| This study examined sixth grade st’udents rational number knowledge usingcomparison tasks and rational number subcontract tasks. Comparison tasks included:comparing two decimals, comparing two fractions and comparing a fraction and adecimal. The subcontracts of rational number addressed in this research include:part-whole, measure, quotient, operator，and ratio.Eighty students were assessed using a written instrument divided into threesections. Nine students were interviewed following the written instrument to probe forfurther understanding. Students were classified by error patterns using decimalcomparison tasks. Students weer initially to be classified into four groups according tothe error pattern: whole number rule (WNR)，zero rule (ZR)，fraction rule (FR) orapparent expert (AE). However, two new patterns emerged: ignore zero rule (IZR)and money rule (MR).The purpose of the classification was to provide guidance in terms of selectingstudents to interview that would represent a range of success working with rationalnumbers and therefore, a range of knowledge that students would possess.Students’ knowledge of the subcontracts of rational numbers was analyzed forthe students as a whole, but also analyzed by classification to look for patterns withinsmall groups of students and by individual students to create a thick, rich descriptionof what students know about rational numbers. Students classified as WNR struggledacross almost all of the tasks. ZR students performed in many ways similar to WNRbut in other ways performed better. FR and MR students had more success across alltasks compared to WNR and7.R On average apparent experts performed significantlybetter than those students classified by errors. However, further analysis revealedhidden misconceptions and deficiencies for a number of apparent experts.Results point to the need to make teachers more aware of the misconceptions anddeficiencies because in many ways errors reflect the school experiences of students. |
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