Monday, June 09, 2014

Test Run: Zero

Note to readers: I am in the process of creating a blog for parents of young children (and possibly older children as well), as a resource for supporting their children's mathematical literacy. Many parents I have talked to are eager to know what they can do to help their children, but don't always know where to start. I'd love to contribute what I can, and before I actually launch the blog, I am test running a couple of the posts I have already developed. I am interested in your feedback! What is helpful and what is not? Do you have any experiences as a parent that you would be willing to share? What kinds of things would you (or people you know) be interested in reading? I want to put something out into the world that is fun, interesting, and helpful, and I appreciate your help!

[I foresee five types of posts on the math blog: (1) games and activities to do with young children, (2) reviews of children's mathematics books with suggestions about how to engage children in the mathematics, (3) principles and guidelines for interacting with young children about mathematics, (4) descriptions of mathematical concepts that children are engaging in, and (5) accessible summaries of research about young children and mathematics. The following post is of the second type.]

Zero, by Kathryn Otoshi (Book Review)
 
It seems to me that children’s math books fall somewhere along a continuum. On one side of the continuum the books practically shout, “I am a MATH book! I will teach you something!” On the other side, the math is so subtle that you might not even notice it’s there.

I’m much more partial to the subtler side of the continuum, where the author weaves math into the fabric of the story, rather than fitting a story onto the math. It’s not that I think kids will only swallow the math if we sneak it into their literary diet. There are some fantastic, mathiest-of-math books that are engaging and fun and fantastic for children. But sometimes when the mathematics doesn’t jump out and hit you on the head there can be a lot more room for conversation. You just need to know what to look for.

One of my students recently lent me her copy of Kathryn Otoshi’s Zero. I had neither seen nor heard of this book, but I fell in love with it from the very first page. This book hits my sweet spot—simple, gorgeous illustrations; an engaging, child-friendly story; solid mathematics; and plenty of conversation fodder. It’s fantastic. I’m going to give it to myself for Christmas.


In this book, there are two big mathematical ideas:  

  1. Zero is a different kind of number. I could write a whole blog post about this idea. (I probably will.) But here’s the short of it: young children don’t initially think of zero as a number because zero is not “part of the count.” When we count, we typically start with “one”. And we never ask our children to count a set of no objects. They’d probably think we were joking if we pointed at an empty tabletop and said, “Count the M&Ms!”  
  2. With only ten symbols, we are able to write numbers as big as we want to. This is an under-recognized beauty of our number system. Many historical number systems (like Roman numerals) can only represent quantities up to a certain size before running out of symbols. But our modern Arabic numerals have infinite possibilities for combining just ten symbols into any number we can imagine. 

So what can you do with this book (besides read it)? Talk about the math! Here are just a few ideas to get you started, but let your child lead the way and see where the conversation takes you.
  • Ask your child, “Is zero a number?” and see what they say. Probe their thinking. You can use the context of the book (but you don’t have to). Why would zero feel left out? What’s different about zero?
  • Have your child write the biggest number they can think of, and the smallest number they can think of. Together, see if you can think of bigger and bigger numbers (and for older children, smaller and smaller). It’s a game, but a game that can help your child think about how writing numbers “works.”
  • Talk about how the numbers in the book can join themselves together. What kinds of numbers could two numbers make? Four numbers?
  • And you don’t have to stop at math. Talk about friendships, fitting in, being yourself, working together.

Test Run: Four Super Simple Counting Games

Note to readers: I am in the process of creating a blog for parents of young children (and possibly older children as well), as a resource for supporting their children's mathematical literacy. Many parents I have talked to are eager to know what they can do to help their children, but don't always know where to start. I'd love to contribute what I can, and before I actually launch the blog, I am test running a couple of the posts I have already developed. I am interested in your feedback! What is helpful and what is not? Do you have any experiences as a parent that you would be willing to share? What kinds of things would you (or people you know) be interested in reading? I want to put something out into the world that is fun, interesting, and helpful, and I appreciate your help!

[I foresee five types of posts on the math blog: (1) games and activities to do with young children, (2) reviews of children's mathematics books with suggestions about how to engage children in the mathematics, (3) principles and guidelines for interacting with young children about mathematics, (4) descriptions of mathematical concepts that children are engaging in, and (5) accessible summaries of research about young children and mathematics. The following post is of the first type.]
 
