The following are some of the people who have had a significant influence on the teaching of mathematics at various periods in history:
Euclid (fl. 300 BC), Ancient Greek, author of The Elements
Tatyana Alexeyevna Afanasyeva (1876–1964), Dutch/Russian mathematician who advocated the use of visual aids and examples for introductory courses in geometry for high school students
Robert Lee Moore (1882–1974), American mathematician, originator of the Moore method
George Pólya (1887–1985), Hungarian mathematician, author of How to Solve It
Georges Cuisenaire (1891–1976), Belgian primary school teacher who invented Cuisenaire rods
William Brownell (1895–1977), American educator who led the movement to make mathematics meaningful to children, often considered the beginning of modern mathematics education
Hans Freudenthal (1905–1990), Dutch mathematician who had a profound impact on Dutch education and founded the Freudenthal Institute for Science and Mathematics Education in 1971
Toru Kumon (1914–1995), Japanese, originator of the Kumon method, based on mastery through exercise
Pierre van Hiele and Dina van Hiele-Geldof, Dutch educators (1930s - 1950s) who proposed a theory of how children learn geometry (1957), which eventually became very influential worldwide
Robert Parris Moses (1935-), founder of the nationwide US Algebra project
Robert & Ellen Kaplan (about 1930/40s-), authors of Nothing That Is, The Art of the Infinite: The Pleasures of Mathematics, and Chances Are: Adventures in Probability (by Michael Kaplan and Ellen Kaplan).