Developing Number Sense through Mathematical Diary Writing: Der-Ching Yang Provides Insights into the Teaching of Mathematics in Taiwan through His Use of Mathematical Diaries as a Strategy for Developing Number Sense
Yang, Der-Ching, Australian Primary Mathematics Classroom
Many documents and reports (Australian Education Council (AEC), 1991; National Council of Teachers of Mathematics (NCTM), 1989, 2000) emphasise that communication is a major component of mathematics education and highlight that writing should be considered as an essential communication skill in learning mathematics. For example, the Principles and Standards for School Mathematics (NCTM, 2000) states that "written communication should be nurtured" (p. 62). It also emphasises that "communication is an essential feature as students express the results of their thinking orally and in writing" (NCTM, 2000, p. 268). Furthermore, A National Statement on Mathematics for Australian Schools (AEC, 1990) highlights that "mathematical communication skills are needed in order to understand, assess and convey ideas which involve mathematical concepts" (p. 13).
Writing can be a useful catalyst because it not only supplies students with an opportunity to describe their feelings, thinking, and ideas clearly, but it also serves as a means of communicating with other people (Baxter, Woodward, Olson & Robyns, 2002; Liedtke & Sales, 2001; NCTM, 2000). Writing "about mathematics, such as describing how a problem was solved, also helps students clarify their thinking and develop deeper understanding" (NCTM, 1989, p. 26).
Even though there is an important math curriculum reform effort under way in Taiwan, the new curriculum pays little attention to mathematical diary through mathematical diary writing. Writing about mathematics is a new experience to many students and teachers in Taiwan because it is not considered part of mathematics learning and teaching in the Taiwanese mathematics curriculum.
Can an emphasis on mathematical diary writing help children develop number sense?
NCTM (2000) and Liedtke and Sales (2001) believe that writing should play an important role in mathematics teaching and learning because it can help children develop conceptual understanding. This stimulated my research topic: can mathematical diary writing help children develop number sense? One of my graduate students, a mathematics teacher with five years teaching experience, asked her third grade students to write a mathematics diary in one class period. The task was to "write a short paper describing the number 12". One of her third grade students wrote:
Ming is a 12 year-old boy. His class has 12 students total. They are all from 12 different families. Ming celebrated his birthday on December 12. On the day of the party, Ming's mother bought a birthday cake and cut it into 12 pieces for them. His mother also bought 12 cans of soda for these kids. The party began at 12 o'clock noon on time.
In this example, the number "12" represents different meanings. This student separately provided the number "12" with multiple meanings and vivid life, showing she could make sense of her understanding of numbers and connect her understandings to real-life situations. As a matter of fact, a number is not an obvious and formal entity but is an abstract symbol. We create the significance and the value of a number. This episode encouraged me to study the impact of diary writing further and was the stimulus for this article.
Why ask students to write mathematical diaries?
Leung and Wu (2000) believe that posing and solving problems at home through mathematical diary writing is useful. They also claim that this is "practical because it makes mathematics learning continuous and promotes teacher-child-parent relationships" (p. 29). Using mathematical diary writing appropriately is helpful in promoting the teaching and learning of number sense. Teachers also can get feedback and check children's learning through the mathematical diary. Diary writing has numerous benefits. The following examples will support several major reasons why mathematical diary writing can help nurture children's number sense particularly in regard to fractions. …