Sunday, February 18, 2024

Free Online Math Circle Has a Few Spots Open Still

 

We picked a time. We're meeting for nine weeks, each Saturday from March 2 to April 27, for an hour, at 3pm PT / 6pm ET. We still have a few spots open. We'll be playing with Triangles, Circles, and Pi, along with the fictional Althea and her friends. Participants will get an introduction to geometry, proof, and trigonometry.

 

I'm writing a new book series, Althea's Math Mysteries. In four young adult novels, Althea and her friends explore some of the mysteries of mathematics. The first two books are nearing publication, and the second book needs folks to test it out. In Althea and the Mysteries of Triangles, Circles, and Pi, Althea and friends, with the help of Althea’s mom, explore geometry and proof in order to then learn the basics of trigonometry.

 

We'd like to find some eager math students to join us in an online math circle, led by me, to explore along with Althea and her friends. Students will participate in 9 weeks of lively small-group sessions: in part a deep and friendly math course, and also a unique book club, with the author refining the story based on student reactions.

 

Do you know any students who enjoy math, know a bit of algebra, and would enjoy "user testing” Althea and the Mysteries of Triangles, Circles, and Pi? We're looking for a few more young people to try out the activities in this book together. 



Commitments: 

  • Attend 9 weeks of 60-minute live online sessions from March 2 to April 27, each Saturday at 3pm PT / 6pm ET.
  •  Read and comment on 1 to 3 chapters of the book each week. 
  • Keep an informal math journal during this time.



For all who stay the course: 

  • You'll learn the foundations of geometry and trigonometry (and will get a certificate for completing the course).
  • You'll get a signed copy of the published book.
  •  Your name or alias will appear in the book's acknowledgements, and you will receive a letter of appreciation for your help with this STEM project. (If you’d like a letter of recommendation later, we will be happy to write one for you.)
  •  You’ll get to build community with math friends and mentors.

 

 

Interested? Please email me at mathanthologyeditor@gmail.com for more information, or to sign up.

Wednesday, February 7, 2024

Openings Now in Free Online Math Circle

 

Join an online math circle for students ages 12 to 15 in March and April, exploring geometry, proof, and the basics of trigonometry.

 

As most of you know, I'm writing a new book series. In four young adult novels, Althea and her friends will be exploring some of the mysteries of mathematics. The first two books are nearing publication at Natural Math.

In Althea and the Mysteries of Triangles, Circles, and Pi, Althea and friends, with the help of Althea’s mom, explore geometry and proof in order to then learn the basics of trigonometry. My publisher and I would like to find some eager math students to join me in an online math circle, exploring some math mysteries along with Althea and her friends. Participants will join lively small-group sessions: in part a deep and friendly math course, and also a unique book club, allowing me to refine the story based on student reactions.

Althea and the Mysteries of Triangles, Circles, and Pi is a fictional story set in the present, in which the characters discuss math, with Mom throwing in a few true stories from the past. Like The Number Devil and Math Girls, this book gives you more the more you put into it by doing the math yourself.

Do you know any students who enjoy math, know a bit of algebra, and would enjoy user testing Althea and the Mysteries of Triangles, Circles, and Pi? We’re looking for 5 to 8 young people to try out the activities in this book together. If interested, please add your name and information here.

 

Commitments:

  • Attend 9 weeks of 60-minute live online sessions in March and April. Times to be determined, most likely 4 p.m. EST / 1 p.m. PST, on Saturday or a weekday (whichever works for more students).
  • Read and comment on 1 to 3 chapters of the book each week.
  • Keep an informal math journal during this time.

 

For all who stay the course:

  • You’ll learn the foundations of geometry and trigonometry (and will get a certificate for completing the course).
  • You’ll get a signed copy of the published book.
  • Your name or alias will appear in the book’s acknowledgements, and you will receive a letter of appreciation for your help with this STEM project. (If you’d like a letter of recommendation later, we will be happy to write one for you.)
  • You’ll get to build community with math friends and mentors.

 

Sign Up Button

Monday, February 5, 2024

The Storytellers of Math

Anyone here reading knows that I'm working on my series of young adult novels with math at the center - Althea's Math Mysteries.

