Mathematical Misconceptions

Misconceptions are as common as any other phenomena in real life situations. Just about any concept, regardless of how well it is taught, could be misunderstood. Needless to say that misunderstood concepts could have disastrous effects on all stakeholders. Having been in academia for 40 years I realize that exposing these misconceptions and addressing them head on is the most effective way of dealing with them. The misconceptions occur in computation, algebra, geometry, trigonometry, linear equations, quadratic equations, similar triangles relations, functions and many other areas. To this end, I have selected some of the more prevalent misconceptions, not taken in any particular order. For each misconception I have indicated all or some of the following: the nature of the misconception, the flaws in the misconception, the correct concept, an example of the use of the correct concept, an example of the use of the incorrect concept, a relevant poem where appropriate, a practice exercise with answers, a few observations/s and reflection(in action and on action).