Before a course to improve basic reasoning skills can be intelligently designed, it will be necessary to determine the exact nature of those skills. Research indicates that: (1) reasoning skills are highly specific, not generalized; (2) a large number of different reasoning skills exist; (3) many reasoning skills are language dependent and widely distributed; (4) patterns of weaknesses in reasoning skills are highly individual; and (5) reasoning skill weaknesses are very hard to change. In a normal lecture approach to reasoning skill instruction, the teacher decides how many skills to cover, then lectures on them in sequence; unfortunately, this type of instruction is ineffective given the specificity, the number, and the difficulty of these skills. The creative response to this situation is diagnostic testing and individualized instruction; students must be pretested to discover their individual patterns of strengths and weaknesses. If this is done, then instruction, homework, and even tests can be designed for individual students. The sequential instruction of reasoning skills in a lecture format is almost certain to fail; at most, there will be a reinforcement of existing skills in the better students and almost no genuine skill development in those who need it most. This paper briefly reviews the author's research in this area and describes in detail a pedagogical experiment based on his findings. (JB)