The purpose of this study was to translate a general cognitive observation system, the "Florida Taxonomy of Cognitive Behavior," into a system specific to mathematics. Firstly, a group of 20 mathematics educators generated a preliminary Taxonomy. Secondly, this taxonomy was critiqued by a group of 55 mathematics educators while, independently, a group of 10 mathematics teachers tested the usefulness of the taxonomy by using it to classify videotaped mathematics lessons. Thirdly, after revision of the taxonomy, six observers were trained in its use and then classified the mathematical behavior shown in 20 videotaped recordings. Satisfactory inter-judge reliability and observer-criterion validity coefficients were obtained. (Author/MM)