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 cjmarchis · Apr 08, 2014 at 03:32 PM
My children tend to hit upon something they like and then keep doing it for awhile before moving on to something else. For example, one day they cut dozens of kirigami designs. Then it was pearler beads. Now it is playing games. It is always legos, creating machines (pulleys, levers, etc), or any kind of construction for my son. I think adults can support creative behaviors by providing lots of raw materials, time, opportunity for & support during failure, excitement about their efforts, and participation with them (but not always, they need time on their own to "play"). I also need to remind myself that these activities are real work, and they don't need to set them aside to complete a workbook page. Sometimes its hard for me as an adult to be ok with not having a way to measure progress, but allowing it to meander in its own way.
Yes, this is something that I remind myself often that just because she is "playing" in the backyard she is creating fairy houses, building things, making up elaborate stories this is real work and valuable learning time that I cannot measure on a page. Nor do I need or want to. But sometimes I think hmm let me see something in writing.Sometimes, it is hard to break out of the internal structure I hold.
A good reminder that kids need time to explore. School teachers must "cover" so much curriculum, the papaceve is usually much too fast.
Answer by LeistCatalano · Apr 08, 2014 at 06:39 PM
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.
Answer by Meggin · Apr 08, 2014 at 07:42 PM
we enjoyed reading this...made us think how many things are math related...My son was trying to stump me. Is beauty math? Is sleep math? We were finding math in cycles, proportions etc...thank you!
Answer by Ms_Matthews · Apr 09, 2014 at 01:14 AM
One of my students likes to play "Stop the Water" when we go to the beach near our school. This is a game where he finds broken bricks, large rocks, etc., and piles them in a tiny streamlet of fresh water running into the ocean. I think you should add this to your list! His is learning about hydro-engineering: what materials will water pass through, what do I do when the water simply goes around the sides of my objects, can I actually stop the water or can I just redirect it???
I can support him by asking these questions out loud when he is playing and running into challenges to spur his thinking. I can give him enough time at the beach to answer some questions. I can provide him with different materials to experiment with. I can present him with images of dams and reservoirs.
Answer by racherinh · Apr 08, 2014 at 11:53 PM
My girls love to play "opposite day" - where they do the opposite of everything that is said. I think this might fall under finding the inverse of a rule? Sometimes it is quite challenging - if mama says to go upstairs loudly, what is the opposite? Is it to go upstairs quietly, or to go downstairs quietly? I like to make up challenging commands with different layers of opposite.
Sometimes we come up with statements that each girl interprets differently, and then they debate which one is really the opposite.
I definitely don't always have the energy for this one - it can get quite tiring to always have to come up with an opposite when its really just time to set the table and get ready for bed. We are incorporating it into vocabulary discussions, though, and come up with an opposite of new words we are learning.
My daughter used to play this when she was 4 and 5. We called it "Yes means no and no means yes." because that is how she would announce to us that she wanted to do it. We would inevitably collapse in giggles when one of us messed up and mistakenly said what we actually meant! I'm not sure I played along as dedicatedly as you seemed to! ;-)
Answer by Kris · Apr 09, 2014 at 01:14 AM
First of all, I love the list of 60 - very concise but sparked so many ideas.
Here is an example of a creative game I have played with my son since he was about 2.5 years old and I foresee adapting for several years to come. After reading "Guess How much I love you," my son created a game based on this children's story. I
Here's how it goes:
1) Person 1 starts off by saying "Guess how much I love you?" 2) Person 2 then says I don't know. How much? 3) Person 1 says some kind of "measurement" (e.g., as tall as an elephant!). 4) Person 2 says a measurement that is bigger than the one provided by Person 1 (e.g., from our house to grandma's house) 5) Person 1 says a measurement that is bigger than the one Person 2 said and the process is repeated.
