Panama

So I was just watching a show on the Panama Canal…it said that a staggering 14,000 ships go through the canal each year.  I started thinking about the numbers a little bit and knew that meant between 35 and 40 per day, on average.  

 

Then it was talking about a ship, the Zim New York, that could navigate the trickiest part of the canal in only 3 hours…

THEN…it said that this tricky part was only wide enough for 1 ship to fit through at a time – so one ship going from Caribbean to Pacific meant that no ship could go through it from Pacific to Caribbean simultaneously.  

I was wondering if that meant there are certain days on which only east-to-west travel is allowed, and some days on which west-to-east travel is allowed.  Is there a long caravan of Fishyback container ships travelling in one direction, or is it like yielding over a one-way bridge?  

OR were they only talking about the enormous ships that make up the Panamac class to which the Zim New York belongs?  I have more pressing things to do, but my curiosity is getting the better of me.  (Watch out, River! [she’s my cat])

If you have been, thanks for reading!

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July!

A new month already?  July-in to me?!  Nope.  Couple of things I’ve been thinking about this morning/early afternoon:

1: 6 months are done, 6 months to go.  That should mean the halfway point of 2013?  31 + 28 + 31 + 30 + 31 + 30 = 181.  Half of 365 is 182.5.  So today’s the 181st day. Tomorrow’s the 182nd. Wednesday, the 3rd, at noon – we are halfway done with the year.  July 4th I will set off fireworks not (only) in celebration of Independence Day, but the beginning of the second half of the year.  This also just got me thinking — is there exactly half a year between equinoxes?  Solstices?  Is this a proof that the orbit around the sun is an ellipse and not a circle?  

2: I’m charged (sort of) with making the school more “mathy.” Simple things — factoring the date, making little equations, math vocabulary. 

     2a: Should I make equations out of the dates ahead of time so I know one will work, or make them up on the fly because I like a challenge?

     2b: Any other ideas how to “math up” the school?

 

Thanks for your help!  And if you have been, thanks for reading. 

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Measurement

Not a post about measuring things.  A post about the book Measurement by Paul Lockhart.  I love this page…it’s from page 15 of the edition I own.

  This is the kind of thing you have to do as a mathematician: try things. Will they work? Will they yield useful information? Usually not. But you can’t just sit there staring at some shapes or numbers.  Try anything and everything. As you do more math, your intuition and your instincts will sharpen, and your ideas will get better. How do you know which ideas to try? You don’t. You just have to guess. Experienced mathematicians have a great deal of sensitivity to structure, and so our guesses are more likely to be right, but we still have to guess. So guess.

I wish for this to be an idea that my (and all) students would have about maths.

“If you want to paint a picture from your heart, there is no ‘answer painting’ on the back of the canvas.”

I had a discussion with my mother the other day, and it went something like this:

Mother: How would you fix math in school?

Me: I don’t know.  But I think it’s reversed.  Kids learn the boring and mundane stuff like memorizing multiplication algorithms and how to do long division and do worksheets and worksheets during “math time” in elementary school.  They learn that all math is, is manually doing the work that a calculator can do; and when they realize this, they feel like they don’t need or don’t like math because it’s not a subject on its own. It’s useful for other things, they are told.  But who cares?  When the students get curious, they are told there’s more interesting parts of math, but they need a foundation first.  Learn the boring stuff now. Gain a hatred for math now. Think that math is all about doing arithmetic now.  The interesting stuff will come later, when the kids will all already discount it as something for nerds.  Then laugh and ask “when will I use this in real life?” Then laugh again as the teacher struggles.  There are a lot of ways to answer this question…I’ve gone with:

You won’t.  But you need to pass this class to get through high school.

(incidentally realized this was not the best option. Never used that more than once or twice.  That’s it Andrew, feed the hatred…)

Well it depends what you want to do.

Ok — leading to further questions and further digression.

You’re right, maybe you won’t. But when will you need to know the sonnets of Shakespeare or know the states and capitals?  You can look them up just as easily as you can use a calculator.

Fantastic.  Lets get into a war of school subjects….

Does it HAVE to be useful? Can’t math just be a subject for the sake of being a subject?  Interesting to learn?

My personal favorite there.  That’s what I generally stick to.  Maybe this isn’t the most interesting to the students, but it is the most personally satisfying to me.

Mother:  okay, so what can be done about that?

