Eliminating Misconceptions & Learning to Love Math
Excerpted from Learning to Love Math: Teaching Strategies That Change Student Attitudes and Get Results by Judy Willis. Get this book at a 15% discount through August 22, 2012, with offer code Z68IS.
With the exception of errors that result from carelessness or incomplete basic arithmetic facts, the errors that students make in math tend to be consistent. The most common involve incorrectly applying a procedure or an algorithm learned by rote memorization. Such errors occur when students have not developed the mathematical reasoning that accompanies constructing the mental patterns of concepts; procedures and facts learned only by rote memory are not available for successful transfer to new situations.
As in other subjects, students have misconceptions about mathematics. These misconceptions hinder the learning process because they are strongly embedded into neural networks that have been activated again and again. Students need tangible experiences to break these misconceptions.
Eliminating mathematical misconceptions is difficult, and merely repeating a lesson or providing extra time for practice will not help. A better approach is to show students common errors and help them examine completed sample problems that demonstrate these common errors. This method also gives you an opportunity to reinforce critical foundational skills.
For example, combining like terms is a concept that needs to be constructed with a framework of experiential learning, that is one can add and subtract only like terms (i.e., objects of the same category, same units of measurements).
Unless this concept is learned with complete understanding in elementary school, it will continue to confuse students when they move on to common denominators and the simplification of algebraic equations. An example of a common error in this category is 2a + 2 = 4a.
How do you help students resolve math misconceptions?