Reflection on chapter 2: At Home with Numbers, of "Learning All the Time"

This is from the collection of my reflections on three selected phrases from each chapter of John Holt’s book; Learning all the time. An online version of the book could be found here.

Book: Learning All the Time

Author: Holt, John Cardwell, 1923-1985

Length: 169 pages

Published by: Addison-Wesley Publishing Company

Year of Publication: 1989

Edition: Eight, August 1995

ISBN: 0-201-55091-1

Chapter 2: At Home with Numbers

Phrase 1:

… when little children first meet numbers they should always meet them as adjectives, not nouns. It should not at first be "three" or "seven," all by itself, but always "two coins" or "three matches" or "four spoons" or whatever it might be. [para 2, page 47]

This is absolutely correct because numbers are nothing in abstraction. Numbers show nothing until they are attached with some object like two spoons or five fingers. If we teach our children that way, the learning they will have would perfectly match with the objects they see in their daily lives. They would then start relating, exploring and learning on their own and would have so much fun while inside or outside of their home.

Phrase 2:

… it is not at all necessary, and indeed not a good idea, to have children meet numbers always in the counting order. Thus, we might at one moment show a child two of some kind of object, but the next thing we show, according to the circumstances, might be five of some other object, or eight, or whatever. Numbers exist in nature in quite random ways, and children should be ready to accept numbers, so to speak, where they find them. [para 3, page 47]

This is all sensible knowledge being given in a meaningful and sensible way. As numbers are nothing in abstraction until they are attached with some object like three kites or ten fingers, teaching numbers in counting order show as numbers are itself some object that can be compared. However, the fact is that numbers are not comparable but the quantity of objects is. This means two oranges and five oranges can be compared and that makes sense. Even when we say two is less than three, that actually means two objects are less than three of such objects but the word objects or things is hidden.

When children start noticing quantity of objects as a property of them like color, shape and size, they will focus on objects itself rather than on numbers in absolute sense. This means, noticing an object like plate they would then be able to tell that it is of red color, a circle, and bigger than the other smaller blue plate. Similarly, they would then be able to identify that they have 6 color-pencils and 3 books in their bag. This is the right way of introducing real world objects to the children so they will be able to analyze their properties, compare them with other and start exploring more and more new objects.

Phrase 3:

. . . our minds are much more powerful when discovering than memorizing, not least of all because discovering is more fun. Another advantage is that so much of arithmetic (and by extension mathematics) that now seems mysterious and full of coincidences and contradictions would be seen to be perfectly sensible. [para 2, page 53]

The first point that discovery is more fun and more powerful than memorizing probably does not need any proves. Everyone of us can easily do an experiment to reach to the same conclusion. However, there is a question, and few teachers need to test it on few groups of children that instead of asking children to memorize, when we give them some activity to discover something, they would not learn everything by heart the very first time. They need to redo that discovery again and again until they learn it by heart. But children get bored doing the same thing again and again. How would the teacher or the parent keep that activity still interesting for the children to keep their interests in it for a long period of time? Not only frequent variations in the activity would be needed, but teachers need to discontinue that activity for some time as well and come back to it after some time to keep children’s interests in it.