Wednesday, June 20, 2012

How Awesome is Measuring?

How we describe the world is incredibly important. This has been a recurring theme for me in everything from therapeutic psychology (where how we describe our processes and history becomes an integral part of how we experience our lives) to my tempestuous love affair with Science (the procedure for hypothesis testing demands precise measurement, and yet how we define our variable and even the act of observing our variables may alter their measurement. Oh Science, you magnificent tease!).

For the preschool set, measurement is important because it integrates a bunch of early math components, and yet it is easy enough for them to do on their own, and is one of those things, like knock-knock jokes, that they seem to happily incorporate into their everyday life so frequently you might wish you had never handed them a ruler. There's counting, obviously, but also the thrills of comparing which helps them understand the importance of the ordinal/relational quality of numbers. The other thing about measuring is that it is so useful in the sort of simple experiments which we do in investigative learning. I've showed them how to measure before, used it in some of our exploratory play, but I had never just talked about measurement in general. And since I love nothing more than a meta investigation, I decided to get them going exploring the idea of precise ways to describe their world.

Footwear Measurement is vital.

Printable Rulers, cut out
half sheets of paper folded and stapled to make observation books
stuff to measure!


1. I printed and cut out the rulers- I thought about trying to dig out some wooden rulers, but these were nice because the kids could wrap them around objects.

2. I made them each a book to write down their observations. I've been trying to get them interested in keeping a science journal, but so far they seem to only use them if I make a little mini-book for each project. I hope that this at least will help them get into the habit of recording their observations. Only one kid is ready to start trying to write and sound out words, so I suggested that they draw a picture of the object and write out its measurement in numerals.

3. I set them loose!


Baby Tiger is 7 inches long- I didn't even need Alex's translation!
Alex particularly loved this project, which was especially nice because unlike Anya, he is not terribly interested in practicing how to write numbers. But when it is in the name of science, he was all over it!

He was stymied by a box that was longer than his ruler. When I asked him if he could think of ways to measure it, he suggested we cut it up and measure the pieces, but was dismayed at the thought of losing the box in the process. I had to hold my tongue not to bring up Schrodinger's Cat which is a bit much even for me to wrap my head around! But the essence of the problem (precise observation altering the subject) seems similar enough that I was tempted! Eventually I showed him how to mark the spot where the ruler ended, measure the remainder and add the measurements together, but he's not quite there yet in terms of comfort with the idea of addition. He was really excited when I did it, though, and went back to measuring smaller things with even greater enthusiasm.

Anya measured her shoe collection almost exclusively, and measured them in ways I was not expecting, which was cool.

She lost interest pretty quickly, but went back to it after she saw Alex still excited ten minutes later.

She also suggested that we could start measuring our trees, and came up with some interesting ways that we could do so, involving Luke scaling to the top and dropping down a very long measuring tape. I told we could measure how high he goes in them next time he's pruning.


After they spent about 45 minutes measuring things, we watched a clip from Sid the Science Kid about measuring, and we talked about why measuring is important. I framed it in terms of hypothesis testing. Recently we had been talking about plants that could continue to grow in water, like green onions after you cut them, and the kids were insistent that they didn't need soil at all and we could plant a water garden. I told them that I thought they would grow more in the soil, and that only certain plants would grow in the water. To show them how measuring could be used to precisely describe the world, I explained that we could try one onion inside and another outside and observe. They both immediately understood that the bigger one would show whether soil or water was best for the plant's growth, but it was only after I mentioned that there might be very little difference that Anya grabbed her ruler and said we could measure the difference to see even a little change.

This brought to mind our chicken scratch notes on the kitchen doorway showing the kids' heights over time. We marked their heights again, then measured the amount that each had grown since last year, as well as the difference between them. I showed them how to use the metric and imperial units. I think the idea of comparisons over time and between individuals became real to them during this part, which was awesome. I hope that we will be referencing the stuff we learned today in our projects in the future. I also really want to find a kid friendly scale! More dimensions! More measurement!

