Andy and Bon (that’s me) commit a crime. Not anything terrible, just something gently bad. (No sense in killing folks for a blog post, right?)

We get caught. (I know – it gets worse!) And they separate us into two rooms for interrogation.

The detective says to me, “If you confess, you may get some leniency.”

**Bon**: Just how much of this “leniency” can I get?

**Detective**: Well, if you both both confess, you both get reduced sentences of 5 years.

**Bon**: What if I don’t confess?

**Detective**: You get 10 years, if Andy confesses.

**Bon**: What if Andy stays quiet?

**Detective**: That’s the great part. If he keeps quiet and you confess, you get NO time!

**Bon**: But what if we both refuse to confess?

**Detective**: We have your DNA, so you automatically get 3 years each.

The Data Science Imposters gave the classic solution:

Suppose I have an attorney and he’s somehow in the know. If he comes and says, “**Andy confessed**,” what should I do?

- If I stay quiet, I will do 10 years.
- If I confess, I’ll do 5 years.

So if Andy confesses, I will too, so I only get 5 years.

But what if Mr. Know-it-all-attorney comes to me with, “He’s sticking to his guns – **Andy is NOT confessing**!”

- If I stay quiet, I will do 3 years.
- If I confess, I’ll do 0 years.

Again, if Andy zips his lips, it’s still far better for me to confess.

Either way, I confess.

I’ve been teaching *expected value* in my statistics class these past few weeks, so I began to think of the problem from that perspective.

Suppose I **don’t** know what Andy is doing. And since Andy is flaky, it’s a total coin toss on what he’ll do. In other words, the probability of him doing either is 0.5.

Let’s say I choose to be a loyal friend (maybe he saved my mom from a crazed escaped alligator from the zoo). So **I’m going to stay quiet**.

We can assign a *random variable X* to the outcomes of what Andy chooses (as his are totally random):

- If Andy chooses to confess, the random variable
*X*= -10 (ten years hard time for me). - If Andy chooses to stay quiet,
*X*= -5 (only 5 years in the big house).

Since each of these are equally likely, the *expected value* of the random variable *X* is the average: -7.5.

On the other hand, let’s say Andy gets on my nerves and I saw him spit in my mom’s alligator gumbo once. So **I choose to rat on him**.

We assign the random variable *Y* to the outcomes like this:

- If Andy chooses to confess, the random variable
*Y*= -3 (a 3 year sentence). - If Andy chooses to stay quiet,
*Y*= 0 (I get off scott free!).

Again, these are equally likely, so the expected value is the average: -1.5.

One way to determine if you should play a game is by examining the expected value. If you play the game a bazillion times, the expected value is what you’ll win on average for each game.

In the game of what-will-Andy-do, the expected value of my confession (1.5 years in prison) is better for me than the expected value of staying quiet (7.5 years).

So I’ll still confess.

Where there are humans, there is variability. The reality is that my partner in crime could be known for being a snitch or being very loyal. Let’s do some crimes with two other people: Charlie and Dean.

Charlie is a great friend. But not only that, out of the 10 times he’s been in police custody, only 1 time did he turn on his partner.

Empirically, the probability that he will confess is 0.10. And the probability that he will stay quiet is 0.90.

If **I stay quiet**, and Charlie chooses to

- Confess, then
*X*= -10 with*P(X)*= 0.10. - Stay quiet, then
*X*= -5 with P(X) = 0.90.

So the expected value is

If **I confess**, and Charlie chooses to

- Confess, then
*Y*= -5 with*P(Y)*= 0.10. - Stay quiet, then
*Y*= 0 with*P(Y)*= 0.90.

Sadly, even with a super loyal friend, I should still turn him in!

Dean has been in police custody 10 times and 7 of those he’s thrown his partner under the bus.

Empirically, the probability that he will confess is 0.70. And the probability that he will stay quiet is 0.30.

If **I stay quiet**, and Dean chooses to

- Confess, then X = -10 with P(X) = 0.70.
- Stay quiet, then X = -5 with P(X) = 0.30.

So the expected value is

If **I confess**, and Dean chooses to

- Confess, then Y = -5 with P(Y) = 0.70.
- Stay quiet, then Y = 0 with P(Y) = 0.30.

As suspected, I still should confess, but maybe with Dean I do so very quickly!

*Share your thoughts in the comments, on Twitter or on Facebook.*

*The Data Science Imposters podcast is one of my very favorites. Jordy and Antonio offer just the right amount of intelligent self-depreciation balanced with great information. I highly recommend them!*

A bit.

