What methods are effective in identifying and eliminating severe math anxiety, this most terrible and unfortunate part of modern mathematics education? This question is not about ordinary math anxiety but about a severe version of the condition that manifests itself in such symptoms as panic attacks, physical symptoms, or inability to function.
In regards to "math anxiety", the 1990 paper by Ray Hembree helped me out a lot. It's a large meta-study of about 150 papers and a total of 25,000 students. Summary of the results, as I wrote on my blog previously:
Whole-group interventions are not effective (curricular changes, classroom pedagogy structure, in-class psychological treatments). The only thing that was effective is out-of-classroom, one-on-one treatments (behavioral systematic desensitization; cognitive restructuring); these have a marked effect at both lowering anxiety and boosting actual math-test performance.
The lesson that I personally take from this is that addressing math anxiety is largely out of the hands of the classroom teacher. Unless the student has access, or the institution provides access, to one-on-one behavioral desensitization therapy, no group-level interventions are found to be effective. When discussing the subject with students one-on-one outside of class, my number one priority is just to get them to physically relax at the moment, and I've become more prone to recommend that they arrange a meeting to see a college counselor.
Hembree, Ray. "The nature, effects, and relief of mathematics anxiety." Journal for research in mathematics education (1990): 33-46.
A while back I posted the related question How can we help students who are very anxious about math?, so that I could offer up a few answers of my own.
My suggestions include a few good books: My students have had some success in decreasing their anxiety with books like Mind Over Math (Kogelman, Warren), Overcoming Math Anxiety (Tobias), and Managing the Mean Math Blues (Ooten).
And a soundtrack I created: I also wanted something that directly addressed their test anxiety in math, and (after much research on math anxiety and the principles of creating guided visualizations) I developed a 14-minute guided visualization, which I titled Math Relax. It is available online for free. Not every student finds it helpful, but some students have felt that it changed their outlook dramatically.
Whether math anxiety is moderate or extreme, it comes from past experiences that we replay in our subconscious (or conscious). Guided visualizations help us to rewrite that script.