Sunday, 28 April 2013

ETC: Doctor Who's Pacing


"I say stuff." -The Doctor
"My turn." -Me

So, the recent episode "Journey to the Centre of the TARDIS". It bothered me. But not for the temporal aspects, as remarked on by some, including at io9 in the article "We're mighty sick of Doctor Who stories where time travel is magic". I think the show got the temporal aspects RIGHT, for the most part. The trouble was in the storytelling, and to a certain degree, in the staging and pacing.

Ok, spoilers ahead.

By the way, speaking of staging, there's storyboards up for the episode.

Also, here's a review from someone who apparently liked the episode a lot. More than their first comment, at any rate.

Have I mentioned that I've written time travel fiction? I also wrote about the movie Looper and "Asylum of the Daleks".

Also, you realize I'm just killing space here, because SPOILERS!  Hello!

You DID catch that, yes?  Sure you want to scroll?

Okay, just checking.



BIG FRIENDLY BUTTON

So, let's start with: There isn't necessarily a problem with a reset button episode. Not when it's done well. I should know, I've seen a bunch and written one into my "Time Trippers" story. In fact, I did mine in a way which, upon further analysis, is not completely dissimilar from this episode. (So, okay, biased.) Yet I think that's also why I find this Doctor Who episode simultaneously really good, and yet rather aggravating.

I think that the point to a reset button episode is character development. Bear with me, I know that sounds weird since the characters don't remember it... but the point is, WE DO.

In this case, we get to see the Doctor being rather manic about who Clara is, while she does the same in turn... we're effectively afforded the chance to look inside their heads, and learn how they would react to certain things, without those things actually occurring. That's NOT a bad thing. It's only bad if it's never brought up again.

Now, there are other ways to do this aside from time travel. "The Zeppo" comes to mind, from Buffy, season 3, episode 13. We see the story from Xander's point of view, we get new insight into his character that the other main characters do not. We can now look at him in a new light. The people in the story don't know what happened, so they lack that ability. Of course, we don't get the benefit of Xander really interacting with the others.

There are also ways to botch this using time travel. "Year of Hell", the Star Trek: Voyager two parter from Season 4 comes to mind. The resolution made no sense, and the actions of the characters (like Chakotay, in investigating temporal paradox) were completely isolated from the rest of the series itself. For an example of it being done well on that show, go with "Timeless", sixth season.

Doctor Who's "Journey"... the rules are consistent, not magic, but it falls down in execution.

TIMELINES

Now, here's why it works. We're effectively seeing the second iteration of a time loop. The same plot device, by the way, as used in Stargate Universe's Season One Episode "Time". (There are no new plots?) In the grand scheme of things, here's what happened:

TARDIS gets zapped. Doctor appears, tells himself how to fix it, time loop gets fixed, end story. Which is (in theory) all Clara knows. But that's barely even a teaser.

So here's what actually happened:

TARDIS gets zapped. Big problems, temporal echoes, people die, maybe even Clara actually dies, then Doctor has a flash of insight, sends the critical device back in time, inscribing it with a message to tell his future self to push it. Bringing us to second iteration. Clara retrieves device, still big problems, still temporal echoes, still people die, this time Clara survives, helps Doctor with his flash of insight, and this time he has the time or inclination to actually interact with his prior self. Time loop closes.

We only see the second part of that run. Which is part of the problem, but at the same time, we don't necessarily want to be subjected to a replay of Haruhi Suzumiya's "Endless Eight". So I can forgive them that. The trouble is, it's not obvious unless you make a habit of thinking four dimensionally.



For instance, the "time will reassert itself" issue discussed in the io9 article comes from the fact that the group is effectively trapped in a room that will burn them alive. The Doctor's 'plan' is that the two salvage guys separate. His theory being that, according to future history, when they die, they get fused together. But if they stay apart, that can't happen, meaning the beings now trapping them won't actually exist, meaning they can get out.

Time hates when you try to rewrite it though. Even future time. Just ask my character, Carrie. So that failed.

Moreover, it seems to me even had separating the guys WORKED, they'd become trapped by two SEPARATED future salvage guys. So that's where even more of the theory falls down. Also, to even be with me at this point, you'd have needed to notice the burn victim parallel, which is where the rest of it potentially falls down. Which brings me to the bigger problems.