Tuesday, June 5, 2012

Flower Challenge

Tinkerlab is an awesome blog about fostering creativity and hanging out with kids doing cool stuff. I've come to rely on Rachelle's fun activities and inspiration, as well as enjoying her perspective. This mommyblog thing is a delicate line to walk- how to write passionately about your beliefs and children without coming off as judgmental about other perspectives or styles; how to talk honestly about the good and the bad, the mistakes and the failures; how not to fall into the trap of bloggy narcissism; how to write about the good stuff without causing others to hateread your blog and doubt your words. Tinkerlab is a keeper, walking that line with a grace and an enthusiasm  that I find infectious.

One of the awesome community-building projects she does over there are her Creativity Challenges, in which she invites other parents to write and link to creative projects related to the theme of the challenge. Unlike the types of projects I typically blog about, these challenges should be child-driven; that is, that the children should initiate and follow through with their own creativity, rather than participate in an activity that the parent/teacher designs and sets up. I love the idea of child-driven work, and my kids certainly do a ton of it on their own, but I seldom set up "invitations" as many child-driven parents do. I prefer, because of my own temperament and the pressure of working from home with no child care, to do slightly more structured work, activities, and then let them children take it wherever they want. I haven't taken part in the previous challenges partly because I imagined that if I tried just setting them loose on a totally child-driven challenge, that they would go in opposite directions and want me to follow- a pretty common problem in raising twins! But on the way home, as we were talking about flowers and root systems, I decided to go for it and join in on the Flower Challenge.

I explained the idea behind the challenge, and at first Anya did not want to do it because she thought the word challenge meant it would be a competition. She's not naturally averse to competition, in fact, both of them are so fiercely competitive that any whiff of there being a winner and a loser and there is sure to be a knockdown drag-out fight- Anya has learned that to maintain her awesome relationship with Alex, they need to just stop competing. I wonder if her dad and uncles will ever learn that! But when I re-framed it as a challenge for her mind to think of cool creative fun projects to do with flowers, she got on board. We talked a little about how they could think of learning experiments to do or questions to ask and try to solve about flowers, or they could gather flowers and do something with them, or they could make flowers out of something else. They decided to gather flowers, and Anya wanted to decorate our windows with them, while Alex wanted to attach the flowers to a piece of paper and paint a scene to go with them.

I asked Anya how she would like to attach the flowers to the window- we couldn't use contact paper because the flowers she were quite large, and she first wanted to use glue or starch, as we had with tissue paper window decorations in the past. Eventually she decided on tape, so I got her set up with some packing tape and left her to work on it while I helped Alex get his paint set up.

Alex arranged his plant bits on his paper and started gluing them, then painting in the scene, then gluing, then painting and so on. Alex is a kid who imagines all kinds of wild scenarios and is usually the driving force behind the complex imaginary games they play, and who spends hours designing and taping together robots made from the recycling, and who will dictate ten page stories to me every chance he gets. So I was surprised to see that he decided to create a very naturalistic scene where the bits of plants were representative of whole plants. The only exception is the dandelion puff as a storm cloud, which may have been influenced by me commenting on a similarity the other day. He's been fascinated with rainbows since we saw two different double rainbows on our drive home from Upper Michigan last week, so he created a sunny and rainy day, but then didn't want to paint a rainbow because he was worried he wouldn't be able to do it without ruining the rest of the picture that he was so pleased with. Kind of a bummer of a feeling, but I didn't want to push him as he seemed to drop it quickly and move on (which is rare for my ruminative son!). I will probably do a more focused project on rainbows, and hope that builds some confidence for painting them.

