Wednesday, April 30, 2014

Day 5: Imitation: Should I Be Flattered?

I have over 100 followers on Twitter now -- not much by celebrity or even teen standards, but pretty respectable for a teacher with a blog and an occasional comic. I follow less than half that. I've tried following more people, but the newsfeed (or whatever they call it) gets a little too busy. Most of those are people I met through my comic or through my geekier side. Yes, there's more that's geeky about me than making comics about math teachers and talking numbers.

I'm slow to add new people, and most of those I've added because someone else retweets them often. And I've dropped a few for differing reasons. Generally, they tweet so much that it seems that they're the only one there, or they always tweet the same thing and never have anything new to say, or they get really, really opinionated about things (whether or not it's an opinion I agree with or not ... but usually not).

The people left are mostly educators who found my blog by word of mouth. I like reading those. It gives me hope that after a dozen years, there are still things that will get better.

And often, fellow math teachers will have a similar sense of humor. Which brings me to the topic at hand.

Yesterday, someone retweeted a comic he'd found on the Net. It's one I've seen before. That exact one. It was black and white and someone had typed a large x2 and x3, and the former was asking the latter, "Do you believe in God?" and the latter said, "Well I do believe in higher powers..."

Hysterical! At least, that's what I thought back in 2008! When I wrote it! Titled Math and Religion, my "x"s had faces to talk with, but the wording is almost exact. It was a interesting transformation: not quite a translation ... more like diluting.

There's nothing to do except be "flattered" by this "sincerest form". Even with the serial numbers filed off, along with my signature, title, border, copyright notice . . . No, not bitter at all.

It gave me a chance to follow up with the original and put myself out there, so that's a positive, I guess.

But it did make me think about "imitation". Not all imitation is sincere. This wasn't a case of someone trying to be like me: they just took the joke. Have I taken ideas from other people? Sometimes, but usually I've said something like, "Oooo, I have to use that." (And I haven't used everything I've said I would.) But then I make it my own. I add something to it. Put a twist on it. Something. Or I don't do it.

For instance, have you heard the one about the Volume of a cylinder equaling pi * z * z * a?
I've mentioned it before, and I think I posted a copy of it:

That was the first version of it I saw. That was good, and I wasn't in a position to make it better. Back then, if I'd tried to imitate that, it would have been a poor copy. It would've looked like a circle or oval and not a pizza. On the other hand, if you search images for "volume pizza", you'll get a lot of variations. Pity. Actually, I wish I knew who did the original so I can credit them.

Moreover, a lot of imitation in the classroom isn't intended to be flattering. Sure, there are some students who imitate the way I solve problems, but that's not a matter of flattery. That's a matter of learning. And that's not what I'm talking about anyway. No, I'm talking about the people who mimic each other (including me) in dopey voices with exaggerated gestures. If they nailed any particular habit or vice of mine, maybe I would be flattered. Problem is tha they don't know enough to make the copy. They won't put the required effort in.

That does sound a little familiar. Not putting in any effort is the reason that they have so much time practicing their mimicry!


(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

This needs to be a website. Make it so.

And it's not just the people taking pictures of their lunch. It's *how many* pictures that they're taking.
Possible excuse if your Photography teacher sent you and your classmates in there, but you still look silly.

Tuesday, April 29, 2014

Day 4: Statistics Review

Note: I have a personal webpage that I use for class -- that is, I use it when I know that students are using it. I spent a good part of the evening updating the page with information about a test on Statistics that we're having on Friday. I copied over the code to the blog. No reason that it can't count toward my daily updates.


We are having an important Statistics exam on Friday, May 2, 2014.
Statistics will be an important part of the Common Core Algebra Exam.
You should review this material.

Measures of Central Tendency: The mean, median and mode. They are numbers used to describe a set of data. See the individual definitions below.

Mean: The average. To find the mean, add up all the data and divide by the number of data items there are. Example: The mean of 6, 3, 5, and 12 is (6+3+5+12)/4 = 26/4 = 6.5.

Median: The middle number when the data are in order. If the data are not in order, than the number in the ”middle” is meaningless. If there are two numbers in the middle, the median is the average of the two numbers. Example: The median of 6, 3, 5, and 12 would be found be first ordering the numbers as 3, 5, 6, 12. The numbers 5 & 6 are in the middle, so the median is 5.5.

