Table 4.5: Student failure rates (%) by Work, Errors, Causes of Errors and Misconceptions on Converting units of Area Volume and Capacity % Failure Student’s work Errors Associated misconceptions rate Noted errors Causes If 1m = 100cm Squaring only the prefix, instead Defined 1m2 incorrectly as 83.9 1m2 = 100cm2 Incorrect use of the relationship of squaring both the quantity 1m2 = 1× m × m Then if 1m2 = 100cm2 1m = 100cm to deduce that and unit prefix. Hence incorrect instead of the correct meaning 100m2 = understanding of the term 1m2 = (1m)2 x By cross multiplication Exclusion of units in the calculation unit’ = (1m) × (1m) ‘Square = x = 10,000cm2 If 1m = then Defined 1m3 incorrectly 82.9 1m3 = 100cm3 Incorrect use of the relationship 1m = Cubing only the unit prefix as 1m3 = 1×m×m×m So if 1m3 = 100m3 100cm to deduce that instead of both the quantity and instead of the correct meaning 10m3 = 1m3 = 100m3 prefix. 1m3=(1m)× (1m)× (1m) x By cross multiplication 1x = 10 × 100 Excluded units in the calculation = = 1,000cm3 x
Table 4.5: Student failure rates (%) by Work, Errors, Causes of Errors and Misconceptions on Converting units of Area Volume and Capacity % Failure rate Student’s work Errors Associated misconceptions Noted errors Causes 83.9 If 1m = 100cm 1m2 = 100cm2 Then if 1m2 = 100cm2 100m2 = x By cross multiplication x = = 10,000cm2 Incorrect use of the relationship 1m = 100cm to deduce that Exclusion of units in the calculation Squaring only the prefix, instead of squaring both the quantity and unit prefix. Hence incorrect understanding of the term ‘Square unit’ Defined 1m2 incorrectly as 1m2 = 1× m × m instead of the correct meaning 1m2 = (1m)2 = (1m) × (1m) 82.9 If 1m = then 1m3 = 100cm3 So if 1m3 = 100m3 10m3 = x By cross multiplication 1x = 10 × 100 x = = 1,000cm3 Incorrect use of the relationship 1m = 100cm to deduce that 1m3 = 100m3 Excluded units in the calculation Cubing only the unit prefix instead of both the quantity and prefix. Defined 1m3 incorrectly as 1m3 = 1×m×m×m instead of the correct meaning 1m3=(1m)× (1m)× (1m)