Alex's Sunny and Rainy Day

Anya came over while Alex was working, and decided that his project looked like more fun, so he gave her some of his collected flowers, and she went out with me to pick some more. She started with a large flat dandelion leaf and immediately declared that it was the grassy hill. This was also surprising, since Anya is often a very literal kid, and I fully expected her to glue the flowers down and paint a vase to hold them. She was playing with a magenta bloom, looking at it from different angles and seemed unsure of what to do next. I asked if it looked like anything and she decided it was a fairy skirt. Once she had that decided, she was eager to go hunt for some petals to be the wings and a round flower to be the head. I let her pick two fresh iris petals, despite the usual picking ban on my favorite flowers, because I knew how perfect they would be as wings- see, I kind of suck at child-driven... I just want to get in there and do it with them! She glued them in herself, and I took myself over to Alex so I wouldn't be tempted to interfere with her vision for the fairy.

Fairy Seeing Flowers She's Never Seen Before by Anya

It ended up being a really fun project, and I love it when my assumptions about the kids are challenged!

Monday, June 4, 2012

Princess Feet

A good friend introduced me to Katy Bowman's work on biomechanics and body alignment a couple of months ago, and I've found her work to be fascinating and incredibly helpful, not just for my own issues, but as a healthcare provider. Many of her posts on the importance of healthy body alignment and the effects of one part on the entire system compliment my own interest in the importance of  breathing technique and body position in working with issues such as pain, anxiety and decreased oxygenation, especially during recovery and physiological stress.

One of the subjects which Bowman talks about frequently is the importance of walking, squatting and the cascade of problems which positive heeled shoes can cause. I was never a big fan of heels, and have been carefully considering the angle of my shoes ever since. But my fashion sense has always been decidedly...unfashionable. I cannot say the same for Anya, and preschool girls have some very particular ideas about what to wear.

The Princess Years

Yesterday morning, my 4-year old daughter wobbled into the room wearing a princess tutu, a princess tiara and one of the 6 pairs of cheap plastic princess heels she was given for Christmas last year. I had thought she forgot about them when I buried them in the costume box, quarantining them from the real shoes. I have socio-political issues with girls and princess culture. My kids know that I hate princesses, know that I dislike that princesses rarely save themselves in stories, are considered special simply by the circumstances of their birth or because of their beauty. When I explained the problems of a monarchy vs. a democracy, Anya was the first to chime in that the people should decide who the leaders are. And yet. The princess culture in the preschool set is overwhelming, infectious, and all-consuming. The fixation with prettiness is problematic but workable; the conflation of "pretty" and "fancy" with "princess", and "princess" with the requirement of pretty above all else!!!1!- that is the spiral of death by pink for me.

When Anya wobbled in in that outfit, all smiles and pride in how pretty she was, I knew I had to pick my battle; all out War, Mom vs Princess was asking for an epic loss. I told her how beautiful the dress was, how impressed I was that she had created a whole costume for herself, and how beautiful she was when she was pretending to be a princess AND when she was being regular Anya. She asked what I thought of the shoes. I told her that I didn't like high heel shoes because the heels were no good for running and no good for the muscles, bones and the whole body.

She twirled for me a couple of times, then wobbled her way out.

Be free!
A minute later she wobbled back in and said, "Why are my pretty shoes not good for my body?" I know what to do with that kind of soft pitch! I leapt up and showed her where her hamstrings are, showed her how to feel them stretch, pointed out where they attached to the skeleton- we did a great activity using a little movable guy with rubber bands attached to his bones to represent muscles and how they move bone, which I'm just realizing I never blogged about- and she was fascinated. Then we lay down and held up our legs to look at the angle of our feet and how a pointed toe shortened the length of our hamstrings. I talked to her about how walking like that and never stretching them out would make the muscles get tighter and shorter, till it was so bad that our feet couldn't even get into a neutral position without some effort on the part of our muscles. And, by the way, our lesson on simple machines has totally come in handy- the kids now often differentiate between things that take work from our muscles and things that don't!