Mode: The most frequently appearing piece of data. Unlike mean or median, there can be more than one mode. There might be no mode if no data is repeated. Mode doesn’t have to be a number: consider the data set (red, red, yellow, blue, blue, blue); “blue” is the mode. Examples: (1, 2, 3, 3, 3, 4, 4): “3” is the mode; (88, 95, 92, 95, 88): 88 and 95 are the modes; (7, 8, 9, 10): no mode.

Frequency The number of times something occurs. In the data (10, 10, 11, 11, 11, 12, 12, 13), “11” has a frequency of 3, and the total frequency of the set is 8.


A Frequency Table is a summary of the data, organized as a table. The data are on in the left column. The frequency of each piece of data is one the right.
There are three examples of frequency tables below.

In the first example, every number in the data is listed, along with its frequency. The interval of the table is 1. Because of this we can find the mean, median and the mode of the data. We can re-create the data if we wanted to by writing out all the numbers.

In the second example, the data is collected into intervals of 10. We don’t know the actual numbers; we only have approximate information. Because of this we cannot find the exact mean, median or mode. However, we can find which interval contains the median and which interval is the most frequent. (There are methods to find a mean, but we aren’t going to calculate that right now.)

In the third example, the data aren’t numbers, they’re adjectives (qualitative data). Because of this, we can find a mode, but not a mean or median.

Finding the Mode, Median and Mode of a Frequency Table

In the first table, the total frequency (the sum of the Frequency column) is 20. If we write out the data, we can see that it has a total of 36. Divide 36 by 20 and we get a mean of 1.8. We can also see that there are more 2s than any other number, so 2 is the mode. And out of 20 numbers, the 10th and 11th are in the middle: both of those numbers are 2, so the median is 2.

However, we don’t need to rewrite all the data. (And if the table were bigger, we wouldn’t want to write out all the data!) The number with the highest Frequency is 2, with a frequency of 7 (mode). If you keep a running count as you go down the Frequency column, you will see that the 9th through 15th numbers are all 2 – that includes the 10th and 11th number (median). And if we know how many of each number there are, we can take a short-cut to get the sum of the data: (0 x 3) + (1 x 5) + (2 x 7) + (3 x 4) + (4 x 0) + (5 x 1) = 36. Divide 36 by 20 and we get 1.8 (median).

In the second table, the mode and median can be found using the same method.

In the third table, because the data are descriptive and not numeric (quantitative), there is no median. A middle size somewhere between Medium and Large wouldn’t have any meaning.

Monday, April 28, 2014

Day 3 of 30: Number Sense? Do You Have It? Can You Get It?

One of my biggest problems in the olden days, i.e., ten years ago or so, which were still "new" teaching days for me, was a lack of Number Sense among my students. This was before the advent of mandatory class sets of calculators, in those dark, Byzantine days when I used to have them -- Horrors! -- work it out! However, with the introduction of decade-old technology (by the standard of those days) ... not much changed. Sure, some problems were alleviated, but others rose to take their place. And the new ones were more confounding because they were less likely to notice something went wrong.

Before I continue, let's come up with a working definition.

What is Number Sense?

Basically, it's the ability to estimate an answer, to "ballpark" a figure, to look at a solution and know if passes the Smell Test, whether or not the answer is on the money. It should be a set of alarm bells ready to go off in your head when the cashier hits the wrong button or the waiter "accidentally" carries an extra "1" to the hundreds column. (New Year's Eve, back in the 90s -- my wife caught it when the "per-person" share of the bill was over $10 more than anything that anyone at the table had ordered! Even with drinks, tax and included gratuity, something was amiss!)

I had a simple check back in those old days. Tell them not to call out because I was going to call on someone. Then I wrote a problem as long division: 4 into 82, and waited about 30 seconds. (They didn't have to do it as long division, but many took it as a suggestion.) Instead of calling on someone, I raised a hand and asked, "Who got 2.5?" Five or six hands would go up, along with a couple of should-I-shouldn't-I hesitations.

I then showed them where the mistake was. There'd be "oh"s and "gotchas" and laughs at how people could be so silly. And then they'd make the mistake again. The thing is that had I asked them for 4 into 80 or 4 into 84, they would've gotten it right. They would know 4 into 80 isn't 2, and there's no 0 to forget in 84. Maybe it was the question, maybe it was how it was framed.

The problem for me is that I know that me students have some number sense. The problem is getting them to use it the right way. For example, when I introduce word problems, I tend to start with simpler problems with "easier" numbers. This makes it easy for them to see that they are getting the right answer. Unfortunately, their Number Sense is telling them that the answer if 14, 15, and 16 and that's all they need to know. They can't explain why it's right (other than guessing and checking), and they don't see the point of doing it my way. Then I try a harder problem, and they're stuck because they didn't learn the correct way to approach a problem.

