Solving simple algebraic word problem Sample questions: Item 37: If and = 3, evaluate the expression n Item 40: Simplify the expression Item 41: Find the of if Item 42: I am thinking of a number when it is multiplied by 3 and then adding to the result, the answer is 1. Find the number I am thinking of. Table 4.11 shows errors noted in solutions of the four items as well as the associated misconceptions and causes. In item 37 respondents were required to evaluate an algebraic expression m2 – mn – 2 by substituting and = 3. The as noted from respondents m= n substitution error –2 work, was in substituting = into They wrote either (–2)2 + (–2)3 2 or m mn. –2 – + (–2 × 3) instead of (–2)2 + (–2)3 2. The misconception was that the –22 –2 – – two signs in (–2)3 make a positive sign outside brackets and hence obtained – + (–2 × 3) instead of +2(3). When subtracting a positive number from a negative as in 2, some respondents obtained 0 as the answer instead of 4. The respondents –2– – were confusing this with the fact that, one number minus the same number, the answer is 0, (a = 0). With this misconception they regarded 2 as a – –2 – subtraction of the same numbers and hence committed an error of confusing The respondents in the Focused-group discussion also numbers with opposite signs. gave 0 as the answer for the two expressions and They thought that the a a a a. – – – two expressions were the same.
Solving simple algebraic word problem Sample questions: Item 37: If and n = 3, evaluate the expression Item 40: Simplify the expression Item 41: Find the of if Item 42: I am thinking of a number when it is multiplied by 3 and then adding to the result, the answer is 1. Find the number I am thinking of. Table 4.11 shows errors noted in solutions of the four items as well as the associated misconceptions and causes. In item 37 respondents were required to evaluate an algebraic expression m2 – mn – 2 by substituting m= –2 and n = 3. The substitution error as noted from respondents work, was in substituting m = –2 into mn. They wrote either (–2)2 + (–2)3 – 2 or –22 + (–2 × 3) –2 instead of (–2)2 + – (–2)3 – 2. The misconception was that the two signs in – (–2)3 make a positive sign outside brackets and hence obtained + (–2 × 3) instead of +2(3). When subtracting a positive number from a negative as in –2– 2, some respondents obtained 0 as the answer instead of – 4. The respondents were confusing this with the fact that, one number minus the same number, the answer is 0, (a – a = 0). With this misconception they regarded –2 – 2 as subtraction of the same numbers and hence committed an error of confusing numbers with opposite signs. The respondents in the Focused-group discussion also gave 0 as the answer for the two expressions a – a and – a – a. They thought that the two expressions were the same.
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