Next, I did some silly poses to try to show her how the whole body has to compensate for the forward lean of the body standing on heels. Katy Bowman's illustrations are better than my clowning around, but when your audience is 4, a little mama slapstick goes a long way towards remembering a complex lesson!

Anya wobbled back out to the living room, then returned, without the heels and said, in the most woeful voice ever, "But how can I have princess shoes if they are bad for my body?" I took her out to examine her shoe collection and tried to push the hot pink, turquoise glittered light up sneakers as sufficiently fancy for a princess. Anya was not impressed.

Then I had an awesome idea.

Princess Feet

"I think that princess FEET are even cooler than princess shoes, don't you?" She looked doubtfully at her feet. "I can make your feet extra fancy and special!"

I collected up red, pink and purple markers, a washable glue stick, gold glitter, and two colors of nail polish. I painted her nails and drew suns, hearts, flowers and swirls all over the tops of her feet, then rubbed some glue stick over the top and went to town with the glitter. She was beyond thrilled.

We went outside to test out her new princess feet. It turns out that not only are princess feet cool-looking and fun to create, but you can run in them way better than in high heeled princess shoes.

 We also did some careful scientific tests of climbing, playing, skipping and hammock pushing. Princess feet outshone princess high heels in all the categories!


Wednesday, April 18, 2012

Marbling Paper

I love the look of marbled paper like Suminagashi, but have been put off by the unknown chemicals and hassle of getting pre-made kits- I was especially worried that a kit would turn out to be too difficult for the kids.

Then I saw this post on Inner Child Fun, about how to do paper marbling using just laundry starch and acrylic paints!

I have tons of old acrylics laying around, so all I needed to buy was a $2 bottle of starch, which is useful for so many projects we do anyway.

I set each kid up with a small, flat-bottomed plastic container and poured in about 1/2-1" of starch. Then each kid chose their colors, and I let them drip the paint right into the starch. Then they used bamboo skewers to swirl the paint and starch. We lay cut pieces of watercolor paper on the marbling solution, then lifted them up and put them in a large container of freshwater, where the starch washed off, leaving the paint in beautiful patterns. We set them to dry on an old sheet.

Some things we learned:

  •  The really old (~18 years old!) ones had often gotten too dry or had changed in some way that caused them to drop to the bottom of the starch, which meant that they would not swirl and could not be lifted off with the paper floating on top- I did try sinking a paper to the bottom, and while it picked up some of the old colors, it was a garbled mess, not pretty and swirly.
  • The more liquid, "soft-bodied" acrylics in squeeze bottles worked much better than the more expensive professional paints in tubes. 
  • Lots of small drops works better, because overzealous preschool squeezing of the paint causes huge glops of paint which immediately sink to the bottom.
  • Glitter can be added after the paint and will transfer beautifully.

  • We ran into a funny issue which I haven't solved yet: Our first prints came out great and very little of the paint came off the paper in the wash along side the starch. But as we progressed, more and more of the paint came off in the wash. I tried changing to fresh water and changing to fresh starch. The new starch helped with a certain muddiness that was taking over - all preschool art must eventually become Preschool Gray- but even with an essentially new set-up, we had a harder time keeping the paint on the paper in the wash. Eventually I tried just not washing some, which caused them to stick a bit to the cloth where they were drying, but I just peeled them off, re-washed them and lost no paint.
  • Note that acrylics do not wash out of clothes, and can permanently adhere to many non-porous surfaces if not cleaned up right away with soap and water. 

Tuesday, April 17, 2012

Simple Machines for Preschoolers

Child-led learning. It all sounds so lovely and peaceful. But really? I end up using child-led inspiration for our activities when the kids are at their worst, when nothing I do can stop the cycle of twin-on-twin aggression, when everyone is too tired or sick or grumpy to concentrate on what I planned.

Alex and Anya were having a bad morning, switching off roles of tattler and mischievous imp, with increasing escalation and contrariness towards each other. Alex shouted from the living room, "No, Anya! Don't stick that in the couch! Mama, Anya won't stop and she's ruining our couch!"

