Operating with Decimal Fractions as a Part-Whole Concept

Most research on both the assessment and teaching of decimal fractions has dealt with the decimal fractions as static units, not ones involved in operations that involve compensation. This study examined 1356 students ’ ability to add, subtract, multiply and divide numbers that included a decimal portion using the appropriate compensation for each operation. A fifteen-item test was given to 12-year-old students that assessed both their ability to use compensation and decomposition with whole numbers and with numbers that included a decimal fraction. Results showed that if students were able to use the appropriate compensation with whole numbers, between 47 % and 64 % were also able to use compensation to solve problems dealing with numbers that included a decimal fraction. This indicated that these students understood the part-whole nature of decimal fractions. It is suggested that while compensation has not been used to teach decimal fractions in our schools, it provides an additional way of enabling students to operate with decimals in ways similar to that used by people outside of school. Decimal fractions continue to perplex many students and adults, as evidenced by studies such as that of Stacey, Helme, Steine, Baturo, Irwin & Bana. (2002). The man