Quote
mathematicians today "write out their answers" a la the style of Everyday Math.
Some may say this statement by the principal presents an opportunity to respond that you'd like to know more about this trend, and ask to see the source: research, articles, etc. Personally I would follow up on this and learn what the principal & teacher are basing their presentation on... setting the teacher's anecdotal experience aside, as it does not speak for the field as a whole.

Meanwhile, a quick websearch on Everyday Math brings us to the website of the University of Chicago, School Mathematics Project, Resource and Information Center, "created by the authors of Everyday Mathematics". There are tabs for home, about, parents, teachers, and teaching topics. Using their website search feature to find the keyword "writing" presents a results list including
- Teaching Topics, Individual Needs, a page in which the word "writing" appears three times in the section titled, "How can I provide enrichment within the classroom to students who are ready to think more deeply about content?" (where thinking more deeply about content may be a code phrase for gifted). Based upon what is presented, some may understand writing to be a form of differentiation for gifted pupils.
- A listserv. The results list shows snippets of teacher inquiries on the topic of having their pupils write.