But not a lot. And I’m no longer full time in the professional math education circuit.

I’ve thought about starting a whole new blog for my new career in data science. But * data science* is just a fancy term for statistics with computers.

So even though math teaching isn’t my main focus, I’m going to roll on with math stuff * and* data science stuff here at MathFour.com.

No doubt math education will be ingrained in each post. Especially since I’m mom to two math learners.

I hope you’ll stick with me on this journey.

Let me know your thoughts in the comments or tweet them out to me.

I was enjoying some middle-of-the-night software development and watching ID-Go, when a horribly offensive commercial came on. I’ve edited it for brevity…

Share your thoughts in the comments, and

Share your thoughts in the comments below, and if you’re horrified too, share this on Twitter and Facebook!

It’s not a medical problem, although it sounds like a mix between ear mites and pinworms – yuck! Turns out earworms are those bits of a song that get in your ear and cause the whole thing to get stuck in your head.

The cure to an earworm is to play the song in its entirety. It’s a psychological thing. It’s been studied.

Yup – if you listen to the whole song, it goes away (you’re welcome).

But what if the song never ends?

By the very definition of the song, it’s infinite. Which means you can never play it in its entirety. Which means it’s the quintessential earworm.

Theoretically, there’s no cure for it. But I have tried, successfully, to displace it with another earworm and then play * that* song in its entirety.

And here we come to the beautiful math part of all this. The next time you get a chance to explain infinity, the concept not the cardinality, you can pull out the song that never ends.

After all it’s already stuck in your head isn’t it?

If you’re a teacher or professor, you know the game I’m talking about: there’s the “demo teach” element of the interview process. You have a handful of other math teachers “learning” how to solve a system of equations (or some other math topic replete with pitfalls for the inexperienced) based on your mini-lecture for them.

At some point, you stop getting annoyed at the demo teach and start thinking how it can show other math teachers a different way of teaching.

As I mentioned previously, I’m making a transition from math teaching to math using. I’m going to be a software developer when I grow up.

But as a mid-life wife, mom and expected half-loaf bread-winner, I can’t just stop to learn. So I’ve been applying and trying to find work in my new field of coding.

And this is a whole new game!

I sent my resume to a local (but pretty big) software company and was sent a “test” to do. It had four exercises, all related to HTML, CSS and JavaScript (my newest tools). I knew very little about any of the tasks, but I researched like a mad fool and ended up making all of them work to some degree. I made sure the commenting included my personality, in hopes that would get me a few more points.

Apparently I did okay, because I was then offered a phone interview. #woohoo

And that’s where things got weird.

I was very excited, but the interview was two weeks away. I could hardly contain myself. So I researched the company. I found and read all about the people who would be interviewing me. And I was all ready with my own questions.

Then the phone rang – finally!

He introduced himself and his colleague briefly and then said, “This is a technical survey so let’s get started.”

Whoa!

What happened to “tell us about yourself…?” Or even, “here’s a bit about the position…?”

It was a rapid fire of JavaScript questions (check out these 85 to get an idea of what I’m talking about).

I had been warned about technical interviews. But I thought they would be a small intermingling of some “puzzle” type questions. Things to check on logic and reasoning and to see how you think.

I never expected a barrage of fact-based questions.

I asked my coding bootcamp teacher about it that evening: “So I could be an idiot but memorize all the answers and get the job. But if I’m a good thinker, can learn fast, but don’t have the right answers, they won’t hire me?”

His only response was, “Yup.”

Heartbreaking.

The phone interview was a test at the lowest level on Bloom’s Taxonomy. The “take home” assessment exercises were at least at the application level. For me, most where at the synthesize level, since I wan’t familiar with them and had to learn while I worked.

I’m a bit worried that they think I cheated. Cheating isn’t beyond me, but this isn’t one of those times. Especially because it was such a good learning opportunity.

But there’s not much I can do about it now. I have to learn from the experience and be differently prepared next time.

So here we are again at the end of a post on MathFour.com and you’re wondering, “What’s this got to do with math learning?”

It’s annoying, but the reality is that you have to “play the game” – in job interviews as well as math class.

If a teacher requires you to show your work, you gotta show it. If you haven’t a clue what to show, then fake it.

If you know what’s going on and can’t play by the rules (regardless of how dumb you think they are), you won’t make the grade.

Grades aren’t everything. Heck, grades aren’t anything, when it comes down to it. But that’s how a lot of people measure things.

And that’s how this company measures ability to develop software.

I may pout for a while. But I’m going to put on my big-girl pants and go memorize those answers.

