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 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 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 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 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 alex73 · Apr 19, 2014 at 12:55 PM
1. Seeing a new machine (real or video) and building it from Lego
2. Please add it, probably.
3. Explain what is probably inside the machine and how it works
Answer by monikkem · Apr 27, 2014 at 10:32 AM
He has special Edu. Needs. He has an analytical mind and needs to see and do to believe. Finds paper folding relaxing. Enjoys nature and anything factual and /or unusual.
Got him to read books and watch online movies about origami. Stwrted very simply-planes, but is starting to make more complex 3D creations.
It has been a pleasure to see the interesting shapes and patterns he is starting to make.
@monikkem - does your son like to follow other people's designs in origami, or does he try to make up his own, or both? Traditionally, origami artists do focus on nature! I wonder why the love of nature and the love of origami often go together...
Answer by njbillips · Apr 28, 2014 at 11:30 AM
Though she hasn't had music class outside of school, my girl (6) loves music. During some of the (many) snow days we had, she spent time writing songs (including the music for them), and "playing" them on the guitar. She played around a lot with the rhythms - we just gave her lots of space and let her work. It can be difficult to give that kind of time, but the snow days were perfect for just letting her explore.
Answer by Silina · May 05, 2014 at 03:11 PM
I absolutely in love with the ideas so TRIZ, especially the ideal system (an absent system) idea. I am always surprised to see how my toddler finds the ways to incorporate different object into ideal systems.
1. She made her a seating spot out of a plastic box, so she can watch me more comfortable everywhere. It is very easy to take with her.
2. 38 I think, though i just realized that her box idea is not math.
3. I offered her another box a table, plus paper and a pencil and she has a research station :)
Answer by jjuday · May 08, 2014 at 09:38 AM
Currently, my child's favorite on this list would be #43, specifically around Minecraft. We support him by playing with him, and getting him to show us what he has been building.
Another area that has been fun has been the hallway chalkboard. It is a space for playing with numbers. One game has been adding and subtracting really ridiculously long numbers, just for the fun of it, because he thinks it is so cool that he can do math that is in the millions and billions and on. So, maintaiing that chalkboard as a place to play is another one.
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.
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 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.
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