PACING

A HUGE problem with the show itself lately is the pacing. Everything is frantic, and the characters talk so fast that I miss chunks of dialogue, and it's all an action adventure, and really? Does no one sit and talk anymore? I watched the episode a second time, and here's a few rather KEY bits of dialogue that breezed by me on first viewing:
1) "This little baby can disable entire vessels." Okay, so THAT'S why the device was so helpful. I was trying to figure out how it acted like a reset.
2) "You're my guides for this." Okay, that's at least a possible reason for the Doctor to trap them inside... they do know salvage, and his ship is a bit of a wreck. He didn't know the half of it.
3) "So that's who." Which I think I only got on the second viewing because I saw a reference to it on the 'net. Maybe cut away even faster and have Clara whisper quieter next time, then no one will get it.
4) "Recent past." Aha, so that's how the Doctor was able to set the time rift. (See? It's never that easy, honestly.)

I also thought the first time that ALL of the salvage operators were androids, because that bit of dialogue was unclear. Oh, and I missed the swimming pool. Yeah, lots of people mentioning the pool as I browsed the net, passed right by me in the initial viewing. Don't blink.

Now, I realize part of the point is that they WANT to pull us into multiple viewings, but can we not always be lurching from crisis to crisis? The bit in "Cold War" when Clara is reflecting on the people who died was genuine, and important in the grand scheme of things.

There was time for that sort of thing here. Just nix some of the stuff where the salvage people are wandering around trying to salvage the TARDIS, with it trying to stop them, because that turned out to be pointless. Or at the least, it could have been done SO much more intelligently. ("Let's split up!" - how was that NOT the plan in the first place?!)

Which brings me to the other big deal...

CHARACTERIZATION

Maybe it's the lack of female writers. But when The Doctor was talking about putting the TARDIS in basic mode for her, and then the talk about driving, my jaw nearly hit the floor. Also, it took how long for The Doctor to realize Clara was still inside? And the way he described her? Oy. (Maybe he was overcompensating after that, what with the self destruct?)

Clara wasn't much better. "A hug is really nice"... pardon me? This guy has just said he saw you DIE in the past, and YOU'VE just recently seen yourself dead, and a hug is nice? No. Just no. A hug is now scary, and this guy you thought you knew is acting kind of creepy insane, and you're smarter than that. Or you should be. And you COULD be.

Again, the point of a reset button episode is CHARACTER development.

Show me Clara giving The Doctor what for about his secrets, and/or the Doctor sincerely apologizing. Show me the Doctor scared; I bought it in "Hide", I didn't buy it here, the script forced him to act too manic. Heck, show the Doctor collapsing to his knees or something when he sees the engine, actively distraught over the TARDIS. Maybe show him choosing the TARDIS over Clara. Show Clara standing up to The Doctor, or leaving him.

SHOW ME SOMETHING OTHER THAN PEOPLE RUNNING AROUND.


Oh, and then there was this gem:
"Don't worry. You'll forget."
"I don't want to forget. Not all of it."

Which leads to... pardon me?! I'm thinking there are a few things you'd want to remember ASIDE FROM A RANDOM NAME. Writers, don't use your "vanishing" episode to drop hints ABOUT THE PLOT. Either state the plot OUTRIGHT (as the characters won't remember it), or have a discussion. About whether they'll still be the same people if The Doctor manages to repair the damage, or whether they have the right to do this if the future is already written (and wanting to assert itself), or what will become of the salvage people should none of this ever have happened. You could have made time for that! Easily! Then people won't end up annoyed in this way.

For that matter, it would make the end line of "Do you feel safe? I need to know you're not afraid." ring true, instead of hollow, as it did for me at the end. Sure she feels safe. Apparently she always has. Boring. Instead, wind back a bit to show me a Clara who's overcome, who isn't sure she can go on, who has been wounded, physically and emotionally, and who isn't sure she'll ever trust again.

THEN reset her and ask her if she feels safe.

If she does, that's not only better foreshadowing, it's far creepier for the audience than a noise in the dark. Don't you think?

