Down the rabbit hole of pretend play? [Week 2 Task]

[Maria Droujkova]

Several parents expressed concerns about kids abandoning math for pretend play or context. Did it happen to your child?

PLEASE REPLY TO THIS THREAD WITH AN EXAMPLE OF YOUR CHILD GOING FROM MATH INTO PLAY

You can just hit "reply" under this email. Then, we will follow the child down that rabbit hole - only to find even more math in the land of play.

Here are two recent examples.

~*~*~*~*~*
Yesterday, Kirsten wrote:
Today's lesson in our household was borrowed from toddlertoddler.com (the specific activity was http://toddlertoddler.com/todaysbutterflies.htm). My husband is a corporate pilot, so we chose the airplane printout. The only problem is that Hailey kept saying "DADDY PLANE!!!" instead of identifying the individual numbers. Cute, but not....counting.... :)

---
Here is the picture from the site:


How to play mathematically with DADDY PLANE? Hailey ran away from counting planes into looking at them as pictures. Let's follow her, with some math.

• Get a toy daddy plane or get a picture. Ask Hailey to prepare stickers for the wings (flags, stars, any other decorations). She will probably prepare a whole lot at first; explain that in this game, planes only have one picture of each kind per wing. If she prepares, say, three stars, don't tell her she's wrong. Just put one star on each wing and tell her: "Oooh, there is a star left!" Next, ask her to prepare another type of sticker, just enough for wings. Take turns with you doing it, too, and making mistakes for fun. Or you can prepare enough seats on the plane for the whole family to fit there.
  
• Get another object she likes, say, a butterfly. Now, prepare enough stickers for butterfly wings!
  
• Ask Hailey to pick another object she likes and prepare something for it.  Shoes for a ladybug? Nail gems for her hand? A flower lei for each head of Cerberus the three-headed dog?

Support Hailey's wish to pay attention to what objects are.

~*~*~*~*~*
Last Thursday, Megan wrote:
FRACTIONS: I only have one idea here and it's pretty plain - would love to hear more. When you're offering your child a fruit, e.g. an apple, asking if they want 1/2 an apple (a butterfly), or a 1/4 (a boat). And same thing for when asking them how much water/milk they want.

Mick replied:
One question though, why do you refer to them as "boat" and "butterfly"? Wouldn't it be just as easy to learn "half" and "quarter" (that even has less characters)?

---
Every time we have a math club, we do "apple math" during snack time. And every time most of the kids, some of them already contemplating topology, infinity, equations and other lofty topics, still go into image play such as calling a piece of an apple "a boat." To answer Mick's question: for the majority of kids, it is not easy at all to learn without such pretend play. Moreover, there is a lot of rich mathematics in these games, famously described by Lewis Carroll's phrase: "Why is a raven like a writing desk?"

Here are a few pretend play games you can do with images:

• Half an apple like like a butterfly. What about half a pear? Half a cube? Half a ball? Cross-sections are hard to visualize, and comparing them to rich images makes the process easier. You can cut real objects, paper shapes, or clay models.
  
• Kids naturally use imagery to remember new symbols! For example, 8 may remind them of a person and 1 of a spear. They like to draw pictures around symbols. Or play with smiley faces - pictures made OUT OF symbols! Here is Princess Leia from Star Wars:
  @(*-*)@
  and here is a cat:
  >^..^<
• Scavenger hunt. What else around you looks like a boat? How about a triangle? What looks like a butterfly? What looks like a cylinder? See what I am doing here - this pretend play develops the same skill that is used for noticing properties, sorting, and taxonomies!
  

~*~*~*~*~*
I am looking forward to your examples!

Cheers,
Maria Droujkova

Make math your own, to make your own math.

 

[Yelena McManaman]

This is what happened today - we played a sorting and comparing game. First, I emptied the pantry and put all the cans into one corner of the kitchen. I gave Mark a set of pink, yellow and green dot stickers (leftovers from when I was doing a garage sale last year). Then we decided that big (tall) cans will be marked with pink stickers, medium-sized ones - with green stickers and small ones - with yellow stickers. We also agreed that after a sticker was taped to the top of each can, it will be rolled to its proper storage space on the floor (we marked those with painter's tape). We had a total of about 20-25 cans.

 

Here's how it went - first, Mark would choose a can from the big pile and estimate its size. He then would compare it to an already-marked can to make sure that his estimate was correct. He marked it with a sticker and sorted into the proper storage place. Everything went smooth until one of the piles (large cans) got about 10 or so cans in it.

 

At this point he started building a tower with the cans, but also continued sorting. Once all the cans were sorted, he built a space ship out of them (the Axiom, from Wall-E movie) and designated one of the smaller tuna cans to be the evil autopilot Auto; a can of condensed milk became Eve ('cause it's white) and a can of beans (brownish color) - Wall-E.

