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 Court · Apr 09, 2014 at 01:14 AM
My son is always coming up with creative, funny names for himself, renaming things and or coming up with creative solutions to problems that are funny. They usually sound funny in your mouth when you say them. I write them down in a notebook so we do not forget them, but he and his brother always remember them because they are so funny and always make them laugh- huge big belly laughs that only they understand. I'm not sure if this is on the list. I think adults can offer support by not trying so hard to force our own ways to connect concepts for the kids. Maybe we should let them come up with what makes sense to them and makes them burst out into fits of laughter every time they think of it. Then the concepts would stay in their minds longer.
I agree with your comment.
"I think adults can offer support by not trying so hard to force our own ways to connect concepts for the kids. Maybe we should let them come up with what makes sense to them and makes them burst out into fits of laughter every time they think of it. Then the concepts would stay in their minds longer." Adults can have a tendency to do just that--force our own ways to connect concepts for kids; experiences then become more about the adults and less about the child(ren). Best.
Answer by KaleSprouts · Apr 09, 2014 at 01:14 AM
1. Often, my daughter (5) will gather some paper, tape, glue, and scissors and set out at making 3-D objects. I'm always amazed at the results. Often she figures out the right shapes in the right orientation to make her desired object, even if it takes a few tries. Her twin brother isn't interested in doing this as his still developing motor skills frustrate him, but he comes up with very interesting ideas to try building in Minecraft. Since Minecraft mostly uses cubes, it has been a challenging to make shapes that need curves, but has inspired him to figure out how to creatively use blocks to represent the curves he wants.
2. Right now things related to time are interesting us.
3. Well, this is more overarching than specific to my example: but if it's not fun, start something new.
Answer by jbrabham · Apr 09, 2014 at 12:47 AM
My students love to use nature in play. Fallen trees on the playground become forts or balance beams or part of a parkour course. They drag limbs from the woods to make structures. They create their own play place. I see true creative minds at work.
This kind of creative activity includes more than one of the 60 behaviors. Kids argue with each other, kids persevere, create games around it, etc.... It's not specifically listed above, but many aspects of this activity are there.
Adults can support this kind of activity by letting it happen and by not insisting on too many rules (just rules of safety) and for providing the freedom for the kids. I find that if I am with the kids - instead of watching from a distance - they limit their activity. They many not want me (the teacher) to hear the arguments or they're afraid I won't let them try something....
Agreeing with you--
That's important isn't it. . . knowing when to let the kids argue and work things out on their own and when to step in.
Answer by Scubadawg20 · Apr 09, 2014 at 01:09 AM
I have a 3 year old and we are currently in the stage of asking why about everything. I have found that as I answer each "why" eventually we each a point where she is satisfied with the explanation. I just have to sometimes remind myself when I'm hearing why for the hundredth time in a day it is for a good reason. This is her way of learning and making sense of this big world around her.
If I may, just a tip that you probably already know. Eventually you'll get questions that you can not answer; don't panic! Make it a learning experience by saying, "I don't know, but we can find out." You might go to the library for a book, visit someone who knows the answer, etc., etc.
When my kids ask just "Why?", I say "Ask a more specific question." It makes them think on their own a little and keeps me from losing my mind. I feel like plain old "Why?" is lazy.
Or, of course even better is "Well, why do YOU think?" (And as someone else said, bite your tongue unless their idea reveals a totally wrongheaded idea of the universe that simply has to be corrected.)
I agree with both of these points. Thank you for sharing. I had never thought of why as lazy but I like that perspective, especially for older children. Now that my son is approaching six years old, I can see the long-term benefit of getting him to ask more specific questions. He's also a child that is very focused on getting the right answer, so I've been responding with "I'm not sure let's explore" a lot more then I used to. Then we try to come up with different ways to do a task or different ways to look at the question. By taking this approach I try to focus more on the process then the importance of finding a right answer-that can come later.
Yeah -- I'm a scientist, and I think there's generally way too much focus on "science facts", memorizing things and getting the "right" answer. Definitely NOT good training for actual scientific research (in which you need comfort with ambiguity, uncertainty, being wrong and screwing up!) I'd much rather my kids practice coming up with ideas on their own, considering alternatives, and, when possible finding a way to test or at least explore their ideas. Encouraging kids to think there's one right answer is counterproductive -- and also gives the impression that science is all figured out and they should look to an authority figure (or text) for the answers. My favorite technique to encourage critical thinking is to give them an answer that is clearly ridiculous...then they say, "No! It's [more likely answer]". This ensures they really evaluate everything I say to see if I'm pulling their leg.
Now, I'm not quite brave enough to do this with math -- I correct them if they think 7+4=10 :)
I've been playing around with how I correct my son if he's adding something. Here's a scenario from today depicting one method that I find works well: He asked me how much I spent on buying tickets to his school musical. I said twenty dollars. He asked me how much I spent on each ticket-I said I bought four tickets, so how could we figure out how much I spent on each ticket. Instead he volunteered a guess, "hmmm... $7 is closest". Instead of saying that's not right or correcting him, I ask him to explain how he came up with that
number (*I picked up this suggestion from someone else in this forum). He said I added them together. We did the addition together and when we got to 28 (7+7+7+7) he explained that he missed one seven when he did it and got $7 so thought that was the answer. So, I rephrased the question and asked, "if four 7's equals $28, do you think I spent more than or less than $7 per ticket?" He said less, paused and then said $5 because two 10's is 20 and two 5's is ten.
