Updates

Teaching: Chalkboard writing

I'm teaching S4 Pre-Calc content this year, hoorays!

However, there are a few problems I've discovered:

• as usual, my students are very silent;
  
• the desks are very segregating;
  
• I'm short;
  
• I'm unexpected (I look strange, I act strangely; it puts the kids who don't know me on edge and distracts them perhaps);
  
• I have messy chalkboard writing (I think I'd write better on an overhead)...

Things I want to do:

• Increase class participation (more group assignments or activities; more in-class assignments);
  
• Get them moving at least once every class (after recess time, most of the kids have little energy for Math);

More Updates

I'm in university again, going for Math (we'll see exactly where, later)...

I'm also in a literature course, and I'm supposed to be focusing on this essay, but, seriously, it's hard to write about something I think is pointless or... "dumb". Yes, yes, there's got to be a better way to describe that--I'm working on it, I'm working on it!

My dad was in the hospital for his leg thing. He was there about two weeks, then got sick of the hospital and came back home. The thing's still leaking, but at least he got his surgery date bumped up! It's....very.....distracting, I think. I don't know the word...

I might be doing modeling! More to come later!

Still in the reserves, still with my unit...

Teaching Math this year; got a good TA, too! Awesome!

University isn't offering the Hons Calc course anymore, and won't be next year, either. So I guess it's regular Calc for poor me. Boo.

Been in the military just over a year now! I'm entitled to new kit starting 23 Oct. I can order my DEUs now (they *might* be ready for Remembrance Day).

Rolled ankle still bothering me. Wrist feels the same, too; it's so aggravating!


...probably more. For now I should get back to that essay...
--Charlie

Mixed Update

Bus Girl

There's a girl on the bus, Shannon. She's adorable; small Chinese girl, 24 years old, always curious or happy--she's got this way of speaking, as though everything is happy and positive. For the most part, she doesn't express negative emotions very well (unless she frowns, and then she looks so hateful), which makes it a little difficult to talk to her, but as long as I'm listening carefully, it shouldn't be a problem.

She says I'm charming. Tehee!


Me

I got a bra fitted the other day. It was in a tasteful "adult" shop; I liked the experience! I'm actually bigger and smaller than I thought! I'm a 34-C or D; and in some cases, 36-B or C. That was impressive. I never thought I'd be a D-cup; even a C-cup seemed generous.


Bible / Christianity

I'm reading through Matthew again--at least, I'm starting at Matthew, and I'm, hopefully, going to get through the entire New Testament consecutively this time. Last time, I finished the Sermon on the Mount, and went, "Hey, yeah!" and left it at that. I guess I'm partly scared I'll find something stupid/disagreeable. But I have to keep in mind it's People writing, not directly God. And context is confusing--it sucks that history gets more made-up as we go along.

Like... A long time ago, THIS was the way it was. A few generations later, it's forgotten, so the next generation researches it and records it in their own context. These are then used as research for more research. To understand context, you have to... I dunno, how does one understand context, if not taught it by someone else? I mean, to an extent, one can GO there, but even when there, things are different NOW than THEN. ... Augh.

So, what I'm scared I'll find is intolerance and hate or fear -mongering. I heard once that religions were made as rulebooks, because following rules actually changed one's consciousness, which is cool!

"Do not unto others unless you would have them do unto you." That's a nice place to start, action-wise. It's not as selfish as "Do unto others as you would have them do unto you", but it conveys a similar message. It's more about respecting others than gratifying self. I like this version.


Photos

Our apple tree had blossoms! I got home from the bikeathon, and the branches were like green and white arms! View album here.

Also available for your viewing pleasure are old photos from the Piano Smash fundraiser. You may view them here.


Teaching

Augh. Been subbing for Calc lately; I know most of the kids by name already (which would be more impressive if there were more than ten).

Last day is tomorrow. Not sure I look forward to it, if it's with my regular class. But I really love those Calc kids!

Also! How cool is this? Leibniz cookies! Woots!

--Charlie!

047:

I went to Perkins with Mark again, and used the ladies' room while I was waiting. A girl came in. She looked at me, exited, and came back a few seconds later. That was hilarious.
Legfest?

So, by now, everyone knows I have Boobfest, which is a collection of drawings of the naked female figure, more specifically, the upper body.

I also want to study legs and hips, because I've never been able to represent poses properly--they always seem off, somehow. So I decided I'd study legs next.


Highschool Art

Back in highschool, we studied the human figure, too. More specifically, hands and feet. Here are a few of my studies:

Army

I've been calling in sick for Army, so there's not much else to cover; except that my BMQ/SQ will be from the end of April to the end of June. Woo.


Teaching

I got to fill in for the Calc teacher on 02-Feb and 09-Feb. I guess I forgot to write about it.

02 Feb
This was a disaster. Alan didn't leave any materials and didn't even e-mail me the topics he wanted covered! I was a nervous wreck. And, of course, the principal came in and started correcting my technique and--horrible mess!

09 Feb
This was much better. I realized that even though it's a terribly small class (ten or eleven), the kids don't talk to eachother, they don't know eachother. I opened with a silly ice-breaker game involving throwing things.

Walked them through a related rates problem.

Then I ranted about Math, which I'm good at doing!

Talked about proofs and what they are; did a very quick walk through Relativity (assume that the speed of light is always constant; can mathematically prove time/space distortion near the speed of light!); One Million Beans problem and proof; introduced the (extended) Monty Hall Problem... Just a nice glance at how awesome Math is--although I probably should have included Maxwell's Equations in there... Dang it!

I mean--how awesome is that! This guy just played around with equations, realized he needed two constants so used Epsilon-nought and Mu-nought; and when finally needed to figure out their values so he could find the speed of electric waves and magnetic waves--he gets the friggin' SPEED OF LIGHT. (Further reading)


Sleeeeepy time.
--Charissa

Concavities and Venn Diagrams

Concavities!

I'm subbing in for the Calc teacher at Maths School on 02-Feb and 09-Feb. He wants me to cover Concavity. As soon as I finish with a proof of concavity, I'll post it up here.

For now, you get this Venn Diagram as I ponder over Necessary and Sufficient. ...Again. Augh!



I'm not sure who else got taught this way, but I was taught that the rectangle (in this example) is "The Universe", so label accordingly! Put a title on The Universe! Label things that aren't in the circles!


Mm, tired.

--Charissa

Maaaath

Relationships

Based on private entry, 13 Jan, 2008 at 13:08 on bus

Been thinking.

Had lunch with James. Was strange. He talks more, though. But, either Istill make him nervous, or he's still that way--at least, around me.

Yet, I find, ... physically ... I think we fit together.

We still have a weak relationship. He talks about things I don't understand; and I talk about things he can't comment on. When I ask him to explain, he usually can't, or, not very well.

Maybe our roles are too loose. If it were a planned or structured get-together / event, maybe it would flow better.

I think that's the biggest issue: we have nothing to talk about. I ask about him, and he doesn't say much. I ask a little more, and then he talks more; but of course he'll start talking about programming, and I won't understand much of it. I ask him to explain, and he becomes hesitant and stumbles over the explanation (or maybe I'm just difficult to explain to?). When I talk about myself, he won't be interested, or won't comment. I guess, the other thing: I jump from topic to topic, and he likes to stay on one topic at a time.

It's so strange to have that physical connection, yet no other connection. I can read his body very easily; but not his mind or heart. And it may be that his body has very contrary "thoughts" from his mind/heart. Afterall, he has much self discipline.



Math

At work, I got bored. So, I figured out that, for each area code, there are 4,251,528 possible phone numbers (8*9*9 *9*9*9*9). Assuming there are 60 people working on that area code at any given time, and each worker can make 90 calls per hour; it will take roughly 13 hours to dial an area code.

Of course, I was at work at the time, so my numbers were totally wrong. It's very hard to find 9⁷ when you can work on it only 20 seconds at a time, with 70 seconds in between, which are spent doing something completely different.

(Just for comparison, I got: 5,373,459 possible numbers, and 1.15 hours, assuming 60 workers and 80 calls/hour. I was 21% off on the phone numbers, and a whole order of magnitude off on the hours--but I think that was just stupid messy-writing error.)

My next task will be to find out how many possible phone numbers in the US and Canada. I've made a list of all area codes that don't exist. It'll be a matter of finding:

(729 - [number of area codes that don't exist]) * 5,373,459

Woo!


Teaching

I mentioned, last post, that we've started transformations. I think, most of the kids don't get it.

Well, I want to make a bonus question on their next assignment:

1. Determine algebraically whether y = f(x) = sinX is even, odd or neither.

2. Determine algebraically whether y = f(x) = cosX is even, odd or neither.

I'll even do this right now, off the top of my head!

1. f(x) = sinX
Step 1: Find f(-x).

f(-x) = sin(-x)
= sin(0 - x)	Trig ID: sine sum-angle identity.
= sin0 * cosX - cos0 * sinX
= 0 * cosX - 1 * sinX	Simplify.
= - sinX	Which is also....
= - f(x)	Therefore, this function is odd. Hoorays!

2. f(x) = cosX
Step 1: Find f(-x).

f(-x) = cos(-x)
= cos(0 - x)	Trig ID: cosine sum-angle identity.
= cos0 * cosX + sin0 * sinX
= 1 * cosX + 0 * sinX	Simplify.
= cosX	Which is also....
= f(x)	Therefore, this function is even. Hoorays!

If we do this in class, then we've just taught them another trig identity, which is always good.

I really want to show the kids the process of how to solve those "Even, odd or neither" problems. Augh. It's so frustrating, the way the teacher teaches... Sigh.


Okay, sleepy time.
--Charissa

Mistaken Sex, Diagrams, and Everyone is Quitting

I got mistaken for a man today!

Well, maybe, sorta, I dunno. I went to get doughnuts and wanted to use the washroom, but you needed to get a key, and the cashier handed me the mens' room key. Woots.

Also, when I went for lunch with James, I had to use the washroom because I'd walked too fast and had started sweating. Two elderly ladies came into the washroom, separately, and had extremely puzzled expressions on their faces! I had taken off my inner shirt so I could dry it using the blow-dryer, and the first lady eyed me so strangely. I smiled back. I dunno, what else could I do? I suppose I could have declared, "I'm a lady!" but maybe that would've been too odd.


Teaching

We started the Transformations unit today. Some kids aren't quite sure what this whole "negative f of x" or "f of negative x" or "inverse f" is, so they're not sure what the whole "even, odd or neither" thing is, too. THERE'S EVEN A HANDY-DANDY CHART!

One of my favourite ways of explaining things is through the use of charts and diagrams, as you may have noticed. Maybe. I love how it's very graphical and intuitive--or maybe it's just intuitive to me. Flow charts are one of my favourites, though.

I decided I'd make another flow chart:

Mostly, I made this because one student has already e-mailed me asking how to do the assignment. Sigh. Sometimes I wonder what they do in class!

As a side-note... I noticed the kids tend to get very restless around 16:00. I should keep this in mind.


Army

Augh. We started off with four untrained Privates. In a few weeks, there will only be two. Few weeks after that, maybe only me.

C-- had a series of personal tragedies, and, next to me, I'd say she was the least "army" of us four. So she left.

K-- is the most "army" of us all. She tried doing Reg Force BMQ several times, but, each time, a few weeks before completion, she'd get sick or injured. She just advanced in her Civi job, though, so she won't have any more time for Army from now on.

And, F-- is thinking he might switch over to Reg Force. He'll decide by Tuesday, but he seemed pretty gung-ho about it already.

AUGH! Why?! WHY?? If I had balls, I'd say this was like a kick in the balls. The person in charge of us is pretty intimidating (although, one of the new Officer Cadets said, "Oh, you're cute!" to her face and stayed un-punched). I would not like to be left alone with her.

Sigh. Well, at least I can do BMQ, and sooner, now that I've talked to my employer at the Maths school. Wooo...


Okay, sleepy time.
--Charissa (or is it Charles?)

Nickels and Trig IDs

I'm bored and was trying to explain Trig IDs to a student. One analogy I came up with was trying to make 25 cents from pennies and nickels. If you know that a nickel is five cents, and a penny is one, you can make 25 cents.

And then I got bored so I made this:

Twenty-five cents:
penny, nickel, dime, quarter.
= 25p
= 20p + 1n
= 15p + 2n
= 10p + 3n
= 5p + 4n
= 5n
= 3n + 1d
= 1n + 2d
= 1q


Recently, my brother had asked me what is the process for writing out all the combinations of elements in sets? For example...

Set A consists of these elements:
a₁, a₂, a₃.

Set B:
b₁, b_2.

Set C:
c₁, c₂, c₃, c₄.

and I want to write out every combination possible; so:

a₁, b₁, c₁;
a₁, b₁, c₂;
a₁, b₁, c₃;
a₁, b₁, c₄;
a₁, b₂, c₁;
a₁, b₂, c₂;
a₁, b₂, c₃;
a₁, b₂, c₄;
a₂, b₁, c₁;
a₂, b₁, c₂;
a₂, b₁, c₃;
a₂, b₁, c₄;
a₂, b₂, c₁;
a₂, b₂, c₂;
a₂, b₂, c₃;
a₂, b₂, c₄;
a₃, b₁, c₁;
a₃, b₁, c₂;
a₃, b₁, c₃;
a₃, b₁, c₄;
a₃, b₂, c₁;
a₃, b₂, c₂;
a₃, b₂, c₃;
a₃, b₂, c₄.

What is the process my brain goes through?

My brother wanted to know the process, because he was writing a computer program, and wanted to make it shorter--fewer lines of code. I'm not a programmer, so I don't know/remember exactly what his code says, but it does something like this:

For every a₁,
for every b₁,
write out an element of Set C.

For every a₁,
for every b₂,
write out an element of Set C.

...

Something terrible like that. And he doesn't just have A, B and C; he has about fourteen of these, so his code gets pretty dang long!

I thought; and thought; and thought about this, but I couldn't simplify it.

And then, I realized, no matter how many (few) elements in each set, there will be more rows than columns (assuming it's organized this way). So, instead of filling out the "chart" one row at a time, maybe it would be shorter to fill it out one column at a time! You'd just have to tell your program how many times to write each element before moving to the next element in the set (eg: how many times to write "a₁" before writing "a₂", etc), and when to stop, I guess, if programs require that.