 

- Yelena

[Megan Haggerty]

Thanks so much for the reply on the apples: 1/2 and butterfly - I didn't know the reason why we did this with my neice (age 2-4), but I knew it worked when used in tandem.

For my own child, she's just 6 months, so I find that for the most part I'm just enjoying getting ideas for the future from you all. Two things, beyond counting, that I've been trying to do:

1. I use sign language. Particularly for "more" and "all done/all gone" - concepts of amounts and time really.  At 6 months, babies start to be able to use their hands - and these are two symbols she can use. (and milk and diapers are two others...but they're not mathematical concepts).

2. during shower time, we have 3 ducks lining the tub. She knocks off each one, and knows that the last duck to go in the water means the end of bath time. sometimes i count 1-2-3. But really, its the idea that there are no more.  We do the same thing when she's eating...we show her her bowl when there is food, and then when it is all-gone. And she knows! and only fusses when she has time/food left.

[Maria Droujkova]

On Thu, Feb 3, 2011 at 7:52 PM, Yelena McManaman <yelena.m...@gmail.com> wrote:

This is what happened today - we played a sorting and comparing game. First, I emptied the pantry and put all the cans into one corner of the kitchen. I gave Mark a set of pink, yellow and green dot stickers (leftovers from when I was doing a garage sale last year). Then we decided that big (tall) cans will be marked with pink stickers, medium-sized ones - with green stickers and small ones - with yellow stickers. We also agreed that after a sticker was taped to the top of each can, it will be rolled to its proper storage space on the floor (we marked those with painter's tape). We had a total of about 20-25 cans.

 

Here's how it went - first, Mark would choose a can from the big pile and estimate its size. He then would compare it to an already-marked can to make sure that his estimate was correct. He marked it with a sticker and sorted into the proper storage place. Everything went smooth until one of the piles (large cans) got about 10 or so cans in it.

 

At this point he started building a tower with the cans, but also continued sorting. Once all the cans were sorted, he built a space ship out of them (the Axiom, from Wall-E movie) and designated one of the smaller tuna cans to be the evil autopilot Auto; a can of condensed milk became Eve ('cause it's white) and a can of beans (brownish color) - Wall-E.

Sounds like fun! Did you take any pictures? You can just attach pictures to this group's emails.

It also looks like Mark was ready and wiling for more complex sorting tasks at this point! One that immediately comes to mind, within this game, is stacking cans of smaller and smaller radii on top of one another for a spaceship. Is it what Mark did? If so, you can use the pretty word GRADIENT to describe the result.

You can also sort cans by other dimensions. They are 3d, but because they are cylinders, their widths and lengths are always the same (the top and the bottom are circles). However, the height is different, and interesting! Some cans may be wider than others, but shorter. So if you sort by heights, it's one gradient and if you sort by radii (as you naturally would for building a spaceship) it can be another gradient, another order. What would Mark make of this discrepancy in his game?! Ask him what he thinks and let us know!

Another complex sort has to do with characters. You have three - Auto, Eve and Wall-E. Put them at the top row of a grid. Some floors have grid patterns, or you can just draw a grid on a large piece of paper. Now start filling each row with their objects. For example, a plate for Auto, a plate for Eve, a plate for Wall-E. Use cups, spoons, forks, etc. You will soon make a grid that you can "read" by rows or columns. This prepares kids for coordinates. For example, "Eve's cup" is in the second column, third row. I attached a picture. It's more fun if you can make sorting a part of the story, but I don't know the story of Wall-E enough to make up anything but sizes. Wall-E gradients, anyone?

[Maria Droujkova]

On Sat, Feb 5, 2011 at 11:49 AM, Megan Haggerty <megan.h...@gmail.com> wrote:

Thanks so much for the reply on the apples: 1/2 and butterfly - I didn't know the reason why we did this with my neice (age 2-4), but I knew it worked when used in tandem.

For my own child, she's just 6 months, so I find that for the most part I'm just enjoying getting ideas for the future from you all. Two things, beyond counting, that I've been trying to do:

1. I use sign language. Particularly for "more" and "all done/all gone" - concepts of amounts and time really.  At 6 months, babies start to be able to use their hands - and these are two symbols she can use. (and milk and diapers are two others...but they're not mathematical concepts).

Baby signs can be so powerful! Some parents are concerned that signing may delay speech, but it's the opposite. The reason is that signing develops the same brain structures that support speech.

There are several books and online communities on baby signs. However, if you just observe the gestures babies do, and repeat them, signs develop naturally. Each family has their own set of signs, by the way. This is normal.

One mathy play babies and toddlers like is "driving" parents by signing directions. I play this on stairs, with the kid in hand. When the baby gestures "up" I move one step up, and when the baby gestures "down" I go down. You can combine this with "all done" when you run out of stairs. To show how this works, gesture with the baby's hand.

