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 

Do snails have tails? - Start of a snail Inquiry

Sid and Nidhi got excited looking at a couple of snails in a planter box in our apartment. They have been peeking at these snails for some days now. So I wanted them to take their time and observe them. It was dark and I switched on the flashlight and we sat there for about an hour just looking at the snails.

I wanted to know what thoughts ran in their little minds. 

So, here is how the conversation goes...

I see...

Me: What do you see?

Sid : Two snails.

Nidhi: A mommy snail, a baby snail.

Me: What else do you see?

Nidhi: The baby is sleeping.

Sid: The big snail is walking.

I think...

Me: Sid, Why do you think the snail is walking?

Sid: Because it is moving.

Me: Do you think snails walk with their legs?

Sid and Nidhi : No! I think the snails don't have legs.

Me: Then, how do you think they move?

Nidhi: Like this! (Shows me like she is crawling by dragging her legs, makes a full round around the planter and looks at the snail and exclaims "Wow! It is still moving!")

Me: You mean it is moving slowly?

Nidhi: Yes! Slow!

Me: What else do you think?

Nidhi: I think its house is on that plant.

Me: Is it where the snail is going now?

Nidhi: I think it is going to its baby.

Me: Why?

Nidhi: Because the baby is crying like ooo-aaa (imitates a baby cry)

Sid interrupts and asks me "Mom, Do snails fly?"

Me: I don't know. What do you think?

Sid: No they don't. Birds have wings and they fly.

Me: So, snails don't have wings?

Sid : No!

Me: What is that on its back then?

Sid: Thats the shell. Turtle has shell. (Look, he is making a connection!)

Me: What do you think snails eat?

Sid : Cream cheese!

Nidhi: Sticks!

Me: What else do you think?

Sid: I think the sticks on its head are ears.

Nidhi: No, those are eyes!

I wonder...

Sid: What is that water?
Nidhi: Can snails jump?
Sid: Do snails have tail?

Nidhi: Where is baby snail's blanket? :)  I love how she is worried about the baby snail sleeping in the cold.


Since the twins are pre readers, I have a voice recording of these details. They get excited listening to it when played back to them.
Our next step would be to reflect on these thoughts and if they are still excited, to dig deeper into the subject. This is how an inquiry often unfolds. 

How does this conversation help them? It teaches them many important skills that are not being nurtured in traditional education environment as well as it should.
This kind of conversation helps them to
1. See - Really observe and deeply think about what we see.
2. Think out loud - It is a required skill for 21st century. Those who attend job interviews know what I mean ;)
3. Nurture Curiosity.
4. Appreciate the environment we live in.

So, the next time your kid notices something interesting and asks a question, try not to answer it by yourself. Instead, ask "What do you think?" and "Where shall we look for the answers?" and most importantly LET THEM THINK.

"Most of all, have confidence in every learner's ability to think and your capacity to nurture that thinking. The results will amaze and energize you" - Ron Ritchhart - Making thinking visible.

  

Deepening an Interest

A child's play is not simply a reproduction of what he has experienced, but a creative reworking of the impressions he has acquired - Vygotsky

How to help your child deepen his interest?

1. Observe

You might remember Sid and Nidhi's self directed project on Puppet Show. It happened on one single day - got inspired, made a plan, implemented and executed the show in one day. I thought to myself, "So that's that! They have tried their hands on it and they'll move on". Boy, was I wrong!
The interest in making puppets sustained. Sid was painting his cardboard box a little at a time every single day preparing it as Gingerbread house for his next show. They were also painting a lot of craft sticks to make their characters.
This sustained interest is the key to take the learning deeper. They want to do more but obviously did not know how. This is my cue to help them dig deeper into their interest. I observed that their interests were in exploring by themselves hands on.

2. Provide required materials and skills to explore 

I added a bit more craft items to their creative box - google eyes, bits of yarn, pipe cleaner etc. The twins transformed quickly into puppet manufacturers. Suddenly there was a whole product line of popsicle stick puppets.

Popsicle Stick Puppet Factory

Puppet Product Line

Notice how finer details are added now that they are provided with more raw materials. Working on creating their own puppets also helped them refine their cutting, gluing skills. They learnt that drawing with black pencil on black felt is not helpful.  They noticed that there are head to body  proportions to be maintained, that hand does not grow from back of our heads. However these learning didn't interfere with their creativity.

3. Provide the right amount of provocations

With so many puppets in hand Sid went back to his Hansel and Gretel story with opera music. Isn't it time for them to explore other forms of puppeteering? So, I switched off lights and put on a flash light. They instantly got excited about the shadows the puppets made and started to explore the shadows.

Shadow Puppet exploration

 Shrini observed that the shadows grew big and also shrunk as she moved. Suddenly, the puppets started talking among themselves about their appearances. Here is a small video of their shadow puppet exploration.


We then watched a small hand puppet show on youtube. Then I added a couple of paper bags to their creative box and showed them a few images for inspiration. They both chose a Monster puppet as their inspiration and worked on creating their own.

Testing out his hand puppet in front of mirror

Shrini said "Mom, I want to make my puppet talk". So I took a video of her Monster's interview. Sid joined in later. It was so fun watching them transform into their characters.

 I have pulled out a small String puppet I had bought during my last India visit to provoke them explore about Marionettes. The twins may not be future professional puppeteers but I hope these experiences give them pleasant memories like the one my grandfather gave me of watching a lady puppet made out of banana peel dancing elegantly.

 I am not sure how far this interest will be taken further but we are enjoying and cherishing every moment of this learning journey. Don't believe me? Try what we did  - Imagine your hands and legs are on Strings and dance like a Marionette!

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 :)