I was hesitant about playing this game at first because I didn't want it to be about one upping someone else, especially for something like love, but I quickly realized that this concern was greatly outweighed by the benefits (at least in my opinion). My son was learning to think of unconventional ways to measure an "abstract" construct such as love. He was learning about the concept of bigger and smaller and eventually we started playing around to introduce math numbers and terminology (e.g., I love you 5 plus 6 times 1000). (side note: a couple months ago I was informed by my now five-year old that I cannot love him more than a sidewise 8 because infinity is a never ending number. That comment led to a discussion about whether or not somethings like love have a limit).
It is a fun game we play and I guess that is the point. Upon reflection he has been developing his math literacy and creativity among other things, through this game. I suppose I have inadvertently supported my son, by introducing unfamiliar terminology, playing devil's advocate and asking him to think critically about concepts (e.g., why can't I love him infinity?), and following his lead by coming up with crazier and crazier forms of measurement.
Answer by corilewis · Apr 09, 2014 at 12:53 AM
My child will make structures out of anything. What sticks out is all of the times she used her "manipulatives" to build something instead of use them to solve the arithmetic. I honestly tried to allow her to build but I'm sure I redirected her also. She builds like crazy in minecraft and likes to play games and solve puzzles with me. She writes or narrates wonderful stories. She definitely has persevered and has practice being "stuck". She will amaze me with how she will see a pattern or shape somewhere that I didn't see it. She will say something like "oh, that looks like two sevens " and I'll look and look until she can show me and, of course, there it is.
Grown ups should wait and honor how she chooses to spend her time when her brain is doing its thing. Oh easy to say, hard to do.
My sons are builders. Love minecraft, but also do very well with duct tape (!). I'm over the moon when they do- I'd rather see them use cardboard than cellphones.
Answer by Sblair · Apr 08, 2014 at 12:54 PM
Number 20. Solve Puzzles.
For us, we love to put together actual jigsaw puzzles. Use this opportunity to look at the box, note the piece count. Help the child separate the ends from the center pieces, then count each group. Create an addition problem and note the total piece count. As the puzzle is almost finished, around 10 or 15 pieces left, estimate how many pieces are currently connected then count the remaining loose pieces and subtract from the total from the beginning of the project to get the actual total. Examine how the puzzle looks minus the remaining pieces. Perhaps discuss the time and days the puzzle took to complete. Multiply the total number of pieces by the active hours working on it to calculate the number of pieces worked on per hour. Making mention of the difficulty or ease a particular puzzle had. Help the child correlate this factor when choosing another puzzle, mentioning time constraints during the week that could also pose a delay in completing the puzzle.
Answer by yileinei · Apr 08, 2014 at 02:03 PM
My daughter loves jigsaws puzzles, so we sometimes take photos of our family and cut them with scissors to put them back together. We often change the pieces so we can make different faces i.e. mum with dad's eyes, or one face with another's hair, etc. She loves playing that!
Answer by perbui · Apr 08, 2014 at 01:27 PM
Number 2: make tables, charts, Venn diagrams, schemes, graphs
I taught my then 6-year-old daughter how to make Venn diagrams one day, and the next morning I found her trying to categorize plant-based foods into a three-way Venn diagram labeled "roots," "leafy veggies," and "starches." (She has this thing about eating well-balanced meals and finds my never-ending argument with my wife over where corn should be categorized amusing.) The problem was that I had never taught her how to do a three-way Venn diagram, so she had the circles side by side, with only two circles overlapping at a time, rather than having all three circles intersecting in the middle. I helped her to re-draw the Venn diagram, and then proceeded to help her write down the plants she had already listed while she told me where to place them. I started naming off other edible plants, and she was off. Finally, I asked her whether she had ever thought about seeds and where they should be categorized. In this example, I helped her in the process when she got stuck. I helped to organize her ideas and to write and record so that she could focus on generating ideas and doing the critical thinking. I extended the pattern with more examples for her to think about. I thought her use of the Venn diagram to be quite creative!