Saturday, 27 April 2013

MAT: Tile and Error


You know that we like using 'x'
To do algebra is not that complex!
Physical models can help you out. (oh oh)

A small square will be one by one
The area, the area is how it's done!
Unknown length shows 'x' without a doubt.

-Avril Lavigne ParaB Conic, "Y-Squared Tile"


Blogging about PD (Professional Development) here. I should do more of this. That way, I'll remember it better, and it could be of more use to others. I sort of did it as part of DITLife, but here it wasn't part of a school day, it was a Saturday morning. The "Ottawa Valley Spring Math Forum", as presented by Claire Bonner, Rebecca Black, Robin McAteer and Anne Holness.

Topic: From Patterns to Algebra.

In other words - at least for me - the bridge from middle school (Using: Input x 3) to high school (Using: 3x). Immediate diversion to write about what's in the parentheses there... since when does "take the number and triple it" become "triple of some unknown that looks like a multiplication symbol"?? Answer: Nowhere in the curriculum. Just, you know, one of those adjustments we expect Grade 9s to make.

Along the same lines, we tell students to always do the parentheses first, before exponents. Then we start writing parentheses as multiplication, and wonder why they have trouble with order of operations. Yeah.




Anyway, here's some of my "take aways" from today:

1) Students - and people - have a tendency to look down the table for patterns (+5,+5,+5,+5) rather than across (value times five). Putting things in order does not help them make the transition.

2) A mistake textbooks make is giving a lovely pattern of squares, then immediately saying "create a table". That changes the context. One should be able to come up with a "rule" even WITHOUT a table. Along the same lines, you don't want to introduce 'x' and 'y' too early, or you're probably doing a disservice. They're very abstract - patterns are concrete.

3) Pausing to ask a student "Why? Explain yourself!" is important not just for that student. Granted, it forces that student to try and articulate their intuition. Good. But it can also allow you to see whether they're seeing what you think, and perhaps more importantly, give OTHER students additional time to think about things.

4) Why DO we kill mixed numbers as soon as students enter high school? If you have "6 times 2 (1/2)", you don't have to do "6 times (5/2)", you can do "6 times 2" PLUS "6 times 1/2". Boom. Distributive law.

5) Patterns show equivalent expressions. Consider "3x+7" and "3(x+3)-2". Equivalent? Well, put down 3 "x-tiles" and 7 "unit tiles". Now put down three groups of "x-tiles" & 3 "unit tiles". Include two negative units. Zero pairs. Boom, same thing. No algebra.

6) Cutting up the "x-tiles" according to values of x makes more sense than swapping in unit chips for x. Which I'm not articulating well, but we sort of need elasticized tiles to represent x. Ones that students won't fire at each other.

7) Possible group activity for solving equations: "You're the right side (3x-4). I'm the left side (2x). We're equal. So of what value are our 'x' tiles to make it work?" (No stealing my tiles! But you can give me zero pairs, aka 'Thanks for nothing!'.)

8) Sequences, which start counting at '1'... I've blogged about that issue before. But it occurred today that RECURSIVE sequences DO run down the table. You need to know entry 98 to figure out entry 99. Inefficient, but there's the connection between recursive addition (of a constant) modeling a linear pattern.

And I'm doing recursion this coming week. I have no idea how much use that connection will be, but here's hoping I remember to incorporate it.



And that's whyyyyyy I smile, it's been a while,
Since every day and everything has felt this riiiight,
And now. YOU turn it all around...

-ParaB  Avril Lavigne, "Smile"

Sunday, 21 April 2013

TCH: Teaching Times


So, as I tweeted last Friday, over a seven day span I worked 84 hours. This is what happens when report cards are due the same week as the school play. Tracking the time was fairly simple, as I was usually at the school itself, though there were times I marked papers elsewhere, so I included that in the total too.

I'M NOT SURE I KNOW THE MEANING OF THE WORD

I now think I'll keep recording, day to day. This for a few reasons:
1) People tend to take note of extreme highs or extreme lows. This presumes we have a baseline to work from, but do we really know what that is?
2) I'm wondering how I stack up against people I follow on Twitter. I feel like I'm an average teacher, but really don't know. If I'm working less than others, perhaps teachers who work more will feel better about what they're doing. Conversely, if it's more, maybe I need to relax a bit.
3) I was listening to the latest "Infinite Tangents" podcast (106), where there was discussion of "Day in the Life". It was remarked that there aren't as many submissions of late. Audio was pitched as an idea, but for now, I'm going this route instead.
4) It's easy, and no one's told me it's a bad idea. You are welcome to correct my thinking.

