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Math-rich baby and toddler environment
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But where is mathematics?! Or, "spiral IS math"
As one of the goals of the course, I'd like to make a map to baby, toddler and young child activities, by math concepts. Here are two map examples I like a lot.
To start, I would like to invite every family here to do something joyful with their kid they think MAY be mathematical, and share the story in this thread. Share photographs or videos of how you do it - always helpful and fun - but stories work too! Then we will discuss how kids can make some math within your activity.
Here is an example: an excellent activity write-up from zetamom (Kenede):
We used two sheets of plain white art paper. I folded one sheet in half and the other in half, twice. She opened the paper and poured the paint kind of in the middle, but she's 21 months, so it was close lol. We refolded the paper, she pressed down a little and when we opened it she had two pictures that were symmetrical. For us this was science, but I'm glad to be opened to learning something everyday. As I read the comments, I remembered that here in DC symmetry is on the "state" test under math. They normally use a triangle and some weird block looking object and the question normally asks which object is symmetrical.
Having done this, what math can the kid do? Here are three examples of math for the above story:
- Sort and conjecture: find out which of the shapes you draw of find could be made with folded paper and paint (symmetrical). For example, can you make letter A this way? A butterfly? A spiral? Even a baby can point to symmetric objects, or enjoy opening and closing a picture folded along the symmetry line. You can prove or disprove the kid's sorting conjectures simply by folding the picture along the proposed lines and seeing if halves are the same. Celebrate the kid figuring out the conjecture was wrong, too! Disproving something is hugely valuable.
- Similarities in differences: enact symmetry with your whole body - become a live mirror to someone! Newborns can mirror facial expressions, but nobody knows why this works: babies do not see any faces in the womb! Mathematics is seeing the sameness of idea (symmetry) in different contexts (paper shapes, gestures). Verbal kids can also talk about what's the same among activities. Here is the photo of kids in a math club being live mirrors:
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- Extend: Can you do this with more than one line of symmetry?!! This is not easily done with paint, but you can fold paper into four and cut with scissors. Kids who are too young to cut can guide their parents' hand with scissors, or just open the papers parents cut. The picture shows kids experimenting with 2 lines of symmetry (also, giant paper is fun):
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Mathematicians sort, cojecture, notice similarities in differences, and extend ideas. Babies can, too!
So, please do an activity and share it here so we can mathematize it!
Thanks for the links to the maps! I'm a visual learner, so they definitely help me understand the concept of toys and experiences that going beyond counting.
Hi All,
Happy Friday:) Today for Marley and I it was art day but because I received a very good response to my question, I included math. Part of art she painted and the second part she frosted cupcakes. I placed 5 unfrosted cupcakes on her table, the number 5(cut-out) and frosting. We discussed the number of cupcakes, counted them and then frosted them. We also compared them to the actual number.
I'm thinking the math besides just counting is comparing the actual number to quantity. If wrong please please tell me. If anyone knows how to upload pics on here, please share. I would love to share some of the things we do but more so on spirals. I would like to share some of Marley's line drawings and paintings. I would be wondering, if once the pictures were viewed, if someone could explain if spirals consist.
What fun (and tasty) activity!
COMPARING is a very mathy extension as well. For example, what else around us has 5 in it? Marley could "feed a cupcake" to every finger on her hand, or every toe on her foot, or her five senses, or the five Platonic solids, or every end of the usual star, or every corner of the Pentagon. But there are too many cupcakes for the three bears and not enough for the seven dwarfs!
I got another mathy extension idea that has to do with the number cut-out you used. The numeral 5 is a representation, a SYMBOL for that quantity. Math question: what other symbols can we use?
There are historical symbols, such as the Roman V or the Mayan __ (they used dots and lines for numerals). These are fun to look up on Google image search. You can use a star (pentagram) for a picture symbol, and a gesture modern people use when they can't hear one another - a hand with spread-out fingers. But a large part of what mathematicians do is make their own symbols, so you can invite Marley to draw a symbol for five, or point to an object she wants to be a symbol for it. Then you can copy her symbol a few times and maybe put it up on the fridge or the bulletin board together with the rest of the collection. If you do that, I would love to see what symbols Marley makes up. My kid called all numbers by animal names, and one of my students thinks of them in colors, which is common among mathematicians (synesthesia).
I included an image of Maya numerals in this comment, which you will not see in email, but on the page. I am addressing the image question in a separate broadcast as well. You need to use the html code "img src" and upload the image to a sharing place first, like Flickr.
WOW!!!!! This is all so great. Thanks a million, I could also use some of these ideas for other numbers :)
We played a game that we decided to call "sea shell families". We have a large vase with all sorts of sea shells. None of them are exact pairs, but you know some are more alike than others. So Mark would pick a shell and then find a mommy-shell or a daddy-shell for it (a larger shell that looked very similar to the baby-shell). This went on for a while and I guess he really needed to concentrate to see the similarities between shells of different sizes and shades. Not sure if it counts as math.
"Family" is such a great metaphor for "common properties"!!! Mathematicians classify all sorts of objects - shapes, curves, equations, functions - by properties. Van Hieles (husband and wife team) built a stage theory of reasoning that many people apply to ages, saying that young kids cannot be analytical about properties. However, I believe kids can become analytical, and notice properties, if they spend enough time in a beloved, interesting context, such as your beautiful shells! Have you ever noticed kids pay attention to minute details of their favorite toys, cartoon characters, cars or space ships or animals - whatever they like most?
Van Hiele levels: http://en.wikipedia.org/wiki/Van_Hiele_model
Mark "really needed to concentrate to see the similarities between shells of different sizes and shades" - absolutely!
One math extension of the family "property noticing" idea is GRADIENTS and it comes from the story "Goldilocks and three bears." In the story, Goldilocks analyzes many properties: hardness of chairs, temperature of the porridge... Mark can find several shells for each family, even extending it to grandparents. Then he can find correspondences with other things, like Goldilocks.
What piano key does baby-shell and mommy-shell and daddy-shell play? Piano keys are a gradient.
What size piece of banana do they usually eat?
What size toy car do they drive?
How loud or how high are their voices? Can you sing "la-la-la" for them?
Kids really like these "family gradient" stories, and they find all sorts of gradated objects to give to the "families." Montessori has a whole lot of sorting (gradient) ideas that go well with this game, such as textures (rough-smooth) or light-to-dark color cards. Which you can also get for free at hardware stores that sell paint.
Love the idea of gradients!!
I didn't even think of extending this game to gradients, but it makes perfect sense. Mark loves making up stories and I think this game will work great with him. Will try tomorrow!
I have to confess, I am still in counting mode with Hailey (a few weeks shy of 2yo). I hadn't had a chance to check out some of the suggestions made here (until tonight!).
I am kind of trying to figure out how to teach numbers to her. One day, we were going through a numbers book and she was pointing at various numbers, and I would "read" that number to her. They were out of order, but I was simply working on number recognition for her. So my husband was hearing me say "seven...three...eight...one...two..." etc. He fussed at me for not going through the numbers in order. I suppose we had different objectives at the time -- his was orderly, mine was recognition. So I am now trying to incorporate both.
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.... :)