Request for Submissions for Playful Math Carnival 186: Math Stories

Calling all math lovers. I'm hosting the fall edition of Playful Math Carnival 186. The theme is once again Math Stories.

 

Have you written a math story?

Have you written an article about stories and math?

Do you have a favorite math story?

Would you like to write something in the next 2 or 3 days, and post it somewhere?

 

I'll be posting this next week Friday, September 25, so I have one week to get the goods and weave them together. September 25 is National Math Storytelling Day. 

 

9-25 is also headed towards being 9-to-5 day in honer of Dolly Parton. She sure loved spreading the joy of stories, and I can certainly imagine her delight at the idea of math stories. I'm so happy to be sharing our math story day with the fabulous Dolly Parton.

 

Got a link? Please send it today

Limit Definition for Derivatives

Calculus courses usually start with limits, and the precise definition of a limit is usually included but barely. There are a number of problems with this.

First off, limits seem alien and "why are we doing this"? It would be better to start with the derivative, connect it to slopes and velocities, and tell a bit of the history (Newton attempting to understand gravity). Perhaps do some hand-waving about the limits, and promise to come back to them.

The second big problem is that the limit definition is never connected with the derivative definition. In fact, the f(x) in the limit definition is not the same function as the f(x) in the derivative definition. After almost 30 years of teaching calculus, I finally wrote something to explain how the two definitions interact. (I found nothing online about this, and I have never seen it in a textbook.)

I've written it up two ways. One is a bonus chapter for my (not-yet-published) book, Althea and the Mysteries of Calculus, in which there is discussion among the kids and 'Mom'. The other leaves out the characters: How the Definitions of Limit and Derivative Interact

 

Math is the Plot

But a plot usually has a conflict. What's the conflict? (I don't know yet.) And there should be some drama, etc.

I'm now in a critique group for people writing STEM fiction. I recommended Math Girls to one of my critique partners. She mentioned how much she loves trying to solve the problems before the characters do. Duh! I figured something like that would be easy to include in Althea and the Mysteries of Calculus. It took me a few days. Now there's a teaser at the end of each chapter. And the list of those questions makes a great outline for a calculus course.

I'm still working on the characters' responses to those questions. I've already rewritten a number of scenes in exciting ways. Sofia is a very visual thinker, and she often finds answers in very different ways from how Mom would explain.  

 

Check it out.

  

1. How can we define tangent lines? (p31)
2. How is it possible to figure out a speed when no time has passed? (p53)
3. To find instantaneous velocity we need two points infinitely close together. How can we do that? (p62)
4.  ... 

 

Book Progress

 

I'm working on removing anything unnecessary from Althea and the Mysteries of Calculus. So far I've only removed 15 pages. At that rate, it would take me a year and a half to get it down to 350 pages. I'd better pick up the pace.

I'm also improving things that beta readers have asked me to. The characters need to move around a little more, and have little physical quirks. I'm working on that. D suggested that one of the characters might chew on their pencil when thinking, and then their pencil would bump into their mask. I like that image. I haven't found a spot yet where it will work, but I hope to.

Someone just asked to read the first book. I wondered what made him ask just now, since I haven't recently asked for readers. I realized maybe it's that school has ended.

 

If your school year has recently ended and you or your kids would like to read one of Althea's Math Mysteries, just get in touch at altheasmathmysteries@gmail.com. I'm still in need of beta readers.

 

More information about the books here. 

 

What is calculus?

It finds slopes on curves,

And areas inside curvy shapes.

So it can find a changing velocity,

Like with gravity.

 

How does it work?

We use two points to find slope of a line, rise over run.

But we want the slope of a curve at one point.

So Newton and Leibniz “cheated”,

Putting the two points infinitely close together.

It works.

 

If you want to learn more,

Althea and her friends are exploring calculus

And you can join them.

 

 

(Email me at altheasmathmysteries@gmail.com.) 

Progress: Althea and the Mysteries of Calculus, version 8.2

 

Minor changes

The front image is much nicer now. It's still not a professional illustration. That will happen after we begin our kickstarter campaign, and that won't be for many months, at the earliest.

I decided the predictability of having Althea's Math Journal after every chapter would feel good to readers. But the first two Mondays had two chapters each, and she can't be writing her journal in the middle of a gathering. So I had to combine chapters 1 & 2 and also chapters 5 & 6. Done.

Also, at 450 pages, the book is way too long. I intend to shave off at least 100 pages. I found some bits in chapter 1 that could go. (Some of that appears in the Activity Book still.) So that chapter is a reasonable length, I think. So far, I haven't found anything to take out in what is now chapter 4. I hope folks giving me feedback can help me with that. I think it comes in too long at 26 pages.

I'm still finding places where I need to add a bit to make the math clearer. But more and more, I'm also finding bits that can go. Adding a touch of color here, removing something out of place there. I feel like a sculptor or painter. Ahh.

I wish it were easier to find beta readers. (I have a story to tell about that. It will be in a blog post soon.) If you're interested, email me at altheasmathmysteries@gmail.com.

 

 

Table of Contents 

Here it is. Does it entice you?

Prologue                                                                      

Part 1. Slopes on Curves and Changing Velocities

Ch. 1.   Areas and Graphs                                        

Ch. 2.   On Our Own                                                 

Ch. 3.   Working On Our Icons                                

Ch. 4.   Velocity, Acceleration, and Tangents           

Ch.5.    Finally, the Derivative                                 

Ch.6.    Measuring Speed                                          

Ch.7.    Derivatives from Graphs                              

Ch.8.    Even More Perspectives                             

Ch.9.    Finishing Up and a Test                             

 

 

Part 2. So Many Derivatives

Ch.10.  All the Powers                                             

Ch.11.  Polynomials and Graphing                          

Ch.12.  Graphing with Newton                                

Ch.13.  Back to Trigonometry                                  

Ch.14.  Derivatives for Sine and Cosine                  

Ch.15.  Quotients and More Trig Derivatives          

Ch.16.  Optimizing                                                    

Ch.17.  Nested Functions                                          

Ch.18.  Exponential Functions                                  

Ch.19.  Exponential Derivatives                                

Ch.20.  Implicit Derivatives                                       

Ch.21.  Linearization                                                 

Ch.22.  Review and Another Test                              

 

Part 3. Anti-derivatives, Areas, and Volumes

Ch23    Areas                                                            

Ch24    Getting Closer to Area                                 

Ch25    That Area Definition                                   

Ch26    Fundamental Project                                    

Ch27    Gravity                                                         

Ch28    Substitution                                                  

Ch29    Volumes of Revolution                                

Ch30    A Final Exam                                               

Ch31    Back to Infinity                                            

Ch32    Infinite Series                                               

Ch33    Infinite Series for Area                                

 

Epilogue.