Four Super Simple Counting Games

Hidden Objects: When your child has counted a number of objects, hide them by covering them with your hand, a blanket, a bowl, or a book, or simply turn around with your child so you can no longer see. Ask, “how many are there?” and see if they give you the same number.
  • Why? Part of learning to count is recognizing that the number you say is how many there are, and that objects don’t have to be seen to have a count. Seeing whether your child can tell that the number of hidden objects is the same as the number they counted gives you insight into what they understand about counting. 
  • Variation: After your child has counted a set of objects, mix the objects up, push them closer together, or spread them farther apart, and ask how many there are. Early on, a child will recount the set. With counting experience, though, they will learn that moving objects around doesn’t change how many there are. 
Guess the Number: Ask your child, “How many [crackers, birds, toys] do you think there are?” Then count together to see how close the guess was.
  • Why? Build number sense! It’s horribly difficult to tell the difference between, say, 12 and 13 at a glance. But a collection of 7 things looks very different from a collection of 15 things. Guessing before counting can help children to get a sense of the relative size of different quantities. 
  • Variation: Give a child two options. For instance, if there are 6 swings at the park, ask, “Do you think there are 6 swings, or do you think there are 10 swings?” 
Now How Many? If your child is counting objects that you can manipulate (beans, toys, spoons, etc.), take one away or put one in after your child has counted and ask, “Now how many are there?”
  • Why? This will help your child learn how to utilize the number sequence for simple addition and subtraction. Initially, children will need to re-count the set of objects, and that’s okay! Be sure to remind them how many there were before, and how many there are now. Eventually, your child may realize that all they have to do when you put one in is to say the next counting word, and all they have to do when you take one away is to say the previous counting word. 
  • Variation: If a child can play “Now How Many?” without recounting, begin removing or adding two objects at a time, or even three. 
Backward and Forward: Count steps as you’re walking. Stop on a certain number of steps and walk backwards, counting down. Make a game of it, counting up for walking forward and down for walking backward. When they get the hang of it, let your child lead.
  • Why? Being able to count backward is an important skill for early arithmetic. It also helps solidify a child’s familiarity with the number sequence. 
  • Variation: Count when you walk up or down stairs with your child. If you’re walking up or down an unfamiliar flight of stairs this could also be combined with “Guess the Number.” Guess how many stairs there are, and then count (up or down) to see if you’re right. 

Wednesday, January 22, 2014

9 Month Picture Flood

I haven't been posting month-by-month shots consistently like I used to, partly because there was about a 3-month period where it was impossible to get Miles to sit still in his bouncer. But with age comes the ability to hold still and pose for the camera, if we can be quick about it, and it's so fun to see how much Miles has grown and changed in such a short time.

(Click the picture for a better view.)

That particular photo montage is still a month behind (the snapshots are 1 month, 4 months, 8 months respectively), and Miles has now very decidedly been alive longer than he gestated, by several weeks. That seems like a significant milestone.

For family and friends who are interested, here are some current Miles pictures, from the last month-and-a-halfish.


Cuddle-bunny. When he's tired, Miles is a great cuddler, and having him curl up on my chest is one of my favorite things in the world. I hope it doesn't go away too soon.

These days he climbs on anything and everything - shelves, couches, laundry baskets, garbage cans, boxes, his carseat.

First visit with Santa at the ward Christmas party. Look at the beard. This guy's the real deal.

This boy sure does love his bottle. And I sure do wish I could figure out how to rotate pictures in Blogger.

Trax!

Salt Lake visit with Grandma and Grandpa Tanner and the Hackings (not pictured, but they were there).

His favorite toy is the washing machine. Whatever the crawling version of running is, that's what he'll do the minute he sees you open the washing machine door.

Miles' favorite Christmas present.

His other favorite Christmas present. Almost a month later he still plays with it every single day. Judging by friends' pictures on Facebook, this was THE Christmas gift of the moment for babies his age.

Still trying to figure out how it works.

Cousins are so fun!

Miles loves his new big-boy baths. Am I supposed to put things like this on my blog? Miles, if this comes back to haunt you as a teenager, I'm sorry. But only a little, because I think this picture is so cute.

He loves his daddy!

And he loves dinnertime. He joins us at the dinner table most evenings now, for a baby puree and some tastes of whatever we're eating. Miles loves trying new foods!


