I want to understand Math, math that once troubled me. I used to score great marks in science and social studies, which I considered a good student, but Maths always remain elusive. I somehow able to score in it, but that was something which I not wanted. So here I am giving another try to understand math and work on it at the same time.
Let’s say I need it more now than ever. So I downloaded all books from the NCERT site and started reading them one by one. First among them is the First-class Math book. Yeah, I am going down. The initial pages say that teaching mathematics is directly related to achieving the important aim of helping children become independent and critical thinkers. Yes, I very much agree with this, as it helps to reach us to a measurable, quantifiable thing. Knowing the finite/correct answer is always better than dwelling in obscurity. Mathematics is more of a way of thinking, which has never been discussed in schools. Most of the time, we cannot garner the interest about the subject in the student, as much we wanted, or it should be generated, even before actually starting with the syllabus, actually this is true for every subject just maths alone.
Inside-Outside
The very first concept that is mentioned here is Inside-outside. What it has to do with Maths? A pic of an Arab, a camel, and a tent has been given, and a story has been told, where camel try to come inside the tent and it sort of funny.
The story ended when the camel came completely inside the tent, and the Arab has to leave the tent due to space scarcity. The idea of sharing this story with pictures gives an idea about different shapes/figures we have in the picture. Children can understand a camel can take huge space. And what is meant by coming inside and being outside?
You start understanding Maths when you start differentiating the stuff. You can recognize that something is different from others, in what manner it is different that is something we will later. There are some parameters to differentiate between two things: size, shape, color, odor, or maybe any other quantifiable parameter.
Bigger-Smaller
The next topic asks to compare, from big to small, which is very much clear to naked eyes. A hippo is bigger than a dog, so does a cow than a squirrel. Various vehicles have different sizes of tires. So it is like, children can understand to differentiate between the different objects based on their size. Again, once you become aware of sizes, only then can you carry out the comparison. So writers of the book are trying to generate questions in the mind of young kids. How you can say something is bigger. It is effortless to tell which is bigger between a cow and a dog, but what if someone asks who is bigger among a dog and a goat? May their sizes be almost the same. Then how would you decide which one among them is bigger? Again food for thought.
Top-Bottom
The next part talks about the differentiating positions, from top to bottom. What is meant to being on top? How can you say someone is on the top or the bottom of anything. Most of the time, it is the height criteria at which a given thing or person is placed. Height of the object/person/animal from a reference, which is Ground in this case.
Nearer-Farther
Again another mathematical comparison and a way to measure something. First, we need to define the point of reference, just like another case we talked about earlier, size (big-small) and position(top-bottom). I am nearer to my laptop while typing this blog, but I am farther from the kitchen, sitting in my study room and not in my kitchen.
Next topic in this first class Math, talks about the topic of shapes around us.
Like sphere(balls), circle(bangles), square/rectangle(boxes) etc. Once we start understanding what is a circular shape, or what is spherical shape, or what is rectangle shape, we can move to the next of part of sorting the various objects around us on the basis of their shapes. That’s a really great activity for young minds.
It is just an irony, that I don’t remember learning about this complex stuff of sorting in the first class.
Please leave the next two para, if you don’t want to. I have tendency to go haywire from the topic. You can start from Rolling-sliding topic.
But to all those parents or aspirants, who will study my blog, I guess we need to talk a bit more about this.
Sorting is essential stuff, and though the ability of great and efficient sorting comes with our ability to understand the shapes and pattern, it’s been introduced so quickly in the first class itself. Sorting has too many use cases. You require sorting in day-to-day life; let me give some examples here.
- In your home: Sorting kitchenware based upon their shapes, you want to keep plates in one place, as it will help you in utilizing the kitchen space judiciously. You want to sort your medicine based upon your family member’s medication plan. God forbid, you don’t want to mix your parent’s medicine with your child’s medicine. See sorting is indeed essential.
- In the market: You need to understand the pattern of prices, for the vegetables, clothes. Pattern recognition helps you in sorting. You need to understand the right price of a vegetable, whether it is expensive than your last purchase. You need to understand that when a festival approaches, gift items, clothes get costlier. When the season is about to change, for example, leaving the winter season and entering spring, the woolen/warm clothes will get cheaper. So you can probably buy for next winter and bargain a little more to save some extra cash.
- In IT/Computer Science: Sorting/Pattern recognition is everywhere. Writing programs for libraries, for an e-commerce company, etc. It is altogether a different level of discussion, and we will take that up some other time.
