Letters in Algebra:Misconceptions and Errors

Students often have difficulty with algebra because of misconceptions in various areas. It is important that teachers are aware of the misconceptions and errors so these could be corrected. When these are corrected, the students seem to grasp the concepts more clearly. One area is the meaning of letters

• More often, especially for Grade 7 pupils, they completely ignore the presence of letters. For example, if 5 is added to x + 7, the answer is 12
• Sometimes students are confused when between letters used as units of measure and as variables. An example is the use of m. Some students could not distinguish the 5 m and
• Some students treat letters as objects.

                 Question: Shirts cost p pesos each and pants cost q pesos a pair. If I buy 3 shirts and 2 pairs of pants, what does 3p + 5q represent?

                 Student’s answer: 3 shirts and 5 pairs of pants.

• There are students who think that letters always have one specific value.

               Question:  What can you say about p if p + q = 12 and p is a natural number greater than q?

              Student’s answer: p = 7

• Some students think that different letters always represent different numbers.

            Example: a + b cannot equal a + c.

• Confuse how to perform addition and multiplication when letters are involved

            Example: 3m + 2p = 5mp