Obvious to You, Amazing to Others

 

obvious to you, amazing to others

Beware the Ides of November (for the Southern Hemisphere)

These days it seems like I turn around and two weeks have just GONE. FOREVER.

For example, I am nearing the end of my first year as a full time teacher. So since I have been in a listing mood recently it seems appropriate to list some of the things I have learnt this year.

1. Be bossier!

Let's face it: being bossy is basically part of my job. Diffidence might be charming but it doesn't help kids learn. And frankly, some times its more important to be confident than right. At least forging confidently ahead despite uncertainty demonstrates where the potholes are (though sacrificing a party member or two is not ideal; not even in the interests of making an accurate map of the terrain).

 
Some of the arenas in which I need to be bossier are discipline, record keeping, note taking and time keeping. I particularly sometimes need to be bossier with my colleagues. When I know what I'm talking about (which I do, occasionally), then I need to insist.




2. Plan more.


A planned week is 100% better than an unplanned week. Don't get the wrong impression - I don't actually FOLLOW my plan. But having lessons ready and resources printed and schedules created and all that jazz still makes a huge difference.

The difficulty is that planning is never as urgent as a thousand other bits and pieces. It tends to feel like procrastination. 

IT ISN'T.

At the moment I'm sacrificing loads of other more urgent work (like admin, marking etc.) in order to plan for next year. And I'm sure that this is the right decision. Not only does planning help me to teach better, it also helps me to teach with a higher level of confidence and fluency. It helps to decrease stress levels and exhaustion levels. It is also easier to be creative in advance. So if you plan, you're more likely to be creative. See points 1, 4 and 5 if you're still not sure why planning more is a good idea!


3. Live closer to work.

This just isn't worth it:

The stress, the time, the petrol money, the stress, the time, the petrol money, the stress, the time, the petrol money, the stress, the time the petrol money, the stress, the time, the petrol money....








 You get the picture. Why choose inefficiency when you could have... THIS:



Hmm, yes, being a glorious 50s housewife has always been a dream of mine...


But seriously, moving to live within ten minutes walking distance from work has probably been the single most life-enhancing decision of the year. 
 We have so much more time to enjoy life. It's the ultimate way of slowing everything down a notch or two.


Our kitties also love our new place (though that's probably more to do with the garden than its proximity to work).


And yes, it has made more time for creativity in the kitchen...

4. Stress less.


I am a champion stresser. I could probably win a medal if they had medals for stressing. NEWS FLASH: stressing doesn't help. The work will get done faster and better if you don't stress about it. Stress is supremely inefficient.

Of course, not stressing is easier said than done (duh). In fact, I have been known to be stressed about stressing. And I have yet to actually succeed in not stressing. But I'm studying to improve. Points 2, 3, and 5 in this list have helped me to stress less. 


But these are some of my anti-stress mantras:

• It doesn't matter that much anyway.
• In two weeks time I won't even remember this.
• Who gives a %#@*!$#? [no matter what they say, profanity always helps in times of trouble]
• It'll get done eventually.
• I shall run away and join the circus.

Saying these repeatedly in any order you choose and with increasing levels of hysteria has been know to not help at all... But they're good to remember anyway.


5. Be more creative.

Being more creative is difficult. It requires proficiency in time management and planning OR a general ability to tell the world to go hang while you get on with your creative project.

BUT it builds your soul. It relaxes you. It gives your "serious" work fresh flair and imagination.

Now the ideal application of creativity is to your work. Because then you can hit time-management/planning/creativity/work buttons all at once and STILL reap the rewards of creativity.

image source

Mwahaha!

Make new, nice resources and share them (this also garners praise which is always nice). Write reflective marathon blog entries (who cares if no one reads them). Dream up new ways of organising the universe. Rearrange your admin under colour coded headings. Invent a new curriculum. Play (*educational*) games in class.

After all, why not?

I need a holiday!

more pictures to daydream about...

I found a new...

So check out this AWESOME BLOG!

Woeful Wednesday - Energising Efforts

It's woeful wednesday again and despite not having taught a lesson yet today I am CAPUT out of energy. So I'm drinking a huge cup of very sweet coffee and trying to hype myself up to start a new and extremely challenging chapter with my grade 11s..

Energising Efforts:

more awesome coffee piccies

1. Get the caffiene flowing in my veins (feel the heartbeat skyrocket!)
2. Music: soundtrack mix (preferably lots of vibey Disney stuff - think Hercules and so on...)
3. Work - preferably something completely non-essential and non-urgent (like making stationery choices for next year :-)

Bar Graphs

W.H. Auden on Reading

To read is to translate, for no two persons' experiences are the same. A bad reader is like a bad translator: he interprets literally when he ought to paraphrase and paraphrases when he ought to interpret literally.