But what is the method to write all the combinations of coins needed to make some amount of money? Wooo, Canadian monies.


Man am I tired,
--Charissa

Last day of school

Today was the last day of school before "Winter Break", and I got to lead the class. It was great!

Something I learned: Saying "Yo!" or "Word!" or "I'm-a get ma shizzle ON!" etc is a very easy way to get the attention of grade ten students. Indeed! One student, in particular, was embarrassed for me :). But it works. It's so outrageous, that they immediately cease all other activity and turn their heads.

We went over the kids' exam first (as planned here). Half the class got less than 50%. The average was 53%. We got through the first two pages before recess. I wanted to finish quickly so we'd have time for their "presents" afterward, so I just picked one of the hyperbolas to graph. They actually stayed the first minutes of recess to see it through.

Recess.

After, I handed back their tests. Not happy. I copied down a summary of How to Complete the Square; after, I gave them the flow-chart.

Handed out the "presents": condensed notes on sketching conics; and "Why Conic Sections are Cool!". Talked about "formula sheets", study guides, condensed notes.

I passed around my first "formula sheet" I ever made. It has taped edges to prevent tearing; sprayed with hairspray to prevent graphite smudging (write in graphite so that you can erase and position everything better); everything is labeled; colour and indents help titles to pop out... Only two things about this are dumb: One, I used pencil crayons, which the hairspray dissolved. Two, I spent too much time making it. On the next formula sheets, I smarted up. No colour, no tape; but the indents keep everything orderly.

I told them about speaking "Ukrainian Math Wizard", and (let's call him) Vasil, my prof for Honours Calculus.

Then, I gave them the One Million Beans problem (but with fixed values), saying that if anyone could solve and prove it, I'd bring doughnuts next class (solution below). The top students (grade-wise) couldn't get it, but two girls who were interested but determined they could not figure it out ended up solving it! Well, not necessarily proving it, but close enough. So I owe them doughnuts next class (January 12).

While they were working on it, I told them an Engineers vs. Mathematician joke; they're on the train, one ticket... They laughed--they got it! Just before class ended, I told them the joke about Mathematicians reducing everything to problems they've already solved whereas Engineers can solve "new" problems with originality. If they don't get it now, I'm sure they'll get it later!


Proof of "One Million Beans" Problem

We know that after the beans have been moved back and forth, each jar still contains P number of beans. Now let's look at the number of red and green beans in each jar:

Jar A has

(P - n) green + (m) red beans = P.

Jar B has

(P - m) red + (n) green beans = P.

Set up equality:

P = P	Number of beans in Jar B = number of beans in Jar A.
(P - m) + n = (P - n) + m	Cancel (P) on both sides.
- m + n = - n + m
2n = 2m	Cancel (2) on each side.
n = m

Therefore,

| n - m | = 0

for all Natural m, n, P, Q < P.


Okay, I have to get up early tomorrow, then work an 8-hour shift. Sigh. Shouldn't have committed to it...

But I'll mention quickly:

I've been blessed with amazing Math teachers over the years, which probably explains a lot about me. Hopefully, this will allow me to pass along that experience to others.

One student remarked how great it was to have a teacher who didn't mumble (which is especially funny because my father teaches the level below and some kids had him last year). Another said I was exciting and that she was having fun. A few others generally remarked that I explained well and was interesting.

And these are the three (recent) things that have made me feel so worthwhile, in chronological order:

1. Finding out my army-boss has harassment issues (it's not everyone--and we're not necessarily bad untrained privates!).
2. My army-boss telling me I look good (dress/deportment).
3. Hearing that the kids enjoyed my teaching.

--Charissa

Quick update

Army

My "boss" called my house the other day, and it was the scariest thing ever. I'm so scared of getting calls from the Military--for every/any -thing, like, "HEY, WHY AREN'T YOU AWAKE?" or "WTF ARE YOU WEARING?!" or silly things like that.

She called for me to work on Wed and Fri, but I had plans Wed... I actually have a doctor's appointment on Friday, but it'd look bad if I didn't work; and I'm learning that being in the Army, image is very important. Sigh. At least, I'm fairly good at bluffing.


Teaching

I'll be in charge of the kids on Saturday! Hoorays! Unfortunately, they just wrote an exam, and it does NOT look encouraging... I wanted to jump into awesome stuff, but looks like I'll have to go over the exams... Sigh.


Plan for Saturday, maybe?

1. Hand back exams
2. Tell: If you have a question about how I've marked your paper, please wait until I've finished going over the solutions.
3. Tell: If you have any questions about what I'm doing, or why, or anything like that, put your hand up; or if I don't see you, just ask me to pause.
4. Go over solutions.
5. Answer questions about papers.

6. Recess should be about now...

7. Tell: I have some handouts that might be useful for studying! If you don't want them, leave them at the front before you're dismissed. I'm also going to show you how to tell what type of Conic Section you have, which I didn't print out.
8. Distribute Handouts: "Why Conic Sections are so cool!", "How to convert to Standard Form", "How to Sketch Conic Sections".
9. Draw: "How to tell what kind of Conic Section you have" flow-chart.
10. Questions?

11. Tell: I'm going to give you some study tips that I've picked up through high school and university.

12. Condensed notes / "Formula sheets" / Study sheets

have the Trig IDs on it

have the Standard Forms on it.

Tell: Every new topic or every month, try to condense as much information as you can onto one sheet of paper. I used to make condensed notes for every unit in Physics, and they saved my arse! Make sure you label everything so that you can tell just by looking what and where everything is. If you're doing one sheet per unit, put a title on that sheet! Use this sheet when you get your review exercise at the end of a unit; use it for assignments. Always improve your condensed notes while you're learning the material--that way, you'll know exactly where to look when you're studying for the final exam.

13. Start: ________ (new topic: graphing polynomials, or logs)

14. Optional: Hand out treats!
15. Dismissal!




Leaving for work now...
--Charissa

Conics and my state of mind

Every two months or so, I go kinda crazy--just a little, though. For about five days, I am restless, pouty, petty, dramatic, anxious, confused--all sorts of nasty things. An additional side-effect is that I can believe anything. I won't know waking reality from dreams; I won't know waking reality from things I read; I won't know waking reality from what I want to believe. Added to this, I have a mild fever that's been off and on for about a week.

For anyone who has an idea the state my mind's normally in, you may have an extra appreciation of the mess this stirs up.


Teaching

We've just "finished" teaching Conic Sections to the kids. I'm not sure what he taught, I was marking their papers so they'd know how they're doing before the exam comes.

In S4 Pre-Calculus, we made a flow chart for identifying types of conic sections. I want the students to have it, but I'm not sure what the teacher has in mind.

That being said...

Because Saturday, December 01 is my fitness test with the Army, I might miss part of Math school that day. That's a review class, and I'd be sorry to miss it. One student is even writing the exam that day because he won't be there next week.

Upcoming Saturdays:
December 01

09:00 - Army fitness test at base. Eep.

14:00 - Review class before exam. One student writing exam early.

December 08

14:00 - Exam on Trig and Conic Sections.

December 15

14:00 - Teacher is away and has not given me any specifics on what to do that day, so I have full control of what we do that day! I want to actually enrich* the students' understanding of Mathematics--because we're supposed to be an "enrichment program".

17:30 - Math School Christmas Dinner. Woots.

* Here is what I want to talk about on December 15...

Conic Sections

History

Way, way back, circa 200 BC, there was a Greek named Apollonius, and he wrote a book called On Conics. This earned him the title, "The Great Geometer". The study of conics has been around for a long time! (Will add more later.)

What are they?

Imagine two hollow cones placed together at their points, sort-of like an hour-glass. By cutting different 2D sections of this, you get "Conic Sections".

Taking a slice of a cone, parallel to an edge gives a parabola.
Taking a slice of a cone at an angle such that you slice through both halves, gives a hyperbola.
Taking a horizontal slice gives either a circle or a single point (if you cut at the joining point).
Tilting that circular slice gives an ellipse.

Definitions

A circle is the set of all points** equidistant from a single point. To draw one, wrap a loop of string around a pin and a pencil and draw as far from the pin as possible without tilting the pencil.


An ellipse is the set of all points** whose distance from both foci is constant (ie: the distance from one point to the first focus plus the distance from the same point to the other focus always adds up to the same number). To draw one, wrap a loop of string around two pins and a pencil and draw as far from the pins as possible.

A parabola is defined as the set of all points** equidistant from a line and a point F (the focus) not on the line (see the right-hand side of this image).

A hyperbola is the set of all points whose distance from one focus, minus the distance to the other focus, is constant.

**(in a plane).


Gravity

The path of a projectile thrown (ie: with another, smaller force in a perpendicular direction) near the surface of the Earth is a parabola.

The path the Earth travels around the Sun is an ellipse.

The path of an object (such as a rocket or comet) on an escape trajectory from a fixed mass (such as the Sun) is a hyperbola.


Reflection

The parabola, ellipse and hyperbola each have "focus points" or "foci". If you've ever seen a satellite dish, you have an idea what this means.

For parabolas, an incoming ray that is parallel to the axis of symmetry is reflected toward the focus.

For ellipses, any ray originating at one focus will reflect toward the other focus (this is still true for the special case of the circle, where the "other" focus is the same focus).

Hyperbolas are a bit more complicated. A ray originating from one focus will be reflected and look as though it originated from the other focus (see this image). (There are a few other cases that work out nicely, that I just can't remember right now.)


Light Cone
...Actually, maybe they won't be ready for this yet. But I'll mention it--briefly.


...I should take that book out of the library again...
--Charissa


Further reading:
http://fti.neep.wisc.edu/~jfs/neep602.lecture8.trajectories.97/neep602.lecture8.trajectories.97.html

"Spacecraft Trajectories"

http://mathworld.wolfram.com/Parabola.html

Mathworld: Parabola

http://mathworld.wolfram.com/Ellipse.html

Mathworld: Ellipse

http://mathworld.wolfram.com/Hyperbola.html

Mathworld: Hyperbola

http://www.practicalphysics.org/go/Experiment_386.html;jsessionid=alZLdQlAHb1

"Drawing" a parabola; teaching aid

Quick Update

Origami

For my birthday, I received an Origam gift box and extra book from Mark! OMG! The gift box has printed paper (strange and elegant designs that remind me of wallpaper), gold and silver foil paper, a protractor, two 'bone' crease tools (one for making sharp creases, the other for "drawing" the crease patterns), a square board with grid and markings on it, and an origami instruction book. I'm only a little irritated that both books contain mostly diagrams that are reliant on cutting paper.

This is mostly an announcement that, as soon as I get my camera, I'll be posting picture of both the modular origami polyhedra and the new models--animals and flat geometric patterns. Man, I can't wait to get that camera!!


Teaching Math

I've been in correspondence with one of the students who had questions about exponents/roots, and after the two weeks between classes when I was helping her with that, she wrote back to say I'm a good explainer! That totally made my day!

We started conic sections on Saturday with the Circle and Ellipse. At the end of class, the teacher wrote this on the board:

"Next week: line, parabola and hyperbola."

The students had mostly never heard of hyperbola, and some never heard of parabola. The teacher said to look it up on the Internet, and I wanted to jump up and say, "MATHWORLD DOT WOLFRAM!!" but of course, that would have been inappropriate, so I didn't. Sigh.


Film Festival

One of my friends has a film in a Canadian film festival, and his film made it as far as a public showing! I'm so excited! I'm going to the showing, hopefully with a friend who is/was a major artistic-film-maker-type-person. In truth, I wonder if she'll like my friend's film, but I invited her mostly for the other films. Heh.


Army

My unit did a field exercise this past weekend. They slept outside with little form of heating for two nights. Yowza! I went on the last day to help with breakfast and tear-down. Man, I suck at moving things. I definitely need to work out. But with the army, I get a personal trainer and access to the gyms, so I'll have to make use of that. Sheesh, though, I wish I had more free time...


Art

I'm donating Boobfest III to the queer student group at the university I used to go to. At least, I'm donating a print--and I think I'll take it back at the end of the school year.

Also, that student group is planning on booking a small art gallery in one of the centres at the university--there's this glass room beside a major traffic junction and across from a Tim Horton's / food court, I think, which is totally a great place to put an art gallery.

If we end up booking it, I'll totally submit: my nude pieces; the Origami I'm proud of (goldfish in the bowl!!), including an enclosed chain of connected coloured boxes that are ordered to make a rainbow (sort of; I'm missing a real *purple* but I have this dull mauve thing); and any other artwork I deem public-worthy--which is not much, so I'll have to get busy making more, dammit! Mmm, I'm excited!


...Will update this entry with links and text formatting later.
--Charissa

018: Exponentiate!

Woo! Just a quick update to post this tutorial (Flash) on exponents/radicals. Check it out here, too!

Woots. Off to work now.
--Charissa

Issues

As much as I want to keep this from being angsty and personal, I sort-of want to write about my state-of-mind.

I've been so apologetic ever since getting the survey job; I haven't spoken fluently and with conviction, it seems, for ages. My sentences are full of "maybe"s and "I think"s and "I believe"; and "it might be"s; and more "like"s than ever before.

I wonder if it's mostly a self-confidence issue, or if it's something else?

I also wonder if doing more proofs will be helpful in gaining more self-confidence. Probably will!


Week so far:

Oct 29

I'm now 19. Hoorays, I guess. For my birthday, I paid $200 in Utilities.

Oct 30

Learned how to properly wear my Army uniform! Woo-hoo!

Had my first "class" in the Army (Dress and Deportment; and Rank Structure).

Oct 31

Started playing Brood War again. Sigh. What a wonderful way to waste time.

Received e-mail from the teacher, who said I should go over the Quiz in class with the students--WHICH IS OMG HOORAYS!!

O, Time...
--Charissa

Webcomics and Teaching

Webcomics

So, I read Irregular Webcomic!, a webcomic run by DMM, pretty regularly. And often, there are totally geeky annotations, including (to point out only a few)...

here, where the joke involves vector calculus;

here, talking about the impossibility of StarWars using Thermodynamics;

here, explaining three Laws of Thermodynamics;

here, explaining how awesome Maxwell's equations are;

here, using the Shroedinger's Cat idea;

here, making Quantum Mechanics jokes;

here, making Fourier Transform jokes;

and now, here, using History and Math!

