Drawing from experiences at Ohio State University (OSU) with remedial college students and with 12th grade students without elementary algebra skills, this paper outlines a numerical approach to algebra instruction using handheld calculators. Introductory material discusses problems with traditional approaches to math education and outlines some instructional developments made possible through the use of calculators. Next, background is presented on the experimental use of handheld calculators at OSU, including information on students' skill and achievement levels and the rationale for using concrete problem situations, rather than axioms and algorithms, and calculators, rather than pencil and paper. Then, several features of the numerical, problem-solving approach used at OSU are explored: (1) students with calculators can effectively use numerical methods to solve problems they are unable to solve algebraically; (2) using calculators, students can encounter concepts and relationships in problem situations before the concepts are formalized; (3) investigating problems in many special cases permits variables to be introduced in a natural way to describe the general case; (4) calculators require students to pay attention to arithmetic ideas that would otherwise be of little interest to them; and (5) calculators permit the early introduction of graphing. Finally, further developments of this approach are illustrated with regard to strengthening the pre-algebra component of 7th and 8th grade courses. (HB)