0.89 as for –8.9 – the case of addition. 3 (–3) Did not know the Thought that − – = + 3 commutative law of the negative and −3 + 3 = −3 −6 = addition. positive signs in −6 40.2 3 + 3’ are ‘– multiplied to give a negative sign as for the case of × +a = –a −a In this study, respondents were required to answer three questions. In the first question, they were required to compute 3. This means to subtract 3 which is a –9 – positive integer from which is a negative integer. Most respondents did an error –9 in the expression to obtain a positive number. of multiplying any two negative signs As it was observed in the findings, respondents obtained either 3 = or 3 –9 – –6 –9 – = +6. Both and +6 were incorrect answers. As revealed from the discussion with –6 selected respondents, such errors were due to a misconception that, the two negative signs in 3 are to be multiplied to make a positive number, as is the case in –9 – multiplying negative numbers. For this reason, it is clear that, respondents had no understanding of the rules on multiplication of positive and negative numbers. They were also not aware of other ways of expressing That is = + = a a. a a a – – –a – – – (–a) + (–a) = The underlying misconception was the misapplication of the rules –2a.
–8.9 – 0.89 as for the case of addition. 40.2 − 3 – (–3) = −3 + 3 = −6 −3 + 3 = −6 Did not know the commutative law of addition. Thought that the negative and positive signs in ‘– 3 + 3’ are multiplied to give a negative sign as for the case of –a × +a = −a In this study, respondents were required to answer three questions. In the first question, they were required to compute –9 – 3. This means to subtract 3 which is a positive integer from –9 which is a negative integer. Most respondents did an error of multiplying any two negative signs in the expression to obtain a positive number. As it was observed in the findings, respondents obtained either –9 – 3 = –6 or –9 – 3 = +6. Both –6 and +6 were incorrect answers. As revealed from the discussion with selected respondents, such errors were due to a misconception that, the two negative signs in –9 – 3 are to be multiplied to make a positive number, as is the case in multiplying negative numbers. For this reason, it is clear that, respondents had no understanding of the rules on multiplication of positive and negative numbers. They were also not aware of other ways of expressing – a – a. That is –a – a = – a + – a = (–a) + (–a) = –2a. The underlying misconception was the misapplication of the rules