Week 1 Task 2: Your child, the divergent thinking genius

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.

How do you work in the 4th dimension?

#61 Cue the music, "Clean up, clean up, everybody do their share!"

Now we can begin again with #1-#60. I like to begin from order, "Mind that you don't hurt yourself or those around you", and I prefer "Handle the materials respectfully." (It's the Montessorian in me.)

I love the list of 60 and this conversation! Best!

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.

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.

I love experiencing thinking through a child's mind. My eyes are constantly opened to a new way of thinkng as they explore patterns and relationships. It's my job to facilitate an environment that allows for their creativity while still embracing the laws of math.

One area that I partaiculary focus on in my classroom is making mistakes. I want mistakes to be comfortable as they allow us to make better sense of our reasoning. Mistakes are so valuable because they provoide opportunities to discuss the "why" in a process.

I think grown ups need to be open to the power and insight a child has. When we work together, we get a better understanding for the task at hand.

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.

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....

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.

My daughter loves to model and bake with sculpey. She makes people and does a great job of capturing many of the characteristics of the people and animals she chooses to make. This winter she created a chart of all the kids in her class, came up with 5 ornament designs she wanted to make and made everyone an ornament.

She also loves to play piano, which has been an awesome way to use patterns, and another annotation for numbers.

Is music an example of ethnocultural math? I haven't been able to find many examples of that, other than the mayans.

I have to admit I find the list of 60 a little overwhelming. Though I do see how some of my children's interests can fit into this list. I think I just need the confidence to do it playfully. I would love to find a math circle in our area.

When I take the time to reflect on some of her activities I can see the opportunity to point out math, I could have easily made a graph of some of the ornaments she made. We could have compared sizes of some of her ornaments, how much material and what colours she needed - we did a quick approximation at the store when we were buying sculpey.

When looking at this list I found some great ideas of creative behavior we've not yet done. My son loved the list. We use a program called processing and scratch that are both free and allow tons of creative energies to be released. Off the list we easily do about 15 of the activities quite regularly. Definitely have more ideas to try! I really think as grown-ups our job is to help our child find some sort of creative outlet and its good for us adults to have creative outlets too.

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.

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.

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).

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.

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.

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.

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!

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 .

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.