Sunday, January 12, 2014

Fifty(four) Books

My New Year's goal at the beginning of 2013, because I anticipated a bit more down time than I was used to with my long maternity leave, was to read 50 books. And even though having a baby around takes up more time than you ever expect (and I even knew to expect this, but you still don't believe it until it happens), by December 31 I had managed 54. Even if you don't count repeats, it was still 51. So just for fun, here's my master list. My personal favorites are highlighted, but I liked most everything I read. There are quite a few non-highlighted books I'd still recommend, and very few I absolutely wouldn't (Divergent and Allegiant, for example...but apparently tons of people love the series and they're making the first into a movie this summer, so maybe you will too. But it's no Hunger Games...). Starred books are re-reads.

Fiction
Cloud Atlas by David Mitchell
The Age of Miracles by Karen Thompson Walker
Sharp Objects by Gillian Flynn
The Cloud Atlas by Liam Callanan
The Snow Child by Eowyn Ivey
Anathem by Neal Stephenson
Middlesex by Jeffrey Eugenides
Ragtime by E.L. Doctorow
The Round House by Louise Erdrich
Eleanor & Park by Rainbow Rowell
The Taliban Cricket Club by Timeri N. Murari
Silver Sparrow by Tayari Jones
Good Kings Bad Kings by Susan Nussbaum
The Storyteller by Jodi Picoult

Classics and Minor Classics
I Capture the Castle by Dodie Smith
The Talented Mr. Ripley by Patricial Highsmith
The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson
Childhood's End by Arthur C. Clarke
And Then There Were None by Agatha Christie*
Wuthering Heights by Emily Bronte
The War of the Worlds by H.G. Wells
A Prayer for Owen Meany by John Irving

Children's and YA Fiction
The Book of a Thousand Days by Shannon Hale
The Fault in Our Stars by John Green
The Last Dragonslayer by Jasper Fforde
Never Fall Down by Patricia McCormick
Gregor the Overlander by Suzanne Collins
Divergent by Veronica Roth
The Westing Game by Ellen Raskin*
Evolution, Me & Other Freaks of Nature by Robin Brande
The Book of Lost Things by John Connolly
The Lemonade War by Jacqueline Davies
Mrs. Peregrine's Home for Peculiar Children by Ransom Riggs
Allegiant by Veronica Roth
Caroline by Willo Davis Roberts*
Unwind by Neal Shusterman

Nonfiction
Wild Swans: Three Daughters of China by Jung Chang
Nothing to Envy: Ordinary Lives in North Korea by Barbara Denick
The Checklist Manifesto: How to Get Things Right by Atul Gawande
Candy: A Century of Panic and Pleasure by Samira Kawash
Big in China by Alan Paul
Bossypants by Tina Fey
Lean In by Sheryl Sandberg

Parenting, etc.
The Happiest Baby on the Block by Dr. Harvey Karp
Bringing Up Bebe by Pamela Druckerman
Bottled Up: How the Way We Feed Babies Has Come to Define Motherhood, and Why It Shouldn't by Suzanne Barston
French Kids Eat Everything by Karen LeBillon
And Baby Makes Three by John and Julie Gottman
Expecting Better: Why the Conventional Pregnancy Wisdom is Wrong--And What You Really Need to Know by Emily Oster
Feisty Fido: Help for the Leash-Reactive Dog by Patricia McConnell (owning a dog is a little like parenting...)

Essays and Short Stories
The Best American Essays 2011 ed. Edwidge Danticat

Graphic Novels
Blankets by Craig Thompson

LDS/Religion
The God Who Weeps by Terryl and Fiona Givens (nonfiction)
The Reluctant Blogger by Ryan Rapier (fiction)






Aiming for quantity didn't really lend itself to long reads (although I did manage to get in some - A Prayer for Owen Meany, Anathem, Three Daughters of China), so this year I think I'll relax my quantity expectations and mix in some length. I'm also not going to worry too much about meeting a reading goal, since I'm back to work full time and balancing work with motherhood for the first time ever. But I'll still read, 'cause that's what I do. Any recommendations?


Sunday, November 24, 2013

Day 8: Object Lesson

 
On Friday morning, at a professional development in Park City, each of our groups was given a deck of cards and told we had 15 minutes to try to build the tallest tower. About 11 minutes in our group was going strong when our possibly-tallest tower collapsed (my fault). With nothing to lose, we threw caution and our sense of structural engineering to the wind, and in 4 minutes we had a tower taller than any of the 15-minute towers in the room. I feel like there's a moral or two to that story.