Table 4.12: Students Failure rates (%) by Work, Errors, Causes of Errors and Misconceptions on Using BODMAS Rule % Errors Associated Failure misconceptions Students work Noted errors Causes rates Did not Thought that the 53.8 (− 8 ÷ 4 ) understand the negative sign − = 8 ÷ 4 two negative outside the − Neglected the negative = 2 signs multiplied brackets have − sign outside the together. the same brackets meaning as the one inside. (− 8 ÷ 4 ) − = + ( 8 ÷ 4 ) Multiplied the two Thought that = 8 ÷ 4 negative signs in division is = 2 (−8, to obtain + as − associated for the case of distributive distributive law of property like multiplication multiplication. (− 8 ÷ 4 ) − Opened brackets as in = +8 ÷ 4 − the case of distributive = 2 − law of multiplication 47.9 12 10 7 Thought that the − = 2 7 computation Performed 12 10 Did not know – = 14 can be done by first instead of 10 × 7 BODMAS rule. starting with 6 8 ÷ 2 − any operation. = ÷ 2 –2 Performed 6 8 first – = –1 instead of 8 ÷ 2 31.0
Table 4.12: Students Failure rates (%) by Work, Errors, Causes of Errors and Misconceptions on Using BODMAS Rule % Failure rates Students work Errors Associated misconceptions Noted errors Causes 53.8 − (− 8 ÷ 4 ) = − 8 ÷ 4 = − 2 − (− 8 ÷ 4 ) = + ( 8 ÷ 4 ) = 8 ÷ 4 = 2 − (− 8 ÷ 4 ) = +8 ÷ − 4 = − 2 Neglected the negative sign outside the brackets Multiplied the two negative signs in − (−8, to obtain + as for the case of distributive law of multiplication Opened brackets as in the case of distributive law of multiplication Did not understand the two negative signs multiplied together. Thought that the negative sign outside the brackets have the same meaning as the one inside. Thought that division is associated distributive property like multiplication. 47.9 12 − 10 7 = 2 7 = 14 Performed 12 – 10 first instead of 10 × 7 Did not know BODMAS rule. Thought that the computation can be done by starting with any operation. 31.0 6 − 8 ÷ 2 = –2 ÷ 2 = –1 Performed 6 – 8 first instead of 8 ÷ 2
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