2D shape exploration with DIY Geoboard

I recently set up a simple DIY Geoboard provocation. It is a tray containing two cork boards, few jumbo push pins and few rubber bands.

A normal geoboard is a mathematical manipulative consisting of a board with certain number of nails half way driven in.
A DIY geoboard gives the kids an independence to set the nails/pins at their will and explore the shapes that pin arrangement makes. Another advantage of setting out individual boards and pins is that it helps in good fine motor skill practice.

When working on this provocation, Sid declared he wanted to make a square and figured out that he needed four pins for the vertices and that he had to place them in particular fashion to achieve his square. Till now, all he knew about a square was that it has four equal sides. But this provocation helped him to get introduced to vertices and angles.

In his quest to make square he figured out pin placement for rhombus and rectangles. Triangles were the easiest.

He then wanted to make a star and almost succeeded in pin placement but placing rubber bands for the sides was too confusing for him.

Nidhi wanted to try making a circle. She set off by placing the pins along the edge of the board and because the number of pins were limited she had to settle for semicircle.

She wasn't happy and insisted that she wanted to make a circle. I suggested that she spread out the pins along the whole board and when she did it, exclaimed "But Mom, this is an octagon. Not a circle".

I explained to her that she needs more pins to make a better circle. "But I don't want a better circle, I want a perfect circle" , she insisted. "Well if you need a perfect circle then you need infinite number of tiny pins." Though she could not understand my response, I wondered "Is circle a polygon with infinite number of vertices with infinitesimally small sides?"

One little discussion with a three year old trigger such wonderings! I explored more and learnt a lot. The power of inquiry is amazing.
 Curiosity is contagious!

PS: Please use discretion in offering young children with sharp small objects.Sid and Nidhi are under careful adult supervision when using objects such as jumbo pins.

Can kids learn Math by themselves?

Can kids learn Math by themselves?

 In my opinion the answer is Yes, but with proper scaffolding and understanding of basics.
Whether kids can learn Math by themselves in discovery or inquiry based, constructivist learning environment has been a hot topic of debate. The arguments from NO side seem to be assuming that the kids are left unassisted to learn everything based on discovery.

Here is what happened yesterday. Nidhi found a piece of cardstock. "Look Mom, I am holding it like I wear my blanket when I pretend like a princess". She was holding two corners of the cardstock together to make it look like a cape.

"Nice! What are you going to do with it?". Thinking a bit she replied "A cylinder." She quickly held two edges together and taped it. We took turns talking through the tube and exploring the sound effects.

Next, she put it on the floor and went in search of things to fill her cylinder. She returned with a pack of writing materials and started to fill the cylinder. When she lifted the cylinder everything fell off.
She then started to count to check how many crayons filled the cylinder. I remember her counting somewhere around 40.

Filling the cylinder with writing materials

Next she brought another piece of paper , asked me to hold the cylinder while she traced the bottom, cut it and taped it to the cylinder. Then she repeated the process to make another cylinder.

Tracing circles for bottom and lid

cutting out the circles

Proud owner of two cylinders

This I feel is a good example of inquiry based self directed learning.

• She set her own inquiry - how to build a cylinder?
• She set her own problem statement - How many crayons are required to fill the cylinder?
• She problem solved by herself - Putting a base and lid helps in containing objects.

However everything she learn was not through discovery. She already knows to identify  3D shapes through provocations. She already has a lot of practice in counting through roleplaying Grocery Shopping.

What she learnt newly is that

1. A Rectangle and 2 Circles are required to make a Cylinder
2. A Cylinder can be used to contain objects
3. Relative measurement terms such as full, half and empty
4. Problem solving skills.

She also tries to master her learning through repetitions.

What is needed for such self directed learning?

1. Curiosity - being inquisitive.
2. Prepared environment.
3. Just the right amount of guidance from facilitator.

Will this way of learning Math help her in future?
I hope that deepening her knowledge by self learning will become easier in future. She might learn or arrive at Surface area or volume formulae of a cylinder tangibly by herself leading to better understanding than traditional method of memorizing those formulae.

You have brains in your head and feet in your shoes,

You can steer yourself in any direction you choose!

 -Dr.Seuss 

Lego Maths

This is a simple provocation set up with some magnetic numerals and Legos. No questions asked or hints given. Just what can you do with a bunch of numbers and Legos?

Here is what they came up with. First obvious choice to both of them was to arrange legos from 1 to 10.

Then Sid started to make two digit numbers and wanted to know what they are.

This is their first interest shown towards learning numbers larger than 20.

Then Sid tried a little bit of number comparison by building towers and finding out the tallest and thereby the bigger number.

Nidhi resorted to sorting of legos by color and then counting them.

Now she declared "I want to count to 100!". But there was not enough Legos and so she came up with the idea of counting pattern board manipulatives. 

So out came beautiful patterns. Patterning as well as counting! Now that's a treat :)

Encouraging Block Play - A Progressive Approach For Young Toddlers And Preschoolers

Blocks are the most versatile, open ended toys that can be lifelong companion to any child.

A lot of research talk about why block play is important in toddlers and preschoolers.

I read up on those research articles and felt pressured that I have been losing time on introducing blocks to Sid and Nidhi. So, I hurriedly bought our first set of blocks from IKEA and presented it to the twins when they were almost 2 years old.

