Week 1 Task 2: Your child, the divergent thinking genius
Today your mission is…
Look at this mini-poster of 60 creative behaviors that support mathematics. Here is the same list in plain text. Recall an example of your child doing something from this list - either in mathematics, or in another context. In hindsight, what would have been a good way for you to support this creativity?
Ready, Set, Go
In Breakpoint and Beyond, George Land and Beth Jarman describe a longitudinal study they conducted on 1,600 kindergarten children ages three to five. They gave them eight tests on divergent thinking and an astonishing 98% of the children scored within the creative genius category. The researchers repeated the tests in five and ten years and separately tested adults. It gets worse and worse with time: only 2% of adults score at creative genius level. The good news is that grown-ups can collaborate with kids.
There are quite a few tasks children do better than adults, especially when adults support them. Other tasks adults do better than children, but even then adults can benefit from inspiration and prompts from children. In a harmonious learning environment, adults and children play complementary roles.
Adults
Children
Ideas
Write ideas down, sort and organize sets of examples, articulate knowledge
Generate diverse, creative, novel, unexpected ideas
Mathematics
Maintain consistency of patterns, extend patterns with new examples
Open up and maintain free play, break patterns to create new patterns
Process
Organize the process, manage time and tasks, maintain group well-being, nurture
Sense poor management practices, quickly show when well-being is in danger (“the canary”), invoke empathy and joy
Applications
Connect ideas to many life experiences and examples
Connect ideas to unexpected examples, look at familiar things from new angles
Aesthetics
Appreciate order and systems
Appreciate beauty and adventure
Frequently Asked Question
Can young children really understand advanced math concepts?
We believe that to be understood, a math concept (and pretty much anything else in life) has to be well-explained. The key is to search for age-appropriate explanations of advanced math concepts. For young children, the most appropriate explanation is through hands-on exploration and free play.
This means we need to find physical objects to represent mathematical concepts. But these should be objects that do not require prior knowledge to be played with. We call such objects and activities around them “grounded”. Grounded activities lower the risk of math anxiety. Plus, by selecting “no prerequisites required” activities, you avoid the “snowball effect” of sequential, prerequisite-filled learning.
The task
1. Find an example of a child’s creative behavior.
2. Do we have your example in our list of 60 behaviors, or should we add it?
3. How can grown-ups support the child in your example?
My children are wildly creative: play acting, making up riddles, 3-d multimedia art, poetry & prose, piano, creating their own games, etc. Much of the list of 60 looks like a snapshot of our home! As the parent, I try to support them by rotating a variety of materials, books, games, etc., in their living space and giving them freedom to explore and play.
My daughter will take odds and ends in the house and make play toys out of them. Sometimes she will make an instrument. Another time she will make a new animal or character in which she can act out stories. It can be hard to keep all of her creations but we try. When have a recycle box in the main room and she often removes things we would normally recycle so she can use them for her 'creations'.
Our daughter loves music - she'll kick her legs along with the beat, and smile as soon as I bring out an instrument to play with her. She also loves creating music on a little iPod game I occasionally present her with (but maybe that's just a fascination with technology). Listening to music is on the list, but not playing music. We support our child by giving her noisy percussion instruments to play with, helping her to dance along with music recordings, and giving her an unusually large amount of live music (with plenty of mistakes!).
Our eldest loves to build things out of stuff we would normally recycle; often humanoid robots. We support that by making sure he has the tools and materials around to build something when he has the urge to use something bigger than Legos.
My son used to notice patterns in everything. He was always finding similarities in different things. Often to my amazement. I guess I did not know how to encourage this in him and turn it into something that would help him with math. I don't know that he does this any more. He no longer talks about it. He does still love games and any kind of scavenger hunt. I have used these as learning tools for math, science & history. He used to make models and structures out of anything he found, graduated to Legos and now works in Minecraft. He is going through a mod design class for Minecraft now. Always looking for ways he can learn that he perceives as fun.
Vygotski wrote about young kids talking out loud and older kids having "internal conversations" in their minds - so maybe your son is thinking, rather than talking, now that he's older. Minecraft is a wonderful tool for mathematics. Maybe you and your son can make some Minecraft models for our course tasks?