I hearts this comic so much!

Also awesome in the Math department is xkcd, by Randall Munroe! I've even used this comic in an animation I'm working on.



Teaching

So, being Saturday again, I went to the Maths school to TA; and, again, it aggravated me. But we had a meeting today, and our principal mentioned some of the duties of the Teacher and TA, which I was wanting to beat my teacher over the head about.

Some things mentioned...

Our school's philosophy/signature: Since we have such a high student-to-teacher-or-TA ratio, we have a "human element"; there is more human interaction: student-teacher/TA and student-student.

Roles of the Teacher and Techniques:

• don't lecture
  
  the kids are 13 and younger, they can't handle lecture-style yet!
  

  create lesson plan
  

  have authority
  

  avoid dead silence; talk! Fill the silence with teachery sounds!
  

  don't talk into the board
  

  do not read lesson plan
  

  don't work out of a textbook
  

  never lose face
  

  never let the student "win"
  

  lose once, lose all

Roles of the TA and Techniques:

• don't supersede the teacher
  
  if the teacher's wrong, don't point it out, no matter how frustrating
  

  make sure the students pay attention
  

  encourage participation
  

  supplement the teacher
  

  interact with the students; learn their names

Tips for Creating Lessons:

• don't copy down examples or problems
  
• not just formulas
  
• walk the students through it all

My birthday party

My birthday parties have been nick-named "Awkwardfest", but this year was pretty okay. In fact, we had a focus on awkwardness, and I even donned my "Awkward Fairy" costume (it's skimpy black spandex with a hole shows off what would be cleavage on a more endowed woman, and a black tie worn over the hole). Awkward! Especially when one of the guests flips the tie up!

But it was good. Kevin and Mark came.


Other Stuff

There's a guy at work who makes tobacco smell handsome. Or, maybe, just the way it smells on him is handsome. I don't know.


--Charisa

Numerals and Teachery Things

I took out the book The Abacus: a pocket computer from the library (because my brother had gotten me an abacus for my 18th birthday, or Christmas, I forget). In the chapter "The Ancients", it discusses ancient number systems, most of which I'd already heard about in "Mathematical Sorcery".


There was an explanation of Babylonian numerals and Egyptian numerals, as well as others; but what I didn't know was the meaning behind the Egyptian numerals, and this book explained some.

After some quick Googling, I've found three slightly different interpretations of the symbols:

1. http://members.tripod.com/kangwei1a14/egyptian.htm
2. http://www.recoveredscience.com/const102egynumerals1.htm
3. this book.

Picture	Explanation 1	Explanation 2	Explanation 3
	A rod.	Upright.	"just a vertical stroke, not much different from [our 'one']."
	Cattle hobble.	Vault.	Heel bone.
	Coiled Rope.	Rope coil.	Scroll.
	Lotus flower.	Lotus.	Lotus flower, "a plant the Egyptians loved."
	Finger.	Finger.	(None)
	Tadpole.	Tadpole.	(None)
	God with raised arms.	Heh-god.	"a man holding up his arms in amazement. To the Egyptians, one million was a tremendous sum."

Awkward sidenote

My good friend Mark told me about this assignment he had (a long time ago), to convert Babylonian numerals into Greek or Roman or something. When converted, the numbers spelled out the words "clitoris", "penis" and "airplane", which confused the heck out of him!

Aren't numerals fun?



I watched the movie Proof last night.

It sucked. It was almost good, and maybe if it hadn't been so "Hollywood", it would have been better; but it truly, truly sucked. Also, movies in which getting it on is part of the actual plot tend to suck.

Plot summary:

• Girl thinks she's crazy, because her dad was a crazy mathematician, now deceased.
  
• Boy is going through the deceased dad's work.
  
• Boy and girl have sex.
  
• Girl has a proof she wrote, but nobody believes she wrote it, not even the boy.
  
• Drama!
  
• Turns out, she wrote it; and maybe she's not crazy after all!
  
• Reconciliation with boy!

Did I mention the movie sucked?



Teaching

As usual, Saturday was another day of TA-ing for the Maths school. We've started on Trigonometric Identities, and I don't think the teacher adequately taught what an identity is; nor what a proof is. He later asked if this was too easy or too hard, and nobody responded.

Sometimes, I want to just jump in front of the class and tell him to shut up, and start teaching. But, the principal must have hired him as a teacher (instead of me) for a reason... At least, I hope there was a reason other than "he's older, so he'll be the teacher."

I think we should walk the kids through what an identity is; walk them through a few proofs. I'm marking their papers, and I can tell that a few just have no idea what's going on. Someone wrote "1 / 0.5" as a final answer, which is wrong on so many levels!


