I believe it would benefit all teachers of mathematics to integrate a diagnostic element to all practice materials and tests that they write. Although there are a variety of things that a teacher can do to determine individual and class weaknesses, diagnostic materials are perhaps the most valuable. Whether in the classroom, coaching, or tutoring on the Internet, I have always integrated a diagnostic element to all of the materials that I write. I make sure that a variety of problems are written that target concepts that I am teaching. When appropriate, I also include problems that feature common errors. When grading practice materials or tests, I focus attention on specific problems that demonstrates to me if a student has actually mastered the concepts that I have introduced. I also look at problems where common errors might occur. Many times, I do a tally sheet that indicates the number of errors that were made on a test. By studying that tally sheet, I can see class weaknesses, which I can address in follow up lessons. When grading tests, I determine individual weaknesses, which I address with individualized tutoring.
Developing diagnostic practice materials and tests is something that parents could also do to help their children. When diagnostic elements are combined with tests that are cumulative in nature, students are provided an opportunity to reinforce what they are being taught. I can assure you that the combination of diagnostic and cumulative elements in tests is responsible for the success that my students achieved in the classroom, in competitive contests, and when tutoring.