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 Nelleke · Apr 08, 2014 at 05:46 PM
For about two months, my 5-year-old used his snack at teatime to create math equations. He would use the strips of cheese to create plus and minus signs, and arrange slices of apple, crackers, etc. to stand for the numbers. Then he'd ask me the answer. "Mama, what is one minus two?" "One less than zero," I'd tell him. "Some people call it negative one." So, yes, you have "snack" in your list of 60 behaviours, and I supported him by answering his questions or bouncing them back at him to figure out.
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 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 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 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 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 nikkilinn · Apr 08, 2014 at 01:29 PM
My daughter (5) enjoys creating clothes for her dolls, sometimes with paper, sometimes with whatever fabric we have around the house. She draws and pieces together some very cute and creative pieces. I support her by keeping all of the craft supplies within her reach so when the inspiration strikes, she doesn't have to wait for me to have a moment to get something for her. I am also her head tape assistant and stapling assistant, and sometimes security guard when her little sister (3) decides to "help". :)
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 Elizabeth02 · Apr 08, 2014 at 01:11 PM
My son likes to create his own games. They often have simple math elements, but also a lot of creation and revision to make the game go well. I usually try to help him with the problem solving process, by asking questions about why some element isn't working well, and what can be done to make it better. I gauge whether his frustration level could take another mess up & re-try, or if he needs a little more help so he doesn't give up entirely. The best support here is to take the time to play the game with them and enjoy.
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.
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