Experience
In general, I am very impressed by the graphing calculator on the Monarch. I wish it had existed when I studied analytic geometry and calculus at secondary school.
On the Monarch, I created graphs of various equations familiar from secondary school mathematics, such as $x^2+y^2=1$, $y=e^x$, $y = \sin x$, and $y = \frac{1}{x}$. (The equations are here given in LaTeX notation.)
I didn’t need to use panning or zooming operations, since the graphs fit the display well enough to be readable without manipulation. More complex graphs might need panning and zooming to be performed during exploration, of course.
I also succeeded in exporting an equation from KeyMath to the word processor, which worked as documented.
Implications for Students and Professionals
So far as I know, the graphing calculator should be sufficient to support secondary school mathematics, except possibly multivariable calculus, which was available at the secondary school level when I was a student (the Australian school curriculum could take students further in mathematics than seems typical in the U.S.). If I am reading the User Guide correctly, it suggests that KeyMath does not support three-dimensional graphs, for instance.
I haven’t studied mathematics at the university level. However, my general understanding is that larger and more fully-featured software packages are used, at least in applied courses, including symbolic algebra systems and statistics tools. For example, [SageMath[(SageMath - Tour) is an open-source example of a symbolic algebra system. The R statistics package is an open-source option for statistics that has been extended to support accessibility features for students and professionals who are blind. Both of these tools include graph plotting capabilities.
Thus, when students need more complex mathematics software than the graphing calculator available on the Monarch, the question becomes how well these tools can be supported by the Monarch’s tactile viewer and any other relevant features. In addition, it isn’t clear what the limitations are of the KeyWord word processor in supporting mathematical notation - in particular, whether it can handle notations used in undergraduate and graduate-level mathematics. If not, the student would need alternative means of entering and editing mathematical expressions that support the full range of undergraduate and graduate-level material.
I would expect a professional with an undergraduate degree or higher in mathematics or a science discipline to require specialized software in the workplace, although there may arise situations in which a graphing calculator such as that found on the Monarch would be useful. However, this is a speculative claim and I think it’s an open question for those participants in Monarch RISE with mathematics and science degrees what software they would expect to use with the Monarch in workplace environments.
Comparisons
I think the graphing calculator as implemented for the Monarch is a major advance over what has previously been available. Sonification has been used, of course, as have embossed graphics, but what the Monarch offers are instantly available and very readable graphs of mathematical equations. This helps to give students who are blind a similar opportunity to their sighted peers in the mathematics classroom, for whom graphing calculators have long been readily available.
Although embossed graphs of equations offer higher resolution and hence more precise images, it doesn’t seem to me that the graphs displayed by the Monarch would be of substantially less educational value, especially once students become accustomed to working with them. The graph of a circle displayed on the Monarch, for example, is clearly an approximation, but it’s still easily recognizable. It is probably best for students to be familiar with both embossed graphs and dynamically displayed graphs (as on the Monarch). However, I think the Monarch’s advantages in generating graphs instantly and in providing full access to mathematics and science textbooks are considerable, and these benefits also need to be carried into workplace settings.