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

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.

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.

#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.

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.).

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.

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.

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.

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.

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.

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 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.

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!"

#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...

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.

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.

My children tend to hit upon something they like and then keep doing it for awhile before moving on to something else. For example, one day they cut dozens of kirigami designs. Then it was pearler beads. Now it is playing games. It is always legos, creating machines (pulleys, levers, etc), or any kind of construction for my son. I think adults can support creative behaviors by providing lots of raw materials, time, opportunity for & support during failure, excitement about their efforts, and participation with them (but not always, they need time on their own to "play"). I also need to remind myself that these activities are real work, and they don't need to set them aside to complete a workbook page. Sometimes its hard for me as an adult to be ok with not having a way to measure progress, but allowing it to meander in its own way.

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?

7. Make as many mistakes as you can, on purpose.

I do this with my math groups, where I allow them (if they're unsure) to give me the wrong answer. The kids find it funny and just say a random number. For example, I have an estimation station in my room and allow the kids to make guesses for a prize at the end of the week. I have them put a number that's too high and a number that's too low to have them set error boundaries for themselves. Unfortunately, they typically do 1 is too low and 1,000,000 is too high. I want to help them narrow down without taking the activity away from them entirely.

Pretend play - this is a big one for my 5 yr old daughter. She comes up with elaborate stories and within these stories are characters who face a myriad of problems. She "plays" with solutions and sees how these characters handle the also imagined consequences of their choices. These stories often go on for days with all sorts of new developments. I think this helps her puzzle out relationships and difficult situations without having to actually experience all of it in reality. It is so fun to join in the stories and throw in curve balls. What I find remarkable is the curves she creates on her own and how she does not follow the same logic I would have.

we enjoyed reading this...made us think how many things are math related...My son was trying to stump me. Is beauty math? Is sleep math? We were finding math in cycles, proportions etc...thank you!