Author Archives: vinaire

I am originally from India. I am settled in United States since 1969. I love mathematics, philosophy and clarity in thinking.

KG MATH 7: Data Analysis & Probability

July 2, 2011 – 9:03 PM

Data refers to items of information. Analysis means to examine something by breaking it down into parts that make it up. Probability is the likelihood or chance of something happening. “Data Analysis & Probability” shows how to do these actions at the elementary level.

Answers to simple questions involving two or more categories or choices may be displayed using concrete materials. This is called a Concrete Graph. When the same information is displayed using pictures it is called a Picture Graph.

The range of a graph is the difference between the highest score and the lowest score in that graph. The mode is the score that occurs most of the time. Here are some exercises in this subject for the kindergarten level.

LEVEL K7: DATA ANALYSIS & PROBABILITY

“Data Analysis & Probability” shows how to display quantitative comparisons graphically. It introduces the estimation of likelihood.

 

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KG MATH 6: Patterns & Relational Sense

July 2, 2011 – 12:25 PM

A pattern comes about because of some repeating characteristic, such as color, shape, size, etc. Different types of repetitions generate different patterns regardless of what is being repeated.

A relation is an existing connection; or a significant association between or among things. Because of a relation, if something is present then we may expect another thing to be present as well. A pattern is made up of relations. To see a pattern is to have a sense of relations among things.

A number line is a pattern that presents relations among numbers. With the help of this pattern we may locate a missing or hidden number.

A symbol may be used to represent a missing or hidden number in a pattern. The position of that symbol in that relationship may then help discover that number. Here are some exercises in this subject for the kindergarten level.

LEVEL K6: PATTERNS & RELATIONAL SENSE

“Patterns and Relational Sense” forms the foundation of the subject of ALGEBRA. It is a study of patterns underlying numbers, and quantitative relationships.

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KG MATH 5: Numbers & Operations

July 2, 2011 – 11:06 AM

An operation is an action done on numbers, such as, counting. Numbers are not only used for counting as one, two, three, etc., but also to indicate sequence as first, second, third, etc.

As numbers are counted they stand for increasing quantity. This may be represented pictorially on a number line, where numbers are placed at equal distances on a line. These numbers increase sequentially from left to right. One may then use this representation to compare numbers, or to demonstrate how numbers may be combined to obtain new numbers.

Numbers may be visualized as sets, or collections of objects. A pile of pennies may be used as a set  for demonstrating basic operations with numbers.

The combining of two numbers together is called addition. This may be done by counting a number to the right from another number on the number line. It may also be demonstrated as combining two piles of pennies together.

Taking a smaller number away from a larger number is called subtraction. This may be done by counting a number to the left from another number on the number line. It may also be demonstrated by breaking a pile of pennies in two smaller piles and taking one of those piles away.

Such opertions may help one develop a sense of estimating quantities without having to count each object.

By pairing pennies from a pile one may determine if they are even or odd. Numbers of pennies may also help one develop a sense of relative value, especially when they are presented as different coins.  Here are some exercises in this subject for the kindergarten level.

LEVEL K5: NUMBERS & OPERATIONS

“Numbers and Operations” introduces the basic operations with numbers and how such operations may be executed with skill. That is the sense underlying the word ARITHMETIC (from arithmos number + techne skill).

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Attitudes inspired by Buddhism

June 25, 2011 – 7:08 PM

  1. There is only the human being. And that human being has the potential to be spiritually awakened. God is merely an extrapolation by the mind. There is no higher being or power that sits in judgment over man’s destiny.

  2. Man’s emancipation depends on his own realization of Truth, and not on the benevolent grace of a god or any external power as a reward for his obedient good behaviour. Each person must develop himself and work out his own emancipation.

  3. Do not be led by reports, or tradition or hearsay. Be not led by the authority of religious texts, nor by mere logic or inference, nor by considering appearances, nor by the delight in speculative opinions, nor by seeming possibilities, nor by the idea: ‘this is our teacher’. It is proper to have doubt, to have perplexity, for a doubt has arisen in a matter which is doubtful.

  4. When you know for yourselves that certain things are unwholesome, and wrong, and bad, then give them up. And when you know for yourselves that certain things are wholesome and good, then accept them and follow them.

