Some consider adding 0 as similar to adding 1 to the other addend, thereby increasing the number by 1. Another common error I have encountered is when students add a multi-digit addend to a single-digit addend, some calculate for the sum of the individual digits together. Some add the single-digit to each of the digits of the multi-digit addend. Some get confused with place-values, thus adding the ones to the tens, and so on. Some even make up a new rule in addition by adding all the numbers in the ones position then placing the sum under the tens. This is followed by calculating the sum of all the numbers in the tens position, and then placing the sum under the ones. There are also ones who seem to think that adding from the left to the right is the correct way. While this may not be obvious in additions that do not involve renaming, this error pattern could be carried over in other mathematical calculations, so teachers need to watch out for such student slips as well. I would say then that in teaching middle school addition, teachers need to help students “never forget” the basic principles of addition, and focus on place-values especially of multi-digit numbers.

Middle school subtraction, on the other hand, has its own set of error patterns apparent in some students. Just like in addition, some students tend to forget that subtraction is just a reversed addition. Sometimes, although not very often, a student makes a mistake in subtraction that could have been easily corrected had the student remembered the connection between subtraction and addition. Some students also do subtraction by forgetting proper renaming and borrowing. Place-values are also sometimes not used properly. This is common especially in multi-digit minuends and single-digit subtrahends. Forgetting to put proper marks when renaming is also common. This causes several mistakes in the subtraction processes. Sometimes, students tend to subtract from left to right. ...Show more