- In Finance: Again, you cannot discuss financial products/services without understanding pattern and sorting.
There are many other places where I can think of implementation/application of our sorting knowledge, but perhaps, I am not qualified to talk about those or just avoiding it at this point e.g. Chemistry, Business, Architecture of buildings, Transportation.
I have mixed Pattern recognition with Sorting, just to indicate that they are connected, pattern recognition, helps us in the categorization of problems/shapes/objects in hand, and this categorization is in fact Sorting. I am sure, these topics we will discuss in the more dedicated manner later.
ROLLING-SLIDING
Why this in the first class Math book? This is an essential question a parent like me can ask. I want to make my kid understand math, and on every damn page, the school book introduces such difficult topics. How will the discussion go? Ok, let me try. Children love slides. At least my 3-year-old son does. Which object can slide and which can roll is dependent on their shapes. So, we can say your SHAPE gives you a special quality. A ball will always roll, and a box, which is rectangular in shape, can only slide and can never roll. Because of this very reason, our car tires are circular and not rectangular shaped. Easy?
It is again a fundamental scientific and philosophical concept. Your shape gives you a special attribute to be successful in a certain condition and at the same time limits you of not being useful in some other condition. But anyway, you will always be useful, as you will definitely carry some shape, you can never be shapeless. In fact, Air, which is formless, is the most important thing I know at this point, I know I am contradicting my point, but you can understand what I am trying to convey here.
Chapter 2: Numbers from One to Nine
The chapter talks about counting the objects, people, animals. The chapter try to build understanding of the kid, that what all we can count, and no matter what is the shape, size and nature, counting of the object can be carried out in the similar way. You need to recognize that they are same based upon object’s shape, size and nature and then you can count it by recognizing how many of them are their in front of your eyes.
Chapter 3: Addition
This is the first mathematical operation, after practicing sorting that a child learns, let me know if I have missed out on any other.
First you need to categorize the objects based upon their similarity, and then count them, once you have individual objects counted, you can add those numbers, after that.
Number1 + Number 2 => Addition
1 + 2 = 3
It clears one more thing, to addition is a mathematical operation, that can be carried out on a mathematical entity i.e. Numbers. You can add two flowers, you cannot add two birds. You add counting of birds. First you count, write the number of that object, and then add those numbers, to reach to final number. It looks sort of basic at this point, but again a very important concept, that define the data type in Computer Science.
Interesting fact:
Chapter 4: Substraction
Do you know that Addition/Substraction/Division/Multiplication was given by an Indian Mathematician, Brahmagupta.
You can read more about it here: https://en.wikipedia.org/wiki/Brahmagupta
Now, what is substraction. Taking away the number which comes after minus (-) sign from the number from the number which is not carrying the minus sign, is called substraction. I mean it is tough to define, need to look for their solutions.
🙂
- 2 – 1 = 1
- 1 -2 = -1
- -1 – 2 = – 3 (What we did Subtraction or addition?) => It is actually addition of two negative numbers. Which can be discussed later. Negative numbers are not discussed at the first standard, and rightly so, therefore you can leave it to later part.
Chapter: 5 Numbers from Ten to twenty
It is a big jump for little minds, when they jump from single digit counting to double digit counting. Nothing much I can explain here, probably later I can come back to it.
Chapter 6: Time
This chapter, introduces the very important concept of time. Why it is so important?
Time is important, as it guides our day, we need to wake up at morning when sun rises, we need to sleep at night, when there is dark. There is almost 12 hours difference typically between sun rises and sun set. It’s better if organize our work/daily routine as per that. Also, building sense of time among kids is very important, not taking proper sleep on time, not spending enough time on constructive time, and not having the limited nature of time we have is actually disastrous for any one.
The chapter does justice in building the sense of time, among students by various pictures and diagrams.
Students have been asked, which activity to carry out at what time in the day, like morning time you wake up, then take bath, brush teeth, breakfast and then go to school. Then in afternoon, have your lunch, do your homework and take a nap. Then in the evening, play with your friends, tell/listen stories. Have dinner, read some book for some time and then go to bed at night. It helps in balancing the life.
The chapter ends with making kids aware about that time also have some kind of dimension, which we all know, can be measured by watch. But kids of first class probably even don’t know how to tell the time from the watch, still building concept about time measurement is important. Just like the book did in the first chapter, building concept about big and small, without getting into measuring shape and size. So how this concept can be build around dimension of TIME?