The format I'd like my students' work to follow

Question number. Question

Work Work Work

/ Side computations / Side computations

Answer

That would be just amazing and so much easier to mark. Maybe I'll have to make photocopies from now on, just so it's easier to explain this to them. Yeah, I'll do that--I'm going to do that RIGHT NOW!

--Charissa!

Math math math math militia

So, a while back, I applied to be a teaching assistant at a Maths school. This Maths school runs on Saturdays, and was originally meant to be an enrichment program: for kids to get ahead, or to just--yeah, "enrich" their understanding of Mathematics.

I want to write a paper on how awesome Math is.

It's just, that's been done so many times already; and, from what I've read, unsatisfactorily. I'm reading Mathematical Sorcery in my spare time right now. It's good, I guess; but there's this one section that tries to induce the reader to look at an equation as one might look at a piece of art, and the author describes how he gets tingles down his spine. I'm not a writer, but I think that was unnecessarily personal; if something is awesome, the reader can figure it out for himself (gender-inclusive "himself").



Tower of Hanoi

Back in Honours Calculus last year, we studied the Principle of Mathematical Induction and then did an example problem using the Tower of Hanoi.

Here is the basic setup: There are three poles onto which you can place some discs. The discs are of different sizes, and start out at one tower, arranged by width: the widest disc at the bottom and the smallest disc at the top.

The objective is to move all the discs from the first tower to form another tower. Usually, you start off with the discs at the far left and must move them to the far right.

A further objective would be to make as few moves as possible.

Rules: Only one disc (the top-most one) may be moved at a time. No larger disc may be placed atop a smaller disc.

Here is what we found (probably):

discs:	0	1	2	3
moves:	0	1	3	7

Let m_d be the minimum number of moves, and let d be the number of discs to be moved. We noticed that m_d = 2m_{(d - 1)} + 1
We hypothesized that m_d = 2^d - 1 for all non-negative integers m.


Proof:

1. We shall test the first/best case scenario, where p = 0.
Plug in values:

m = 2^0 - 1
m = 1 - 1
m = 0

If there are no discs to move, there are no moves to make.
This is true!

2. We shall now test if the following scenarios are true; ie, whether or not m_{(d + 1)} = 2^(d + 1) - 1 Go!

m(d + 1) = 2 md + 1
m(d + 1) = 2 [ 2^d - 1 ] + 1	Substitute md = [ 2^d - 1 ]
m(d + 1) = 2^(d + 1) - 2 + 1	Multiply through. There's a common base of 2, so add one to the exponent to simplify.
m(d + 1) = 2^(d + 1) - 1	Hoorays!

So, by the Principle of Math Induction, we have proved that m_d = 2^d - 1 for all non-negative integers of m. We could even add to the table:

discs:	0	1	2	3	4	5	. . .	n
moves:	0	1	3	7	15	31	. . .	2^n - 1

Sometimes, a story goes with the Tower of Hanoi. There are variations, but the idea is that, at the beginning of the world, there were these monks who had this game set up in their temple. When they had finished the game, the world would end.

Supposing it takes one second to move each plate (not very realistic), and there are 64 discs, when will the world end?

d = 64

m = 2^64 - 1
m = 18 446 744 073 709 551 615

So, the world would end in roughly 585.442 billion years. The universe is roughly 13.7 billion years old, +/- 1%. Hehehe.




Being a Teaching Assistant

Being a teaching assistant is conflicting right now. On the one side, it's like job-shadowing, except I get paid--quite well. On the other side, it's incredibly tedious and painful to see what I would consider bad teaching, and not be able to do much about it.

I got such fulfillment today when one student called me over to explain something.


The way I teach

When a student puts up his hand, I come over. If there is a seat available, I'll sit down; if not, I'll kneel on the ground (this usually puts me just below his eye level). Then I ask, "How can I help you?"

After the student has explained his difficulty, I will confirm that I understand it. This helps me to be clear what I'm trying to do; and also gives me a little thinking time.

I used to be afraid of stuttering, so I'd take silence over stammering or filler. But when I teach, I have to remind myself it's okay to show that I don't know everything or that I'm not infallible; so if I'm having difficulty, I might make a short, "Um," to let him know I'm thinking.

I try to use at least two different methods to explain or solve a problem. I have a habit of asking, "Does that help?" afterward. I think maybe I do this too quickly sometimes; but I found it to be very helpful.

If someone else wants my attention at the same time, usually, I will tell him to wait; because if a student calls for my help, I want to show I am available.

After, if I feel that the student has time or interest, I'll go a little further and tell how it relates to other fields, where else it can be seen, or other cool things that can be done with it.



I think that's all for tonight. I'll just mention that on Tuesday, I'm going to be enrolled in the Militia. They asked me to bring a small recent photo of myself (photo booth at a mall works well) for my temporary ID card; so I went to the mall, and, wow, not one of those four shots turned out well. At least, I'm identify-able, don't look terrible, and I'm wearing clothes I like.

I'm very excited, though.
--Charissa