Table 4.11: Students Failure Rates (%) By Errors, Causes of Errors and Misconceptions on Simple Algebra % Failure rate Students work Errors Associated misconceptions Noted errors Causes Did not know the rules of Thought that: (–2)2 = 60.8 = (–2)2 + (–2)3 2 addition, subtraction and – –(2)2 = + × 3- 2 = –22 –2 multiplication of positive and –22 –4 = 6 2 –4 – – negative numbers. = –12 Thought that: if a a = 0 then – = 0. Misused the fact = (–2 × 3) a a – –22+ –2 that a number its self is = (4 +(–6) 2 – zero = 2 = 0 –2 – 2 = 0 –2 – 3m 3n + (8n) Confusing the rule of Thought that: – = 3m 3n + 8n multiplying negative signs to since 59.6 Wrong application of = 3m + + 11n the rule of adding integers of = +a the rule a a – – equal signs. then: × -ve = +ve –ve + = +a –a –a Does not know how to group 3m 3n + (–8n) – terms. Thought that the grouping of = 3m (3n + – –8n) like terms by using brackets = 3m Wrong placing of – –5n has no effect on signs of the = 3m +5n brackets coefficients. 1 = 2 + Did not know the rules of: Thought that the sign of the x – += 2 1 i. Changing the sign. number/term remains – 6 = 1 ii. Collecting like terms when unchanged when a shifted 1 and + x – = solving an equation. number/term is shifted across across the equality sign equality sign without 54.6 changing their signs Let the number be y Then: Thought that the term is
Table 4.11: Students Failure Rates (%) By Errors, Causes of Errors and Misconceptions on Simple Algebra % Failure rate Students work Errors Associated misconceptions Noted errors Causes 60.8 = (–2)2 + (–2)3 – 2 = –22 + –2 × 3- 2 = –4 – 6 – 2 = –12 = –22+ (–2 × 3) –2 = (4 +(–6) – 2 = –2 – 2 = 0 –22 = –4 –2 – 2 = 0 Did not know the rules of addition, subtraction and multiplication of positive and negative numbers. Thought that: (–2)2 = –(2)2 Thought that: if a – a = 0 then a – a = 0. Misused the fact that a number its self is zero 59.6 3m – 3n + (8n) = 3m 3n + 8n = 3m + + 11n 3m – 3n + (–8n) = 3m – (3n + –8n) = 3m – –5n = 3m +5n Wrong application of the rule –ve × -ve = +ve Wrong placing of brackets Confusing the rule of multiplying negative signs to the rule of adding integers of equal signs. Does not know how to group terms. Thought that: since – a – a = +a then: –a + –a = +a Thought that the grouping of like terms by using brackets has no effect on signs of the coefficients. 54.6 – 1 = 2 + x += 2 – 1 6 = 1 = shifted – 1 and + x across equality sign without changing their signs Did not know the rules of: i. Changing the sign. ii. Collecting like terms when solving an equation. Thought that the sign of the number/term remains unchanged when a number/term is shifted across the equality sign Let the number be y Then: Thought that the term is