Hence time can be long, or short too.
Interesting point: In Indian scriptures even 1/4 time of blinking of eye has been also given a term.
*1 परमाणु = काल की सबसे सूक्ष्मतम अवस्था | *2 परमाणु = 1 अणु | *3 अणु = 1 त्रसरेणु | *3 त्रसरेणु = 1 त्रुटि
*10 त्रुटि = 1 प्राण | *10 प्राण = 1 वेध | *3 वेध = 1 लव या 60 रेणु | *3 लव = 1 निमेष | *1 निमेष = 1 पलक झपकने का समय*2 निमेष = 1 विपल | (60 विपल एक पल होता है) | *3 निमेष = 1 क्षण | *5 निमेष = 2 सही 1 बटा 2 त्रुटि | *2 सही 1 बटा 2 त्रुटि = 1 सेकंड या 1 लीक्षक से कुछ कम। | *20 निमेष = 10 विपल, एक प्राण या 4 सेकंड | *5 क्षण = 1 काष्ठा | *15 काष्ठा = 1 दंड, 1 लघु, 1 नाड़ी या 24 मिनट |
*2 दंड = 1 मुहूर्त *15 लघु = 1 घटी=1 नाड़ी |*1 घटी = 24 मिनट, 60 पल या एक नाड़ी | *3 मुहूर्त = 1 प्रहर | *2 घटी = 1 मुहूर्त= 48 मिनट
*1 प्रहर = 1 याम | *60 घटी = 1 अहोरात्र (दिन-रात) | *15 दिन-रात = 1 पक्ष | *2 पक्ष = 1 मास (पितरों का एक दिन-रात) |
*कृष्ण पक्ष = पितरों का एक दिन और शुक्ल पक्ष = पितरों की एक रात।*2 मास = 1 ऋतु | *3 ऋतु = 6 मास | *6 मास = 1 अयन (देवताओं का एक दिन-रात) | *2 अयन = 1 वर्ष | *उत्तरायन = देवताओं का दिन और दक्षिणायन = देवताओं की रात। | *मानवों का एक वर्ष = देवताओं का एक दिन जिसे दिव्य दिन कहते हैं। | *1 वर्ष = 1 संवत्सर=1 अब्द | *10 अब्द = 1 दशाब्द*100 अब्द = शताब्द | *360 वर्ष = 1 दिव्य वर्ष अर्थात देवताओं का 1 वर्ष।
Chapter 7: Measurement
Till this point kids should started becoming curious, that we can recognize and differentiate between shapes, sizes, distance, and even length of time span, but how we are going to measure it?
So, in this chapter, concept of measurement has been introduced.
First kids have been introduced by relative terms for measurements like:
Shorter-Longer | Shortest-longest | Taller-Shorter | Tallest-Shortest | Thicker-Thinner|
Thickest-Thinnest | Heavier-Lighter | Heaviest-Lightest
These kind of relative measurements are bit easier to make, but at some point you need some scale to measure some of these terms.
Chapter: 8 Numbers from Twenty-one to Fifty
In this chapter kids have been introduced to numbers from 21 to 50.
Chapter: 9 Data Handling
In this chapter, first time kids have been introduced to the concept of data handling.
How they categorize different sort of data, count them and analyze them. Some activities have been introduced, like counting similar shapes in a given pic and counting the letters in the names of few friends. Interesting activity, which try to make little minds curious about how they can manage some information.
Interesting Point: Raw facts => Data
Processed data => Information
Chapter 10: Patterns
Observing the repeated trend is actually recognizing pattern. As we talked during our sorting discussion, pattern recognition has great potential to anyone who understands it. Knowledge of this is useful not only in clearing several competitive exams, but also improve your aptitude to problem solving.
So many activities are given in the chapter to train young minds, infact some are too good even for some mature minds to.
E.g: Extend the sequence, Patterns in shape, patterns of missing numbers etc.
Chapter 11: Numbers
Students have been introduced with place value system of numbers. Like 10th place, one’s place, and this place value system introduced to higher order numbers.
33 = 3X10 + 3X1 = 30 + 3 = 33
It is also again very useful concept when in higher classes will learn about various types of number systems like, decimal number system, binary, octal, hexadecimal number system.
Chapter 12: Money
This chapter introduces kids to the concept of money and various currency notes available in India. How prices of something can be interpreted in terms of available currency.
