Research shows that a significant number of students are anxious about mathematics, which can affect their school performance as well as their academic trajectories and emotional well-being. It is important to understand this problem and identify the best strategies to address it. In a recent study, the authors concluded that the most effective strategy may ultimately be the training of mathematical principals.
We all recognise the importance of mathematical knowledge for school education, but also for scientific and technological development, or for everyday life. Yet this is one of the subjects that generate most anxiety in students. The negative beliefs associated with it, namely that it is a "difficult" subject, can contribute to that. Often, this kind of beliefs is at the root of the psychological effect of "self-fulfilling prophecy". In short, the lower the students' expectations of their own ability to perform a task (low sense of self-efficacy), the more likely they are to divest themselves of that task and consequently experience failure and see their expectations of failure confirmed [3,4,5]. It is not surprising, therefore, that many students develop anxiety about mathematics and try to avoid it, with the consequent damage to their future school and career paths.
In general, anxiety about mathematics is defined as "a feeling of tension or anxiety that interferes with the manipulation of numbers or the resolution of mathematical problems in academic or everyday situations" . The most recent research points to an early start of the problem (already in the 1st cycle of Basic Education) and to an incidence that is not exclusive to students with difficulties. For example, a recent study  with primary and secondary school pupils showed that 77% of participants with maths anxiety had an average or high academic performance. It is therefore important to understand the role of cognitive and emotional factors in solving this problem.
In general, mathematical anxiety is defined as "a feeling of tension or anxiety which interferes with the manipulation of numbers or the resolution of mathematical problems, in academic or everyday situations".
In an attempt to answer this question, a group of researchers  tested the effectiveness of cognitive and emotional strategies for anxiety management in 224 students in the 4th grade. The children were randomly distributed over three study requirements:
1. a first intervention requirement, in which students trained emotional capacities for identifying and managing anxiety;
2. a second intervention requirement, in which the students trained mathematics skills - more specifically, solving calculation tasks and discussing arithmetic knowledge learning strategies; and
3. a control requirement, in which students performed tasks on comics (reading and design).
Each requirement corresponded to a weekly training programme, consisting in total of eight sessions of 60 minutes each. Students were assessed on measures of verbal intelligence, before the start of the training, as well as on measures of general anxiety, anxiety in relation to mathematics and knowledge of mathematics, at the beginning and end of each training programme.
The results found are doubly enlightening.
1) Effects of the type of training on anxiety reduction
None of the training programmes has had an effect on reducing students' general anxiety levels. For the reduction of (specific) anxiety in relation to mathematics, the control training (comic book tasks) also had no effect. However, both the emotional management training and the mathematical knowledge training significantly reduced the anxiety towards the subject (without its effects differing from each other).
2) Effects of the type of training on learning
The control group training (comic book tasks) and anxiety management training had no effect on knowledge acquisition. In turn, mathematical knowledge training has significantly improved student performance.
Conclusion: "knowledge is power"
According to this study, knowledge training in mathematics improves students' performance and reduces anxiety in relation to the subject; emotional management training only reduces anxiety in mathematics, but does not improve learning. In scientific jargon, this means that knowledge training produces a double transfer effect: i.e. it benefits the trained capacity (knowledge) and it benefits different but related capacities (management of anxiety in relation to the subject).
In practical terms, knowledge training has proved to be just as effective as emotional management training for the reduction of anxiety in the face of mathematics, with added benefits for students' school performance. These results have useful implications for the design of maths learning programmes which simultaneously contribute to a virtuous circle of increased knowledge and decreased anxiety.
1 Passolunghi, M. C., De Vita, C., & Pellizzoni, S. (2020). Math anxiety and math achievement: The effects of emotional and math strategy training. Developmental Science, e12964. https://doi.org/10.1111/desc.12964
2 Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551–554. https://doi.org/10.1037/h0033456
3 Usher, E. L. (2009). Sources of middle school students’ self-efficacy in mathematics: A qualitative investigation. American Educational Research Journal, 46(1), 275-314. https://doi.org/10.3102/0002831208324517
4 Williams, T., & Williams, K. (2010). Self-efficacy and performance in mathematics: Reciprocal determinism in 33 nations. Journal of educational Psychology, 102(2), 453. https://doi.org/10.1037/a0017271
5 Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.
6 Devine, A., Hill, F., Carey, E., & Szűcs, D. (2018). Cognitive and emotional math problems largely dissociate: Prevalence of developmental dyscalculia and mathematics anxiety. Journal of Educational Psychology, 110(3), 431. https://doi.org/10.1037/edu00 00222