GROUND RULES


A weekly tally runs from Sunday through to Saturday. Because, calendar. So my previous 84 hour week was TECHNICALLY only 79.4, because the 4.6 hours on the prior Saturday don't count. In terms of the individual days, I figure on counting - or not counting - events in the following way:

1) TRAVEL TIME: No.
It takes me about 25 minutes to get to work. I might be thinking about math at the time, but not always, and it seems silly to think that someone living closer would be "working less". That said, I may include travel time from school to meetings related to education; I'm on a few committees.

2) LUNCH: Yes.
Mainly because it's rarely the full 45 minutes anyway. The two 14.5 hour days I worked last week featured only 10 minutes for me to actually eat. Besides, the 8 hours of a 9-to-5 job would include lunch too, AFAIK.

3) PROFESSIONAL DEVELOPMENT: Yes.
It relates to the job. Also, if I go to a conference instead of to school, it doesn't make sense to me that I'm talking about math and teaching methods all day... then recording that I worked zero hours.

4) DISTRACTIONS: Not really.
In other words, if I take five minutes here and there, I'm not about to be deducting that. But if I take a twenty minute time out during lunch, or during my 75 minute prep period, I'm going to nix that time to the best of my abilities. (For instance, time checking Twitter or researching my web serial.)

Related to #4, if I'm distracted at home, I'll be making estimations. For instance, today I started doing some work around 2pm... but I was simultaneously catching up on Linkara videos, and playing Sims online. I took a break for Dr. Who, and at some point, I went shopping. It wasn't until 8pm that I really focussed in and worked for two solid hours. So, going to call that 4 hours overall.

My estimates will probably lean on the low end, because I don't give myself enough credit. I'm not sure how long I'll keep this up either, it's an experiment in progress. If you want to backcheck on my feed, I was tagging #WeekOfHeck for the last week, and now I'm thinking I'll use #TchTag or #TchDay.

Enjoy?

Saturday, 20 April 2013

WRI: Mind The Gap


Have you ever worked a twelve hour day? Now take it and multiply by a five day work week. Still with me? Okay, now picture trying to update a web serial at the same time.

Could you do it? I'm here to tell you about how you might pull it off.

Pull it ALL off.


BUSY SIGNAL


First, let's kill the notion that people who put up webcomics and web serials have lots of spare time on their hands. Either they're employed elsewhere (to pay the bills and such), or they're unemployed and finding a job is taking up a lot of their time (and certainly their mental energy, as the stress of needing a job can sap your will). Ergo, it's rare that web efforts themselves are the sole activity of the author.

So what happens on those occasions where you're supposed to post something up... and you don't have anything ready?



I was recently faced with such a situation.  I even lied a little above - I didn't work 12 hours for 5 days. I worked an average of 12 hours for SEVEN days, including the weekend. That's 84 hours, folks! Yet only 15 of those were on the weekend. Do the math to get my actual five day work week.

The key is, I saw this coming. From a mile away. Because report cards were due in, on the SAME week I was helping with the school play. Don't often get the double whammy, normally performances are later in the month. (For the record, I'm not even the director, you should see her hours, as she's also a department head!)

What I DIDN'T quite see coming was that this was also happening right when my math personified web serial decided to wrap up Series 4, and move into Series 5.


EVEN INSERTING SERIES 4.5 WOULD REQUIRE MATERIAL

I had a choice. 1) Push on through into Series 5 using random clip art, meaning by today my buffer would be empty, and I might have done a shoddy job at a possible pivotal point in my story line. 2) Go on hiatus for a couple weeks in between the two Series', and risk losing what few readers I might have gained over the last few months.

Naturally, I took the third option.


CHEESECAKE


Yeah, I know. You're thinking about this. But it can just as easily be something like this. The author calls that second "Filler", but isn't cheesecake also filler of a sort? It's a creative way of filling in a gap, and more to the point, it's something you have the ability to prepare in advance, then pull out of your hat in a time of need. Besides, we all have different likes and dislikes, so I'm re-appropriating the term "cheesecake" to represent any diversion that makes the reader smile.


