Despite what Tsui & Mazzocco (2007) found (the study was conducted on a group of mathematically gifted 6th graders), in general, students with higher levels of math anxiety performed poorer on assessments than their less anxious counterparts. According to Ashcraft & Kirk (2001), this anxiety doesn't manifest with simple arithmetic operations (ie, operations involving single digits), rather it manifests with relatively more complex operations like those between two 2-digit numbers, especially when "carrying" is involved in the operation.
Ashcraft & Kirk also theorize that working memory is a major contributor to arithmetic performance and that math anxiety acts as a detriment to working memory, leading to the observed declines in performance. The idea is that harboring an anxiety over a math problem takes up one of the items in our working memory, rendering our mental computations less efficient.
This suggests to me the importance of automaticity in math education. High levels of automaticity would decrease the student's working memory load.
They note that math anxiety tends to be a self-perpetuating phenomenon. Anxiety leads to worse performance which leads to increased anxiety which deteriorates performance further. They also note that students with math anxiety tend to not only perform worse on arithmetic assessments, but they are less likely to engage in mathematics later on in their academic careers (eg, high school and university course work, and STEM careers), performing worse in those endeavors when they do.
One thing to keep in mind with math anxiety is that it has no relationship to intelligence. According to Ashcraft (2002), the small correlation that does exist (r = -.17) is likely due to questions involving quantitative processes on the IQ test.
Another interesting finding of this review was that the negative performance associated with math anxiety primarily manifests with more complicated problems such as those involving "mixed fractions, percentages, equations with unknowns, and factoring."
One of the most effective methods of reducing math anxiety is a technique called systemic desensitization, or graduated exposure therapy (Hembree, 1990). Hembree doesn't go into the details of how this was applied, however.
According to the Wikipedia article on systematic desensitization, the process involves three steps:
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Establish anxiety stimulus hierarchy. Identify the source of the anxiety in other words.
Since we're talking about math anxiety this step seems trivial.
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Learn the mechanism response. Develop a coping strategy.
I think starting each new skill or strategy with trivial examples and gradually ramping up, helps address this
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Connect stimulus to the coping method by counter conditioning. Exposure to the anxiety followed by the coping method.
Induce some kind of intrinsic reward when completing a strategy
One source of anxiety seems to be lack of control and the teacher/student dichotomy (Finlayson, 2014). I think this program addresses that by putting all the control in the user's hands.
This does call into question something I had planned to do: making a mode that was the completion of an instructor task or skill.
One of the coping strategies put forward in this paper was practice. I agree this is part of the puzzle as practice increases competence which increases confidence. It also ties back into the Tsui & Mazzocco (2007) paper that found students performed better on timed tests after having taken an untimed test beforehand.
The abstract of a paper by Feng, et al (2014) suggests that slow-tempo classical music relieves math anxiety.
I have mixed feelings about putting music in any program but it doesn't really make a difference if the user can turn it off easily.