-W.H. Auden, poet (1907-1973)

So who decides on the "ought"? Surely this statement implies that there is a single "correct" way of interpreting a text... You're letting the postmodern side down W.H., pull yourself together!


I find myself agreeing with the sentiment though.

Postmodernism is overrated.

Goals for the Week (or at least what's left of it)

Goals for this week:

• Be prepared for the chance of a lifetime (if it should happen in the next seven days!)
• See challenges as growing experiences.
• Persuade Gauss and Pascal to stop killing baby birds.
• Set my last exam for the year :) 
• Sing more.

Punting Down the Cam

[WARNING: this is a sentimental post about bygone days...*sniff*]

I believe I am actually a child of the 20s. Probably my favourite novel of all time is Dorothy L. Sayers' Gaudy Night, set in beautiful Oxford in the stately interwar days when women had just been admitted to universities and everyone still wore academic dress to College dinners... And, of course, when the best Sunday afternoon activity was to take a leisurely punt down the river. Sigh.






When I was fortunate enough to be sponsered on a "literary tour" of the UK a few years back, one of my most favourite outings was when we went punting. It certainly made a nice change from yet another stately home... Though Blenheim et al are stupendously magnificent, they are also terribly hard on the feet.








Not that punting is an art for the lazy. For those of you that don't know, punting is the art of pushing a boat down the river by means of a long pole prodded repeatedly into the muddy river bed and used as a lever.

Apart from negotiating bridges which are mainly too low to get the pole (or yourself) through upright, one also has to cope with steering (mainly with the assistance of the ardent paddlers) and going upstream. Going upstream is mostly a case of one punt forward - two floats back.


 

And of course: very HOT work (unless you fall in, which I fortunately didn't!) ... By the end of the outing I was much thinner, mainly due to removing layers of clothing!

Nonetheless - oh to return to those stately days...

Statistics (with a pitstop by the Oxford English Dictionary)

So there's this nifty spot where you can go look at the stats of your blog. And it's very interesting. One of the most interesting things about it is this: when I post something new, my readership skyrockets in South Africa (i.e. here). When I don't post anything new, most of my readers come from the US (though I had a brief spate of popularity in India after I posted a mini-series involving Indian mathematicians).

Is this just because more people use the internet on a regular basis in the US? 'Cos I have a nasty feeling it's mostly incidental/search-engine/accidental traffic.

What is driving this particular pattern??? Any suggestions?

***

Pitstop!!

What is the difference in meaning between incidental and accidental in this context?

The pocket OED that I have in my classroom (call me old fashioned but I still haven't gotten used to online dictionaries) says that incidental means "having a minor role in relation to more important thing or event".

Accidental (helpfully) means "happening or done by accident". Well thanks OED. Accident is defined as "event that is unexpected or without apparent cause".

My analysis - incidental relates to the importance while accidental relates to the intentionality of the event in question (i.e. visiting Daydreaming in Maths).

Do you agree??

***

excuses excuses

-  lost camera - lost phone - no internet at home - hectic time at work -

- I miss blogging -

Whiteboard Wednesday

by Simon and Caitlin

The Life Cycle of a Box

We are busy moving house and have lots of fun with cardboard boxes. There is an entire world of interest behind the common cardboard box!

We got a whole bunch of boxes (like 20 or so) second hand from the Pick 'n Pay up the road. Turns out they have a whole container out the back, next to the loading area where trucks come and go, wholly dedicated to the sorting, distributing and recycling of cardboard boxes.


Once the omo, chips, whiskey, apples and cooldrinks have been removed from the boxes, they are ferried in elderly reject shopping trolleys through to this gentleman who rules over the box container...

He works from 8am to 7pm in the small, dark container, which makes loud farting noises if you tread on the floor in the wrong place. Anyway, you tell him what kinds of boxes you'd like (he's got lots - all the way from teeny tiny to enormous) and then he helps you to pull them out of the heap. He's really good at divining what size a box is just by looking at the flap that's sticking out of the pile.

After all that, it seems quite ungrateful just to take the boxes off, put them back together with packing tape and stuff a whole lot of books, crockery, clothes and kittens in them.

But of course once the kitten is tired of sitting in the box...

 

...he can always eat it!

  

"Look mom, I killed it!"

I'm not sure if this is a fitting end to such a noble creature as the cardboard box. On the whole I think it might be. 

Baby Tree - Big Tree

At the moment I am a Baby Tree. I still need support.

But one day I will be a BIG tree.

Room With a View

We're nearing the end of winter, and the pink flowers outside our window are finally giving up the fight for survival... soon they'll be reborn in a burst of colour.

most this amazing

i thank You God for most this amazing
day:for the leaping greenly spirits of trees
and a blue true dream of sky;and for everything
wich is natural which is infinite which is yes

(i who have died am alive again today,
and this is the sun's birthday;this is the birth
day of life and love and wings:and of the gay
great happening illimitably earth)

how should tasting touching hearing seeing
breathing any-lifted from the no
of all nothing-human merely being
doubt unimaginable You?