When I got to the living room, Anya was scowling at Alex and mumbling something about a lever while gripping a long skinny paintbrush. She had been shoving it into a hole in the couch so she could make a lever to push and pull.

Things were getting dire. I needed something to distract them. Science to the rescue!

I asked them if they would like to learn about levers.  I took the paint brush and showed them how moving the whole thing moved it only in one direction, while if I balanced it on a Lego, I could push down on one end and watch the other end rise. I introduced the idea of pivoting, and that there was specific point at which the brush pivoted, which is also called a fulcrum. We looked at some levers around the house, like scissors, and I had them identify the pivot point.

I looked around for a quick and dirty way to show them the difference in the amount of work that it took to lift things with a lever and without. We had an old box filled with Playmobil parts, and I duct taped the trusty paintbrush to the bottom of the box and had the children lift it straight up. Then I had them add in our Lego fulcrum again and try pushing down to lift it up. I described how when we did it the first way, our muscles did all of the work, but in the second way, the lever did some of the work, meaning less work for our muscles.

I asked them to think about if we would be able to lift more or less with a lever. I asked them if they could think of any outside toys we had that were levers. They struggled with that question a bit, so I asked if they could lift each other up in the air- which backfired, because Anya can totally lift Alex- but then asked if any of their outside toys made it easy for them to take turns lifting each other up in the air. I sat in front of them going back and forth with my finger on a pencil lever held over a Lego fulcrum, and eventually they realized that see-saws are simple levers.

Since Anya's desire to push and pull levers was the start of all this, I gave them plenty of time to play with all our improvised levers and make some new ones of our own- though I did convince her to avoid poking more holes in the couch to do so.

Next we moved on to ramps, which were much easier to grasp- perhaps I should have started with them? I demonstrated how a little car needed me to push it on a flat board, but would move on it's own down a ramp, again emphasizing that in the former, my muscles had to do the work and in the latter, the simple machine did the work.

I was hopeful that if I set them up with a good ramp that I could take a kid-break while they explored. I love doing these projects, but I think we all do better if I can have plenty of downtime between projects!

I grabbed the remains of the (poorly constructed) dollhouse that I built for Anya a couple of years ago and duct taped two boards together. One side we propped up in the couch, the other was to let the cars run on after they built up speed on the ramp. I was going to have them measure the length that each car got on the board, but all of them went much further, so I settled for giving them a piece of tape to mark the farthest any car got on the rug a couple feet out from the ramp.

They tried a ton of different small vehicles, and seem to realize quickly that the cars with motors never built up speed- we had a good but brief talk about how those cars are designed to go forward powered by the motor, and that the wheels could not move freely with gravity, like simpler cars could. I did have to remind them to not fling the cars down the ramp, but rather than phrasing it as a rule, I explained that we were measuring the work that the ramp was doing, and that if we used our muscles to propel the car, we wouldn't be measuring just the work of the ramp.

They also experimented with pulling the ramp farther out or pushing it in, changing the angle, and the behavior of the cars going down it. Very cool to watch them exploring!

Eventually Anya started wandering off, but I thought we could milk the ideas I had introduced just a bit more. As we were walking to the backdoor, I asked them to look around for more levers and ramps. Alex, who was still very into rolling things down ramps, went flying over to the fridge and announced, "Ramp!" proudly at the magnetic marble run. Yay!

Anya and I went ahead outside while he played and Anya peered around and told me in that condescending preschooler way, "Now, Mama, the slide, right here? That is a ramp, Mama, did you know that?"

She also decided that the rocking horse was a lever, pointed out the see-saw to me, and told me that we should use a ramp to get the snowballs on top of each other for a snowman.

Science FTW!

Wednesday, April 4, 2012

"Tis a gift...

