Is there a literature database like MathSciNet for mathematics education?
Yes, there is one called MathEduc.
MathEduc (formerly MATHDI) is the only international reference database offering a world-wide overview of literature on research, theory and practice in mathematics education. MathEduc also covers education in computer science on the elementary level. The scope includes literature for all school levels up to university education, teacher education, general and vocational education. About 500 journals from all over the world are evaluated as well as books and teaching material.
Update 09 July 2020:
There is now the following message at the linked page.
MathEduc no longer available. At this address, the MathEduc database, published by FIZ Karlsruhe and the German Society for Didactics of Mathematics (GDM), has been available until December 31, 2019.