This article describes current goals for K-8 school mathematics and outlines 7 critical areas in which students frequently experience difficulty. Effective mathematics teaching is related to teaching that takes into account the 3 learning principles articulated in the National Research Council (2006) publication, "How Students Learn". Research supporting instructional strategies advocated by the National Council of Teachers of Mathematics is used in describing aspects of effective teaching. Continuing and increasing pressures to raise students' mathematics achievement often leave teachers looking for advice on teaching mathematics (Romberg, Carpenter, & Kwako, 2006, p. 3). Consequently, educational and instructional consultants should be familiar with what is known about mathematics instruction and where to find additional guidance for teachers.