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 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 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.
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 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 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 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 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 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 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 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 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 jaaane · Apr 09, 2014 at 03:11 PM
Looking at this list I can see that a lot of the free play my kid does involves these activities. Right now he is obsessed with lego and minecraft. The lego is taking over my house a little bit and I could probably be a bit less neat-freak ish about that. One thing I would like to do is to try to stop rushing through the stuff we have to do (homework, dinner, etc.) so that we can relax enough to talk about these concepts and enjoy them. One thing we do a lot of is make lists. About everything. Activities we want to do together, ideas for making getting ready for school/work easier, food we want to try, etc.
Lego suggestion: IKEA Trofast bins, and a train table for working on. That helps us. Of course, we are lucky that we can allow it to take over a whole room of the house ("The Lego Room").
Answer by juggling_ginny · Apr 09, 2014 at 10:37 PM
I think my daughter often expresses her creativity, in maths and in many other things, with repetition. If we learn a new game, she likes to repeat it again and again (until I am thoroughly sick of it) to hone and refine her strategy. If she comes across an idea that captures her imagination, she wants to repeat it again and again to enjoy the same results or see if something different happens - whether this is mixing baking soda and vinegar or doodling crashing hydra heads in the manner of Vi Hart.
I think I'm still learning how best to encourage this creativity - I think a certain amount of what seems to me to be at times almost mindless repetition is necessary for a child to internalize knowledge and gain familiarity and confidence with something new. Then I think there is a risk of a child becoming stuck in an increasingly unsatisfying repetition of something that is getting stale. Sometimes a variation occurs, either accidentally, or on purpose, that changes the outcome and sparks a whole new level of learning. But sometimes this doesn't happen and I need to learn when to intervene, to suggest changing the rules of the game, varying the initial conditions of the experiment or making mistakes on purpose to see what happens then.
Answer by tselie · Apr 10, 2014 at 01:35 AM
Using graphs in the explanation of problems like Venn diagram, creating her own puzzles and crosswords, drawing - these are just some examples. About supporting, this is a different issue, I give her some space and allow her to do her own stuff and then she explains to me what,why and how she did this or that. But mostly she prefers to work with me by following the particular algorithm.
Answer by CynthiaDadmun · Apr 10, 2014 at 02:52 AM
To answer the posed questions -- my five-year old's major source of creativity is building crazy things out of his Lego sets, which are quickly dismantled and re-purposed as soon as the "official" model is built. I support this by trying not to be broken-hearted seeing the awesome original model go back to pieces :) The "product" he creates may not be totally amazing, but the "process" he goes through to build it definitely is. (Often the product is pretty good too.)
And if I can be a divergent thinker myself here, I'd like to add my comments regarding items in the list:
14 Surround yourself with a Math Circle --- What is this and how do I get one?
24 Rotate, reflect, shrink and stretch your pictures --- Fun project with photocopier! Maybe tracing paper.
27 Tell stories about problems --- I like this, like a backwards story problem. 2+3=5...what's the story?
30 Seek your favorite number in the Encyclopedia of Sequences -- What is this?
33 Plan to spend a long time stuck; if you are not stuck, pretend you are --- Love this!!! Must encourage kids to SEEK OUT stuckness (ie, true challenges). How exactly to do it?
35 Make rough estimates --- Must find new ways to encourage estimation, very imp real life skill
42 Make your own rules, formulas, theorems --- Fun game idea, make your own rules... how to make math-y?
44 Cultivate favorites among each type of math objects: your favorite polynomial, prime, surface, identity and so on --- Yes! Good general motivator technique, not just math.
47 Go on a scavenger hunt looking for a math concept --- Fun! Two kids could set up items for each other to collect (ie pile of five blocks, a written numeral five, etc.)
Answer by mirandamiranda · Apr 10, 2014 at 04:37 AM
The last couple of days my daughters, especially my eldest, have been engaged in building a 'clubhouse' in the back garden. They are using plenty of "old parts' to make a 'new thing' including bits of mouldering wood, broken play equipment, old window screens, blankets, old shelves... There are bedrooms for each of them, a kitchen, a living room with puppet theatre tv, a garden with pot plants and no doubt more will be added tomorrow! It is great to see how creative they can be about repurposing things and how their imagination imbues their surroundings with so much promise and potential.
I think the best way I can support this behaviour is by repressing any feelings along the lines of 'get this eyesore out my garden!' and instead appreciate, as in the untidy room cartoon, what it represents for the children.
I am not sure how mathematical this is though. There is certainly some engineering going on but I wonder if I should try and draw out mathematical concepts or just let well alone. I don't want to threaten their ownership of their creation, or turn it into a chore.
Answer by kata · Apr 10, 2014 at 06:28 AM
1. Last winter my daughter (11) started to make a lead so that she can take her rabbits for a walk. She stuck to it as various things didn't work, changed to different fabric, adjusted the size, changed the closing mechanism, etc.
2. She persevered, took breaks (sometimes several days), drew pictures about it, estimated size and area, made a big thing form little things, used old bits of fabric for the body and crocheted the lead itself.
3. I supported her by letting her have the time, place, she had access to the tools and materials. It was important for her that I stayed out of it and didn't take over, but I did make the odd suggestion when she was figuring out each of the problems she encountered. With my encouragement it could have led into another activity, such as learning some stitches, designing and cutting out patterns, enlarging etc.
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