% Failure Errors Associated rates misconceptions Students Noted errors Causes work (+78) ÷ (−13) Did not know the Thought that the = 37.0 rules for dividing positive and = 6 Neglected the positive and negative signs are positive and negative not involved when negative signs in numbers. performing the computation division as it applies for multiplication. Did not have Thought that, it clear was unrealistic to -91 Skipped a zero understanding of write 0 as the 13 between 7 and 1 using the long number of times 1 -13 in the quotient. 30.3 division method. goes into 13. 00 The zero was the of times ‘number 1 goes into 13. In item 28, respondents were required to divide a positive integer by a negative integer, while in item 14 they were required to divide positive integers. As shown in Table 4.15, the proportion of respondents who failed item 14, was greater than the proportion of failures in item 28. The common noted on division of positive error and negative numbers was omission of the positive and negative signs in the Respondents in the Focused-group discussions from schools C3SGB computation. and NG2SGB appeared to know only the products of two negative numbers, two positive numbers as well as products of the numbers with opposite signs. However, some of them were confusing the result of: dividing two negative numbers, two positive numbers, negative and positive numbers. As such, they conceptualized wrongly the rules governing division of positive and negative numbers by confusing
% Failure rates Students work Errors Associated misconceptions Noted errors Causes 37.0 (+78) ÷ (−13) = = 6 Neglected the positive and negative signs in the computation Did not know the rules for dividing positive and negative numbers. Thought that the positive and negative signs are not involved when performing division as it applies for multiplication. 30.3 -91 13 -13 00 Skipped a zero between 7 and 1 in the quotient. The zero was the ‘number of times 1 goes into 13. Did not have clear understanding of using the long division method. Thought that, it was unrealistic to write 0 as the number of times 1 goes into 13. In item 28, respondents were required to divide a positive integer by a negative integer, while in item 14 they were required to divide positive integers. As shown in Table 4.15, the proportion of respondents who failed item 14, was greater than the proportion of failures in item 28. The common error noted on division of positive and negative numbers was omission of the positive and negative signs in the computation. Respondents in the Focused-group discussions from schools C3SGB and NG2SGB appeared to know only the products of two negative numbers, two positive numbers as well as products of the numbers with opposite signs. However, some of them were confusing the result of: dividing two negative numbers, two positive numbers, negative and positive numbers. As such, they conceptualized wrongly the rules governing division of positive and negative numbers by confusing
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