In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. Similarly in linear algebra there was a linear algebra curriculum study group which produced some really good ways of teaching linear algebra and also highlighted curriculum changes. This was produced in the January 1993 College Mathematics Journal. Has any similar work been covered in number theory. I am looking for what are the important topics to cover and any work or research on the teaching of number theory.
You might be interested in looking at some of the work of the Mathematical Associations Special Interest Group (SIGMAA), RUME: Research in Undergraduate Mathematics Education.
See also MAA Online: RUME for more information on the group, and abundant resources to sort through, as well as links to the RUME Community Website, where you may be able to get targeted answers and suggestions from folks who know the current research very well, and have ready access to effective syllabi for undergraduate mathematics courses across topics.