Now, you may be thinking that's easier to do with images... and you're probably right. As an aside, publishing images along with a text serial is a good move; maybe I'll blog about that in future. But "cheesecake" can be done with text too. As far as my serial writing goes, I use mathematical song parodies.

It was simultaneously quite brilliant and very stupid of me. 

Brilliant because:
1) They were written a month ago, and could be easily dropped in.
2) There's precedent, I bridged Series 2 and Series 3 with a set of Trig Song parodies.
3) It gave me the time I needed to set Series 5 properly in my head.
4) I could cheat. Since I don't post the songs on my main blog page, I could set them up in advance, and then simply Tweet and Link the posts on the day of the update.

Stupid because:
1) Since the songs DO have a separate archive, a casual reader could have missed the links going live.
2) To do it properly, songs require more specialized images. I was cropping photo files in the week previous, and doing added inking and scanning last Sunday night.

There's also the fact that it's sucked up my song buffer, meaning I now have no fallback position in event of an UNSCHEDULED problem in my life. The last time that happened, I went on hiatus for over two months. That said, it's made me think about what other things someone could potentially do, aside from songs.


FILL THE VOID


I'll conclude by offering ideas that can be trotted out for those times when you just don't have the ability to write new material. The key is these can be written at any time, and might even give you more insight into the characters and world that you've created.

A) Character Diary Entry. Their thoughts on current events. Easily put into the serial any time after the fact too, as the character 'finds' the diary or 'recalls' events/emotions just when you need them to. Alternatively, if your character doesn't do diaries, maybe they do fanfic? Maybe they're even shipping your other characters together?? (Oh my.)

B) Commercial Break. Is your series taking place in a fantasy or futuristic setting? Pick an item. How would a commercial scan for a "Jedi Lightsaber"? Or a "Sonic Screwdriver"? Alternatively, you've gotta figure there's a black market for knockoffs, what features do they have that you might not have necessarily anticipated? Because one day, when you're terribly busy, the main character of your story could simply run into this shady guy in a trenchcoat, and he pulls it open to offer something...

C) Origin Story. Where/When DID that item first get discovered anyway? And what ARE the origins of that girl's superpower? Alternatively, who was REALLY the best kisser? Two characters debate it. Maybe they're both wrong. Maybe this sparks an idea for later, maybe this is never used - or maybe it's useful filler. A more cheesecake flavoured supplemental can involve re-enactments.

D) Omake. Meaning "extra" in Japanese, it may be extra material (like a follow-up explanation, or a parody), but can extend right up to another story within your story. Use this with care, as it's an undertaking in and of itself, and you don't want it to get away from you. For instance, "Gekigangar III" in the anime "Martian Successor Nadesico".

Notice also that these are things you could do to get your creativity rolling, to the point that you feel energized enough to return to the main story. So happy writing!



All this, and still no re-edits on the second book of "Time Trippers"! Readers, you have NO idea how displeased I am with the author right now...

Saturday, 13 April 2013

MAT: Irrational Exponential

LYN

Once upon a time, people got tired of writing things like 5+3+3+3+3+3+3+3+3+3+3 and went with 5 + 3(10) instead. And so there was multiplication, as a form of repeated addition.

Later on, people found themselves writing 5*3*3*3*3*3*3*3*3*3*3 so some other short form was deemed necessary. This gave rise to 5*3^10, and the notion of repeated multiplication.
EXPONA

But is the exponent seen as such? Particularly when, in this post, we haven't determined how to make it look like a superscript? Though maybe that's a benefit, it's more clearly not a single multiplication when we use an actual symbol...




BACKGROUND


Michael Pershan recently ran an experiment looking into Why Kids Mess Up Exponents. The issue seemingly being an intuition that leads towards the wrong places. He had a set of questions, and you should check out that link to see the breakdown.

I mention this as I recently ended up running my own experiment based off of his, though rather more spontaneously.

Quick backstory: My Grade 11U level class started exponents earlier in the week. They would have seen negative exponents in Grade 10, though I started with contextual stuff anyway, which refreshed the notion of negative giving divisions. So too late to gain anything there.

