If 1m = 100cm Cubing only the unit- prefix Defined 1m3 as 1,000m3 = 100,000cm3 Incorrect use of the relationship instead of both the prefix and 1m3= 100cm3 Since 1,000cm3 = 1l 1m = 100cm to deduce that quantity expressed in instead of 81.9 100,000cm3 = x 1m3= 100m3 centimeters. 1m3 = (1m)3 By cross multiplication = 1m × 1m × 1m = 1,000 × cm3 = 100,000cm3 × litres = 1,000,000cm3 = x =100 litres There were two types of errors noted in the respondents’ work of converting square metres into square centimeters, cubic metres into and The first is a conceptual error. Over 81% of respondents applied incorrectly the cubic centimeters cubic metres into litres. relationships of units. This error occurred because they did not have a good understanding of the relationship between metre and centimetres. They knew that but did not understand the definitions or rather the expanded forms of square metre’ and 1m = 100cm, ‘a cubic metre’. These respondents had a misconception that since the relationship of one metre and centimetres was that 1m = 100cm, ‘a then Likewise they deduced that Clearly, the respondents squared or cubed only the prefixes, 1m2 = 100cm2. 1m3 = 100cm3. forgetting to do the same for the numerical quantities as well. Therefore, respondents lacked correct conceptual understanding, that 1m2 = Similarly, they did not understand that 12m2 = (1m)2= 1m × 1m. 1m3 = (1m)3 = 13m3 = 1m ×1m ×1m.
81.9 If 1m = 100cm 1,000m3 = 100,000cm3 Since 1,000cm3 = 1l 100,000cm3 = x By cross multiplication 1,000 × cm3 = 100,000cm3 × litres x = =100 litres Incorrect use of the relationship 1m = 100cm to deduce that 1m3= 100m3 Cubing only the unit- prefix instead of both the prefix and quantity expressed in centimeters. Defined 1m3 as 1m3= 100cm3 instead of 1m3 = (1m)3 = 1m × 1m × 1m = = 1,000,000cm3 There were two types of errors noted in the respondents’ work of converting square metres into square centimeters, cubic metres into cubic centimeters and cubic metres into litres. The first is a conceptual error. Over 81% of respondents applied incorrectly the relationships of units. This error occurred because they did not have a good understanding of the relationship between metre and centimetres. They knew that 1m = 100cm, but did not understand the definitions or rather the expanded forms of ‘a square metre’ and ‘a cubic metre’. These respondents had a misconception that since the relationship of one metre and centimetres was that 1m = 100cm, then 1m2 = 100cm2. Likewise they deduced that 1m3 = 100cm3. Clearly, the respondents squared or cubed only the prefixes, forgetting to do the same for the numerical quantities as well. Therefore, respondents lacked correct conceptual understanding, that 1m2 = 12m2 = (1m)2= 1m × 1m. Similarly, they did not understand that 1m3 = (1m)3 = 13m3 = 1m ×1m ×1m.
Victor_Mwesiga_%2D_PhD.docx