Thanks Cynthia for sharing a method for encouraging critical thinking. I'd love to hear about other people's creative suggestions for promoting critical thinking or "correcting errors" (especially for younger children)
Yeah me too! Critical thinking in little kids is one of my obsessions right now. Strangely, there seem to be plenty of resources on specific subjects (reading, math) but few on critical thinking. There are a few logic and analogy workbooks available. This Can You Find Me? book is okay for my 3yo and 5yo:
http://www.amazon.com/gp/product/0894557947/ref=wm...
And there are books to train analogies (for acing GATE tests!). But many of the other books on "critical thinking" turn out to be books promoting Creationism! (who knew?) I just went to a seminar about reading skills in the common core, and really its all about critical thinking. Main take home was encourage kids to read nonfiction, ask questions and insist they point to evidence in the text to support it. Even have them annotate text to find evidence (ie, underline, circle, make notes).
I like your desc of your kid figuring out the math -- so fun to see the gears turning! Like you said, its all about focusing on the process, not product.
@CynthiaDadmun Thank you so much for the book suggestion. Always love a good recommendation for a read. I just ordered a bunch for promoting creative thinking. You referred GATE tests. What are they?
Oh that's the acronym for Gifted And Talented Education here -- I think it's funny that the main incentive for parents to teach their kids logic is to ace the entry tests for gifted programs, which I believe are basically IQ tests with analogies of various kinds. You'd think logic and critical thinking would be a priority just because!
Answer by AGray · Apr 09, 2014 at 04:50 AM
Today my kids were painting butterfly pictures - we folded them in half and talked about symmetry. I should let them paint and do "messy" projects more .
Answer by Cat · Apr 09, 2014 at 02:41 PM
It's not hard to find examples of my children's creative behaviour; it's continuous. One simple example is how they come up with novel and interesting ways to use every day household items or items I've put in the recycling bin; because I have already categorized these same items in a particular way, I would never imagine to employ them in the manner my children do. Their creative use of things can lead to absolute chaos in a house so a way a parent could support this is to recognize the creativity inherent in this chaos rather than only chastising children their children about it. What I've come to know is that, to a child, a tidy living room is a blank canvas... :)
"to a child, a tidy living room is a blank canvas..." - a whole story in a phrase! It reminded me of this comic strip by lunarbaboon:
I love the cartoon that you've posted! I even sent it to my son who sometimes despairs at messy rooms. That said, I feel that children need order, some more that others. The great observer of children, Maria Montessori, tells a story about a crying children, seemingly for no apparent reason, until the adults realized that mama was carrying her coat, not wearing it. (In the child's mind a coat was to be worn, not carried.) It's the biggest job children have is to make sense and order of adults and their world. I feel that it's important to start from order–in the classroom, a day at home, in life. I liken it to great abstract painters beginning their careers by first learning to paint like the masters of realism. Balance is my mantra this morning. Best.
I think everyone has a need for the personal balance between order and chaos. Some people need relatively a lot of order, and others relatively a lot of chaos. There are some gender differences, too. For example, many females prefer to play games with stationary, busy fields (such as "Where is Waldo?") and many males prefer to play games with a single moving object on an empty field (like soccer). In mathematics, there are sequential problems that require one formula to follow the other, and insight problems that make you review a lot of pieces of information at once, and put together a holistic conclusion. As long as people can try various levels of order and chaos, they usually find their own balances.
Whoa... Waldo is a berry in the bushes, and the soccer ball is the wild boar to be chased. Just think of all those Big Fish Hidden Object games...they probably have a major gender imbalance too.
I really appreciate the quote and cartoon -- thanks for posting. As much as I like the Montessori approach generally, that whole "ordered environment" thing just makes me feel like a Bad Mom -- cause ours isn't!
I like (and can maintain) order in some parts of my environments, and then for other parts, I like and can maintain chaos. The balance is very dynamic, like riding a bike. I do use a lot of Montessori methods for the order part of it all!
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... :-)
Answer by lisa.koops · Apr 16, 2014 at 02:37 PM
My daughters create "mash-ups" of songs - take one line from one song, one from another, and add a little bit of their own - with consideration for how the phrases fit together musically. This fits with #37 in a way. I believe the grown-up support depends on the child. I did a research study on this, actually - adult behaviors that enhance or inhibit children's musical play. For some children eye contact, encouragement, and interest was supportive, but for others it shut down their play. My 7-year-old blooms creatively under adult interest and affirmation; my 2-year-old seems to thrive with her sister's presence or that of a peer.
Answer by charlotte.mazur · Apr 26, 2014 at 02:36 AM
She is so creative it is tough to pick out just one example. One really neat way she just started is writing her own songs/tunes and writing down the patterns in a way she understands so she can play the same tune/music over and over again. She doesn't read music and hasn't been to a music class outside of the music they teach in her 1st grade class so she doesn't have formal education surrounding it but she has come up with a way that works for her. It is fascinating to see.
