Jiminy, looking back at my posts during the past month, I’ve been waaaaaaaay too serious. Here’s something a little lighter — but be forewarned, it’s PG-13.
Overheard at the math department holiday party:
- I’m like π — I’m really long, and I go on forever.
- I’m algebraically divorced. Will you replace my x without asking y?
- What do math and my genitalia have in common? Both are hard for you!
- I know the first 1,000 digits of π. But that don’t mean nothin’ if I can’t get the 10 digits in your phone number.
- On a scale of 1-10, you’re eπ.
- You must be an asymptote… I keep getting closer and closer, but you won’t let me touch.
I was at an Internet cafe yesterday, and my server went down on me.
Please enter your new password: penis
Sorry, your password isn’t long enough.
Sex is better than logic, but I can’t prove it.
Were your parents married before you were born?
Yes, my father was married, my mother was not.
Today is 11/12/13, a rather pleasant-sounding date because the numbers form an arithmetic sequence, albeit a trivial one. It’s not the only date in 2013 for which the month, date, and year form an arithmetic sequence. How many others are there?
Several nights ago, my sons asked if they could do bedtime math, but Eli asked if we could do problems other than those on the Bedtime Math website, because “they’re a little too easy.” So instead, I navigated to the MathCounts website and opened the 2013-14 MathCounts School Handbook. We scrolled to page 9 and attacked the problems in Warm-Up 1.
Things were going well until we reached Problem 8 in the set, which read:
The angles of a triangle form an arithmetic progression, and the smallest angle is 42°. What is the degree measure of the largest angle of the triangle?
Eli asked, “Daddy, what’s an arithmetic progression?” pronouncing arithmetic as “uh-rith-ma-tick” instead of “air-ith-met-ick.”
I could have just answered Eli’s question by stating the definition:
An arithmetic progression is a sequence of numbers for which there is a common difference between terms.
But such a definition isn’t very helpful, since I’m not sure that either Eli or Alex know what sequence, common difference, or term mean. It would have led to even more questions.
Plus, I’ve always believed that kids understand (and retain) more when they discover things on their own. Call it “discovery learning” or “inquiry-based instruction” or any of myriad other names from educational jargon, it just means that giving kids the answer is not the most effective way for them to learn.
So instead, I said, “Let me give you some examples.” And then I wrote:
1, 2, 3
3, 5, 7
Alex said, “Oh, I get it! An arithmetic progression is a nice pattern of numbers.”
So I said, “Well, let me give you some patterns that aren’t arithmetic progressions.” And then I wrote:
2, 4, 8
“That’s a nice pattern, isn’t it?” I asked. “But it’s not an arithmetic progression.”
“Oh,” said Alex. He thought for a second, then revised. “You have to add the same amount every time.”
And there you have it. Three examples, and my sons were able to define arithmetic progression. It’s not as sophisticated as “a common difference between terms,” but “add the same amount every time” is a sufficient definition for a six-year-old.
So they generated an arithmetic progression with 42 as the smallest term:
42, 45, 48
Eli said, “I don’t fink vat’s enough.” When asked to explain, he said he thought that the angles in a triangle add up to 180 degrees.
“Are you sure?” I asked. He wasn’t. Nor was Alex. So I asked if they could convince themselves that the sum of the angles is 180°.
Alex said, “Well, the angles in a square add up to 360°, and you could cut it in half.” So we did:
They then reasoned that each triangle would have a sum of 180°. “But maybe that only works for a square,” I said. “How do you know it’ll work for other shapes?”
Eli suggested that we could cut a rectangle in half, too:
Understand, this is NOT a proof of the triangle sum formula. When they get to high school and need to demonstrate the rigor that the Common Core State Standards are demanding, well, then we’ll worry about formal proof. But for now, I’m okay with six-year-olds who can demonstrate that kind of reasoning.
They then took another guess, but this time they chose three numbers that added to 180:
42, 59, 79
Realizing that the difference between the first and second terms was 17 and the difference between the second and third terms was 20, they revised:
42, 60, 78
They concluded that the largest angle had a measure of 78°. And all was right with the world.
So why am I telling you all this?
Partially, it’s because I’m a proud father.
But more importantly, it’s because this vignette demonstrates that teaching is an art, and successful teaching doesn’t happen by accident. It’s not easy, as many people believe. What’s easy is the perpetuation of bad teaching, a la Charlie Brown’s teacher, or textbooks that simply present information with the belief that students will absorb it by osmosis. Good teaching, however, requires content knowledge and pedagogical knowledge, and it demands teachers who can handle unexpected classroom twists and turns and have the ability to adjust on the fly.
A student is convinced that a right triangle isn’t a right triangle because the right angle isn’t in the lower left corner? You better find an effective way to clarify that misconception. (Hint: Don’t use a traditional textbook where every picture of a right triangle shows the right angle in the lower left corner.)
Students think that 16/64 = 1/4 because you can “cancel the 6′s”? Uh-oh. Better find some counterexamples pronto, and help them understand why 16/64 can be reduced to 1/4.
Your students don’t know the definition of arithmetic progression? Then you better figure out a way to help them define it, and just writing your definition on the chalkboard isn’t gonna cut it.
Someday soon, I hope to add my project at Discovery Education to the list of examples of good teaching. Until then, I’ll just keep blathering about my sons.
Today is 11/7/13, which is a semi-lucky/lucky/unlucky date.