(now the ears of my ears awake and
now the eyes of my eyes are opened)

- ee cummings 

 

Soup

I've been making a lot of soup lately. As in, a large volume of soup, not many different types of soup.

My recent soups have fallen into two categories:
1) Tomato soup: lots of tomatoes + garlic + a can of tomato puree + plenty of brown sugar
2) Pea and Potato Soup: split peas + lots of garlic + however many potatoes are turning greenish + plenty of Italian herbs, salt, pepper and other seasoning

What's quite fun is that even in our teeeeny tiny kitchen these soups can both be cooked at once in our two big pots - one on each stove plate. You have to be careful that the handles of the pots are angled away from each other though, because otherwise they don't fit after all.

The downside of this is that when they're both cooked and whizzed and generally ready to eat we then have upwards of six litres of soup and no matter how delicious that soup might be it is impossible (trust me on this) for two ordinary people to finish upwards of six litres of soup before the aforementioned soup goes funny. Not funny haha, funny yuchhhh.

But that's okay, because it's precisely why the freezer was invented. And there is something very satisfying and homely about a freezer full of soup in ice-cream tubs.

Not labelled ice-cream tubs, unfortunately. But once again it's okay, because tomato soup is RED and pea soup is GREEN. And in any case once you've defrosted one of them well that's the one you're going to have for supper so you might as well get used to it.

A Discourse on Purpose

For some reason today I realised that I haven't written a "proper" blog post for ages. My "hectic maths" label is becoming quite empty, and even photographs taken by myself have been pretty scarce.

Part of the reason for this is that I've started a cellphone experiment at school which involves being online with the kids a LOT, via twitter, class blog and so on. So I've been using up all my internet energy - or a lot of it anyway!

Another reason is that I've been thinking quite a bit about what the purpose of Daydreaming in Maths actually is. My class blog has a clearly defined purpose, but in some ways its purpose has eroded Daydreaming's.

Is this a blog for my students? Well, not really. But not NOT either.

Is this a blog for ME? Well, if its just for me maybe I should get a diary and stop filling the internet with random cr**p.

Is it a blog for the general public? Er...not sure if the general public is that interested in Maths and my crazy musings.

Is it a blog for other people that know me? Well in that case maybe I'm better off emailing them more regularly.

So what s the purpose of Daydreaming?

Aaaah...there's a question to please the soul of irony!

Message from the soul of irony (i.e. the brain):

Dear JJR - please note that daydreaming does not serve a purpose. It represents an absence of purpose. Therefore your question is irrelevant. Kind regards etc.

 
Well that's helpful...any suggestions from anyone else?

Message from the id:

Dear JJR -please note that this blog represents nothing more than a place to stash your ideas and impressions. The fact that it is open to the public simply provides you with an illusion of importance. Kind regards etc.

Not sure I like that answer - can I have another one please?


Message from the ego:

Dear JJR - please note that you are providing an extremely insightful and important service to society by writing this blog. If you stop, the world will surely be lacking that certain something. You fulfill a crucial role in the continuance of our cultural identity. Kind regards etc.

I'll shut up now...for now!

The Coolest School Ever

from the wayfaring website

Random Quote for Monday

"It is our best work that God wants, not the dregs of our exhaustion. I think he must prefer quality to quantity."

- George MacDonald

Wonderful Whiteboard Wednesday

An original artwork by Simon (grade 8)

Random Quote for Monday

"When I'm a veteran with only one eye,

I shall do nothing but look at the sky" 

incredible artwork from...

Profound Realisation

In the past few days I've spent a lot of time staring blankly out of my classroom window (which, by the way, I thought was purely the province of naughty children) while my students were writing tests, working on tutorials and exercises and generally getting on with things without my immediate assistance.

My profound realisation is this:  

distance lends grace

Interpret as you choose.

Limits of the Imagination

This evening I'm doing an "academic lecture" as part of a series at school. My lecture is going to be on "The Limit". Here's a preview:
 

Are we getting somewhere?

Maybe not...

When it comes to limits, expect the unexpected!

So let's create an accurate definition:

Any Questions?

Human Experimenting (but not what you think)

I've been reading all these fabulous, exciting articles about getting students online and connecting and interacting etc..., and been feeling more and more like this is something I want to try. But doing something so different is SCARY. No-one else at my school had tried anything like this before as far as I could make out. And my syllabus time is pressurised, and and and... But at the end of the day, I felt like these were just excuses. On Friday I decided to book the computer room, in the hopes that this would force me to just do it!