Algebra isn't about being able to solve the problems you did in Junior High. (Or earlier, if you're teaching Algebra in Junior High. And if you are: God Bless You! Me? Never again.)

Scientific calculators have eliminated some of the problems, but there are new ones. For instance, there's little point in quizzing them on the Order of Operations if the calculator will do it for them. I can test their calculator knowledge by making the key entry a little trickier (e.g., fractions with subtraction in the denominator), but they won't know until they get their papers back that their answers are incorrect. And then there's the biggie, the one that kills them with evaluating any quadratic: squaring a negative integer.

We all know that (-3)2 is +9. If I were to say this out loud, I would say "Negative three squared is positive nine." But the calculator has to know that you what "negative three, squared" and not "negative, three squared". This is made more confusing by the fact that there are separate keys for subtraction and the sign and the fact that the sign is considered part of the number (it's what makes it negative), but the convention is (and the calculator follows it) that if there is a "minus" and an exponent, the exponent wins. The problem gets compounded by the fact that even if the student is aware that a negative squared should be positive, if they evaluate -32 + 5(-3) - 14, they won't know what to expect for an answer, so no alarm bells go off.

Score one against the calculators.

How can we get student to develop this without endless drills? I don't know. Practice helps. Endless drills? After a decade of this, I'm starting to wonder if there isn't some merit in them, other than the fact that good students are so nice, they "help" the unmotivated students. (I'll be nice, too, and say "unmotivated".) When you see numbers in action more and more, they start to make sense. But even older kids aren't immune.

I have junior and seniors in a Financial Algebra class. On a recent test, a couple of students gave me incorrect answers like "$6,170" for the total of a bar graph. All of the numbers in the graph ended in "00". The answer couldn't end in "70". My first guess was confirmed when I realized that they were off by $630 -- they entered $700 as $70 and never noticed the mistake. Imagine doing that on your taxes! (We filled out 1040EZ forms a month or so ago.)

Likewise, these students still have problems with complicated fractions in graphing calculators. I have to add extra parentheses to formulas because they forget to use them otherwise. The students working with the four-function calculators don't have this problem. They break things down step-by-step, but they fall behind because they are doing so much work. However, a few of the students don't have to worry: they have the latest operating system on the calculator that enters fractions and exponents so that they look like you expect them to, without requiring the extra parentheses.

It looks good. I just wonder what new problems it will create.

Sunday, April 27, 2014

Day 2: A Word From Our Sponsor?

I haven't decided to jettison my plan just yet, what little of a plan that I have. However, I've been part of an interesting conversation and there are some unusual circumstances going on right about now.

My friend Rob has a gaming blog, Twilight of the GM, which has been picking up hits lately. (And that's without me giving a free plug and sending traffic that way.) He's built it up by being active on Google+, something which I've hesitated to participate in. For one thing, Facebook soaks up way too much of my time, and for another, I would have wanted to use Google for personal stuff, not just yet another extension of the outreach for this blog. It seems that the blog is stretched thin and wide -- keep of like the old Grade 9 math curriculum.

The conversation we had was about his numbers. He asked me if he was reading it right and if he could possibly be getting as many hits as Blogger was reporting. (Oddly, Google Analytics reported somewhat different, but still encouraging, numbers.) So the subject of advertising came up.

Up until now, I've resisted the siren call of banner ads. I remember the crazy schemes of the 90s that never sounded like they would yield anything more than a few dollars for me while a whole otta traffic went flying off to some other site. Assuming that anyone ever actually clicked on those banner ads. Now, I do have banner ads on the (x, why?) comics-only site, but those came with the space. I wanted the free platform and the support, then I had to have the ads. They should only be advertising comics (and perhaps games) and the ratings for those shouldn't be higher than the rating for my comic, in terms of "maturity" level. So it isn't a big deal to me.

I figured that if I had a following big enough to support ads, then I would have ads for my own stuff. What stuff? I don't know. Books, maybe. T-shirts. Mugs, pencils, bookmarks, notepads, magnets. Whatever I could draw from the comics, so to speak. As soon as I figured out how.

Well, I haven't exactly got that kind of pull yet, and many of those who come to the blog are here for the articles, not the comics. I don't even know how many (or which) comics who lend themselves to T-shirt and bookmark design.

And the biggest obstacle: yeah, I don't know how to accomplish any of that anyway.