We also played this with paper "remote control buttons" (arrows up and down) I taped to myself where the baby could reach. And if the baby pressed twice in a row, I would walk two steps.

This is a prep game for coordinates. You can also play it with walking forward and backward and sideways, one step at a time, for example, if you have to wait.
 

2. during shower time, we have 3 ducks lining the tub. She knocks off each one, and knows that the last duck to go in the water means the end of bath time. sometimes i count 1-2-3. But really, its the idea that there are no more.  We do the same thing when she's eating...we show her her bowl when there is food, and then when it is all-gone. And she knows! and only fusses when she has time/food left.

This is amazingly cool. So, your baby knows ZERO!

Zero games are fun. Clap with baby's hands, etc. and a toddler or a young child can clap for herself.

Let us clap two times (clap, clap). Let us clap three times (clap, clap, clap). Now let us clap zero times! That's when a lot of giggles happen!

I have three ducks in the tub. I have two shoes by the tub. But see, I am hiding zero elephants in my hand! Want to see? Open your hand, which of course will be empty. Giggle!

Can you splash with one hand? Can you splash with two hands? Can you splash with zero hands?

I found these zero games in John Holt's "How children learn" and they are even fun for seven-year-olds or so. Babies love them too if you joke with them and laugh and have fun.

[Yelena McManaman]

I didn't even think of gradients! I learned the word when I was already in college and hating math and I think I still have this fear of gradients. I'm attaching the picture. BTW, after finishing the Axiom, we decided to build a robot with an empty can and all sorts of junk. I'm attaching the picture of the end product. Mark's job was to design it and mine - to hot glue everything exactly as Mark would tell me. This was a good exercise in learning why symmetry is so important (without making the robot symmetrical, we couldn't balance it). Also, Mark insisted on making round tire tracks. But after a while trying to balance his bot, he realized that he'd have to squish the tires to make them flatter on the bottom. Turns out, cylinders are great for rolling, but not the best for keeping the bot upright when it doesn't move.

 

I love the idea of building a grid with physical objects (as opposed to just drawing a table - something that Mark avoids as much as possible for now). And it can be combined with gradients, I guess. I think Mark will love it as well. I'll try it and will let you know.

 

- Yelena

[Mick Weiss]

On 2/5/11 6:04 PM, Maria Droujkova wrote:
>>
>> 1. I use sign language. Particularly for "more" and "all done/all gone" -
>> concepts of amounts and time really. At 6 months, babies start to be able
>> to use their hands - and these are two symbols she can use. (and milk and
>> diapers are two others...but they're not mathematical concepts).
>>
>
> Baby signs can be so powerful! Some parents are concerned that signing may
> delay speech, but it's the opposite. The reason is that signing develops the
> same brain structures that support speech.

From what I've seen, signing could possibly delay speech. I know two
parents who have had issues with their child not speaking (I forget the
exact age) -- the child preferred to sign and simply refused to talk, so
I guess every child is different.

I went with the approach of giving some important things simpler names.
A bottle is a "nee nee" (those are sounds that even the smallest of
babies can make).

I don't think that it is a coincidence that words like "Mama" and "Papa"
work across so many cultures- they are simple enough for most babies
from most any cultural background.

If pointing counts as sign language, then I guess I did sign with my
son. I chose to talk a lot to my son and explain everything around him.
I forget exactly when my son said his first word, but it was relatively
early.

I'd like to know if any other parents signed with their children and how
the did or didn't affect their speech development as they were getting
older.

My data set that I'm working with is too small for any real statistical
analysis or concrete conclusion on the topic.

- Mick

[Maria Droujkova]

On Mon, Feb 7, 2011 at 12:33 AM, Mick Weiss <p2...@mickweiss.com> wrote:

On 2/5/11 6:04 PM, Maria Droujkova wrote:
>>
>> 1. I use sign language. Particularly for "more" and "all done/all gone" -
>> concepts of amounts and time really.  At 6 months, babies start to be able
>> to use their hands - and these are two symbols she can use. (and milk and
>> diapers are two others...but they're not mathematical concepts).
>>
>
> Baby signs can be so powerful! Some parents are concerned that signing may
> delay speech, but it's the opposite. The reason is that signing develops the
> same brain structures that support speech.

From what I've seen, signing could possibly delay speech. I know two
parents who have had issues with their child not speaking (I forget the
exact age) -- the child preferred to sign and simply refused to talk, so
I guess every child is different.

Thank you for sharing. As you said at the end, the data set is small: there is no way for these families to know what would have happened without signs. They would like for their kid to speak earlier - but would it happen without signs? Only statistical studies can answer this, and they show no delays across the board - at least those I've seen. I would be interested in learning more.