Chapter 13: How many
The final chapter of first class talk about counting again, but this time in more advanced manner. Recognizing the numbers based upon the place value system and deciding which one is bigger.
CLASS- 2
chapter-1: What is long and what is round
In this playful first chapter, kids are introduced to various fun activities to recognize the shapes of round and long. The two things which remain very much accessible in schools. Like Pencil and Balls.
Kids been asked to notice their shape, a round object doesn’t have any corners, a pencil has pointed end at one side and flat surface at the other and on the sides it is just long. Kids been asked which among them can roll, which among them can slide. It’s more like the revision of first class.
Chapter 2: Counting in groups
I am observing that class 2 math is more playful than class 1. Lots of activities of counting in groups and various activities for students to notice various numbers in different household objects. Like match sticks in matches, number of seeds in orange, number of teeths in human mouth. All sorts of activities to make kids aware of countable objects around him/her. These counting activitites further followed by activities where students need to follow increasing order of numbers.
Chapter 3: How much can you carry
Kids have been introduced here with the concept of weight. A wet woolen cloth is heavier than the dried one. For enjoying a see-saw ride, two friends have to be of similar weight, if one among them is too heavy, then both friends can’t enjoy the see-saw.
Various activities explaining the weight and size of the object.
Chapter 4: Counting in Tens
Again a chapter where counting in the group of tens have been taught to young minds. So they start counting big numbers.
Chapter 5: Patterns
Just like class1, there is the cahpter on patterns. Which try to make kids aware about various patterns available in front of their eyes, patters in saris, patters in road pavements, patters in iron grill in the park. Then some exercises to find correct patterns.
Chapter 6: Footprints
By tracing activity, kids have been made aware of various shapes available in nature. Like round spherical shapes of common vegetables like tomato, potato. Like rectangle shape of eraser, like cone shape of softy etc.
Chapter: 7 Jugs and Mugs
You might be thinking that I must be running in these chapters, but the thing is concept explained in these chapters are more sort of building due to activity. Terminology wise it is not advisable to try to explain it to small kids. Also, I am nearing some deadlines, hence sort of running.
Anyway, chapter 7 talks about many important things.
- How you can prepare lemon drink, what ingredient and in what quantity these ingredients are required. What if instead of one glass you need to prepare 10 glasses. What will happen with quantity of ingredients? What will happen if you try to sell the lemon drink in some in some fair? Do you think 5rs. a glass will justify the cost of 1 glass preparation. These are very important questions that kids should be encouraged to ask. It will give them all sorts of ideas of how things work and real life implementation of mathematics knowledge.
- Then comes the concept of vessels. How small vessels can be used to fill large vessel. How different sizes of vessels carry different quantity of water/milk?
- The third and one more important concept is about, the volume displaced by same quantity, when your drop pebbles into water pitcher. Since pebbles are heavy than water, water gets displaced and comes up. That was the concept behind the story of thirsty crow.
- Then in the last kids have been exposed to importance of water and asked to find out about the quantity of water used in various house hold activities. Nice one, really appreciate the editors of the book.
Chapter 8: Tens and ones
A similar chapter like in class first, where the kids have been taught to understand, counting ways. How to club big quantities. By means of pencil buying activity using ten rupee notes and 1 rupee coins, kids have been encouraged to count the sums like 35 rs., 40 rs. and distribute their counting in terms of ten reupees notes and 1 rupee coin.
Chapter 9: My Funday
In this chapter kids have been exposed to sequence of days in a week, like Monday, Tuesday, Wednesday, Thursday etc. Kids know that week has 7 days. Similarly kids have been encouraged to make this concept familiarize by means of class time table. Kids like the day which has most number of playing periods like Friday, isn’t it? Then they have been asked to carry out the activity where, then can tell what is their favorite flower and in which month you can see them bloom. What are the favorite months of kids, like the month which carry festivals. These are the fun ways you can make kids aware about 7 days in the week and their different names and 12 months of the years and their respective names. What if all 365 days had different names in an year, we might be in for great trouble then. Isn’t it. Pattern of 7 days makes a week, pattern of 30-31 days make a month, and pattern of 12 months make an year.
Chapter 10: Add Our Points
The chapter talks about adding up points, and numbers one after the other. Various exercises prompt students to add fast and think new ways to reach to a certain sum, after adding numbers in different ways.
