics is considered as an abstract subject. Students find it dull and boring. There are so many on this planet who always say " Mathematics is not my cup of tea". Do you know the reason for this indifferent attitude towards Mathematics ?

Have you ever realised the presence of Mathematics around. One thing which is very interesting to note is...the people who say that they are afraid of Math or they hate Math or they try to run away from Math are using/applying it in daily life.

Aren't these people managing house budgets ?

Aren't they not paying bills for their dinner in a restaurant ?

Aren't all of them not using number manipulations, mathematical operations etc?

Aren't they not seeing/observing beauty of geometry all around?

There is not even a single place where the knowledge of Mathematics is not applied. It is very important to make students realise the presence of Mathematics around and how important the subject is in our daily life?

I have created a blog Exploring Mathematics Around where you can find pictures from daily life depicting the presence of Math everywhere.

Soal Ujian Nasional 2009

Setelah hampir satu bulan ngga ngeblog ( hanya diselingi oleh postingan tentang penulis tamu ) karena kesibukan menyiapkan Ujian Nasional dan rentetan Ujian lainnya, akhirnya hari ini bisa menyempatkan kembali menyapa anda semua yang udah bolak - balik ke blog ini karena ke sasar. Yup hampir sebulan sudah blog ini tidak mampu untuk berbagi soal matematika yang biasanya terus berusaha untuk

Stigler on training teachers

Michael Goldenberg over at Rational Math Ed pointed this out on his blog and it's worth spreading out.

See this thread at the Math Forum for a transcript. Dr. Stigler is the co-author of The Teaching Gap and The Learning Gap, which distill research from The International Math and Science Study (TIMSS) into fresh and relevant information for any teacher, but especially math and science teachers.

The big points to me:
-Teaching is cultural => really hard to change
-Teaching needs to change <= student achievement data
-Teaching can only change gradually, but it can change, by focusing on teaching instead of teachers, and evaluating based on students' thinking and reasoning.


A relevant quote: "A review of research by Hiebert and Grouws identifies two features of classroom instruction that are associated with students' understanding of mathematics:
- CONNECTIONS: Making mathematical relationships-among concepts, procedures, ideas-explicit in the lesson
- STRUGGLE: Students spend at least some time struggling with important mathematics."

Check it out.

A programmer's view of the Universe, part 3: The Death of Richard Dawkins

We're getting close to the end of my blog. After today's entry, I only have three left to write. After that, I'll only blog anonymously or (more likely) not at all.

This is part three of five in my "Programmer's View of the Universe" series. I struggled for a while with how best to introduce the ideas in this installment, and ultimately opted for a short story.

This is a science fiction short story. It's different from many other sci-fi stories in that it is set in the "near future", but it has realistic schedule estimates. So unlike 1984, 2001, The Singularity is Near and all the other sci-fi stories that grossly underestimated their project durations, this one is set 1000 years in the future. I.e., right around the corner.

The story is disrespectful to pretty much everyone in the world. It will create a fantastic shit storm. This is probably a good time to point out that I don't speak for my employer. [Edit: Yay for fiction! Apparently marking something as fiction placates people. Nice to know.]

The story is 18 pages (PDF from Google Docs print preview). That's not unusual for my blog, but I went ahead and published it as a standalone document.

I'd encourage you to enjoy it, but I'm old and embittered enough to know better. You probably shouldn't even read it. Just wait for someone to summarize it for you.

Installments 4 and 5 will not be short stories; they will be regular old blog rants. In them I will further develop these ideas, and I will also attempt to clear up any gross misconceptions about the story, of which there are bound to be many.

My final blog-rant entry is the only one I care about anymore. I've been working on it so hard that my fingers have started to fail. It's been tons of fun, aside from the chronic pain. It's about a neat programming language, and Emacs, and lots of other stuff. I can't wait!

Oh yeah. Here's the link to the story. I've never done a read-only Google Docs link before, so it's probably broken. Or editable. I don't know. We'll see.

This week is going to suck. People are going to be mad. Maybe I should take a vacation and come back when the whining is finished. Can someone email me and let me know when it's all blown over?

Penulis Tamu

Ujian Nasional memang sudah berakhir lebih dari 2 minggu yang lalu, akan tetapi tugas selain Ujian Nasional terus menghadang. Setelah Ujian Nasional rampung siswa juga harus menyelesaikan Ujian Praktik untuk beberapa mata pelajaran yang kemudian harus berjibaku lagi dengan soal - soal Ujian Sekolah. Yup, semua kesibukan itu benar - benar menenggelamkan saya dalam rutinitas yang tidak ada

Ken Robinson

So I showed the Ken Robinson video to my class on the first day and it was quite interesting. The video started with medium engagement, but by the end everyone was tuned in. The story about the choreographer (Gillian Lynne) seemed to really connect.



The first connections were to elements of their own stories, and were interesting. Then one of the students brought up a connection with how Robinson describes us as being educated out of creativity. Her sister is interested in being a soloist, and it took ears of retraining or untraining to get her out of what she had been taught to do as a choral member. I'd never heard of that before, but it connected exactly to the point I wanted to make.

They have been educated - and successfully so, as college calc students - in school mathematics, which has almost nothing to do with mathematics as practiced by mathematicians. (Which really needs a descriptor. Real mathematics isn't going to interest anyone. Creative mathematics? Cool vs. school or cruel mathematics?) Instead of being able to repeat what someone shows you, it should be about solving problems that you don't know how to solve. In which situations mathematicians excel, because they are entirely willing to be wrong, and even glad to be wrong if they learn from it. They're willing to, as my friend Dave says (quoting his favorite Australian, Brian Cambourne) to "Give it a go!"

As long ago as 1982, my calc instructor, John Hocking, worked mightily to convince us to have no fear. To be wrong 100 times if it teaches you something. That math was exploratory, and creative. He shared his topological research with us... which was amazing and fun. He's the reason I added the math major in the first place. Often he put it as "blank pages are just waiting to be filled."

Now can I help my calc students to do the same?

Hani

Perbedaan antara yang mustahil dan yang tidak mustahil terkletak pada tekad seseorang. -Tommy Lasorda-
Pada hari aku bertemu Hani irmawati, ia adalah gadis berusia tujuh belas tahun yang pemalu, berdiri sendirian di tempat parkir sekolah internasional di Indonesia, tempatku mengajar bahasa inggris. Sekolah itu mahal dan tak menerima murid orang Indonesia. Ia menghampiriku dan bertanya apakah aku