Errors and misconceptions committed by respondents in solving items 10, 27, 28 and 29 as well as causes of the misconceptions are given in Table 4.13. Table 4.13: Students Failure Rates (%) by Work, Errors, Cause of Errors and Misconceptions on Subtraction of Integers % Errors Associated Failure misconceptions Students Noted errors Causes work 3 = Did not know the Thought that, the –9 – –6 54.1 different ways of two negative signs Obtained 6 as – writing in‘ 9 are the answer a – b, – –3’ and (+a) multiplied to give b instead of –a – – + 3 hence + 3 = –9 –12 They were also –6 confusing the rules Thought that the two 3 = +6 –9 – of adding two consecutive negative Gave +6 as the consecutive positive in are ‘–9 –3’ answer instead of and negative multiplied to give a –12 integers. positive sign as for the case of × = +a –a –a 6 (+ 3 ) Did not know the: Thought that the − − = 6 + 3 51.4 i. 6 = +6 − − i. of opening two signs in ‘ ii. (+ 3 ) = + 3 − brackets 6 are – – ‘ multiplied to give + 6 ii. meaning of (+ a ), − (–a) – Thought that it was 47.6 Interchanged the Did not know the not possible to –8.9 terms from meaning of (– – a) subtract from –0.89 –8.9 0.89 (–8.9) to – 0.89 –8.19
Errors and misconceptions committed by respondents in solving items 10, 27, 28 and 29 as well as causes of the misconceptions are given in Table 4.13. Table 4.13: Students Failure Rates (%) by Work, Errors, Cause of Errors and Misconceptions on Subtraction of Integers % Failure Students work Errors Associated misconceptions Noted errors Causes 54.1 –9 – 3 = –6 –9 – 3 = +6 Obtained – 6 as the answer instead of –12 Gave +6 as the answer instead of –12 Did not know the different ways of writing a – b, –a – b and – (+a) They were also confusing the rules of adding two consecutive positive and negative integers. Thought that, the two negative signs in‘ – 9 –3’ are multiplied to give + 3 hence –9 + 3 = –6 Thought that the two consecutive negative in ‘–9 –3’ are multiplied to give a positive sign as for the case of –a × –a = +a 51.4 − 6 − (+ 3 ) = 6 + 3 i. − 6 − = +6 ii. − (+ 3 ) = + 3 Did not know the: i. of opening brackets ii. meaning of − (+ a ), – (–a) Thought that the two signs in ‘ – 6 – ‘ are multiplied to give + 6 47.6 –8.9 –0.89 –8.19 Interchanged the terms from 0.89 – (–8.9) to Did not know the meaning of – (– a) Thought that it was not possible to subtract –8.9 from 0.89
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