 

But did you know that this drive to tell math stories is growing among budding storytellers across the lands? 

Sue in California (me!) is writing Althea's Math Mysteries. Four of them!

Shayla (aka SK Bennett) in New Mexico is writing the next book after Marco the Great and the History of Numberville. (I'm loving this one. I'm so glad there will be another.)

Sarah in Washington has written some wonderful fairy tales about physics and math. I'm reading Newton's Laws: A Fairy Tale right now.  (Currently free.)

And of course there are about a dozen lovely stories from the authors who work with Natural Math.


Who else is out there, writing tales of mathjoy that I haven't discovered yet?!

Friday, December 8, 2023

Illustrating Althea

I'm not much good at drawing, but most of the illustrations in Althea and the Mysteries of Triangles, Circles, and Pi are math work. I can do those. So I've put my own illustrations into the manuscript as placeholders. There will be a professional illustrator, later.

This past week, I was looking for where more illustrations are needed. I decided Althea would draw a map of California while thinking about their summer trips. So I drew it. Their home is in Berkeley, they go to camp in Quincy, and they're planning a trip to San Diego to visit Legoland (because her younger brother Rudy would love that, and their moms met in San Diego).

I had fun drawing the map. First I downloaded a map of California into goodnotes, as the template for my document. Then I outlined it, and then changed the template to make the original fancy map go away. Finally, I got to add the places of interest to Althea.

As one friend on facebook pointed out, it would help to make the line weights different for the outline versus the routes she's imagining. The professional illustrator can either take care of that, or show me how it will work best for the published book.




Sunday, November 26, 2023

Althea's Math Mysteries


 

This blog may not be as active as it used to be, but it's a good way for me to remember some things. My first post about my Althea stories was in September of 2019, so I've been working on the first two books in this series for four years now. I'm hoping we'll be able to publish them in about a year. 

I have a very hopeful timeline that puts publication in October. But we all know that things never go as well as we hope. (And I'm wishing we could do it just a bit faster than that, so they'd come out in time for Math Storytelling Day, September 25, Maria's and my birthday.)

I have pretty complete drafts done of Althea and the Mystery of the Imaginary Numbers and Althea and the Mysteries of Triangles, Circles, and Pi. Soon I'll be asking for folks to read the manuscripts and comment on them. (Email me at mathanthologyeditor@gmail.com if you'd like to be one of our readers.) After that's done, we'll do our usual (Natural Math publishing's usual) crowdfunding campaign. And then there will be illustration, copy editing, proofreading, page layout, and books!

Here's my mock-ups of the covers, and lots of information that goes with the books.

At a few points, I've really wanted to see what these would look like as actual paperback books. lulu.com made that easy. Two books cost me under $25. I've done that 3 times, while I've polished up the books. What you see in the photo above is me holding the 3rd printed draft copy of Althea and the Mysteries of Triangles, Circles, and Pi.


In other news, I retired on May 20 from my full-time job teaching math at a community college. Teaching online was way too much work, and less satisfaction than teaching in person. I'm still covid-cautious, so I also didn't want to go back to teaching in person. Retirement has been wonderful. I'm working hard on the books, visiting Michigan where I help my dad (who's 90), cleaning up my house a bit, and working on my yard. 

All that was plenty for about the first five months. When I noticed that I sometimes felt like I had nothing to do, I posted in a Beast Academy group on facebook that I was thinking of offering a class. Someone suggested that I apply for a position with AOPS. (Art of Problem Solving is an amazing online resource, providing great math textbooks and classes, and they wrote the fabulous Beast Academy curriculum.) I did that, and I'll start teaching for them soon!

I will definitely be blogging more over the next year, to let anyone still reading my blog know what's up with these books. (If you're out there reading this, I'd love to hear from you.)


Monday, July 31, 2023

Playful Math Blog Carnival #166

This blog carnival has been around for 14 years. Almost every month for 14 years, someone has added a post to this collection. That's quite a long life for an internet phenomenon. (Congratulations, Denise, for keeping this going!) If you'd like to see any of the previous posts in this series, check them out here. For many years, blogs were a big part of my time online. But not so much lately.