It's not hard to find examples of my children's creative behaviour; it's continuous. One simple example is how they come up with novel and interesting ways to use every day household items or items I've put in the recycling bin; because I have already categorized these same items in a particular way, I would never imagine to employ them in the manner my children do. Their creative use of things can lead to absolute chaos in a house so a way a parent could support this is to recognize the creativity inherent in this chaos rather than only chastising children their children about it. What I've come to know is that, to a child, a tidy living room is a blank canvas... :)
"to a child, a tidy living room is a blank canvas..." - a whole story in a phrase! It reminded me of this comic strip by lunarbaboon:
I love the cartoon that you've posted! I even sent it to my son who sometimes despairs at messy rooms. That said, I feel that children need order, some more that others. The great observer of children, Maria Montessori, tells a story about a crying children, seemingly for no apparent reason, until the adults realized that mama was carrying her coat, not wearing it. (In the child's mind a coat was to be worn, not carried.) It's the biggest job children have is to make sense and order of adults and their world. I feel that it's important to start from order–in the classroom, a day at home, in life. I liken it to great abstract painters beginning their careers by first learning to paint like the masters of realism. Balance is my mantra this morning. Best.
I think everyone has a need for the personal balance between order and chaos. Some people need relatively a lot of order, and others relatively a lot of chaos. There are some gender differences, too. For example, many females prefer to play games with stationary, busy fields (such as "Where is Waldo?") and many males prefer to play games with a single moving object on an empty field (like soccer). In mathematics, there are sequential problems that require one formula to follow the other, and insight problems that make you review a lot of pieces of information at once, and put together a holistic conclusion. As long as people can try various levels of order and chaos, they usually find their own balances.
Whoa... Waldo is a berry in the bushes, and the soccer ball is the wild boar to be chased. Just think of all those Big Fish Hidden Object games...they probably have a major gender imbalance too.
I really appreciate the quote and cartoon -- thanks for posting. As much as I like the Montessori approach generally, that whole "ordered environment" thing just makes me feel like a Bad Mom -- cause ours isn't!
I like (and can maintain) order in some parts of my environments, and then for other parts, I like and can maintain chaos. The balance is very dynamic, like riding a bike. I do use a lot of Montessori methods for the order part of it all!
We have a variation on #3 "Carry graph paper everywhere." We have a chalk board in our kitchen next to the table where we eat. The kids are free to draw on it at any time. We often write words, numbers or draw pictures on it to help explain concepts.
Ditto. Every house with small kids should have a chalkboard or white board out. We use it all the time. I think it helps make learning more part of everyday life.
After we've had a shower or a bath my son jumps at the opportunity to use the foggy bathroom mirror.
My son plays Lego almost all free time. He does not need any help from adults. He likes to make his own constructions from parts of different sets. We gave him an idea to sort detailes from each set and put them in separate boxes. And then he saw his friend sorts his Lego by color and now he likes this idea and uses it frequently.
My daughter likes to play a lot of small things at one moment: small toys from Kinder-surprise eggs, beads, places of papers, etc. She also likes to sort these objects and put them in "beautiful" order everywhere. My help is usually to provide enough amount of boxes, caskets and small bags for all this staff.
1. Pretend play--it's a biggie in our house. 2. Yep, you got it. 3. My son is an only so parents and babysitter are frequent playmates. Have not explicitly tried to work math into pretend play but I'm sure it's gotten in there by accident.
Hmmm. This made me think. The list helped, there are several in there that I see my children doing. They love treasure or scavenger hunts and we've been on a "shape walk" before taking pictures of shapes we see around the neighbourhood. My 8 year old has recently discovered and loves playing minecraft and amoung many other things has recreated his room and the our local swimming pool - complete with a dive pool with a moveable floor! We often have conversations about huge numbers, infinity, negative numbers. Supporting him seems to be enjoying his enthusiasm and helping him when he asks. I wish I could be more creative in my questioning during some of our conversations. My 4 year old daughter notices patterns and is into pretend play in a huge way. She tells us what we have to do and say and we have to follow the rules! She also explores all kinds if scenarios, consequences and feelings in this safe way. Supporting her is joining her but also spotting if frustration is getting too high and intervening. I'd love to have examples of grounded manupulatives and activities.
1. My 8 year's old girl love to create from things she find in the house. For example she made a gift for the brother with a card-board box, she create an arena where he can play fighting his little monsters ones against the other. Another time she created a new game from a half toilet paper and a little paper ball inside: you have to make a path around the house with this game in a hand without having the ball fall down to the ground (i think this is her version of the path with the spoon in the mouth and egg inside). 2. Add "Making creative games and useful things from recycled" 3. We can support her organizing a place where we can put all materials in the right way, separate and give box to each material (a box for recycled paper, a box for card-board, a box for plastic jar nad so on)
My daughter often uses physical activity for planning her problem solving. Swinging, riding her scooter or jumping on the trampoline are things she does when she needs to "get some ideas," as she puts it.
My children enjoy measuring and mixing; exploring taste, smell and texture as they help with the cooking. We explore ratios, fractions, multiplication, volume, mass etc as we produce tasty snacks.