Spring break means many adventures with cousins who are off school; we went to the Milwaukee Zoo all day Monday (started with tree climbing at 9:45 in the morning and didn't get home till almost dinner time!), then on Tuesday drove to Madison for the Children's Museum and an afternoon with our extended family.

It was awesome exciting and more action that we usually have all week smashed into 36 hours.

But there's something to be said for simple pleasures at home.

This morning we ran some quick errands while still in pajamas, then came back and worked on our project for the rest of the week, "Making Our Home More Beautiful" which is my happier sounding re-framing of "Clean the Shit Out of Our Pigsty".

I was amazed at how much the kids have changed in the past couple of months. I took them into our very messy utility room, where they aren't usually allowed without a grown up, and had them take turns sweeping the room, with the non-sweeping one putting dishes in the washer for me nearby. Then I taught them our to use the lightweight string mop I bought for the occasion, and they went to town, mopping the whole area twice, and  probably almost effectively as I would have done on my own- and this is a floor that is filthy, since it had a soda (?) spilled on it and not cleaned up AND it is where everyone tromps in after being in the yard or (shudder) the firepit.

After they were done they were excited to keep helping, and they collected laundry, put it in, measured soap, started the machine, carried clean laundry out. I supervised, but stepped in for physical helping very rarely.

By the time lunch rolled around, everyone was still cheerful, and it had turned into a beautiful day. I let them loose outside with the hose on slightly and a watering can with instructions to water certain areas of the garden, then went inside. 6 months ago, They would have done all of the following in the first five minutes:

  • Turned the hose up so high it would have drained our well and overheated our pump.
  • Sprayed each other in the face with blasts of the icy well water.
  • Started a screaming fight with one another over control of the hose
  • Blasted all the delicate new plants with the water and ignored the plants I asked them to see to.
  • Ran into the front yard without permission or worse, into the yard of the decidedly unfriendly dogs who are behind an invisible fence next door.

But now? They watered all the plants, pulled some dandelions, then came up with an awesome imaginary game involving making a mudpit for the pig statue in the garden and baking mud pies. No fighting, no destruction. They came in together when they were cold and with just a reminder from me, did NOT track mud through the house, but carefully stripped off their muddy clothes and put them in the washer (and Alex even added more dirty stuff and started the machine) got washed up, and are now hanging out with snacks on the couch together.

I know there is no age at which the parent child relationship stops having periods of being fraught, but the last year has been hard. I  dislike discipline of any sort  and yet have become takes-no-guff authoritative parent, which involves maintaining boundaries all. the. time. Sometimes it felt like I was trying to do the impossible, trying to tame ferocious little beasts- and of course I know there is an entire realm of parenting philosophy that disagrees with any sort of authoritative boundary setting, but that is not my bag! Sometimes I felt like they were like some sort of powerful duel force of erosion, wearing down my very soul. But today? When they seem to understand why I want there to be boundaries and rules, where they know they can discuss those rules and we can work together to create and enforce them, when we can finally start approaching our home and our world as a team? Today is a good day, and I think there may be more good days coming. 

Sunday, March 25, 2012

Math Fun: The Counting Corn Game

I wanted to come up with a math game that would be helpful to both of my kids, even though they have very different skills sets/ ability levels. This is a fun activity to set up with the kids as well as fairly open-ended in how exactly you play and process the experience, so that you can let the kid guide how much they want to continue to explore the ideas. It'll also be fun even if kid doesn't want to "work" on specific counting skills; playing around with little objects in and out of little containers is just fun on its own!

1 ice cube tray (or other sectioned container like a bead/tackle box or silverware tray) per kid
Blank stickers and a pen (or any other way to label each little section)
Unpopped popcorn/ dried beans/pennies/ other small counting object
Small shallow containers like large jar lids

1. I showed the kids how I would write on number on each sticker, then asked them to tell me which number to write next. I think they enjoy getting to tell me what to do, and it makes them have an active role in the creation of the game. Plus, while they are busy bossing me around, they are practicing their counting!

