A lot of the math literature suitable for academic research is written at a level far too advanced for undergraduates. The periodicals listed here include content accessible to undergrads and/or informed readers.
Undergraduate Mathematics and Its Applications is published by the Consortium for Mathematics and Its Applications (COMAP). Note: Searching the COMAP site is clunky so use an alternative if provided.
"contains timely articles organized into the following sections: Statistical Practice, General, Teacher's Corner, History Corner, Interdisciplinary, Statistical Computing and Graphics, Reviews of Books and Teaching Materials, and Letters to the Editor." -- from the publisher's website
"Math Horizons is intended primarily for undergraduates interested in mathematics. Our purpose is to introduce students to the world of mathematics outside the classroom." -- from JSTOR
"Mathematics Magazine presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years." -- from JSTOR
"The American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. Its readers span a broad spectrum of mathematical interests and abilities." -- from the publisher's website
"Designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. It publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum." -- from publisher's website
"Devoted to improving mathematics instruction from grade 8-14 and supporting teacher education programs. It provides a forum for sharing activities and pedagogical strategies, deepening understanding of mathematical ideas, and linking mathematics education research to practice." -- from publisher's website
Online coverage is limited to 1997-2003. Current access is only made available to individual members of the National Council of Teachers of Mathematics (NCTM). "Intended as a resource for middle school students, teachers, and teacher educators. The focus of the journal is on intuitive, exploratory investigations that use informal reasoning to help students develop a strong conceptual basis that leads to greater mathematical abstraction." -- from the publisher's website
"Intended as a resource for elementary school students, teachers, and teacher educators. The focus of the journal is on intuitive, exploratory investigations that use informal reasoning to help students develop a strong conceptual basis that leads to greater mathematical abstraction." -- from the publisher's website