Errors and Misconceptions

It is important to understand the difference between an error (mistake – which is a one off) and a misconception (misunderstanding). For example, a common algebraic error might be 3a+5a = 7a, whereas believing that a letter can only stand for one particular number and that different letters must stand for different numbers is a misconception. This reminds me of a famous Peanuts cartoon where Charlie Brown – the main character, instructs his classmate to “Just put down 11 and don’t worry about it.’x’ is almost always eleven and ‘y’ is almost always nine. With the final telling comment, “One thing I have learnt about algebra, don’t take it too seriously”. (https://www.pinterest.com/pin/math--159385274285066889/). A more in-depth exploration of misconceptions in algebra is provided in the research study in 2011 by Gunawardena Egodawatte. The underlying issue with incorrect solutions in algebra is more often based in a misconception rather than an error and therefore teachers need to take extra precaution when teaching algebra and must constantly and consistently remind their students of these misconceptions (Bicer, Capraro & Capraro, 2014).