Friday was going to be the day for rational exponents, which they had not seen in a classroom context. So we had a bunch of snow (yes, on April 12), nine people were absent, I still wanted to at least talk about the topic, and had a brainwave. Thus, after going through some review questions based on the previous day's work, I went through a single question three times, collecting in the answers as I did. Here's the results.


DEPENDING ON YOUR
DEFINITION OF 'FINE'


SET ONE


Straight out:
What do you think 100^0.5 is? How confident are you? (5 being most confident)

ANSWER: 50 [11]
Confidence Breakdown:
1- 4 ppl; 2- 0 ppl; 3- 6 ppl; 4- 1 ppl; 5- 0 ppl

ANSWER: 10 [6]
Confidence Breakdown:
1- 0 ppl; 2- 0 ppl; 3- 3 ppl; 4- 1 ppl; 5- 2 ppl

ANSWER: 0.5 [1]
Confidence level of 1


SET TWO


I then gave some context based on what we'd seen previously, by writing the following table on the board:

INVERT THE COLOURS, IT WAS
ON A BLACKBOARD...

NOW: What do you think 100^0.5 is? How confident are you?

ANSWER: 10 [15]
Confidence Breakdown:
1- 2 ppl; 2- 1 ppl; 3- 5 ppl; 4- 3 ppl; 5- 4 ppl

ANSWER: 50 [1]
Confidence level 3

(Two people didn't give me papers. I wasn't keeping track that closely.)


SET THREE


I indicated that whatever the answer is, it has to be multiplied by itself to get the base back. Demonstrated 100^0.5 * 100^0.5 = 100, along with a couple similar examples, and then outright confirmed the growing suspicion that the prior answer was 10. Then...

Straight out:
What do you think 100^(1/4) is? How confident are you?


ANSWER: root(10) [5]
Confidence Breakdown:
1- 0 ppl; 2- 1 ppl; 3- 2 ppl; 4- 0 ppl; 5- 2 ppl

ANSWER: 5 [4]
Confidence Breakdown:
1- 1 ppl; 2- 2 ppl; 3- 1 ppl; 4- 0 ppl; 5- 0 ppl

ANSWER: 2.5 [2]
Confidence Breakdown:
1- 1 ppl; 2- 0 ppl; 3- 1 ppl; 4- 0 ppl; 5- 0 ppl

ANSWER: 0.1 [2]
Confidence level 2 (for both)

ANSWER: pi [1]
Confidence level 2

(This time four papers missing. Also, when I gave the pi guy a curious look after glancing at his sheet, he said 'pi always figures in somehow'. Amusingly, the answer IS 3.16227766...)


CONCLUSIONS


There's something more going on than merely treating it like multiplication. Even in set 2, a couple of the 10's were based on students having written down a moving of the decimal to the left. (I don't know if it was the same ones who then came up with 0.1)

My suspicion is that there's a search for patterns going on. Because that's what human beings do, we look for patterns. And after two years of linear patterns, that's what students gravitate to, in absence of any other context. So, provide them context? Even then, we may grab moving decimals before anything else. (If it had been 50^0.5, would the response have been 5? Possibly.)

Trouble is, for this problem, a root is not immediately seen as part of a pattern. A root is irrational. Which is kind of ironic given that it's a rational exponent. Or maybe that too is part of the problem.



For further reading on exponents that came up in blogs this week:
1) Rational Exponents - Third Grade Style
2) Exponentials in Context

Was this exponential week? No one told me!! Hmph, so much for happily ever after.

Saturday, 6 April 2013

MAT: Simpson's Paradox


YES. YES IT IS.




So a student came into class the other day and asked if we could talk about Simpson's Paradox.

No!

It happened to be the very day I was going to talk about it anyway.

What?!

Strictly speaking, it's not even in the curriculum.

Get out!

I'm serious!

Me too. Get out of here, you're not allowed to divert from curriculum.


PARADOX WHAT NOW?


Simpson's Paradox, or the Simpson-Yule effect, effectively means that, by aggregating everything together, you might get the OPPOSITE results from what you see individually. In other words, A beats B at poker, A beats B at chess, A beats B at checkers, so the overall winner? B, naturally. (Since he's not being hassled by the paparazzi like A is.)