@charlotte.mazur - can you photograph and attach here a sample of your daughter's music notation? Sounds fascinating! Glad you are not trying to replace it with the traditional notation right away. Designing your own symbols develops the mind, and it is a staple of their work for both scientists and artists!
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 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 kclauser · Apr 08, 2014 at 07:42 PM
I immediately thought of noticing patterns because my son does this all the time, and yes it is on the list.
He will notice visual patterns or patterns in sound and he always shares that with us. I tell him he's correct and it's such a good job, but I need to really jump on those moments to engage him more; ask him what other patterns around he sees or hears and not just gloss over it when he does that. He does other items on the list frequently, like making models with found objects, making charts, asking about large vs. small numbers and what happens when you combine them. I need to foster this behavior by encouraging it and having a dialogue about his ideas without rushing him.
So much about this statement I like. "I need to foster this behavior by encouraging it and having a dialogue about his ideas without rushing him."
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 Tia Knuth · Apr 08, 2014 at 08:24 PM
my 20 month old uses tools in unexpected ways, differently than I am accustomed to using them. Oftentimes instead of drawing with a pen or pencil he will stab and rip the paper. I am saving it to frame. He did this with a beautiful mandala coloring page when my inclination was to stop him because I had an expectation for him to do it a certain way.... My way. I let him do it his way.This type of creative exploration is the kind that kids are better at because they don't yet have preconceived ideas about things.
I would add to the list. Safely use a tool in a way that is not it's primary function.
Adults can observe, ensure the activity is safe and follow the child's lead with their own exploration or mimic the child's action. What else can a pen do on paper?
Answer by pkouch · Apr 08, 2014 at 11:05 PM
My child had a sharp eye and mind for patterns. She would notice pattern in shapes, colours, sizes and other things even words. She also made patterns using Lego bricks. Sometimes she would rebuild a pattern that she had seen somewhere during the day and sometimes she would get creative and build her own structure with perfect symmetry. She did this when she was between 8-18 months old. She grew up being quite comfortable with grasping math concepts.
I wish I had more knowledge about how to support her. I just came up with the idea that she might be interested in music and provided her with a decent music knowledge and skill. She really enjoys and appreciates that, but I am sure I could do much more to encourage her creative mind.
Answer by fcogan · Apr 08, 2014 at 11:48 PM
My 2 year old granddaughters love shapes and puzzles. They persevere at matching shapes and patterns while learning various shapes and colours and learning how many sides make each shape. I like to watch and encourage them to work the puzzle by themselves without my input. My 4 year old grandson loves numbers, counting, simple adding and subtracting using his toys and his fingers. I love to now watch as he designs lego models to fit around some of his toys to make shelters, hangars for his little planes or garages for his cars - simple understanding of volume and 3D modelling.
Answer by Kerrycapp · Apr 09, 2014 at 01:14 AM
My kids like to build, particularly with Legos and we play with them daily. In recent months my six year old's creations have become sleeker, often symmetrical and it is obvious that he's building with an idea in mind. We usually borrow books on legos from the library as well as watch building videos where he can pick up on ideas, building techniques, etc. Also, as part of supporting his passion and learning we tend to let him build without interruption unless it's absolutely necessary. Lately the weather has warmed where we live and we've put materials in the yard - logs, sticks, stones, buckets, rope - that the kids can build with (theory of loose parts). It tends to look like just a bunch of stuff in the yard but it's so much more. They spend hours devising, planning, reworking their creations and it often keeps them engaged for an hour or more.
Answer by MerrilySpinning · Apr 09, 2014 at 12:37 AM
#43. My three younger children love playing Minecraft. They have built a world and have a few friends they invite to play in it with them. They've each built their own houses with rooms for each family member, taking care to supply each room in a way that would be pleasing to its owner. They have animals and gardens, and floating palaces... it's amazing.
I'm pretty good about letting them have time for this sort of play but I need to ask them to tell me more about it -- what things they have to mine in order to have the resources to build things, why they chose a particular material for a certain project...
Answer by JenAM · Apr 09, 2014 at 01:14 AM
My girls spend a lot of time acting out play situations with dolls or themselves. I can continue to support this creative play by suggesting props, or storylines that help their play continue and not get stuck in the same area over and over again but transcend into new genres and problems.
Answer by Joyce · Apr 09, 2014 at 12:51 AM
1. The grandparents bought my kids a gigantic set of Kapla blocks. They are identical blocks about 4.5" x 1" x 1/4", and you can build amazing structures by stacking them in creative patterns. My kids all got into this task at one time or another and we had so many structures on the floor of our living room.
2. # 37: Make a big thing from many small things
#43: Make realistic shapes out of blocks - the kids once made statues of each other!
3. We made room in our living space for these creations, for days at a time, and we let the kids take photos of their creations. Then we enjoyed watching them attempt to bombard them into collapsing. These structures were amazingly sound and could withstand having holes and other partial damage without falling completely down! Here are some of the photos they took. Check out the "bug!"
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