When our number (166 now) was in the 20s, 30s, or 40s, I'd make sure to have that many links. Nope, I don't have time to find 166 great links (and you'd get tired just looking through them). But they're out there. I have learned so much from bunny hopping around the web of math bloggers over the years. And even though blogs aren't the popular thing now, most of the old ones are still out there, waiting for you to find them and get excited.

 

The 166 puzzle: It turns out that 166 is a 'centered triangular number'. If you start with a dot, and then you put a triangle around that, and a bigger one around that, etc, you get up to 166. How many triangles did you use?


 


I have just run out of envelopes. How should I make myself one? (a puzzle from Fawn Nguyen) What shape of paper will you use?

 

 

Online Mathy games


Geometry Puzzles


 

Find the blue area

This one stumped me (no trig required).

 




 

 This one's a lot easier.

 

 

 

 

 

 

What fraction is shaded? Catriona Shearer (@Cshearer41) made this, along with gobs more, mostly pretty challenging, which she posts on twitter. And here's a collection of over 300 of them.

 


Beyond the Games & Puzzles
 
 
 
Searching for more? Some good hashtags are:  #MTBoS #ITeachMath  #Elemmathchat #MSmathchat
 
 
 
If you've seen some good math pedagogy out in the wilds of the internet, add a comment. 

Friday, February 24, 2023

Althea's Math Mysteries

 I've been working for a few years on Althea and the Mystery of the Imaginary Numbers. It's almost ready for the illustrator. But I wanted to dive deeper into the characters, and started working on the second book in the series, Althea and the Mysteries of Pi. I'm about 80 pages in on my first (very rough) draft. It has been a blast writing this, because I pretty much know where I'm headed. (Although sometimes I worry that there's too much math, and not enough character development. And then I back up and think about Althea, Kiara, Sofia, and Aiden some more.)

Today I wanted a good place to put links that the book refers to, so I made a temporary website for all the books. It's a google site (for now). And I made mock-ups for the book covers. It helps me to organize my thoughts, and it is super exciting to see. So even though the books won't be published for another year (or 2?), maybe this will tantalize you. Here's the site for Althea's Math Mysteries.

When this book is pretty much done, I'll start working on the third one, Althea and the Mysteries of Infinity. I have lots of ideas for that one, but they have no structure. I have no idea where I'll start or end. 

When I'm all done, and these 3 books are published, maybe I'll have realized that there are more books in the series. For now, it's looking like just the three.


Thursday, September 8, 2022

What does it mean when we feel we "understand" something?

On facebook, I'm in a group for people who use Beast Academy (even though I'm not using it), because Beast Academy fascinates me. I love most of what they do.

A parent today posted that she was confused about the BA way of multiplying 59*59. They have you draw a 60 by 60 box, and then take off one row (of 60) and one column (which is now 59). Your box is now 59 by 59, and its area is 60*60 - 60 - 59. Cool.



She wasn't seeing it, so she taught her kid the standard algorithm. Lots of people were giving her flak for that. (We each do our best, so I don't see why folks would jump on her.) She replied to them that she thought learning it multiple ways was a good thing.

I wrote: "Sure it's great to do things multiple ways, but does he really understand the algorithm you showed him? (Do you really understand why it works?) I think that's why you're getting pushback here."

She said they both understood it. I replied that I'd have trouble explaining to a young kid why you "put a 0". She wrote: "
I just told him we put it to show that the one number is done. I don’t know if it’s accurate but he understood it. I don’t really remember it ever being explained in school."

So what she originally meant when she said he understood it, was that he could follow the steps and get it right. Not that he understood why it worked.

I think this is common with math.  People think 'understand' means the same as 'can follow the steps'. But I'm afraid that doing math without really seeing why each step makes sense is part of why a lot of people don't like math. It's surely why we easily forget how to do those things.

Here's an article by Richard Skemp, written back in 1978, about why the deeper understanding, which he calls "relational understanding" is a better way to approach math. (He calls being able to follow the steps "instrumental understanding".) I wrote about this topic and this article ten years ago here, but people's ideas about math haven't changed much in that time.

Of course, this parent can still explain to her son why the standard algorithm works, so she hasn't somehow wrecked the beauty of Beast Academy, as some people seemed to feel. And that's what got me writing - I want to see how well I can explain the standard algorithm.

