The beautiful and talented Heather at Freebies4Mom.com sent me a post on An Easy Way to Convert Celsius to Fahrenheit.

It inspired me to draw the graphs of Celsius in terms of Fahrenheit and Fahrenheit in terms of Celsius.

Notice these two intersect at (-40, -40). Which means that -40°F is -40°C!

Use it to convert temperatures.

The x values on the red line are Celsius - so find the °C you have and then look at the y-value to convert to °F.

It's just the opposite on the purple line.

Okay, fine. This isn't the greatest way to convert - but it's exciting to see it graphically. And it might be easier to convert this way for someone who's more visual.

Use it to teach math!

These two lines are inverses of each other. So the coordinates of one are switched to make the other.

Also, they mirror image across that 45° line. I marked the line with dashes and wrote on it.

And if you're into this, their functional composition (both ways) is... x! (not factorial)

Compare and Contrast...

Take a look at the way J.D.Roth did it and then look at the graphs I have. Let your students find the way they like the best. And encourage them to create new ways!

Oh, yeah - and share what happens in the comments!

How do you eat an elephant?

One bite at a time.

But where do you begin?

And that's what creating this Problem Based Learning Finite Math class feels like. There are 17 million entry ways into this.

Find one book and stick with it.

The voice of my housemate in grad school is haunting me: "Quit trying to use every book in the library. Find one book and stick with it!"

He's right. Even in today's online over-googled world.

I've found various sources and I've decided on one source for my course content creation: Samford University's Problem Based Learning Archives.

I need support too!

Since I don't interact face to face with anyone that does this, I'm going to use some resources online for support.

First is the #pblchat twitter chat on Tuesdays at 7pm CST. They normally talk about Project Based Learning, but it's good stuff for the Problem Based Learning people, too.

I'll also follow the #PrBL hashtag on Twitter - it's specific for Problem Based Learning.

For comfort and solidarity, I'll read Emergent Math's Blog - he's got lots on math PrBL. And my super hero in this, Chris Fancher, has a PBL blog that I'll be stalking too!

How about you?

Do you do Problem Based Learning? Or even Project Based Learning? What resources do you use?

Share them in the comments - and with your PLN on twitter!

This is part of the Five Minute Friday series. Today's prompt is: Brave.

Doing math (and teaching math) is a nutty act of bravery.

And sometimes it's just a nutty act.

But we do it - both teach and learn.

Bravery in Learning

Here are some of the amazing things I've seen in math learning - the bravest of the brave:

• Student in tears at the beginning of the course, but there anyway.
• Student in tears at the end of the final exam (different student, btw).
• Student continuing to come to class even though the instructor made her cry. (That was me.)

Bravery in Teaching

Here are some of the brave acts of teaching math:

• Teacher telling a joke and not laughing at himself. (This takes courage!)
• Teacher asking a question and sitting in the silence until someone answers. (Very hard to do!)
• Teacher taking on a different learning style - like Problem Based Learning. (That's me and I'm scared to death!)

How about you?

What's your bravest moment in math teaching or learning?

Share in the comments!

Learn more about the Five Minute Friday writing challenge here…

And that's really easy for me to preach. Because it's easy to practice. For me.

I've never struggled out of control in math.

It's not easy to "just say it."

I've been asking people to say things that they're extremely uncomfortable with. But I've not stepped up to the plate myself and done the same!

I've been reading a book called Daring Greatly by Brené Brown. She writes, "Be the adult you want your children to be."

I want K8 to be happy with math. No problem - I'm happy with math.

But I also want her to be happy with her body, eating healthy and enjoying exercise.

Faking it is hard.

I have body image issues. I eat garbage and I don't work out.

And I don't want K8 to be like this.

Suppose someone told me, "All you have to do is say you like your body, eat right and exercise. Then your daughter will be fine."

My response would be, "That's great - for you. But it's not so easy as just saying it. Jerk."

It's really hard for people to just say it.

I'm going to do what I'm asking you to do.

I'm going to step up to the plate and put my money where my mouth is.

I'm going to make a conscious effort for 25 days to be the adult I want K8 to be.

And it's way outside my comfort zone.

I'm going to tackle my issues as if I don't have them. I'm going to just say it.

Here are the things I'm going to do:

1. First thing in the morning, I'm going to dress in workout clothes. When I workout, I'm going to say, "I'm going to exercise now."
2. I'm going to cut up some fruit for breakfast and say, "I'm eating fruit for breakfast, K8 - do you want some?"
3. In the evening, I'm going to do something active with K8. Either throwing a frisbee, jumping on the trampoling or some Wii Dancing. I'm going to say, "Isn't this fun being active together?"
4. I'm going to eat vegetables with the evening meal. I'll say, "I'm so glad we're having broccoli tonight - vegetables are good for us."
5. And at least once during the day, I'll comment on how how much I like my body.