Answer by Kristin · Apr 08, 2014 at 02:03 PM
My daughter is very creative in many aspects. She finds really creative solutions to all types of problems. She likes to solve puzzles and create things out of recycling, found objects, nature etc... Sometimes this is art and sometimes she is building something that she wants either to solve a problem that she has or to make something just for the sake of making it.
I think the best way that I can support her is staying out of her way and not getting involved unless asked. Certainly, there have been times when I think to myself "there is a way to do" whatever it is that she is trying to accomplish. However, I restrain myself from doing so and watch her figure out the problem herself. She almost always comes up with a way to solve her problem. When she becomes overly frustrated and it is negatively effecting her process ie. she is ready to give up I reflect what I see happening ex. "I see you are doing x and it looks like you are really frustrated." I then try to ask open ended questions "what do you think would work to help you solve this problem?" "what if you tried it a different way or used a different material? I might supply a number of different items or suggest places we can look for an answer on how to solve her problem. Sometimes I ask is there something I can do to help you?
I try to avoid giving her "my solution" if possible. Even when she asks I'll explain why it might not be beneficial to give my input. If she insists I may walk through the process I see her going through with her and sometimes she hits on where the problem is in her solution. If not we will then collaborate on possible solutions and I allow her to teach me along the way. Generally, this helps her find what she is looking for. If not I may suggest she take a break from it and we'll go for a walk.
• Saying what you see, "I see you are doing x and it looks like you are really frustrated."
• Validating feelings.
• Asking, "Who?", "What?","Where?","When?", "Why?", questions
• Collaboration
• Taking a break and going for a walk.
Loving your approach. Are there books that you've read? Courses you've taken? Or does this all come naturally to you?
Answer by Eogruen · Apr 08, 2014 at 01:52 PM
My 7 year old loves nothing' better than to be in her room listening to a good audiobook and doing her own art- drawing, making paper dolls, creating collages from paper and fabric scraps... One day she asked me for an old plastic bottle. An hour later I walked in and it had become a doll with a cardboard head and fabric clothes. mathematically, I think she has learned a lot about patterns from drawing and she is really interested in geometry, probably as a result of all this art and from being a very visual person. My 3 year old, on the other hand, learns a lot right now by asking WHY? And why not? And "if x is true, then why not y?" And if I can't do this, can I do that? She hasn't applied this questioning to math, but just about every conversation involves five why questions In a row! My 10 month old is very creative in learning to get around. She is not quite crawling but becoming increasingly ,mobile through a combination of scooting and reaching. Watching her, I am in awe of the inate drive we are born with to learn and explore.
"…in awe of the inate drive we are born with to learn and explore."
(I'm just appreciating your comment.) :-)
Answer by Sapphyrblue · Apr 08, 2014 at 07:42 PM
Pretend play - this is a big one for my 5 yr old daughter. She comes up with elaborate stories and within these stories are characters who face a myriad of problems. She "plays" with solutions and sees how these characters handle the also imagined consequences of their choices. These stories often go on for days with all sorts of new developments. I think this helps her puzzle out relationships and difficult situations without having to actually experience all of it in reality. It is so fun to join in the stories and throw in curve balls. What I find remarkable is the curves she creates on her own and how she does not follow the same logic I would have.
Answer by oxanavashina · Apr 08, 2014 at 04:06 PM
My younger son loves to jump, climb, roll, dance - move, in short. I sometimes try to make a game out of it - ask him e.g. if he can walk like a table. Or would he like to be a lawn mover, me holding his feet. Or ask him questions so that he tells me a story of his being Zorro and climbing a high wall to resque a friend. Short, I try to create a context and a play out of what he does. The elder ones loves to build contraptions out of basically any garbage. I have to provide ressources and organize the workspace - meaning I have to make sure that we have enough cardboard, plastic bottles, wire, electronic modules etc. Moral support as well - in case something doesn't work as expected - and in case it does!
