2.110 Did not know the Thought that a 26.3 1.173 − significance of zero in 0.937 can ‘a 937 zero’ on the left of be ignored as in The answer has a decimal point. the case of a zero no decimal point in 937.0 1.173 Computed i. Thought that 2.11 Had no − -1.063 1.173–2.11 .173 is larger understanding of instead of than .11 the rules for 2.11–1.173. As therefore a subtracting decimal such they large number numbers. interchanged the can not be numbers. subtracted from a small. ii. Thought that decimal .11 and .173 were independent of integer parts 7.030 Obtained 6.956 The idea of Thought that as the answer −1.174 is not is ‘borrowing’ ‘borrowing’ 6.956 instead of 5.856 clearly understood. done only once ------------ 7.03( ) No subtraction 24.3 They had no idea −1.174 Thought that if a was done in the 5.864 of placing zero(s) digit is missing in thousandth to fill gap(s) in a the vertical value. The digit number with digits. alignment, then (4) was simply no subtraction brought down to can be done in the thousandth the respective place value in the column. answer. Numerous errors were on subtraction of decimal numbers as cited in the respondents’ work in Table 4.24. First, in the question to find 2.11– 1.173, the digits were correctly vertically aligned with a replacement of a zero in the thousandth place
26.3 2.110 − 1.173 937 1.173 − 2.11 -1.063 The answer has no decimal point Computed 1.173–2.11 instead of 2.11–1.173. As such they interchanged the numbers. Did not know the significance of ‘a zero’ on the left of a decimal point. Had no understanding of the rules for subtracting decimal numbers. Thought that a zero in 0.937 can be ignored as in the case of a zero in 937.0 i. Thought that .173 is larger than .11 therefore a large number can not be subtracted from a small. ii. Thought that decimal .11 and .173 were independent of integer parts 24.3 7.030 −1.174 6.956 7.03( ) −1.174 5.864 Obtained 6.956 as the answer instead of 5.856 No subtraction was done in the thousandth value. The digit (4) was simply brought down to the thousandth place value in the answer. The idea of ‘borrowing’ is not clearly understood. ------------ They had no idea of placing zero(s) to fill gap(s) in a number with digits. Thought that ‘borrowing’ is done only once Thought that if a digit is missing in the vertical alignment, then no subtraction can be done in the respective column. Numerous errors were on subtraction of decimal numbers as cited in the respondents’ work in Table 4.24. First, in the question to find 2.11– 1.173, the digits were correctly vertically aligned with a replacement of a zero in the thousandth place
Victor_Mwesiga_%2D_PhD.docx