I figure that the standard algorithm packs in a lot with as little writing as possible. (Maybe when we didn't have calculators, and had to do lots of by-hand multiplication, writing as little as possible was considered an important goal for the way we write things down?) So I figured that it needs to be unpacked a little. That's what I tried to do here.

 


The first calculation is adding up all 4 areas. The one to the far right is the standard algorithm. The first number in the standard algorithm (531) is the 81 and the first 450 added together (with carrying), and the second number (2950) is the other 450 and the 2500 added together. It's surely as little writing as possible, but it hides so much! Does my unpacking on the left help?


It all makes sense to me, but the Beast way feels more fun. (And I don't have to write anything that way. I can hold it all in my head!) What do you think?


Tuesday, August 16, 2022

Prepping for Fall, Calc II: Lovely Arc Length Example

I'll be teaching Calc II for the first time in a few years. This is my first time starting out online with it. So I'm preparing my Canvas shell and thinking about how I want to explain each topic in Canvas. (I know the material well enough that I didn't have to prep this much when we were in person.) The extra prep before we start is so much work, but today it feels totally worthwhile.

 
 
For arc length I was excited to use "crinkle crankle walls" as an example. Isn't that a pretty wall? And you can actually use fewer bricks this way than for a straight wall, because one layer of bricks here is stronger than it would be straight (so the straight wall would need extra bricks for support). I'm thinking we'll try to prove that assertion in my Calc II class.
 


It turns out that arc length uses an integral which often has no "elementary solution", meaning there is no anti-derivative using the functions we are familiar with. 
 
The arc length for y=sin x is...

 
 
 
And this has no "elementary solution".
 
 
I often tell my students that we study infinite series to solve the integrals with no easier solution, but I just realized that that won't work here. (Can't do a square root of an infinite series!) 
 
Ok, no problem. I'm also teaching numerical integration. So I made a google sheet to do Simpson's method, and it turns out beautifully!! (Beautifully meaning that my answer matched the answers on Math SE that people explained in ways that were above my head. I don't know a thing about "elliptical integrals".)
 
I still need to remember how to explain Simpson's rule, but I'll get that back easily enough. 
 
If this wall follows a sine wave, then for 6.28 feet (2π feet) of straight distance covered, it has a length of 7.64 feet. That's just over 20% extra length. (Now to think with my students about whether that's better than the straight wall with supports.)

Wednesday, August 3, 2022

Technology Woes and Cheers: Venn diagram edition

I'm writing questions for my Discrete Math course that will be available to my students (and others) through MyOpenMath, a free online homework system. I'm not very good at programming in their environment, but I'm learning. The cool thing about MyOpenMath is that it uses random numbers in the questions so that each student might get a (slightly) different question.

I wanted a way to ask, for a random Venn diagram: What is the set notation for this?

First, I needed a way to make lots of Venn diagrams, all pretty, and all in the same style. I searched the internet for a free online Venn diagram maker. Nothing right showed up. I looked at over a dozen sites. Many wanted me to sign in. That should not be necessary and I skipped those. None of the others were even close to what I wanted, which is pretty simple. Really?! Isn't this something lots of people would want? 

I asked about it on Math Educators Stack Exchange. Within hours, Cameron Williams posted an answer. He made it on desmos for me. (How sweet is that?! Amazing.) I know desmos well, so I was able to modify his version to be exactly what I wanted, in less time than I had already spent searching. (I suggest you go play with it - it's lovely.) And, if you want orange shading instead of blue, it's very easy to modify this to get exactly what you want.

Then I made 17 screenshots of various combinations of the basic regions, and named them based on the set notation. So "(A un B) int not C.jpg" is the filename for ...

 

Next I went back to MyOpenMath, and wrote most of my multiple choice problem. I'm still stuck on how to get it to display a randomly chosen image file. I think the folks at the help forum there will help me out on that. Once I finish fixing it, I'll edit this post to show the question. MyOpenMath allows attached videos to explain how to answer the questions. I think I might do a video for this one. 


So if you want a free online Venn diagram maker, it's here.  I don't know how to help google move this up in the searches so people can find it. Do you?




 
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