2. I placed the first couple of stickers along the "back wall" of each ice cube section- so that they could see the number even when it was filled with stuff. Then I had them put the remaining stickers on, though I did hand them to the one at a time to prevent skipped numbers and to make sure they did them in a row. I think that counting and  early addition and subtraction work is so much easier for them when things are neat and precise, so despite my intrinsically messy nature and my slight preference for rebellion over order, when we do math, I try to teach them to do things with an inherent sense of order that includes things like counting in rows and not skipping steps of a process.

3. I gave them each a  bowl full of unpopped popcorn and showed them how to count one kernel at a time to get the right number in each section. The kids will pretty much take it from there. I just let them guide me as far as what extra guidance they might need, and we brainstormed solutions to problems together.

Results & Discussion:
Here are some of the things that came up:

- Alex, who has a lot of fixed-mindset traits, and is hesitant to try something if he thinks he can't master it immediately, was very concerned that he didn't "know how many are the big numbers". He already has some of these traits, but the fact that Anya often masters skills like comfort with the "big numbers" just makes it more difficult for him. We talked about how each of our number slots was one number higher than the last- I had him verbalize that after asking leading questions about the lower numbers which he hasn't expressed any anxiety around. And then we came up with a plan that if he got to a number that he was worried about, he would look at the last number and add one more, which he was excited about as a solution, and I was excited about as proto-addition work!

-The physical act of manipulating the kernels and (especially) fishing them out of the ice cube trays if they accidentally added too many was a great fine motor activity. It was challenging for my guys, I would probably use bigger objects (like dried garbanzos, mancala stones or large wood beads) and bigger containers for kids any younger or for anyone that wanted to focus more on math and less on fine motor.

- Once they were done, I went through and counted each container, using a knitting needle to sort of arrange the kernels in rows and point to each as I counted aloud, encouraging the kids to count with me so that it wasn't so much me checking their work as us looking at it together- the kids usually noticed their mistakes before I said anything and were really great at figuring out if they needed to add or remove one or two to get to the right number. It also, I hope, functioned as a demonstration of how I count things. Demo would normally come in the beginning of a lesson, but I really liked how they worked out their own ways of doing it, then watched me, then added certain parts of my method to theirs as they liked.

-After a while, I got out the large jar lids and gave them to the kids to be their counting trays. They would fish out the kernels and could then manipulate them in the lids without losing any, which was very helpful for lining them up in rows in order to make counting easier. Anya has been very interested in skip counting, and lining up in rows was a great way to add a visual/real life component to something we had only talked about and tried out while driving in the car.

Coming up with math activities doesn't come as naturally to me as for science activities for the preschool set, but I was pleased with this. I'd like to start working on more skip counting, and perhaps some abacus work, or something which helps start conceptualizing the meaning of the digits in larger numbers and the meaning of place value.

Wednesday, February 1, 2012

Marshmallow Estimation

The kids were intrigued by a contest at the drop-in care at the gym*, one of those ones where you estimate the number of candies in a jar and whoever is closest wins. They carefully wrote out their names and guesses (Anya said 101, Alex said 100 right after- he's almost got the Price Is Right strategy down. So close and yet so far.) and dropped them in the box.

This seemed like the perfect chance to get them interested in the idea of estimating, especially since the most frequent question I get is, "How could you know?" They are both eager for learning new tools to understand the world and predict how it will work.

I took four identical mason jars and put miniature marshmallows in each- five, ten, twenty and one hundred.

Then I made up quick sheets for the kids to fill out- a dotted line on top for their names, then four rows, each with a sketch of a jar and a box.

