Describe common misunderstandings students often have about algebraic concepts

Question

What will be an ideal response?

Answer 1

Complete answers will include the following: Several types of misunderstandings are associated with the use of letters to represent numbers (Booth, 1988). Some children believe that variables represent objects rather than numbers. Children sometimes think that the particular letter used as the variable in an expression corresponds to the first letter in the quantity being represented. For example, in one study a subject said that 8y would have to mean eight yachts or yams or some other word starting with y, and could not represent apples or dogs or any quantity not beginning with the letter y. Writing "5 times n" as 5n also leads some children to write 56 when n = 6. Wagner (1981) found that many children believe that changing the letter in an equation changes the problem. Subjects were shown the equations 7 x W + 22 = 109 and 7 x N + 22 = 109 and asked whether W or N would have a larger value. Some children said that they couldn't tell without solving the equation, whereas others believed that the order of the letters alphabetically must correspond to the order of the size of the numbers, so W would be larger because it comes after N in the alphabet.