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 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 amyhrn317 · Apr 09, 2014 at 02:29 PM
My boys have millions of Legos. They spend hours daily building their own abstract creations from their loose Lego collection. I enjoy watching them work on these projects....working and then revising their projects. I try to support them by providing them with lots of free time to be creative. And I ask them to describe their creations.
Answer by Carlough · Apr 09, 2014 at 09:51 AM
My son asked me to get out graph paper for him the other day. I was holding the baby and was tired...so I didn't do it. I'll get it out right now so it's ready for him in the morning, and resolve not to miss the moments when he's ready to learn in the future.
Answer by CHabq · Apr 09, 2014 at 09:51 AM
My son has been working with Legos a lot lately. Sometimes, he builds exactly as the instructions dictate. Other times he makes an addition or modifies a part or two. Sometimes he is inspired by other lego creations he sees. And still other times, he creates completely new creations. These creations stay around for anywhere from 2 minutes to 2 months and are also part of his pretend play. I try to support his work by creating spaces for him to keep and display his work, by engaging him to talk about his pieces and his thought processes and finding ways to show him that his work has value (for example, taking pictures and compiling them into an album or creating instructions for his original creations).
Answer by MindfulMommy2 · Apr 09, 2014 at 09:51 AM
My kids like to make up their own version of piano songs they learn. Some of the major elements of the original song are left in so you can still tell which song provided the base but maybe they will just change the order of the notes. Or perhaps they will add their own ending for a dramatic effect to the song.
Grown ups can support the children in this activity by listening to the made up songs and showing interest by asking the children to teach them the song.
Answer by Shannon · Apr 09, 2014 at 07:11 AM
38 - making new things from old parts. My daughter is in the middle of making a "root beer dragon" out of soda bottle caps. I'm not sure how to encourage this from a mathematical angle yet. I do think it is important to allow them to create without scrutiny. She intends to use the bottle caps as scales for her dragon, but I'm not sure the scale (proportion) is correct (I guess there's a math lesson!). I think it is important to discover this on her own. Then the doorways will be open to redesign her project, abandon it, or perhaps select a section of the original concept to work on. Either way, this self-discovered learning not only works her creative muscles, but learning without pressure of assessment or critique maintains her comfort in attempting her (divergent) ideas.
Answer by annettehaddad · Apr 09, 2014 at 07:08 AM
My daughter was playing with her fairy dolls today and began sorting them by colors of the rainbow. I sat down and joined her play, asking her what other ways we could sort them. We came up with all kinds of categories, ranging from hair color to what type of fairy they were. She was so happy and I realized that I need to do more of these things with her- just playing with her, following her lead and making small suggestions, not so much directing. I think this would be 16 and 17 in the list.
". . , following her lead and making small suggestions, not so much directing." I like this.
This suggests a neat directed activity! Could pull out a box of random toys or hot wheels cars and sort five different ways...
Answer by Valerie · Apr 09, 2014 at 07:05 AM
We wanted to support our 5 yr old's creative play in maths so bought her some mirror tiles and she played with them, putting them together in different patterns to show concepts like symmetry and angles. She loved the way that by putting a favourite toy in the middle of a house made of mirror tiles she could see an infinite number of her toy reflected back at her.
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 Goya55 · Apr 09, 2014 at 04:49 AM
we did an decanomial multiplication work with the Montessori beads and found the squares of numbers in the diagonal line of our bead lay out of the multiplication table. We also went to a park today that had a huge structure that had a triangular base and going up to a single point were there were ropes making a geometrical web for people to climb up. It wasa mathematical problem to climb!
Answer by Vanessakb · Apr 09, 2014 at 03:31 AM
These pictures are the result of a group of children I work with exploring growing and repeating patterns using cuisiniere rods. They are very tactile objects and this activity was repeated with enjoyment many times by different children. They taught each other.
My support in this activity was to introduce the concept and give the students the language they needed to talk about it. I also gave them the authority to photograph their own work so they could keep a record of it rather than finish up by tidying it away.
This activity encompasses many of the activities listed on the creative math behaviours. play, explore, represent, talk, doodle, give time.....
I think that an activity to be added to the list so that it is explicit, particularly in this day and age with our digitally cognizant children is use technology to experiment with maths concepts.
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.
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 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 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 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.
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