# Kindergarten and First Graders' Knowledge of the Number Symbols: Production and Recognition

By Mark-Zigdon, Nitza; Tirosh, Dina | Focus on Learning Problems in Mathematics, Winter 2008 | Go to article overview

# Kindergarten and First Graders' Knowledge of the Number Symbols: Production and Recognition

Mark-Zigdon, Nitza, Tirosh, Dina, Focus on Learning Problems in Mathematics

The Hindu-Arabic number system represents amounts of objects by number symbols, without referring to other properties of these objects (e.g., color, size). That is to say that the number symbols, like many other symbols, are linked to the objects that they represent in an arbitrary but agreed upon manner with fixed representation rules (Vygotsky, 1978). Therefore, when the number system is used in a teaching-learning process, the child is required to perform a relatively complicated cognitive process. He has to refer to the meaning behind the symbols and to make the connections between the symbols and the quantities (Bialystok, 1992; DeLoache, Miller & Rosengren, 1997; Dorfler, 2000; Kaput, 1991; Lesh & Doerr, 2000, Thomas, Jolley, Robinson & Champion, 1999).

One question that is naturally raised regarding child's knowledge of the Hindu-Arabic number system is: What are the factors that determine the child's grasp of this symbolic system? One of the major factors that ought to be considered is the development of symbolic thinking. The development of symbolic thinking addresses the cognitive processes that take place in the structure of the mental representation during the change from the "unity level" to that of the "differentiation level" (Nemirovsky & Monk, 2000). In the early stages of the development of symbolic thinking, children are at the unity level. At this level, children believe that the symbolic representation reflects the nature of the object it represents. Thus, for example, children will write names of large objects with large letters (Thomas, Jolley, Robinson, & Champion, 1999). When differentiation occurs, the child separates between the object being represented and its symbolic representation. At this differentiation level the child understands that there is no connection between the size of the symbol and the size of the object that the symbol represents.

The ability of a child to employ symbols of numbers as symbols representing the mathematical meaning of the number is a result of a developmental process (Bialystok, 1992; Bialystok & Cobb, 1996; Worthington & Carruthers, 2003; Hughes, 1986, Munn, 1998; Worthington, 2003). However, newborns are cognitively equipped from the very outset to recognize objects and their quantities and almost immediately begin to accumulate knowledge about numbers (Butterworth, 2000; Dehaene, 1997; Wynn, 1992, 2002). Moreover, symbolization ability begins to develop in children from the earliest life stages (Kamii, Kirkland & Lewis, 2001; DeLoache, Miller & Rosengren, 1997; Mandler, 1992, Piaget 1962), and as a result, children acquire various types of knowledge about the written symbols of numbers (Bialystok, 1992; Carruthers & Worthington, 2005; Hughes, 1986). Tolshinsky-Landsmann (1986) found, for instance, that four year-olds differentiate between Hebrew letters and numerical symbols and that they consider one numerical symbol to be a number, whereas they do not think of one letter as a word (indeed, in Hebrew, one letter does not constitute a word). Tolshinsky-Landsmann and Karmiloff-Smith (1992) reported that children from England and from Spain at the age of about four distinguish between symbols that belong to the number system and those that do not.

As previously stated, the ability to attribute quantities to numerical symbols develops gradually. Two of the prominent researchers that have significantly contributed to our understanding of this developmental process are Bialystok (1992, 2000) who describes the different stages of the development of number symbolic thinking and Hughes (1986), who describes the development of the numerical symbolic representation.

Bialystok (1992) describes three hierarchical stages of number symbolic thinking. At the first stage children recite number sequences from their memory and employ the appropriate name for each number in the number sequence. At this stage children understand that counting is a way of describing quantities. …

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes

#### Cited article

Style
Citations are available only to our active members.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited article

Kindergarten and First Graders' Knowledge of the Number Symbols: Production and Recognition
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.