PATHWAYS TO EARLY NUMBER CONCEPTS: USE OF 5- AND 10-STRUCTURED REPRESENTATIONS IN JAPAN, TAIWAN, AND THE UNITED STATES

Aki Duncan

Northwestern University

aduncan@northwestern.edu

Hsiu-Fei Lee

Northwestern University

feifei@northwestern.edu

Karen Fuson

Northwestern University

fuson@northwestern.edu

This study examines what representational supports for early number concepts appear across curricula in Japan, Taiwan, and the United States and what related supports exist in everyday lives in those cultures. Although there is some difference between Japanese and Taiwanese representational supports for early number concepts, their practice can be characterized as the extensive use of concrete and semi-concrete objects and a focus on the numbers 5 and 10 as units. Textbooks and teachers often show numbers in a vertical and/or horizontal 2x5 ten-pattern array. Linear representations organized by groups of ten help children see other numbers in the relation to 5 and 10. The groups of ten are clearly stated in the number words in these languages (12 is “ten two” and 53 is “five ten three”), but the groups of 5 are not reflected in the language. The use of groups of ten and of five is long-standing; present teachers used such representations as students.

In Japan and Taiwan, many aspects of the cultures emphasize groups of 10. Money is grouped into tens as it is counted. The metric system is used in many places in children’s lives; rice, their staple food, is sold in 5kg and 10kg bags, and bottled drinks come as 1 liter and 500 mg. The fives and tens both appear in the abacus that has been used for calculations for centuries in both countries. In both abaci, one bead stands for a group of 5. In the classroom, however, all five entities in a group are shown. Few everyday uses of five are present in Taiwan. In Japan, five and ten are used frequently to package objects for sale, such as eggs, dishes, dried noodles, socks, and postcards. Children have rich exposure to the number 5, as heroes often come in groups of 5s in their stories, and 5 dolls are displayed as a part of traditional girls’ day celebration.

In the United States there are few everyday occurrences of groups of five or of ten except for money. Dozen (12) and half dozen (6) rather than 10s or 5s are used pervasively in packaging, and the metric system still makes relatively few appearances. Some textbooks use ten-frames for a few pages, but the 5-structure as a way of seeing the numbers 6, 7, 8, 9, and 10 is infrequent. Therefore, using 5s and 10s in adding and subtracting numbers is less familiar and seldom arises spontaneously.