I want to share with you some ideas about assessment. I always taught in a school where there was open enrollment to all AP courses. