The path through mathematics is full of such pitfalls, and sadly many who fall by the wayside do not return. How can we restore math-confidence in those who have lost it? I don’t believe there is a single answer to this question, but here are some thoughts.

Someone who is traumatised by mathematics cannot simply be expected to just try again, but try harder, and reminding them that they will need this skill in the real world will just compound the shame of failure. So, instead of trying to put them back onto the road they fell off, find them a different road.

I teach first-year mathematics students, and I recall one student in particular who was traumatised by simultaneous equations. He would flatly refuse to apply the standard high school methods. But he would gladly solve simultaneous equations using a matrix. The matrix method is technically excessive, but for him, it had the single important advantage of being different.

Now, let’s imagine a student who is unable to perform arithmetic. Arithmetic is the goal, and the fastest path is memorisation. But the student’s experience on this path has been traumatic and now the student reasonably believes that further attempts along these lines will only lead to failure. How could a teacher help? You might like to pause for a moment and consider what you would do or have done to help such a person. Here are some ideas that could work in this situation:

- Teach them to use an abacus. Arithmetic can be understood as the purely physical activity of moving beads on a frame. Addition, subtraction, multiplication and division can all be performed by repeating a pattern with your hands.
- Teach them binary arithmetic. Binary arithmetic looks strange to decimally-minded people, but it is actually the simplest form of arithmetic. The idea of learning the binary number system might be both achievable and palatable because it is does not immediately reignite traumatic thoughts.

Other ideas would be to use Cuisenaire rods, or modular arithmetic. These are just some of the many paths to understanding the fundamentals of arithmetic, and I’m sure there are many others, besides. Mastering a different strategy doesn’t teach arithmetic as directly or easily as memorisation. The advantage, however, is that the student can circumvent trauma by finding a different path to understanding.

The real question is matching the person to the path. Students do not need to stay and suffer on a path that does not work for them. They can and should get off and try something different. While arithmetic may be fundamental and even universal, it is a concept understood by humans, and this human element permits an unlimited number of different and legitimate understandings.

**Dr Daniel Mansfield is a lecturer in the School of Mathematics and Statistics at UNSW.**