Visualising 4 digit numbers by an 8 year old

Today was math class for 4 digit numbers. Introducing the place value and identifying 4 digit numbers was the plan.
the task was easy and Chaaru could follow based on the previous learning. Infact she picked up quite fast.

As per the design approach, we started discussing the relevance of 4 digit numbers in real life.
Where do you find 1000 to 2000 people together?
Chaaru: In India?
Me: the whole of India onlu 2000 people?
Chaaru: Coimbatore?
Me: hmmm
Chaaru: Vadavalli?
Me: Chaaru think and tell me, dont just say something.
(suddenly her eyes were swelling with tears)
Chaaru: I dont know. I cant nderstand.
Me: No problem (hugs and smiles). Lets try and understand. ok how many people will be living in our apartment...
thus begun the analysis and we computed the following:
52 houses - 4 people in a house - 52 + 52 + 52 + 52 =208 people. this is less than 1000

School where she studied:
1 class = 5 sections
1 section = 32 students
5 sections = 32 + 32 + 32 + 32 + 32 = 160 students
there are 12 classes = how many students?

""Amma should we count 160, 12 times :( "
Me: No, lets see if we can do it any other way. 12 can be written as 10 + 2 or 5 + 5 + 2

Chaaru: I can do this, (she added 160, 5 time and then 2 times)
SO 12 classes = 820 + 820 + 320 = 1960 students

In a School there are around 2000 people (and that was an achievement, you should see the happiness to believe it)

This was a very meaningful exercise where the child could visualize 4 digit number. Unless this understanding is initiated, the learning will be a mere calculation/technical mastery, without any relevance to her life.

The next step is to give different perspectives of 4 digit numbers, in terms of weight, distance, money, etc. Once the child is able to visualise the numerical context, application/operation of numbers will be more relevant.

Welcome home schooling :)

A Designer Math Teacher – My Approach

What is design?

Design conveys any intended message to people.

Art is a creative expression of an artist.

Unlike art, success of a design lies in, how easily it is understood by a common man. This is the reason designs are the most popular medium of communication.

A design encompasses different mediums, ideas, interactions, information, objects, books, posters, products, packaging, places, signs, systems, services, furniture, websites.

Every design involves a process, from research, conceptualizing, prototype, testing, implement and evaluate.

What is designing in math teaching?

Math is a language with its own vocabulary. We say, or we are aware of this… But never approach it that way.

Visualize the following classroom scenarios.

English class - Children we read the story of Rapunzel today.

I hope you all enjoyed it. Now let us try and understand the difficult words in this lesson.

1. Tower - a tall building from where you can see far off

2. Tangled - something which has lot of knots in it, ex. wire, rope or hair

Math class - Children we learnt two digit addition today.

So tell me what is 20 + 5? (30 the teacher corrects by adding/counting after twenty 5 more so 25) Very good. What is 12+12? (24) Excellent!.

Observe, in the English class, the focus is on understanding the vocabulary.

Where in the math class the focus is on understanding the technique.

Has any teacher asked, "children what is the meaning of the word addition?” The problem starts from here.

What we do not understand, we do not enjoy. This lack of understanding in math vocabulary keeps piling through the years of schooling. Eventually even after 12 years of education, we do not understand math.

Some of my friends (age 40+) comments on math

"Till today I do not know what a denominator means, except for it is written below the numerator"

"Guess what, tangent always went in a tangent. Could never place it in the right place"

"I always run in the opposite direction when someone takes the name of LCM and HCF, never can tell the difference..."

So is designing for math just explaining the vocabulary?

No. It is just a part

My approach to designer math learning

1. Explain the need with a bit of history. (If I do not feel the need for it, I am not going to be interested in it)

2. Conceptualize (can give perspectives, eg add is including, increasing, more than, etc)

3. Help the students visualize, it can be a story or an experience

4. Teach the technique and allow discussion on the same

5. Practice (not like 100 sums to drive you insane)

6. List the vocabulary and give meanings (this can get creative and funny)

7. Have a conclusion (mind map helps). It can also be a connection to the next concept.

All this need a truck load of creativity, patience and the luxury of time.

More successful in a 1-1 environment. (Will this improve score/marks? I do not know)

Welcome home schooling :)