And to track my progress, I'll post all of this on the Facebook page.

The "Just Say It" challenge.

As I post my journey on the Facebook page, I'll suggest things you can say for math.

You can join the talking-health challenge or the talking-math challenge. Or join both!

Either way - together we'll learn to "Just say it!"

Ready... GO!

I stopped when I was prompted to "share this on Facebook" to get an extra entry.

I thought, "I don't want more people to enter. I want me to win. And if I share, I'll let others in."

Bad Bon! I know - but that's how I am.

Which sparked me thinking about the math behind winning - and losing - if you get more entries.

Entering a blog giveaway is easy.

In blog giveaways you enter by commenting on the post. The blogger also gives you the opportunity to earn more chances of winning by doing other things.

These include following her on Twitter or Pinterest, or liking her Facebook fan page. And you get even more chances to win by sharing the giveaway.

And that's where things start to go bad for you.

Increasing your chance of winning actually decreases your chances!

The more you share, the more you water down your chances to win. Here's how:

Suppose you find a blog giveaway with five entry opportunities. One of those requires you to share the giveaway on Facebook.

You do everything that's required. You even posted on Facebook, "I just entered this giveaway, you should too!"

So you got all 5 chances. Yay you.

At the time you entered, there were 19 other people who entered, and each got five chances, too.

You + 19 = 20 people entered

20 people 5 chances each = 100 entries.

So now you have 5 chances out of 100 to win the giveaway - that's a 5% probability of winning. Not bad.

But wait... you shared on Facebook!

Since you shared this on Facebook, tons of your friends saw the giveaway. Five entered and got five chances each. (Which means they shared on Facebook too.)

Your friends changed your chances to win:

20 people before + 5 more people = 25 people entered

25 people  5 chances each = 125 entries

So now you have 5 out of 125 chances to win - bringing you down to a 4% probability of winning.

Okay, sure. That's still not bad.

But your friends shared on Facebook, too!

Supposed the Facebook "share" from your 5 friends got five more people each. So that's 5 5 = 25 more people. With 5 more entries for each of those!

Now the numbers are:

25 people from before + 25 more people = 50 total people entered

50 people  5 chances each = 250 entries

So now your chance is 5 out of 250 - a whopping 2% probability. You've more than chopped your chance of winning in half - just because you wanted another entry!

Am I pessimistic?

I'll admit that this sounds very negative.

What's the real point in sharing something? Human connection.

Bloggers have good stuff to offer, and their readers know it. And they want to share with others.

But there is math behind all this.

Just don't forget that part too.

Post your thoughts in the comments. And share via Twitter, Pinterest and Facebook - you won't change your chances to win anything!

This method looks like a great way to get students involved - really involved!

Grownups in math classes have been uninvolved for more than a decade. So I've decided to try problem based learning in my next college class: Finite Math.

What is Problem Based Learning?

Problem based learning is a student centered style of learning where students learn by solving problems (instead of being lectured).

I'm new to it (that's an understatement) so that's about the only definition I have. Hopefully I'll grow a better understanding of it as I continue on my journey.

What I understand about it is this:

1. The instructor presents an ill-defined problem.
2. The students work in groups to solve it.
3. The instructor answers questions, guides and gives "lectures" on material as requested.
4. The students end up with a deeper understanding (and appreciation) of the material.

I'm scared.

I've been teaching the same way for 18 years.

I'm a pretty old dog. And switching methodologies is a new trick.

So digging into this is scary.

Actually, it's terrifying.

I'm gonna mess up. A lot.

Chris Fancher the PBL expert at EdCamp this weekend said, "You're going to mess up. A lot."

And strangely, that's what I tell students. And it's okay to mess up. For them and for me.

So I'm going to embrace this.

Every time I mess up, I'm going to go read the "daring greatly" quote by Roosevelt.

I'll probably cry, worry and freak out a little.

Then I'll keep going on my journey.

I have to be all in.

I know me. Three days into class I'll want to say, "Well, this isn't working like I thought it would - let's go back to lecture."

Doing this would be a huge fail.

It'll feel safe. But it'll be in service to me - not to the students.

So I have to be all in.

No excuses. No turning back. And no hesitation.

So I'm pushing the chips across the table. I'm standing up. And I'm saying, "I'm all in!"