  5. A disciple should examine even the Teacher himself, so that he (the disciple) might be fully convinced of the true value of the teacher whom he followed.

  6. The root of all evil is ignorance and false views. There must be doubt as long as one does not understand or see clearly. Doubt is not a ‘sin’. In order to progress further it is absolutely necessary to get rid of doubt and see clearly.

  7. Just to say ’I believe’ does not mean that you understand and see. To force oneself to believe and to accept a thing without understanding is political, and not spiritual or intellectual.

  8. Let all listen, and be willing to listen to the doctrines professed by others. Whosoever honours his own religion and condemns other religions, does so indeed through devotion to his own religion, thinking “I will glorify my own religion”. But on the contrary, in so doing he injures his own religion more gravely.

  9. Truth needs no label. It is neither Buddhist, Christian, Hindu nor Moslem. It is not the monopoly of anybody. Sectarian labels are a hindrance to the independent understanding of Truth, and they produce harmful prejudices in men’s minds.

  10. When we label a human being as English, French, German, American, or Jew, we may regard him with all the prejudices associated with that label in our mind. Yet he may be completely free from those attributes which we have put on him.

  11. The love of a mother for her child is neither Buddhist nor Christian: it is mother love. Human qualities and emotions like love, charity, compassion, tolerance, patience, friendship, desire, hatred, ill-will, ignorance, conceit, etc., need no sectarian labels.

  12. To the seeker after Truth it is immaterial from where an idea comes. In fact, in order to understand Truth, it is not necessary even to know whether the teaching comes from the Buddha, or from anyone else. What is essential is seeing the thing, understanding it. If the medicine is good, the disease will be cured. It is not necessary to know who prepared it, or where it came from.

  13. Emphasis should be laid on seeing, knowing, understanding, and not on faith, or belief. One must have (a) full and firm conviction that a thing is (b) serene joy at good qualities, and (c) aspiration or wish to achieve an object in view.

  14. The question of belief arises when there is no seeing (seeing in every sense of the word). The moment you see, the question of belief disappears. If I tell you that I have a gem hidden in the folded palm of my hand, the question of belief arises because you do not see it yourself. But if I unclench my fist and show you the gem, then you see it for yourself, and the question of belief does not arise.

  15. A man has a faith. If he says “This is my faith”, so far he maintains truth. But by that he cannot proceed to the absolute conclusions: “This alone is Truth, and everything else is false”.

  16. To be attached to a certain view and to look down upon other views as inferior – this the wise men call a fetter.

  17. It is unnecessary to discuss metaphysical questions, which are purely speculative and which create imaginary problems.

  18. Discuss those things that are useful, fundamentally connected with the spiritual holy life, and conducive to aversion, detachment, cessation, tranquility, deep penetration, full realization, and Nirvāna.

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KG MATH 4: Counting & Measurements

June 25, 2011 – 4:13 PM

To measure a distance would be to determine how close or far a location is, such as, the distance of school from home. To measure a size would be to determine how small or big something is, such as, the size of a house. To measure capacity would be to determine how much something can hold, such as, the capacity of a pool. In short, to measure is to determine the extent, size, capacity, etc. of something.

To measure anything we need a unit. For example, to measure the length of a table, we may use span as a unit. To measure the size of the floor we may use square tile as a unit. To measure the capacity of a tub, we may use bucket as a unit. In short, the unit used in measurement is a small but definite amount of what is being measured.

Suppose we want to know how long a football field is. We may walk the length of the field and count how many steps it took. This will give us the number of steps that fit in that length. We can then say that the measure of the field is so many steps. Here a small length called ‘a step’ is the unit used to measure the length of the field. 

If we want to compare two lengths then we must measure them using the same unit, and the unit must be of the same size each time it is applied. To be able to compare measurements around the world, we must use the same unit the same way anywhere in the world. Thus, we have standard units of meter for length, kilogram for weight, hour for time, etc. Here are some exercises in measurement for the kindergarten level.

LEVEL K4: COUNTING & MEASUREMENT  

The measurements make the numbers meaningful. It is important to get the sense of numbers in terms of units by measuring as many things as you can, using as many different types of units as you can.

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