The most common error committed by students is the sign error. Consider, for example the following instance. A seventh grade teacher is to provide instruction in the multiplication of signed numbers. The teacher walks through the room, observing progress of each student as they work on a number of sample problems at their seats. The teacher notices that several students consistently make the following error:
(-5) x (-6) = -30.
One misconception is that the students think that signs do not matter. In solving these kinds of problems, they tend to disregard the number signs. This might be because of lack of knowledge of the concept. The teacher may not have given the importance of number signs. In this regard, the teacher should give the reason why they should not disregard number signs. This will help students be more careful in solving numbered signs because they know its importance.
Another is that some students tend to believe that since the sum of two negative numbers is a negative then their product might also be a negative number. Students may overlook the details on the difference between adding and multiplying negative numbers. The teacher, for this matter, may have not emphasized or given a thorough detail on multiplying a negative number. This misconception can be diminished if the teacher gives the difference between adding and multiplying negative numbers. This will help students to keep in mind that the product of two negative numbers is NOT a negative number since they know that multiplying two negative numbers is different from adding two negative numbers.
There are many other underlying causes on why students commit this common error. One major reason is because teachers often overlook the details and skip the important ones. This error may be reduced if teachers emphasize on the details especially the importance of what they are doing.
SOURCES:
Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching. American Educator.
Conference Board of the Mathematical Sciences. (2001). The Mathematical Education for Teachers. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America.
Misconceptions in Mathematics: Calculations with Negative Numbers. Retrieved November 1, 2006
Patterns of Error. (2002). Retrieved November 1, 2006, from http://math.about.com/library/weekly/aa011502a.htm
Schechter, E. (2006). The Most Common Errors in Undergraduate Mathematics. Retrieved November 1, 2006, from

http://www.math.vanderbilt.edu/~schectex/commerrs/#Signs
Yetkin, E. (2003). Student Difficulties in Learning Elementary Mathematics. ERIC Digest. Retrieved November 1, from http://www.ericdigests.org/2004-3/learning.html