I was eagerly awaiting to watch them start stacking right away but to my dismay it laid unattended. If you are in that phase right now, relax! We are well past that stage now and blocks are an integral part of play in our everyday life now. How we did it? OK, Let me share my step by step progressive approach in keeping my then young toddlers( now young preschoolers) interested in blocks.

1. Start with building Horizontally and use pattern/idea cards

       Start slowly introducing blocks for very young toddlers.Though our mental image of blocks are tall stacked towers and castles, using them for particular task gives the toddler focus and a sense of accomplishment. Start with shape and color matching or sorting activities.
I made simple laminated pattern cards of cars, trucks, trains etc with the blocks I had and put them on their montessori shelves for matching. Make sure each card has not more than 4-5 blocks to start with.
Using magnetic blocks on cookie sheets can help reduce frustrations.

Laminated card made to match blocks

2.  Shift to building vertically and use pattern/idea cards

       Once you feel your child is ready for some tumbling excitement present the same blocks with idea cards such as a bridge, a house, a rocket etc.. The cards can be hand drawn 2D shapes or photo print of simple structures built by you.  This is basically a copy and build activity. To keep the interest alive you can present them with progressively complex structures.

An inspiration card for building a Rocket

3. Set up provocations with pictures of real structures

       Once your child has mastered copy and build with blocks or his interest has moved on, challenge your child to build with pictures of real structures. I set up provocations with pictures of castles, downtown, bridges etc and ask them if they can replicate the structures.
Take care to provide block shapes equivalent to the shapes in the real structure to avoid frustrations when introducing this step.

A provocation set to build castles

4. Enhance block play with add-on materials

       As your child gets older his play gets structured, imaginative and intentional. He starts to build with intent. To encourage this phase, introduce other materials in your block play area. The materials can also act as subtle hints on what they can build. For example, adding animal figurines with blocks can lead to building a barn/zoo. Adding peg people/cars can lead to building a community or race tracks...
Follow your child's current interest and add materials accordingly.

A Barn built with Magna Tiles and Animal Figurines

5. Encourage Tinkering with Blocks

        This suggestion is useful for older preschoolers who are interested in creating or tinkering. Present materials for tinkering such as glue sticks, velcro, scotch tape, masking tape, straws, cardboard tubes etc in the block play area. We found that foam blocks are great to tinker with.

A Tower crane lifting a bunch of sticks - built with Foam blocks, Tape, Cardstock and Straws

PS:
1.  These ideas came out of  my experiences with my kids and we are still exploring. There are many other ways to encourage block play if these don't work for you.
2.   Leave out the blocks for easy access and your kids will surprise you one fine day.
3.  If blocks are left unattended for long time, sit and build something by yourself and the kids will surely follow you.

Finally, there is no one way of playing with blocks. If your child only loves to knock off your beautiful structures, so be it! Just relax and have fun!!

Math Provocation - Button grouping

I arranged this simple provocation with a bowl of buttons and muffin tin.

  "How many different ways can you group/sort these buttons?"

I was very curious to see what kind of answers Sid and Nidhi could come up with. 

Number Sequencing

Provocation : Glass gems numerals and a muffin pan
What can you do with these numbers?

I set up this provocation yesterday asking the kids "What can you do with these numbers?" I also presented a chart from 1-20 hoping to give a hint on number sequencing. Sid instantly picked up on the hint and started to arrange the numbers in sequence in each muffin cup. Shrini also helped him pick the numbers he wanted out of the bowl. Soon, they had sequenced numbers from 1-20.

 Then they encountered a gem marked with zero. They both had a brief discussion on where should zero go.  It was not in the chart I had given them.I was curious to see what they conclude and they both agreed to place it after 20.

So much of thinking, team work and decision making process behind such a simple open ended question!
Next, it was Shrini's turn.She quickly filled the muffin cups with a gem each in random order. Then she counted the empty cups and said "Mom, I need 3 more of these (gems) to fill this tray." Yup, that's another way of doing this Math! :)

Simple Provocation: Household Objects

The idea behind this provocation is to encourage the twins to view the world around them in 3D. At first I thought of presenting them a few pictures of buildings such as the Louvre museum, Pisa tower, Egyptian pyramid. However apart from identifying the shapes of those structures, I wasn't sure how far they will take the inquiry further.

I also wanted to present to them the fact that most of the structures are made of multiple three dimensional shapes.

So I printed out a couple of castle images and presented it along with a few household objects.

Here is a snapshot of the provocation that was presented.

Simple Provocation - Household Objects

"Hey! Look at all those shapes!" exclaimed Shrini. I am glad she could perceive those objects as shapes rather than considering them as is.

I showed them the castle images and asked them what do they see. They listed all shapes they could identify. 

"Can you build your own castle?". They happily obliged and here are the snapshots of structures they built.

In the background, Shrini carefully studying the castle image before starting to build hers.

 Tada! Look at my castle!

"No Sid! This castle has a cone. You don't have one"- Shrini. "OK, Here's one with a cone"

Sid trying to balance a cube on top of the funnel. 

"Look Amma! Here is the gate that opens and closes"

"Will it stay or fall?!!" It stayed!

This was the most complex of all structures they could build.

Of course, blowing away the structure is more fun than building it.

Sid and Shrini started enacting the scene from Three little pigs - "Iam going to huff and going to puff and blow your house down!"

They discussed about different shapes, balancing them and wondered why it was easy to blow the cardboard tubes but not wooden cubes. Without a doubt, they had a blast!