For support, we regularly invite the children to make something for us all to share, we use as much mathematical (and scientific) language as I know, we alter our recipes and experiment with new ratios and ingredients, convert US measurements to metric and observe, describe and eat the results.
1. Last winter my daughter (11) started to make a lead so that she can take her rabbits for a walk. She stuck to it as various things didn't work, changed to different fabric, adjusted the size, changed the closing mechanism, etc.
2. She persevered, took breaks (sometimes several days), drew pictures about it, estimated size and area, made a big thing form little things, used old bits of fabric for the body and crocheted the lead itself.
3. I supported her by letting her have the time, place, she had access to the tools and materials. It was important for her that I stayed out of it and didn't take over, but I did make the odd suggestion when she was figuring out each of the problems she encountered. With my encouragement it could have led into another activity, such as learning some stitches, designing and cutting out patterns, enlarging etc.
The last couple of days my daughters, especially my eldest, have been engaged in building a 'clubhouse' in the back garden. They are using plenty of "old parts' to make a 'new thing' including bits of mouldering wood, broken play equipment, old window screens, blankets, old shelves... There are bedrooms for each of them, a kitchen, a living room with puppet theatre tv, a garden with pot plants and no doubt more will be added tomorrow! It is great to see how creative they can be about repurposing things and how their imagination imbues their surroundings with so much promise and potential.
I think the best way I can support this behaviour is by repressing any feelings along the lines of 'get this eyesore out my garden!' and instead appreciate, as in the untidy room cartoon, what it represents for the children.
I am not sure how mathematical this is though. There is certainly some engineering going on but I wonder if I should try and draw out mathematical concepts or just let well alone. I don't want to threaten their ownership of their creation, or turn it into a chore.
To answer the posed questions -- my five-year old's major source of creativity is building crazy things out of his Lego sets, which are quickly dismantled and re-purposed as soon as the "official" model is built. I support this by trying not to be broken-hearted seeing the awesome original model go back to pieces :) The "product" he creates may not be totally amazing, but the "process" he goes through to build it definitely is. (Often the product is pretty good too.)
And if I can be a divergent thinker myself here, I'd like to add my comments regarding items in the list:
14 Surround yourself with a Math Circle --- What is this and how do I get one?
24 Rotate, reflect, shrink and stretch your pictures --- Fun project with photocopier! Maybe tracing paper.
27 Tell stories about problems --- I like this, like a backwards story problem. 2+3=5...what's the story?
30 Seek your favorite number in the Encyclopedia of Sequences -- What is this?
33 Plan to spend a long time stuck; if you are not stuck, pretend you are --- Love this!!! Must encourage kids to SEEK OUT stuckness (ie, true challenges). How exactly to do it?
35 Make rough estimates --- Must find new ways to encourage estimation, very imp real life skill
42 Make your own rules, formulas, theorems --- Fun game idea, make your own rules... how to make math-y?
44 Cultivate favorites among each type of math objects: your favorite polynomial, prime, surface, identity and so on --- Yes! Good general motivator technique, not just math.
47 Go on a scavenger hunt looking for a math concept --- Fun! Two kids could set up items for each other to collect (ie pile of five blocks, a written numeral five, etc.)
Looking at this list I can see that a lot of the free play my kid does involves these activities. Right now he is obsessed with lego and minecraft. The lego is taking over my house a little bit and I could probably be a bit less neat-freak ish about that. One thing I would like to do is to try to stop rushing through the stuff we have to do (homework, dinner, etc.) so that we can relax enough to talk about these concepts and enjoy them. One thing we do a lot of is make lists. About everything. Activities we want to do together, ideas for making getting ready for school/work easier, food we want to try, etc.
Lego suggestion: IKEA Trofast bins, and a train table for working on. That helps us. Of course, we are lucky that we can allow it to take over a whole room of the house ("The Lego Room").
My daughter was playing with her fairy dolls today and began sorting them by colors of the rainbow. I sat down and joined her play, asking her what other ways we could sort them. We came up with all kinds of categories, ranging from hair color to what type of fairy they were. She was so happy and I realized that I need to do more of these things with her- just playing with her, following her lead and making small suggestions, not so much directing. I think this would be 16 and 17 in the list.
". . , following her lead and making small suggestions, not so much directing." I like this.
This suggests a neat directed activity! Could pull out a box of random toys or hot wheels cars and sort five different ways...
Using graphs in the explanation of problems like Venn diagram, creating her own puzzles and crosswords, drawing - these are just some examples. About supporting, this is a different issue, I give her some space and allow her to do her own stuff and then she explains to me what,why and how she did this or that. But mostly she prefers to work with me by following the particular algorithm.