The Situation Lately

I won't be bashful: I could use the extra money, if it were worth the effort. My son's going to college in the fall, and any little bit will help. But there are only so many after-school hours that can be dedicated to per-session work before it begins to take its toll. There needs to be some secondary source.

I did spend the weekend researching Math for America only to have all of that blow up in my face. It seems that the "priority" deadline, whatever that is, is today. I don't have all the information I need or any of the forms or letters. There's a regular deadline at a later date but there's another problem. To be a part of this, I have to take a PRAXIS 2 exam. No problem with taking the test itself, but registering for it, well, that's a completely different problem. Their site has been having problems, and their forms don't work right. I check a box, it says nothing is checked. After much hoop-jumping, I got it to acknowledge the correct test. It then gave me a list of 10 sites in NYC to take the exam. Actually, there were only two, listed multiple times.

Big shock: every listing said that there wasn't any test being given at that location for the date indicated. (Come to think of it, there was nowhere to select a date: there was an "open window" for when tests would be given. Except that there wasn't.)

So this brings me back to the question: Should I turn on AdSense and start running ads for the people who come looking for answers to Regents exams? Should I create a store that sells notepads, bookmarks, T-shirts and books? Do I keep talking to myself and hope someone's listening.

Any suggestions would be appreciated. And freelance job offers may be considered.

Thank you for sitting through a mini-rant on Day 2.

Saturday, April 26, 2014

Day 1: 30 Posts in 30 Days? That's a Problem to Solve

There I was, minding my own business, just reading my Twitter feed when I see that a fellow teacher I follow retweeted a comment about something with a hashtag #MTBoS30. What could that be, I wondered. It's a 30-day blogging challenge. A new entry every day for 30 days, made for people who can't do the 180-day challenge, which I won't even contemplate at the moment.

Now, is that something that I could do? I think so.

Is that something that I will follow through on? That remains to be seen!

I currently post about 3 times every week. Don't laugh! It's almost true! I try to get 2 or 3 comics posted, and there's always something else of interest (to me) that I post now and then. The question that I should ask, however, is it of interest to you, the reader?

(The unspoken question is: are there any other readers other than me because if not, I'm debating myself and that could be indicative of a problem.)

At the very least, this is a problem to solve. Today's Teachable Moment: And how do we go about solving a problem?

We make a plan!

This is true for word problems or what to teach on Monday's lesson. (There's a reason why it's called a lesson plan after all.)

Break it down into steps. Make a list of topics I'm interested in or can talk about. Make a list and check it twice. Checking is always an important part of solving a problem. So I'll be checking my comments for feedback to see if I'm on the right track with the things I want to about.

There are things I'm good at, and things I'm knowledgeable on. There are things I'm curious about, and things I want to learn better. There are problems from old tests and problems from the classroom. And there are problems in the classroom and other parts of school life which need to be addressed.

All of this is fodder for a column. Along with Martians, vampires, time travel, Game of Thrones and anime, among other things. Hey, I'm a geek. I enjoy that kind of stuff. And that stuff helps solve one problem: connecting with students.

Unlike my last position, where I was lucky to find any geeks other than computer geeks, here there are students with whom I can discuss Doctor Who and Yu-Gi-Oh, if I wanted to. This led to a student this week asking me if I'd be interested in taking over an moderator of the school's new Anime/Manga Club. I was quite thrilled to be asked. Unfortunately, it meets Thursdays and I've agreed to do tutoring after school on Thursdays, starting next week. Also, I don't know if anyone's approached the current moderator about the situation. I don't know many teachers outside of the (very large) math department, and that would be a poor way to make an introduction. (That said, I did try to introduce myself the day of the first meeting but I couldn't seem to get her attention, and she never inquired why a grown man was standing around with all the teenagers.)

That's another problem for another day.

Let's see how many days I can compose relevant material. Or do what I always do: fall back and make a joke instead. Or a comic.

Friday, April 25, 2014

Public Service Announcement

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

I've wanted to do a PSA for a while now. Several, actually.

Actually, I wanted to do one more Easter joke, but it's nearly a week later and it was too much work for one evening. Maybe next year, if I don't lose my notes.

Tuesday, April 22, 2014


(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

That's the yolk.

I was working on the monologue for a while before I realized if anyone were willing to read more that two paragraphs of my prose, I could sell a few stories.

I couldn't tag this one "PI", because it's not "pi". And if I make a new "P.I." tag, I'd have to go back and tag most of the "Pi" comics.

Feel free to contribute your version (or continuation) of the monologue!

Sunday, April 20, 2014

Happy Easter 2014

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

That's only for fresh eggs. It's okay to put hard-boiled eggs in one basket because you want them all to break so you have an excuse to throw them all out!

