Number & Operations for Teachers 

    Copyright David & Cynthia Thomas, 2009

1.1  Counting

 

English:           one, two, three, four, five, six, seven, eight, nine, ten

Crow:              hawáte, núpe, dáwi, cope, tsexó, akáwa, sá'pua, núpu'pi, á'pie, pireké 

Dutch:             een, twee, drie, vier, vijf, zes, zeven, acht, negen, tien

Cantonese:      yat, yih, saam, sei, ngh, luhk, chat, baat, gáu, sahp

 

Eager to engage the world around them, young children are born explorers … observing, naming, describing, manipulating, and counting the objects in their world.  For them, learning to count is as natural as play.  Counting also serves as an informal introduction to the set of whole numbers, represented here as the infinite set {0, 1, 2, 3, 4, 5, 6 …}.

 

Tech Resources

Read about counting at Cut-The-Knot

 

http://www.cut-the-knot.com/arithmetic/Rote.shtml

 

Visit the website Numbers from 1 to 10 in Over 4500 Languages http://www.zompist.com/numbers.shtml

 

There is more at stake when naming numbers than sound and rhythm, however.  In some languages, the naming conventions lead naturally to important mathematical insights involving the structure of the number system.  In other languages, naming conventions tend to obscure important relationships.  Unfortunately, the naming conventions used in most European languages, including English, fall into the second category.  A brief review of English language counting conventions will illustrate the point. 

 

0

Zero

10

Ten

20

Twenty

30

Thirty

40

Forty

1

One

11

Eleven

21

Twenty one

31

Thirty one

41

Forty one

2

Two

12

Twelve

22

Twenty two

32

Thirty two

42

Forty two

3

Three

13

Thirteen

23

Twenty three

33

Thirty three

43

Forty three

4

Four

14

Fourteen

24

Twenty four

34

Thirty four

44

Forty four

5

Five

15

Fifteen

25

Twenty five

35

Thirty five

45

Forty five

6

Six

16

Sixteen

26

Twenty six

36

Thirty six

46

Forty six

7

Seven

17

Seventeen

27

Twenty seven

37

Thirty seven

47

Forty seven

8

Eight

18

Eighteen

28

Twenty eight

38

Thirty eight

48

Forty eight

9

Nine

19

nineteen

29

Twenty nine

39

Thirty nine

49

Forty nine

Table 1.1:  Base Ten Counting

 

Read across any row in Table 1.1 from left to right, other than the first.  In each case, the numbers in the “teens” column are named using a different method that that used in the other columns.  This may seem a minor inconvenience to you, but to young learners, this inconsistency poses an obstacle that, all too often, obscures the structure of our system of numeration.  For instance, most preschools train children to count from one to twenty.  Upon entering kindergarten and/or first grade, children continue to focus their attention on counting, reading, and writing activities involving small numbers.  Unless their teachers make a sustained, conscious effort to teach them otherwise, children are unlikely to recognize or understand the most important concept in primary grades mathematics, place value, and its role in our base ten numeration system.  For many students, the consequences of this failure are far-reaching and significant.  How much easier things would have been if the numbers 11-19 had been named something like tenty one, tenty two, tenty three, and so on.  Interestingly, many Asian and languages do not share this failing … and the children who grow up speaking those languages have fewer mathematical difficulties related to base ten numeration. 

 

Tech Resources

Read about place value at Cut-The-Knot

 

http://www.cut-the-knot.com/ctk/SelfDescriptive.shtml