Answer by mjones · Apr 08, 2014 at 04:32 PM
7. Make as many mistakes as you can, on purpose.
I do this with my math groups, where I allow them (if they're unsure) to give me the wrong answer. The kids find it funny and just say a random number. For example, I have an estimation station in my room and allow the kids to make guesses for a prize at the end of the week. I have them put a number that's too high and a number that's too low to have them set error boundaries for themselves. Unfortunately, they typically do 1 is too low and 1,000,000 is too high. I want to help them narrow down without taking the activity away from them entirely.
Error boundaries is great, you might try asking for a number you are sure is wrong, but someone else might think it right.
Answer by Percy · Apr 08, 2014 at 07:42 PM
My son expresses his creativity through creating inventions and musical composition. He needs the support of adults to provide interesting materials, long periods of uninterrupted time to explore inside and outdoors, someone to listen to his length explanations of his creations or songs, and someone to help him find the answers to his many questions.
Answer by jess · Apr 08, 2014 at 07:42 PM
1.During Centres time, some of my students were playing with Kapla blocks, creating structures and patterns. Working together, they arranged them in a pattern and began to add layers. They wondered how tall they could make the structure. When they ran out of blocks, we took a picture. Next they wondered how strong the structure was. They placed various items on the structure & it still held. They thought that perhaps it would hold one of them? At this point more students were becoming involved. I supported a student in climbing onto the structure. It was very exciting.
2. Notice patterns…
3. Grown ups can support by providing the materials, documenting the process, encouraging the testing & questioning of an idea, encouraging the excitement.
Answer by dnamkrane · Apr 08, 2014 at 07:42 PM
There's a lot here that both of my sons do, but "games" is something that they do together and frequently. The concept of "rules and regulations" comes up frequently, and they constantly butt heads about whether or not the good guy always has to win. For the most part I'm happy to stay out of the way, but I think it is my job to step up when needed and make sure things are done fairly by both. Games aren't fun if one person always gets their way, and that's not a lesson I want them to learn.
One of them really likes strategy games like chess, while the other likes puzzles. I think they're both getting to the same thing, but using a different route. I'm happy to do both with them.
Answer by Brianna · Apr 08, 2014 at 07:31 PM
My kids have done some really fun dramatic play. For a while- they were playing restaurant (together!) and my 7-year-old would order food and my 5-year-old would prepare it for him. I would love to support this type of play more by taking them to a restaurant (or a doctor's office or a grocery store) and really thinking about all the things that happen there. Then I could help them to integrate this understanding into their play. (Other creative things that I am so happy to see are my 5 year old asking "Why? Why? Why?" and lots and lots of construction around our house. They build some truly wonderful things. And it is wonderful for me when they play with toys in non-traditional ways.-- My little guy would pick up anything and pretend it was a telephone to call his Nona or his favorite teacher. :) ) p.s. Thanks for this awesome list! Inspired by so many great ideas! (Used to love doing math scavenger hunts in the classroom and would love to do some at home too!)
Answer by dendari · Apr 08, 2014 at 07:38 PM
How do you work in the 4th dimension?
I usually think of time as the fourth dimension. One of my favorite ways to work with this dimension is animation or cartooning, stop-motion, or just motion in real time, like dance.
Another way to work with dimensions is through projections or sections. This one is more abstract.
Flatland has some good ideas for visualizations.
ted lesson on space time came through my facebook feed today
http://ed.ted.com/lessons/the-fundamentals-of-space-time-part-1-andrew-pontzen-and-tom-whyntie
Regarding flipbooks--I've ordered from http://fliptomania.com before. Long ago. Now I see that there are so many more sites to google.
We were just talking about this today! My kids suggested that in the 4th dimension we would either explode or turn into something crazy like a flower. Then they very quickly started multiplying dimensions and imagining millions of them...
I resisted very hard suggesting time as a fourth dimension, because I didn't want to direct their thinking too much. But I like Maria's resources as expansion suggestions!
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