I have taught mathematics to all age groups ranging from very young kids to adults. No two people learn maths at the same rate. Formal maths teaching starts at pre school or primary school. It is usually taught in groups or as a whole class. From the very first lesson, the little maths learners begin to realise that they are either really quick at understanding the teacher, or they realise that there are others in the class who are faster than they are, at understanding the mathematic concept being taught.
Unlike literacy, where every child is able to use their imagination as quickly as the next person in the class, in maths you either get it quickly, or you immediately discover that you are not so quick on the uptake.
For the slower learner, over time, they begin to lack confidence, they are constantly reminded that the others are working out the sums faster than they are and this is easily diagnosed as 'bad at maths'. As weeks become months and months become years, the student is constantly reminded, every single time, that they are not learning maths at the same rate as some of the others. Over time, the student, believing they are bad at maths, behave like they are bad at maths, thus creating a self fulfilling prophecy.
Every person has a preferred style of learning whether its visual, auditory, kinesthetic or any combination of these. This preferred style of learning translates to a preferred style of teaching. Unfortunately, for the students who do not have the same learning style as that being taught by the teacher, they will lose out to those students who do.
For example, imagine a student who is not an auditory learner but rather, learns best visually. The teacher, being an auditory teacher, insists on explaining the concept by way of talking. The visual student will have to absorb the information using a learning style that is not as effective for them than if the teacher had explained it in their preferred style, thus causing the slower rate of learning than that of their auditory learning counterpart.
The teacher who is able to incorporate all the learning styles into their teaching will inevitably reach a wider audience.
Now given that the slower learner has not fully grasped a concept, the teacher has moved on to the next concept. This will now leave a small gap in the students knowledge. This gap is never really filled. As the lessons go on, more and more small gaps are created. The student knows they have gaps but become too embarrased, as they get older, to expose that they never really did grasp that concept that was taught to them years ago. They try to hide their gaps, especially if it is a concept that they know they should know by now. This fear of exposing themselves leads them to become resentful of the subject. It gives them the courage to say out loud, "I hate maths!" It gives them the courage to say, "I'm not good at maths!"
I have taught privately on a one to one basis. I have taken these very students that feel they are not good at maths or even feel that it is their worst subject. A one to one lesson takes away the pressure of having to answer a maths problem under a timed constraint as they are no longer competing with the faster students. They are able to work at their own pace.
I've had to go back to elimentary concepts to fill gaps that these students have accumulated, filling each hole one by one. The student, though initially embarrased that I have dug up and exposed these holes, start to feel relief that they no longer need to pretent that they know concepts that they really didn't but should have. They now know it. In every single case, I have managed to turn a person from maths being their worst subject to it becoming their favourite subject. From hating maths to enjoying it.
So does this mean that these students are bad at maths? I think not!