Using Ordering Tasks to Determine Fraction Magnitudes

The focus of this study was to investigate the students' ability in ordering four types of proper fractions. Type I: same numerators; Type II: same denominators; Type III: different numerators and different compatible denominators; Type IV: different numerators and different incompatible denominators. The researchers used library search and survey methodology through document search and questionnaire methods. The respondents of this study were 100 fourteen-year old students in two secondary schools from two districts. The results revealed that (i) students could easily order Type I and Type II proper fractions; (ii) students had less difficulty ordering Type II proper fractions compared with Type I proper fractions; (iii) students had difficulty ordering Type III and Type IV proper fractions; and (iv) when presented with tasks on ordering of Type III and Type IV proper fractions, students had most difficulty when ordering Type IV fractions. This showed that students still struggle with determining magnitudes of Type III and Type IV proper fractions. The findings of this study revealed that an appropriate method of instruction should be developed to teach students to order fractions of Type III and IV because the skill of ordering proper fractions is necessary for the development of fraction sense and overall mathematical development.