Just like you or your students are going to get out that paper and start doing the 50 math problems that are all the same.

Because sometimes to show your worth, you gotta just play by their rules.

(Yes, that’s unfortunate, but it’s true. To deny it is foolish.)

I’ve enrolled in The Houston Coding Bootcamp Powered by UT Austin and am tickled pink at my decision. I have a bazillion projects in my mind dying to get out (including a fully robust version of the That’s Math text messaging service).

I’ve been itching to share the news on MathFour.com, but have been hesitant to do so.

“I’m all math all the time,” I’ve been thinking. “How do I stop writing about math?”

*Duh!*

I’m not going to stop writing about math. I’m just going to *also* write about programming. Which IS writing about math.

I hope this fresh perspective on things lifts me up and encourages me to share more.

I’ve already gotten a chance to use some nifty arithmetic skills writing my first game – Rock Paper Scissors. It’s pretty cheesy, so don’t judge. But if you’d like to experiment with it (or see my code), play the game here and look at the code here.

I hope this new direction will continue to be helpful to the MathFour-ticians out there who follow along & contribute to the discussions.

Will it be? Share your thoughts in the comments below, or on Twitter or Facebook. Oh – and if you’re a software developer (current or aspiring), come follow me on github too!

A big thanks to TryInteract.com for sharing a complementary super version of their quiz maker.

]]>Rush Hour is a game of logic and skill.

The colorful cars are fun for other things too.

The object of the game is to move the cars and let the target car “escape.” But at 4 years old, K8 was happy to figure out how to fit all the cars in the game board.

Get a copy of Think Fun’s Rush Hour – it’s a no-screen, single player logic game that appeals to girls and boys alike!

Assuming I run a steady 13:45 minute/mile pace for the whole 26.2 miles, I’ll finish exactly in the 6 hour time limit.

But of course my pace will vary. I’ll be faster at first. And I’ll likely want to crawl across the finish line.

So how fast do I need to go at the beginning so I can go as slow as possible at the end?

Without a backpack (which I wear running to work), I can do about a 10:30 minute/mile pace.

So here’s the math problem: **If my first mile is at 10:30 and my last mile averages with the first to be 13:45, what will my last mile be?**

10:30 = 10.5 minutes

13:45 = 13.75 minutes

(10.5 + last mile pace)/2 = 13.75

So the last mile pace = 17 minutes per mile!

Holy cow! I totally can do this!

If I go from 10:30 min/mile to 17:00 min/mile for the last mile, what should the pace be for each mile in between?

Mile # => Pace

1 => 10:30

2 => 10:45

3 => 11:00

4 => 11:15

5 => 11:30

6 => 11:45

7 => 12:00

8 => 12:15

9 => 12:30

10 => 12:45

11 => 13:00

12 => 13:15

13 => 13:30

14 => 13:45

15 => 14:00

16 => 14:15

17 => 14:30

18 => 14:45

19 => 15:00

20 => 15:15

21 => 15:30

22 => 15:45

23 => 16:00

24 => 16:15

25 => 16:30

26 => 16:45

0.2 => crawl across the finish line!

With that breakdown, I feel quite confident that I can make it.

I’ll pop into the comments after I’m done and let you know how it went.

As a “I’m queen of the world,” question, it’s easy. I’d quadruple the salaries of teachers.

As a “this is real” question, it’s not so easy. Because I’d have to figure out the budgetary requirements for quadrupling the salaries of teachers.

Regardless, I think the extreme salary bump could do the trick.

Why I think it will work…

I know that teacher salaries in other (more successful) countries is super high. Higher than engineers, for instance.

Which gives us indication that it may work.

Apart from that, let’s consider what happens when you have high salaries in something.

- Good teachers will be motivated (or considerably less de-motivated)
- Bad teachers (yes, there are some) will be motivated and might become good
- People in industry who’ve long dreamed of teaching will be motivated to do it.
- People in industry who turn out to be good teachers, will replace bad teachers (those that didn’t turn to good teachers)
- People in industry who turn out to be bad teachers will go back to their industry jobs.

The end result will be that we’ll have tons of good teachers that we can KEEP as teachers. They won’t run off to other fields because they have to starve to be a teacher.

Furthermore, if we bring tons of non-academic people into the teaching field, we’ll also have diversity in thinking. And we can push out the “that’s just the way it’s done” attitude.

Is this a reasonable solution? Am I nuts? Should I be kept away from the position of Secretary of Education? Or might my ideas have merit?

Share your thoughts in the comments, on Twitter or Facebook!