I asked them to tell me what an estimate is ("A guess!"), then talked to them about the difference between a guess and an educated guess. I tried to emphasize that an estimate involved using your senses and mindfulness/"using your head" since they are always interested in the body and we are struggling with both of them not thinking about what they are doing, from rushing to put on clothes and doing it backward to tenaciously clinging to every conclusion they jump to, no matter how much that conclusion flies in the face of their experience of the world. I asked them to tell me times that people used estimates, and they mentioned counting stars, contests (Thank You, Curious George!) and when prompted about things I do in the house, they mentioned that when I am cooking I estimate ingredients, but that they still have to measure.

I had them each take a jar, and encouraged them to pick it up, turn it around, look at the marshmallows from all different sides, feel if there was any difference in weight (could really do a lot more with this using lighter jars and heavier counting objects). We put the jars in ascending and descending order based on how much each looked to be filled.

Once they had explored them for a bit, I asked them to draw a picture of what the marshmallows looked like in the jar, then write the number of marshmallows that they estimated was in each next to the picture. I wanted to encourage them to really look at the different volume that each number took up, rather than just focus on trying to count.

It was really cool to see them working up from being able to simply count the marshmallows to actually having to work out a way to estimate. As I suspected, both of them had an immediate inclination to count, even when it was impossible. When they got stymied by that I encouraged them to look at the jars, compare them with the jars they had already done, and make their estimates from that. I started to talk about the amount of marshmallows doubling, but while Anya especially has been very interested in proto-multiplication (3 sets of 2 makes 6, take a away 2 and 2 sets of 2 makes 4), the abstract idea of doubling was a little more than they could do right now.

In the end, we went through and talked about each of their estimates while looking at the jars together, then counted each jar to see how close they got. Then I let them eat the marshmallows. Math = Fun, guys! Remember that (not the obscene number of marshmallows)! Now let's go run around the yard for an hour!

* I recently conquered my fear of going to the gym, which has allowed me to restart the Couch to 5K program (because it turns out that running outside in Wisconsin is not for the out of shape and feint of heart). It's a post for another day, but running again has made me feel like a new woman. I did not realize just how much of my energy was being burned up simply by trying to stay afloat rather than get pulled down by the dark undertow of depression. I am extremely thankful to Luke, for keeping my gym membership alive even when I didn't use it for so long, and to my friend Jenny who inspired me to get back to running. I am also thankful that my kids will finally allow themselves to be left at the drop-in care, so that I no longer have to push 90+lbs of kid-and-stroller in order to run. Seriously, this is the best development in my life since finishing nursing school!

Thursday, January 12, 2012

Rainbow Snow!

We just got our very first snow of the winter, but I was loathe to dig out their snowsuits from the packed suitcases waiting by the door for our trip up north tomorrow... so I decided to bring the snow into the kids instead!

Inspired by this post at the Chocolate Muffin Tree about painting snow outside with colored water, I filled an ice cube tray with water, then put a couple drops of food coloring/gels in each.

I went outside and scooped up some fresh snow, careful to get only the cleanest, since I had a feeling it was going to end up being eaten.

I handed the kids paintbrushes at first to drip the color into their bowls, but the little brushes didn't carry much of the colored water and were difficult to control, so I grabbed a couple of used, clean medicine syringes (the kind without needles, obviously!) and let the kids start filling and squirting them into their snow how ever they liked. And they *loved* it all, doing the whole thirty minute activity twice in the same night!

They kept the paint brushes for stirring and poking. I had thought that scooping and packing the snow would be fun, so I brought out spoons and small containers, but as soon as they had spoons they both just set to eating it like ice cream, delighting in the silliness of it all. In fact, after the first round when we had to stop to eat, they drank their colored snow water with dinner.

Anya explored how plain water squirted made a clean tunnel to the bottom of the bowl, then set about making a blue green lake at the bottom, so the snow had "something to float on"

We also tried squirting separate drops of all the colors onto the bottom of a bowl, packing fresh snow down into it, then inverting the bowl and looking at the rainbow patterns that the snow took up (the first photo of the post is from that experiment).

Overall, tons of fun, very little mess, no expense, a little color theory and a little physics as we talked about temperature. Win!