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 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 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 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 mistermarty · Apr 10, 2014 at 03:45 PM
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 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 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 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 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 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 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 Noursler · Apr 12, 2014 at 11:33 AM
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.
Answer by Isabella17 · Apr 12, 2014 at 11:33 AM
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'.
Answer by mamaof3creates · Apr 12, 2014 at 11:48 AM
My son just turned seven and has been taking guitar lessons for a few months. I have been told that this is young to be starting. Like someone posted earlier, play an instrument is not on the list.
At first, I had him taught in the traditional, learn a note, chords, and songs from the beginner guitar books. This was killing his desire to play the guitar.
He started because he wanted to make his own music. So, we changed our approach, instead of practicing other peoples songs, the teacher will teach him chords that work well together and his job is to make his music.
He now includes "bongo drums" which means that he flips his guitar over and taps on the back of it or any other part of the guitar that suits his fancy.
He now will play many pieces from his repertoire. :)
Answer by zzzeee2000 · Apr 12, 2014 at 07:03 PM
As a teen with learning disablitys I find that 8,10,11, and 15 all help me out a lot.
Answer by Caroline_Prochazka · Apr 13, 2014 at 12:03 PM
My youngest (5yo) LOVES to draw (#23 Draw a Picture). It is his go-to activity and he can spend long stretched of time at it. I support him by asking lots of questions and trying (sometimes it is very difficult to tear myself away from whatever I want to accomplish in these moments where he is peacefully occupied) to listen carefully to all the details he wants me to know about his illustration. We talk about foreground/background, colour/shade, scale/size - because he wants his pictures (of star wars spaceships, lately) to represent the 'real thing' as best as they can :)
My eldest (9yo) is keen on Lego (#43 Make realistic shapes out of...Lego blocks....), and lately he has been holding a project in his mind to create a hybrid house - a very modern design (all windows and glass) built on an old ruin. We finally got to this one together, yesterday. He needed a helper to work on sorting out certain sizes of blocks, another pair of hands to balance an incomplete structure, a critical eye to help correct asymmetry in order to get all the columns to arranged equally. Mostly, he really loved that I was playing with him
In general, we aspire to include a lot of #32 Do More of What Makes You Happy in our home - and this question was a good reminder of how we can all engage in helping each other achieve that goal.
Answer by AnnMarie · Apr 13, 2014 at 07:06 PM
This is a wonderful exercise for me. I feel like my kids do a lot of creative activities. I do not feel like I do a good job supporting or capitalizing on these activities. Sometimes...I'm pretty sure I'm hindering things. Some recent creative thinking that comes to mind from my 7,5, and 4 year olds. 1. Son looking at speedometer on the way home, "Mom, if we are going 65 mph, can we figure out the car's newtons?" 2. Making a simulation of the watercycle in Minecraft. 3. Creating a variety of pirate paraphernalia from leftover pvc parts from sprinkler project. 4. "Mom, I'll bet I could figure out the area of this space that my swinging is taking up now that I know about pi." I didn't really follow up with any of them. Often times I don't have the math or science knowledge at the top of my head. Then it seems like it is so far removed by the time I get around or start to get around to it. I think I can use some things on the list to extend things out and provide myself more motivation and accountability. Like," can you make me a model of the car, so we can use it to see if we can figure out how Newton's since we know the car's speed and mass?" Or get some sticks and string and ask the same about the swinging. It will clue me into which questions they are really interested in, and help motivate me to figure it out since they've put the extra effort. Hopefully after doing courses like this maybe I can better the frequency and quality of my responses to their interests.
Answer by michellepelot · Apr 14, 2014 at 01:15 AM
My daughter likes to imagine people living parallel lives. She writes short stories about this and illustrates them...number 55 on the list. A grown up can support her by giving her the materials she needs to get the job done, as well as plenty of uninterrupted time to complete her mission.
Answer by Jackroyd · Apr 14, 2014 at 02:41 AM
My 3 year old loves singing and has recently started making up her own songs including new words to tunes she already knows, and new tunes to words from other songs she knows, as well as totally original songs. She particularly loves making up tunes just singing numbers, which is quite fascinating!
This activity covers numbers 11(listen to music), 27 (tell stories about problems, as often she sings about either real or imagined issues "what shall we do?" "how shall we do it?" "how can we find it?" etc!), 28 (pretend play), 32 (do more of what makes you happy), possibly even 38 (make a new thing from old parts?) and 55 (represent a concept).
As adults we can support her in this activity by giving her the space and time to create and develop her ideas, try not to interrupt the creation (unless she obviously is needing some interaction) and encouraging her to continue developing her new ideas. Allowing her time to hear more new music, singing new songs with her (when allowed...most of the time I'm told "no mummy, not you, just me" ...I didn't think my singing was that bad!) and perhaps reflect back the ideas she has come up with so that she can see that they were interesting to others and successful.
These are all things that I try to do but this is a useful exercise to remind me to spend more time allowing her the freedom to be creative when the mood takes her ( for whatever creative thing she is doing, not just this specific one) not interrupting and cutting it short when I am not in the mood or feel I am too busy to listen.
This was also an interesting exercise in that it shows how many different skills and creative processes can be involved in just one single activity...it's not just a 3 year old making a lot of noise, she is actually learning and developing and being creative in many different ways every time she does this. Sometimes as adults I think we lose sight of this.
Answer by Jackroyd · Apr 14, 2014 at 02:54 AM
It is interesting to see that musical performance is something that has been mentioned as a creative outlet /activity in some of the responses to this task, and it is (as others have pointed out) surprising to see that playing and creating music is a glaring omission from the above list. It has been proven that Math and Music are very closely related activities, particularly in the parts of the brain that are used to process them. In my experience as a music teacher I have seen many examples of how those who have a natural gift for learning and understanding music tend to be very good at, and confident with, Mathematics too (and also those who struggle with learning a musical instrument often struggle with math too). Just something to throw out there... :-)
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