Having said that, there IS a period when signing babies keep their old signs for months or years after they can speak. Actually, they tend to use gestures as they get older, as well. Gesturing is a respected part of rhetoric, IF you use it well. As kids get older (4-6), as a part of learning to give speeches, to tell stories, to present at science fairs you can polish gestures, too.

Another difficulty you can observe happens when kids transfer from speaking mostly to their primary caretakers (parents, nannies) to speaking with everybody. Those of us who have older kids know this period to be difficult, especially for introverted kids. Translating gestures can help a lot - so, repeating common words and gestures after you respond to the "baby sign."

Stopping to react to previously understood and loved "family language" is not a good way to teach toddlers the common language. None of the psychologists who worked with baby signs recommended this as a tool. The good way: show that you understood the sign, repeat in the common language, react as usual if it's a request or a part of the conversation. The same works the best for foreign language training!

I went with the approach of giving some important things simpler names.
A bottle is a "nee nee" (those are sounds that even the smallest of
babies can make).

This is a great way to construct your own baby/family language, as well! 

I don't think that it is a coincidence that words like "Mama" and "Papa"
work across so many cultures- they are simple enough for most babies
from most any cultural background.

If pointing counts as sign language, then I guess I did sign with my
son.

Pointing is as universal a "word" as "mama"! I bet you used more sign than one, though :-) Because adults use gestures too. How about "good-buy" or "no" - were there gestures?
 

I chose to talk a lot to my son and explain everything around him.
I forget exactly when my son said his first word, but it was relatively
early.

I'd like to know if any other parents signed with their children and how
the did or didn't affect their speech development as they were getting
older.

My data set that I'm working with is too small for any real statistical
analysis or concrete conclusion on the topic.

- Mick

I will start. We used signs and gestures as they came up. I just repeated a gesture I noticed Katherine making, as well as sounds. I helped her choose toys or clothes for the day by pointing, which she understood. Sometime around a year, we also got touch screen for her computer (which we kept on the floor) and pointing became the way to play toddler and young kid games, such as Living Books (point at a word and it's read to you) or mazes (point to a spot and the character goes there) or simple puzzles. Katherine started to say some words out loud at nine months, but gestures, and now graphic representations (diagrams, mind maps) are still a big part of her expression and thinking. She's twelve years old.

Here is an episode from when she was 13 months. We went to Florida and Katherine was hugely impressed by a palm tree, which she has not seen before. She played with the "hairs" on the trunk for a long time. Then turned to me, pointed at the trunk, did her gesture for "cat" (stroking the air as if petting a cat) and her gesture for "looks like" (tapping the right index finger on the left hand). I laughed: "The palm tree trunk looks like a fluffy cat, eh?" She said "Yes" happily.

We often had longer conversations of this sort with the help of our signs, our private words, and common words.

[Maria Droujkova]

Thanks so much for sharing your pictures, Yelena! It's like we got to visit with you briefly!

On Sat, Feb 5, 2011 at 8:08 PM, Yelena McManaman <yelena.m...@gmail.com> wrote:

I didn't even think of gradients! I learned the word when I was already in college and hating math and I think I still have this fear of gradients.

Here are a few baby and young child toys and games that use gradients and grids with two-dimensional gradients... Tell your browser to show the pictures in this email if you don't see them.

Gobblet Junior http://www.amazon.com/gp/product/B0000E1P87/

We made our own boards in the math club, which kids loved. Cylinders are easy to make for 3-4yo. We made them without the tops.

Matryoshka dolls! And if you have several, you can make a grid (two-dimensional gradient)


Many shape sorters use gradients. Montessori has a lot of them. Here is an example of a grid sorter: https://www.littlezenminds.com/large-shape-sorter-board-from-haba.html


Again, I find it more fun to make our own boards and shapes, because we can customize them to our pretend play!

A Montessori sorter with loooong gradients: http://www.amazon.com/Kid-Advance-Co-SE004-Montessori/dp/B003KWBV3A

I'm attaching the picture. BTW, after finishing the Axiom, we decided to build a robot with an empty can and all sorts of junk. I'm attaching the picture of the end product. Mark's job was to design it and mine - to hot glue everything exactly as Mark would tell me. This was a good exercise in learning why symmetry is so important (without making the robot symmetrical, we couldn't balance it). Also, Mark insisted on making round tire tracks. But after a while trying to balance his bot, he realized that he'd have to squish the tires to make them flatter on the bottom. Turns out, cylinders are great for rolling, but not the best for keeping the bot upright when it doesn't move.

From math to engineering, now! Good call!
 

 

I love the idea of building a grid with physical objects (as opposed to just drawing a table - something that Mark avoids as much as possible for now). And it can be combined with gradients, I guess. I think Mark will love it as well. I'll try it and will let you know.

This is the general principle of working with kids. Try multiple ways of working - physical objects, large motor movement, drawing, stories, sounds...

Cheers,
MariaD