The numbers in today’s date are 7, 11, and 13, which are the same numbers used in my favorite math trick. I shared that trick on 7/11/13 in A Great Day for a Math Trick — which, honestly, was the best day ever to share it (unless you’re in Europe, in which case today is perfect). For U.S. audiences today, do the division by 11 before the division by 7:
- Multiply your age by 12.
- Now add the age of your spouse/brother/sister/friend/uncle/aunt/whomever.
- This should yield a three-digit number. Now, divide by 11.
- Then, divide by 7.
- Then, divide by 13.
- The result should be a number of the form 0.abcdef…, with a 0 and a decimal point in front of a long string of digits. Add the first six digits after the decimal point.
Here’s the cool part. I don’t know your age, nor do I know the age of your spouse, brother, sister, friend, uncle, or aunt. But I do know that after you completed those steps, this is your result.
Now, how did I know that?
That’s for you to figure out.
Math Major: I’ve found that 67% of Literature majors are stupid.
Literature Major: I’m part of the other 13%.
I was walking past a mental hospital the other day, and all the patients were shouting, “13… 13… 13… 13.” The fence was very high, so I peeked through a little gap in the planks to see what was going on.
Some bastard poked me in the eye with a stick.
Then they all started shouting, “14… 14… 14… 14.”
Thanks to the folks at Quizlet, I’m able to offer you an opportunity to prove how smart you are.
Know what a polygon is?
Do you know the value of a trillion pins?
Think you know about polar bears?
Try your hand at this 26-question quiz. For each definition, just enter the term to which it is referring.
Post your results in the Comments, or share other math definitions.
Several nights ago, as we were having dinner with a neighbor and his kids, we started talking about cherries. (I have no idea why.) But not willing to let an opportunity slip away, I offered, “I have a friend named Merah (pronounced mare-ruh) who works in an ice cream shop, and her job is to place cherries on top of sundaes.”
My neighbor looked at me funny. Then he saw where I was going. “Is her last name Sheeno?” he asked.
“It sure is! Merah Sheeno!”
Nothing. Not even the slightest hint of recognition from the boys or from either of my neighbors’ kids.
But I was not deterred. “And she has a brother named Whatduzz.”
Everyone looked at me blankly.
“Whatduzz Sheeno! Get it? ‘What does she know?”"
My neighbor nearly fell off his chair. “Oh, that’s good!” he said. “I hadn’t heard that one before.”
“That’s because I just made it up, Hunter.”
“No wonder your sons say you’re the funniest man they know!”
It’s true. That’s what my sons usually say. But not that night. That night, they just thought I was weird.
Someday, I hope to use my ability to make up funny names to write a bestseller under a pseudonym. (At this point, putting my real name on a book would surely lead to negative sales.) Some of my ideas are:
- Putting the Pieces Together, by Lois Carmen Denominator
- Step by Step, by Al Gorithm
- The Longest Side, by Hy Potenuse
- Much Ado About Nothing, by Zee Row
- Big Wheels Keep On Turning, by Cy Cloyd
- Calculus for Tan Gents, by Anne T. Derivative
- Nothing to See Here, by M. T. Set
- Mirror, Mirror, by Reif Lection
- Below the Line, by Dee Nominator
- Can’t Tell Up from Down, by Vin Q. Lum
- Pushing My Buttons, by Cal Culator
- Petal to the Metal, by Rose Curve
- I Lost My Parrot, by Polly Gon
- Three Dimensions, by Polly Hedron
- What My x Got in the Break-Up, by Al Jabra
- Less Than That, by Lisa Perbound
- Local Extremes, by Max Imum and Minnie Mum
- Out In Front, by Lee Ding Coefficient
If some of those names look familiar, you may have seen them in Mathy Names. Thanks to Jim Maher, who contributed some of the names in a comment.
A joke about a graveyard, a dead person, and being frightened. All good things for All Hallow’s Eve.
A man was walking through the Alexander Nevsky Monastery when he heard someone say, “x2 + 2x = (x)(x + 2).” Sure that his mind was playing tricks on him, he kept walking, but then he heard, “x2 + 2x + 1 = (x + 1)2.” He paused again, then heard, “x3 – 4x2 – 7x + 10 = (x – 1)(x + 2)(x – 5).” Concerned, he approached a cemetery worker. “Why do I keep hearing math equations?” he asked.
“Oh, that’s Leonhard Euler,” said the worker. “He’s decomposing.”
Driving through Paris (Virginia, not France) on Saturday, we passed a field of grazing cows. I asked the boys, “What do you think a French cow says?”
Eli said, “Moo-la-la!”
Funniest. Kid. Ever.
Perhaps because I grew up in rural Pennsylvania, I’ve always had a bovine fascination. I envy their laissez-faire existence. What I wouldn’t give for a life where I could roam freely, eat when I wanted to, lie around listlessly in the sun, and defecate whenever and wherever the urge strikes. The only aspect of their existence that I don’t envy is the end-of-life trip to the grocery store on Styrofoam plates wrapped in cellophane.
The following are some pseudo-mathy cow jokes.
What does a Greek cow say?
What is a cow’s favorite subject?
What does a cow use to compute?
Why does a milking stool only have three legs?
Because the cow has the udder.
What do you call a cow with two legs?
What do you call a cow with one leg?
What do you call a cow with no legs?
And here are some cow jokes that aren’t mathy at all.
What did one cow say to the other?
Two cows were out in a field. One turns to the other and says, “Moooooo!”
“That’s funny,” says the other. “I was just about to say the same thing!”
The first one says, “Holy cow! A talking cow!”