Seriously, I know some people who eat them, but I know few who enjoy them.

Friday, April 18, 2014

Good Friday

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

Or possibly labeled "Passion, Death, Resurrection"?

Good Friday is part of the Paschal Triduum, which can also be spelled "Pascal", but I wanted to avoid confusion and basically hang a lampshade on it.

Thursday, April 17, 2014

"If Tomorrow Starts Without Me"

My cousin Patricia (she'll always be "Patty" to me) read the following poem at her mother's funeral yesterday. (That would be my Aunt Pat.) There wasn't a dry eye in the place. And if that didn't get you, then her sister Debbie, in her eulogy, remembering those who have left us since last August did: my Mom, their sister Barbara, my niece Lisa and most recently, our cousin Mary Ann.

To that, I'll add a few more: my Uncle Eddie (on the other side of the family) last week, my colleague Ms. Judith Brown (a one-woman welcoming committee at my last job) at the same time as my cousin, the fathers of two friends and the grown son of a former coworker. And there have been so many that I'm sitting at my keyboard wondering if I forgot someone, and counting the list, thinking, "How could there be more?".

Here is the poem. From the Internet, I've discovered that it is attributed to David M. Romano, from 1993.

If Tomorrow Starts Without Me…

If tomorrow starts without me, and I’m not here to see,
If the sun should rise and find your eyes all filled with tears for me;
I wish so much you wouldn’t cry the way you did toda...y,
While thinking of the many things we didn’t get to say.
I know how much you love me, as much as I love you
And each time that you think of me, I know you’ll miss me too.
But when tomorrow starts without me please try to understand,
That an angel came and called my name and took me by the hand.
He said my place was ready, in heaven far above
And that I’d have to leave behind all those I dearly love.
But as I turned and walked away a tear fell from my eye.
For all my life I’d always thought, I didn’t want to die.
I had so much to live for, so much left yet to do.
It seemed almost impossible that I was leaving you.
I thought of all the yesterdays the good ones and the bad.
I thought of all the love we shared, and all the fun we had.
If I could relive yesterday, just even for a while,
I’d say goodbye and kiss you and maybe see you smile.
But then I fully realized that this could never be,
For emptiness and memories would take the place of me.
When I thought of worldly things I might miss come tomorrow
I thought of you and when I did my heart was filled with sorrow.
When I walked through heavens gates I felt so much at home.
God looked down and smiled at me from his great golden throne
He said, “This is eternity and all I’ve promised you”
Today your life on earth has passed but here life starts anew.
I promise no tomorrow, but today will always last
And since each day is the same there’s no longing for the past.
You have been so faithful so trusting and so true.
Though there were times you did some things you knew you shouldn’t do.
You have been forgiven and now at last you’re free.
So won’t you come and take my hand and share my life with me?
So when tomorrow starts with out me don’t think we’re far apart,
For every time you think of me, I’m right here in your heart.

Wednesday, April 16, 2014

Funny How Things Work Out

It had been my intention, if I could muster the discipline and determination, to have a new comic each day this week because I'm off. Funny how things work out. It seems like every day is booked with something, the first three days being the worst. Sure, I might have something by Thursday, but that's hardly "every day" of the week. That's catch-up time.

There will be an update, and if I can spend Friday working on things, I'll plan out next week ahead of time. I hope. And next Monday and Tuesday are professional development conferences, meaning that I might be sketching little cartoons in the margins during the boring bits as topics present themselves.

And, of course, by "funny", I mean exactly the opposite.

Friday, April 11, 2014

Circular Logic

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

Would triangular logic be a three-sided argument? On the one hand ... on the other hand ... on the gripping hand ...

And, on a side note, happy birthday to the author of this comic.

Tuesday, April 08, 2014

Texting Problems

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

That's the trouble with texting problems. Or even probs.

Friday, April 04, 2014

Part of the Whole

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

You can't be part of the class if you aren't given it your whole attention.
Or something like that.

Tuesday, April 01, 2014

Shape Up!

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

Regular exercise with a regular polygon!
At least, she used to be regular, but now she's trimmed down a bit. Admit it, you like her better this way. Who wants to be regular anyway?

When Dinosaurs Roamed the Halls!

(Click on the cartoon to see the full image.)
(C)Copyright 2014, C. Burke.

History has been repeating itself for a very, very long time.

Except that I haven't done a silly April Fools comic in three years. Don't know why. I guess it just didn't work out.

What's Dinosaur for "LOL", anyway?