Posted by eoffg on October 04 2005 09:01 AM
Hi Countess, and welcome to the Forum!
You write that the your Daughter loved maths until it came to the magic number 10?
This is a most important issue, where I'll add some quotes from a research paper by Joan A Cotter, which looks at the difference between the Asian and Western approach to Maths:
A difference is that of naming numbers. Most Asian languages refer to 23, for example, as "2-ten 3" and 67 as "6-ten 7." In English the quantity ten has three names, ten, -teen and -ty. Another confusion are the numbers, 11-19; words eleven and twelve seem to make no sense and for the numbers from 13 to 19, the order is reversed with the ones stated before the tens. All European languages have some irregularities in naming numbers."
So we have this confusion at the basic level of the words that represent numbers.
Related to this, is understanding numbers as 'groups'? Where the above Asian approach, where 23 is spoken as '2 ten 3' highlights a different way of speaking and thinking numbers.
The following quote, also shows how the Asian approach to learning Maths, is to begin by learning numbers as groups!
Not as 1,2,3,4, and so on in the Western model?
"Visualization vs. Counting
Another major difference is the view of counting. In the U.S. counting is considered the basis of arithmetic; children engage in various counting strategies: counting all, counting on, and counting back. Conversely, Japanese children are discouraged from counting; they are taught to recognize and visualize quantities in groups of fives and tens. Children using counting, which is slow and often unreliable, to add and subtract develop a unitary concept of number. For example, they think of 14 as 14 ones, not as 1 ten and 4 ones. Such thinking interferes with understanding carrying and borrowing in larger numbers.
To understand the importance of visualization, try to see mentally 8 apples in a line without any grouping--virtually impossible. Now try to see 5 of those apples as red and 3 as green; the vast majority of people can form the mental image. The Japanese employ this sub-base of 5 to make quantities between 6 and 10 easily imaginable. Thus, 8 is seen as 5 and 3. "
So that instead of beginning by learning numbers one by one.
It begins by learning numbers as groups.
So that it reverses the way numbers are learnt?
13 = 8 + 5.
Not; 8 + 5 = 13.
Anyway Countess, perhaps you can let me know if this made any sense to you?