Foundations of Mathematical Thinking
This book is the first of six Kindergarten books focused on math education. The Kindergarten series is a part of the K - 12 'Mathematics as a language' books - a new mathematics book genre.
These books are the world's first 'Family edition' curricular books. They are meant to empower parents to ensure the best quality education for their children, with or without schools. Parents should use the books for the most 'whole-child' development context at home. Ideally, an hour together with children, guided by the books' contents, will ensure the family's 'happy hour' of the day. Math education would be a secondary outcome!
The pre-primary years shouldn't be grouped into 'subjects.' The books aren't math books; the development of language, observational skills, drawing, craft, awareness of things around, better living, etc. integrated into the books.
School textbooks and teaching hurt children's development, and parents have no tailored curricular resources to achieve children's right educational development. The books are innovative resources for the most educationally efficient years of human development – childhood, unique to humans. It presents the most rapid and broad growth avenues and opportunities. Developmental deficiencies in these years can be recovered later, but at a far greater time, effort, attention, resources, and friction.
The books may also be used as a resource in tutors' hands (with love for children as the only qualification). The books are rooted in everyday living and are conversational; parents can easily collaborate with tutors for the most impactful education.
The books have 'nothing to teach.' The content is the navigational guide to support children with contexts, resources, experiences, conversations, and goals to 'make sense of things.' It nurtures observation, an extension of knowledge, application/generalisation, estimation, and joy of collaborative/social learning.
Four other books of the series on the 'Foundations of Arithmetical operations' - 'Foundations of addition,' 'Foundations of multiplication,' 'Foundations of subtraction,' and 'Foundations of division' are already published. They demystify the operations and lay the foundations for 'love with math, and unparallel insights into the new economy/society.'
Children around the Kindergarten years have to follow these six books in the series. No distinction is possible and meaningful in the series to be relevant to the different KG years - I and II, as in the formal education system.
Math education in the pre-primary years may be the poorest in the formal education of math. For eg., the numbers are introduced too early, and math is not rooted in everyday things, situations, and conversations.
In these years, parent-led education works magic, and the books have dramatically simplified the demands on parents.
Parent-led education (within or without schools) will also achieve much greater outcomes and a developmental pathway unique for the children and the family.
Mathematics must be taught and introduced as another language, much like the languages well known to children at their age in Kindergarten – mother tongue, a second language for children in some countries, art/music/dance/play.
Indeed, music/sound is every child's first language (music is pleasant/melodic sound, and children react to such sounds). Play/gestures/facial expressions are the second ones. Drawing is the third. And dance is the fourth.
Our Kindergarten mathematics heavily draws on other languages. There is little difference in math and other languages in KG – math is drawn from everyday living; there is no abstraction.
Thus, every 'lesson,' called Learning Outcome, has most of the following components:
- Exploring a range of everyday things and situations
- (Specific) Discussions
- (Mathematical) Story
- (Specific) Observations
- Vocabulary building
Befriending a car to know the car (motorbike or bike is equally great)
Don’t we know our parents more than other adults? And the siblings more than friends. Why does this happen? Isn’t it because they care about us the most? And we share more with those who care more for us. Taking care of others is the best way to know more about others. We befriend people when we care for them.
Interestingly, this is true for everything, plants and animals, and non-living things too. I hope you believe this and would love to see if such a thing is true. Let us try this on a car/motorbike/bike that you like/love. Let us see how taking care of the chosen car/motorbike/bike will help you know more about it.
But what can we do to care for a car/motorbike/bike? There are a few ways, but the best may be giving it a wash! Have you ever washed a car/motorbike/bike with care (with love)? Let us try that once (again).
The discussion on the wash may be split into two sessions:
Pre-wash: Discuss whatever children remember about the car/motorbike/bike, including dents, scratches, spots, damage, fading, etc.
Post-wash: Discuss the new knowledge, including dents, scratches, spots, damage, fading, etc. discovered during the wash.
Also, discuss if the wash, or the act of taking care, did help in knowing the car/motorbike/bike better
Discuss with children
- How much new information do you found after the wash? One/pair/few/many/very many.
- How much time did it take to wash? Little/a lot/half an hour/one hour. Just being informed of half an hour/one hour is expected.
- What else takes a similar amount of time? Again, just a sense of similarity. It is to help nurture a sense of estimation.
- How many parts of the vehicle are made of glass? Again, it is in terms of one/pair/few/many.
- Why was glass used? One, or two, unique property of glass is good enough. The name of the parts may be discussed.
- How many parts are made of steel? Again, it is in terms of one/pair/few/many.
- Why was the steel used? One, or two, unique property of steel is good enough. The name of the parts may be discussed.
- Similarly, discuss parts made up of rubber/plastic, shapes of different parts, and other colours in vehicles.
- When would you rewash the vehicle? In a few days, many days, or never. What are the benefits of washing a car/motorbike/bike?
- How else can you take care of a car/motorbike/bike? Beyond washing.
Let us practice I
- Let us take some cars to their garage. Drive the cars into their garages (house for cars) by tracing the paths.
Let us explore
- Have you noticed things of different shapes in cars? Here are some different kinds of shapes found in cars. Trace the shapes given below the car and colour them in different colours. After that, colour the car in the same colours as the colours of the shapes.