Without a firm foundation in basic arithmetic, algebras (I, II) and geometry a student will struggle in precalculus and above.
The following programs reflect what I believe is meant by foundational math.
From the University of New Mexico
http://news.unm.edu/news/foundational-math-taking-fear-anxiety-out-of-learning-mathematics
The course is called Foundational Math (Univ. 103) and is a division of University College’s Academic Foundations Program. Primarily computer-based, the class is designed for students who need brush up on some general math and algebra concepts before going into higher level courses required for most majors.
Community college of Philadelphia
https://www.ccp.edu/college-catalog/course-offerings/foundational-mathematics-courses
Courses in:
arithmetic
elementary algebra
Introductory Mathematics
intermediate algebra
Retail Mathematics & Merchandising
Sonoma State University
https://education.sonoma.edu/programs/FLM
Foundational Level Mathematics Teaching Credential program.
The FLMTC authorizes teaching general mathematics, all levels of algebra, probability and statistics, geometry, and consumer mathematics, but not calculus or mathematics analysis.
Queens University(Canada)
https://files.eric.ed.gov/fulltext/EJ1068208.pdf
A College-Level Foundational Mathematics Course: Evaluation,
Challenges, and Future Directions
All three courses cover basic number facts and operations—addition, subtraction,
multiplication, and division—with rational numbers, including positive and negative integers
and fractions; linear algebraic equations; the order of operations—brackets, exponents, division,
multiplication, addition, and subtraction; ratio, proportion, and percent; basic graphical
techniques; and, basic manipulation of equations containing variables. The level of difficulty of
the GAS course is comparable to that of the Ontario grade eight curriculum while the CV and
CV+ course are at a grade six level.