Can I publish a paper in mathematics education on a computer program?
I agree with user2768's comment that it will be most convincing if you can publish a user study and/or test of the program's impact. However, if your program is designed around some part of learning theory that is important but hard to implement, or focuses on a neglected area of mathematics, the program itself may generate interest. You allude to interviews with children when designing the program--so if you can illuminate what the misconceptions are that kids have (or other needs you found) and how the program is designed to address those, that might be compelling.

You may want to take a look at the Bootstrap project, which started as a teacher's classroom tool to teach algebra and became a dissertation topic and then an educational tool.  http://www.bootstrapworld.org/community/

It's also not fully clear to me how far along in your thesis you are. You'd benefit from reading about Design-Based Research (see, e.g., the 2004 special issue of the Journal of Learning Sciences, starting with this article by Barab &amp; Squire: https://www.tandfonline.com/doi/abs/10.1207/s15327809jls1301_1?journalCode=hlns20), and possibly also this conference paper on how to build that into a dissertation: http://ro.ecu.edu.au/ecuworks/1612/ This method may offer you a framework to help you publish design work-in-progress, as well as knowledge you gain as you test and develop it. 

Also, you may want to ask your advisor about good outlets to publish this, and whether getting a paper out at this point is a top goal. Since most education conferences are non-archival (double-check whether the individual conference publishes archival proceedings), this may also be a good thing to submit to a conference.