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 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 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 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 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 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!"
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 corilewis · Apr 09, 2014 at 12:59 AM
BTW, I'm not sure what a concept map looks like...
I'm not sure what context you are asking this question, but in general terms a concept map is a visual representation that illustrates how different concepts are related. You can create them in different ways. I have used pictures to create concept maps (e.g., http://www.accessexcellence.org/AE/AEPC/WWC/1995/concept-map-4.gif) as well as more traditional formats (e.g., http://blogs.nature.com/ericwubbo/CMapSummary.jpg) Typically, as material is understood "better" (aka more deeply) concept maps become more sophisticated. Examples of how you can use them: 1) show learners how ideas fit together either before or after ideas are presented, 2) help to clarify your understanding of how several concepts fit together, 3) as a work in progress as you learn material. The key to a concept map for me is to think of it as a work in progress - revise, revise, revise
For a second there, I thought your "mutation" link led to a unicorn.
Regrettably I cannot take credit for the concept maps :) I just found a couple on the internet to illustrate the two types of concept maps I've used (I should have made that more clear) - although I must come up with an excuse to create a concept map that includes unicorns and dragons ;)
Maybe a combination chart for chimeras? Bird + Lizard = Dragon? Like Creebobby comics archetype times table:
A concept map shows connections between ideas or objects. Here is one map out of several my kid and I made from Peter Gray's Free to Learn:
BTW – I know and embrace "The Value of Free Age Mixing" as a main principle of Maria Montessori. Best!
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 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 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 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 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 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 scpnorman · Apr 09, 2014 at 01:15 AM
My 19 month-old son loves patterns and puzzles. When he had mastered some of his wooden peg puzzles, we started to turn them upside down, to give them a new twist. Like most children, he also likes to use his toys in nonstandard ways. Recently, anything that he puts on his head has been a "hat" (wooden blocks, toy cars, etc.).
Answer by champalto · Apr 09, 2014 at 02:32 AM
#43 jumped out at me. My children love to create in Legos and Minecraft, both realistic structures and fanciful ones. I can support them by giving them plenty of time and space for this important play.
Answer by Plasticflywheel · Apr 09, 2014 at 02:33 AM
One of the kids in my math group was trying to show us how he does multi-digit division last week. I had him write out the problem on the whiteboard. No one, including myself, could get any idea of what he was trying to do, but I felt that he had a valid concept. Today, I asked him to explain what he was doing out loud while I wrote it on the board for him. In this way, we were able to get his thought process in a way that him doing the writing didn't accomplish. ( In essence, what he is doing is rephrasing a division problem as a multiplication problem.) The other kids began to catch on to his idea and it game them (and me!) a new way to think about division. I would call this: Do something your own way and then teach others how to do it your way.
Answer by PruSmith · Apr 09, 2014 at 03:13 AM
Pretend play and noticing patterns are two items on the list I've seen a lot of recently. In both cases I've found the best responses come from a passive involvement on my part: there to engage, but not direct, their interest. Those are the moments the kids seem the most energetic, focused, and creative in their explorations.
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