I’ve been able to fix the problem by changing the default-calendar-grid.php file to change the contents of the buttons that they noted above. I ended up replacing the chevron icons in the file with stylized “<” and “>” characters, respectively. This allows a screen reader to see that there is actually content within the button, and furthermore within the table header, and as a result fixes the errors it has with the calendar.
Hey Casey, this is one of the areas where things get a little weird because the W3 doesn’t actually have any say over the ADA guidelines, it is more than the ADA guidelines adopted the WCAG 2.0 guidelines as just that, a guideline to help. As far as I know, the tool you’ve linked to hasn’t been used in any judgements I’m aware of. Usually when it comes down to making a decision on if something is/isn’t compliant they have people use the actual PAWS tools and show what elements do/don’t work as intended or are otherwise inaccessible. Hope this helps!
The pressure is mounting to implement technology that more directly connects with residents, but balancing the shift to enable all citizens – including the approximately 19 percent with disabilities – can seem insurmountable. Beyond ensuring your organization is doing right your community, being in compliance with the Americans with Disabilities Act (ADA) or Section 508 standards is daunting – especially with the threat of a fine or lawsuit for non-compliance.
The 2014 case involving Peapod, an online grocery retailer emphasizes that being ADA compliant goes beyond your website. The settlement required Peapod to make its mobile applications accessible by March 2015 and its website accessible by September 2015. Since mobile apps are fast becoming the preferred method of online shopping, e-commerce sites must focus on app accessibility too. 
An accessible and ADA compliant website has the potential to increase your sales by over 20%. The market segment of persons with a disability is very loyal to businesses and websites that make legitimate efforts to increase their quality of life. Your businesses social media presence can also be improved as visitors share their favorable interactions with your businesses. Offering your business a significant and fiercely loyal revenue stream.
Another important consideration is that the ADA does not allow businesses to simply provide an alternative such as a phone number. Lastly, include accessibility issues as part of your website and mobile strategy. When new technologies are implemented or pages added, part of the process should include the implications for persons with disabilities. 
Many deaf-blind individuals use support service providers (SSPs) to assist them in accessing the world around them. SSPs are not “aids and services” under the ADA. However, they provide mobility, orientation, and informal communication services for deaf-blind individuals and are a critically important link enabling them to independently access the community at large.
Not to be outdone by their Southern neighbors, the Canadian government site is highly accessible. The home page is a simple page, beautiful in its perfect symmetry between English and French. The default language as specified on the element is English (lang="en", hey they had to pick one) but all French content is marked up with lang="fr". It's actually quite pleasing, and very Canadian, to listen to this page with JAWS as it alternates between the two languages.
The Americans with Disabilities Act (ADA) prohibits discrimination against people with disabilities in several areas, including employment, transportation, public accommodations, communications and access to state and local government’ programs and services. As it relates to employment, Title I of the ADA protects the rights of both employees and job seekers. The ADA also establishes requirements for telecommunications relay services. Title IV, which is regulated by the Federal Communications Commission (FCC), also requires closed captioning of federally funded public service announcements.

Title III of the Americans with Disabilities Act (ADA) requires that businesses and nonprofit services providers make accessibility accommodations to enable the disabled public to access the same services as clients who are not disabled. This includes electronic media and web sites. While the ADA applies to businesses with 15 or more employees, even smaller businesses can benefit from ensuring that their websites are ADA compliant. Doing so opens your company up to more potential clients and limits liability. Web developers should include ADA compliant features in the original site and application plans.
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