Welcome to the game!

Will you come along for the ride?

This is the first in the series... But of course I don't know what will come next. So I'll just come back and link here as they happen!

If you have any resources or thoughts, will you share them? Drop them in the comments and don't forget to share this on twitter.

I was a bit excited about attending EdCamp Waller today!

I was horrified.

Apparently some professors are doing this!

Requiring evaluations is unethical.

There are many reasons professors shouldn't do this:

1. It decreases anonymity
2. It can skew survey results
3. It's a violation of student rights

To add to these (which I cover in detail below), professors must give credit for it. If they don't give credit, they can't enforce the "required" part.

Which adds a third problem:

4. You're skewing the students' grades!

1. It decreases anonymity.

Suppose 3 students out of 20 decide to honor the requirement. They do the evaluation online and show the prof the "completed" form.

When the prof gets the results of the evaluation back, he has much better chance at "guessing" who wrote what.

And if only one student did it, he knows exactly what the single student wrote - thus destroying the student's anonymity altogether!

It might be okay - if they never take a class from him again. But who's to prevent him from telling other professors what they wrote?

2. Requiring evaluations can skew survey results.

These professors are externally motivating students to take a survey that will have no bearing on their future. So why should students answer honestly?

Students only need to print the page that shows "you've submitted the evaluation." Who cares what answers they pick - they surely don't!

Which means they'll likely go down the left or right (or maybe middle) of the checkboxes and check them as fast as they can.

Which means the survey isn't giving an accurate picture of how well (or poorly) the professor is teaching.

3. It's is a violation of student rights.

Evaluating a course is a right, not a requirement. Just as the freedom of speech is a right.

But that doesn't mean we try to force people into blogging, posting on Facebook and giving their opinion at cocktail parties!

People have the right to speak their mind - or to not say anything if they want.

Students have the right to evaluate their instructor - or to not evaluate him!

4. Requiring evaluations skews the students' grades!

In order to "require" something - you must be prepared to reward (or punish) the behavior. Which means you give credit for it.

So these instructors are giving extra credit for completion of the evaluation.

Which means they are giving credit for non-course related activities!

In fact, it's helping students pass when they have not learned the course content. One of my students asked me outright, "Could you wait until the semester's over before you tell them to stop? I really need those points."

How is this any different than allowing students to wash my car in exchange for extra credit in College Algebra?

It isn't.

The road is paved with good intentions...

Back in the 1990s we posted grades next to Social Security numbers outside lecture halls. We naively thought, "They want their grades - this'll give the grades as fast as possible."

Our hearts were in the right place back then. But it didn't make what we were doing right.

I'm sure professors that require evaluations (and offer extra credit for them) have their hearts in the right place.

But requiring evaluations is still not right.

Back to you...

What'd I miss? Do you do this? Will you stop?

Share your thoughts in the comments.

It's up and running. And we have big plans for it!

Building a "Back End"

The plans are to build a teacher login section so teachers can:

• Input and save all parent email addresses.
• Send pre-written emails to parents based on the content they'll be working on that week. These emails will link to That's Math! content which is free for parents to view and comment on.
• Print a record of that info to send to state agencies requiring reports of parental involvement (like for U.S. Title I funding).

We need help!

In order to build this, we'll need some high end programming - much more than I can do. We'll need "for real" marketing. And a sales team to make sure schools know about it.

And that means we'll need funding.

Yes - we could do crowd-funding, traditional venture capitalists or love-money. But getting on the Shark Tank TV show could be the first step in marketing the idea of parent involvement activities!

Will you donate 2 minutes?

I timed it.

If you follow these instructions, it will take you two minutes to vote for That's Math! on SharkTankZone.com.

1. Go to SharkTankZone.com.

2. Click on "Register" in the top right corner. (Don't worry, you won't have spam coming from this!)

3. Fill out the registration form - use a throw away email address. I've not gotten any emails from these people, yet. But no doubt they're harvesting them for evil plans in the future (there's no "don't subscribe me" checkbox!).

4. Head back to the That's Math! page to vote. Click on the "thumbs up" and you're done!

Now tell others!

Okay, that's not built into the 2 minutes. But if you can share this with your PLN, that would help. You can tweet, share or pin it.

And make sure you share your thoughts in the comments!

If you tap into you basic counting nature, it gets easier.

Counting Reference Angles in Radians

I made an animation showing how to "count" reference angles in radians.

Notice the way the angles count around using the numerator of the fraction, while holding the denominator constant:

Can you use it?

How about it? Will you be able to use this to teach reference angles?

Share your thoughts in the comments!