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?
Answer by James · Apr 11, 2014 at 09:07 PM
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!).
Answer by mngiggle · Apr 11, 2014 at 02:49 PM
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.
Answer by Ekaterina.ermakova · Apr 11, 2014 at 05:15 AM
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.
Answer by Reenie · Apr 11, 2014 at 04:06 AM
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.
Answer by Sutrali · Apr 10, 2014 at 05:57 PM
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?
Answer by nabennett · Apr 10, 2014 at 05:08 PM
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.
Answer by Lamhita · Apr 10, 2014 at 03:53 PM
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)
Answer by mistermarty · Apr 10, 2014 at 03:45 PM
Answer by Katec · Apr 10, 2014 at 12:41 PM
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.
Answer by SarahKrieger · Apr 10, 2014 at 09:01 AM
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.
Answer by kata · Apr 10, 2014 at 06:28 AM
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.
Answer by mirandamiranda · Apr 10, 2014 at 04:37 AM
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.
Answer by CynthiaDadmun · Apr 10, 2014 at 02:52 AM
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.)
Answer by tselie · Apr 10, 2014 at 01:35 AM
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.
Answer by juggling_ginny · Apr 09, 2014 at 10:37 PM
I think my daughter often expresses her creativity, in maths and in many other things, with repetition. If we learn a new game, she likes to repeat it again and again (until I am thoroughly sick of it) to hone and refine her strategy. If she comes across an idea that captures her imagination, she wants to repeat it again and again to enjoy the same results or see if something different happens - whether this is mixing baking soda and vinegar or doodling crashing hydra heads in the manner of Vi Hart.
I think I'm still learning how best to encourage this creativity - I think a certain amount of what seems to me to be at times almost mindless repetition is necessary for a child to internalize knowledge and gain familiarity and confidence with something new. Then I think there is a risk of a child becoming stuck in an increasingly unsatisfying repetition of something that is getting stale. Sometimes a variation occurs, either accidentally, or on purpose, that changes the outcome and sparks a whole new level of learning. But sometimes this doesn't happen and I need to learn when to intervene, to suggest changing the rules of the game, varying the initial conditions of the experiment or making mistakes on purpose to see what happens then.
Answer by sherylmorris · Apr 09, 2014 at 05:30 PM
#61 Cue the music, "Clean up, clean up, everybody do their share!"
Now we can begin again with #1-#60. I like to begin from order, "Mind that you don't hurt yourself or those around you", and I prefer "Handle the materials respectfully." (It's the Montessorian in me.)
I love the list of 60 and this conversation! Best!
Answer by jkshuler · Apr 09, 2014 at 04:05 PM
I love experiencing thinking through a child's mind. My eyes are constantly opened to a new way of thinkng as they explore patterns and relationships. It's my job to facilitate an environment that allows for their creativity while still embracing the laws of math.
One area that I partaiculary focus on in my classroom is making mistakes. I want mistakes to be comfortable as they allow us to make better sense of our reasoning. Mistakes are so valuable because they provoide opportunities to discuss the "why" in a process.
I think grown ups need to be open to the power and insight a child has. When we work together, we get a better understanding for the task at hand.
Answer by WendyGee · Apr 09, 2014 at 03:25 PM
My daughter loves to model and bake with sculpey. She makes people and does a great job of capturing many of the characteristics of the people and animals she chooses to make. This winter she created a chart of all the kids in her class, came up with 5 ornament designs she wanted to make and made everyone an ornament.
She also loves to play piano, which has been an awesome way to use patterns, and another annotation for numbers.
Is music an example of ethnocultural math? I haven't been able to find many examples of that, other than the mayans.
I have to admit I find the list of 60 a little overwhelming. Though I do see how some of my children's interests can fit into this list. I think I just need the confidence to do it playfully. I would love to find a math circle in our area.
When I take the time to reflect on some of her activities I can see the opportunity to point out math, I could have easily made a graph of some of the ornaments she made. We could have compared sizes of some of her ornaments, how much material and what colours she needed - we did a quick approximation at the store when we were buying sculpey.
Answer by jaaane · Apr 09, 2014 at 03:11 PM
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").
Answer by babyhclimber · Apr 09, 2014 at 03:06 PM
When looking at this list I found some great ideas of creative behavior we've not yet done. My son loved the list. We use a program called processing and scratch that are both free and allow tons of creative energies to be released. Off the list we easily do about 15 of the activities quite regularly. Definitely have more ideas to try! I really think as grown-ups our job is to help our child find some sort of creative outlet and its good for us adults to have creative outlets too.
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