But no, seriously, it's explained better on the Less Wrong Blog at that site, and by James Grime in this YouTube video - which I've shown in class. It's gaining a fair bit of awareness out there these days... I'm not even the first person to blog about it this year. That last site has a few nice images with the explanations too.

Your takeaway? Summaries are always obscuring the truth, if not outright lying to you. It's better to have the individual data - then you can create an overall aggregate if you choose. Yet in our busy lives, we tend take percentages at par! Ignoring that they're useless without knowing what made them. This news article from 2009 references the problem as well, with lots of practical examples, including one in sports.


PARADOX. THE GOOD ONES MAKE YOU THINK.

I forget exactly when I stumbled upon the scenario - probably in the maths book I own by Martin Gardner - but I have since grabbed examples from a statistics text to use in a class handout for one day, when I teach Data Management (statistics).


WHAT ABOUT THAT STUDENT?


He'd been reading up on the Paradox after having a disagreement with his employer. The employer had taken the individual sales averages (for each employee), and averaged them together to create one for the store. Apparently, store sales were slipping.

The student rightly pointed out that, if you added up the individual sales for the units, you would get a different answer then by averaging all the averages. This actually had to be DONE, before the employer would believe the values would be different.

Don't take my word for it - make up an example for yourself. What if one guy always makes his sales, and another never does?

It's not strictly an example of the Paradox, since nothing is reversing direction, but it is an example of how averages are completely meaningless without a sense of the totals involved. It's also what led the student to investigate and find the Paradox, and explains why we have this thing called the weighted mean!


Oh, and actually - it IS in the curriculum. Kind of. We're supposed to learn about the variability inherent in data. So there.


You win on a technicality then... but next time...

Monday, 1 April 2013

BLOG REBOOT


The index of my 55 prior entries is below.  Why?  Read on.


Comments by Education Realist on my last blog entry (Why Do You Blog?) have me thinking about my writing style. I feel now like I've been writing words on a window for myself, then inviting others to comment.

Shouldn't I at least be writing the words in reverse, so that you, someone on the outside, can understand more of what you're seeing?

Moreover, doing that should not only force me to think more carefully, but is a better invitation for you to come inside, and see what else I have to offer. So, the time has come.
REBOOT!

1) This blog will now be categorized, with three letter cues in the header. For entries related to Writing, look for WRI. For entries related to Mathematics/Math Instruction, look for MAT. For entries related to Teaching in general, look for TCH. For entries related to anything else (like reviews or opinion pieces), look for ETC.

2) This blog will now involve less first person writing by me. First, because I feel I'm better at imparting my thoughts through a narrative. Second, because doing so should help me to decide what's really necessary, or at least interesting.


PERSONIFIED MATH will
handle the MAT and TCH
CARRIE WATERSON will
handle the WRI and ETC
One more thing: There will be an additional tag, MIX, if more than one category applies, and it doesn't make sense to break it into two posts.



The best way to make the distinction clear is through examples, so I have classified all 55 of my prior entries below.  This has the added benefit of being a junction point between my future entries, and the inherent randomness that the blog has been to this point.

Let me know if you have questions, or think something doesn't fit. The most recent entries are on top.


Tag: MAT


2) Ontario Teaching - Allegory 2004-2012


"OOOOH. TEACHING, THAT'S WHAT IT'S ABOUT."
"MY PENCIL WILL CONVINCE YOU OTHERWISE."



Tag: WRI



1-5) JulNoWriMo Musings (Parts: 1 2 3 4 5)

Tag: ETC


9) Identity Crisis Online
2-5) Analyzing Zynga Games (1 2 3 4)
1) Intro

"PICK A CATEGORY!"
"HEH, I, UH... CAN'T?"

Tag: MIX - Worlds Collide


9) Why Do You Blog? (Writing/Mathematics)
8) The Web Serial: Who (Writing/Mathematics)
7) The Web Serial: What (Writing/Teaching)
6) Seeking New Personifications (Writing/Mathematics)
5) Notoriety: Blessing or Curse? (Writing/Teaching)
4) Writers Make Poor Teachers (Teaching/Writing)
3) Week as Math Educator Roundup (Mathematics/Writing)
1) If You Build It... So What? (Teaching/Writing)



...and no, this is not an April Fools.