I then spent most of the weekend madly planning and trying to work out how to make the best use of the internet/geometer's sketchpad time. The lesson itself was an introduction to the sine/cosine/area rules in Trigonometry, with a very strong group of grade 11s. So I planned the first half of the hour and a half lesson to be a "collaborative research" style lesson, where we all searched for and posted links (under a twitter hashtag) about sites which we thought were interesting/useful/funny around the topic of applications of trigonometry, and proofs of the laws.

This went okay, though by the time the kids had logged in, and sorted Twitter out and so forth there wasn't that much time to actually get the interactions going properly. Keeping the class on-task was also tricky, but I'd hope that that would improve with time and practice (on my part as well as the class').  I also found it tricky to "sell" the value of the whole exercise to the kids. My most frequently asked question was "Is this for marks?"!

The second part of the lesson was an investigation of the sine rule, followed by a guided proof. The idea was that they would follow instructions to form a conjecture regarding the sine rule, and then prove their own conjecture (again, following instructions). Well, that went...okay...but you'll gather from my hesitation that it didn't go quite as I intended.

It was mainly slow. My instructions needed a certain amount of streamlining, but there were decent, especially since I was there to facilitate. But I underestimated how difficult it is to PROVE stuff when you're in grade 11. Even if you're very good at Maths.

To summarise:

• Advantages - Not a total disaster. I saw some potential for developing the ideas and activities. I think it started to develop some (non-curricular) skills which are important to acquire.
• Disadvantages - Time-consuming, and not necessarily always directly relevant to the (curricular) abilities that the kids need to acquire. Inefficient (but is real learning ever efficient?).

All in all, I think I will try this again...not every lesson or for every topic, but I will definitely try it again. In the immediate context, I think we will return to the computer lab on Wednesday to complete our proofs!

-oids Part IV

-oids Part III

-oids Part II

-oids Part I

Counting at the Seaside

I'm on holiday folks, so no hectic maths for a bit... instead I've been collecting pictures of numbers. Today I counted from 0 to 5 on and around the beautiful beach at Muizenburg.

 Hum...the usual problem with "counting" zero. Am I encroaching on hectic maths after all?

One clock-tower on Muizenburg station. Not one o'clock.

Two walking people (husband and father-in-law if you must know)

Can you spot the three?

Four beach huts...

Five (or is it six?) steps gone adrift...

To Infinity and (not) Beyond: Part II

photo from the nytimes archives

 
I'm sorry that this post is so belated, but the creative side of my brain has been dead, and understanding Maths  takes a lot of creativity.

everything maths

I promised you a discussion of Mr Cantor and his contribution to infinity... Cantor realised that there is more to understand about infinity than previously thought.

He started by thinking about different sets that we use everyday and think about as "infinite", such as the natural numbers (0,1, 2, 3, 4...). And the real numbers (0, 0.1, 0.0000000002, -0.0547829 etc...). In fact he thought about a lot of sets, and these are just two simple ones. But they will suffice for my highly simplified explanation.

Most of us would agree that there are infinitely many natural numbers. You could keep counting forever (though why you'd want to I'm not sure) , and you would never "run out" of natural numbers - even if what you were counting was the number of stars in the sky!

To briefly introduce some terminology, Cantor called the number of elements in a set the set's cardinality. He called the cardinality of the natural numbers "aleph null" (HINT: the squiggly N is the Hebrew letter aleph).

Well so far so good. All we've really done is make another label for infinity. Who cares?

The really exciting part comes now! Cantor went on to observe that the real numbers behave...differently...to the natural numbers. In fact, he demonstrated that there are infinitely many real numbers between every two natural numbers.

This is the core of the Cantor's insight, and it is demonstrated visually by Cantor sets, which you can learn how to draw here.

The idea is that if you keep dividing the interval between 0 and 1 into thirds, deleting the middle third each time, you could keep dividing forever. Since the real numbers between 0 and 1 essentially represent every possible fractional value between 0 and 1, they can in some sense be represented by the infinitely many "segments" you would have at the end of this process. If there was an end, which there obviously wouldn't be!

And yes, the Cantor set is a kind of fractal - go here for another (probably more rigorous) discussion!

Cantor went on to say (very reasonably in my view) that you can't say that the real numbers have the same cardinality (number of elements) as the natural numbers if there are infinitely many real numbers between 0 and 1 and further between any two natural numbers. It just doesn't make sense! So he labelled the cardinality of the real numbers aleph, with the rider that aleph is bigger than aleph null.

Um, aren't we forgetting something here??? We agreed that both the natural numbers and the real numbers had an infinite number of members. And do you remember Galileo: ...“it is wrong to speak of infinite quantities as being the one greater or less than or equal to the other”?

Cantor disagrees. According to him, there are at least two types of infinity. The first has the same cardinality as the natural numbers. This he called a "countable" infinity. The second has the same cardinality as the real numbers. This he called an "uncountable" infinity.

As you can imagine, this has some interesting consequences...but that's a story for another time.

from here