Me:  I don’t know.  Don’t hand kids multiplication tables to memorize.  Hand them pictures. Hand them basic word problems. Read to them and ask them questions.  Give them calculators.  If they keep pressing 6 times 4 long enough, they’ll realize that it’s 24 and memorize because it’s convenient for them, not because there’s a test on it on Tuesday.

Mother: How do you measure how well they’re doing?

Me: (again) I don’t know. Give a project. Ask questions. Assess on the quality of the work, not the quality of the answer. On the descriptions they give you. On how well they communicate their thoughts to you.

Mother: Would that really be a math teacher’s job?

Me: Maybe we need to rethink what a math teacher is.

**end discussion (which I now realize was more of a soliloquy.) 

So that’s it.  Sure, I made it a bit more formal for the sake of typing instead of just conversation while driving to get batteries for a loupe.  I don’t know if it was useful for me to think about or not, or if I just got frustrated because by the time the students are in high school, they have such a concrete attitude towards math that I have to spend my time convincing them it’s useful when in reality I just want to show them it’s interesting.  As the year comes to an end, maybe I’ll focus my energies on getting ready for next year.  Stop asking the “how much paint will she need to buy to cover this…” questions, and abstract it to “we have a rectangle.  What’s the area? You want to know why anyone would ever want to know this? Here’s a computer. Figure it out. Then write a paragraph telling me why or when area is useful.”

Ugh…frustrating, stressful, time-consuming?  Yes.

Thought-provoking? Absolutely. So I wouldn’t trade it for anything.

 

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Scavenger Hunt

We did a scavenger hunt the other day to start the week.  Perhaps you’re aware of these ideas, but I figure I’d write about it anyway.

Students were grouped in teams of 3 (the teams were made for the whole week.  Finish last during the scavenger hunt?  No problem! Maybe you’ll fare better in the basketball toss).  Anyway, next time the teams might be smaller because there were naturally students who kind of rode the coat tails of the members who worked well.  Of course, the goal was that they would help each other.  When there are points and a prize involved, the speedy kids speed through and leave the others behind.  Not sure how to avoid that…help?

But yeah, each team got a started card.  There were 2 questions of each “type,” (exponent rules, simplify radicals, etc…) for a total of 8 questions.  Once they worked out the first answer, they were to hunt for the card with the answer.

Show the teacher the answer.  Once confirmed correct, the next question is on the back of the previous answer.  Keep going.  Last card has “congratulations” or something like that on it.

The biggest concern I have for next time is that it was sort of a pain to make 72 problems (8 questions, 9 teams).  It was sort of a pain to re-hide 72 cards at the end of class in the few minutes between classes.  I think it was worth it because it did work well, but for next time maybe I’ll have like 20 questions, but have them in a loop?  Number the problems so each team has a starting point, but make sure the answers do not go in numerical order.  I don’t know, thoughts?  I’m just worried that if a team takes a card, the next team may not be able to ever find their answer because it simply doesn’t exist.

Anyway — thoughts?

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Lego my…Lego!

How many Legos?

Lego Knight

So I’m 5’11”

http://shop.lego.com/en-US/Pick-A-Brick-ByTheme

There were several of these statues around the exhibit.

How much would it cost (assuming no bulk discount) to build such a thing?

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Origami

Origami Symmetry Oriagmi2

So the personal side of me went to the museum to see the Lego exhibit this past weekend.

The math teacher in me was just about as giddy when I saw a secondary exhibit highlighting the geometry involved in origami.  Well duh!  Of COURSE it’s math.  In any case though, here’s evidence that math is used.  Needless to say I will share these pictures with my students regardless of what topic I teach.  Hey look — it’s math!

Have a great day, all!

 

 

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419

4/19.  Four-Nineteen.  April 19th.  I can’t think of anything spectacular about today’s date.  Nothing *good* anyway.  I could look it up and find some interesting things I’m sure, and I will after I post, but I want to know these kinds of things, not have to look them up.  

It’s raining very hard outside.  There’s actually a tornado watch for the next couple of hours here.  I don’t really know what to write about today, but I’m going to keep to my goal of once per day for a year.  I just set that goal.  I think I’ve tried it before and it didn’t work.  And I know it won’t work this year, unless you excuse me for the time I will be away and not with access to the Internet.  If I make it until May, I’ll be impressed.  That’s all for tonight. No teaching today, so no fun stories today.  I did read that some schools in Jersey are implementing Singapore Math for K-2, and rolling it out for 3-5 the following year.  Thoughts?

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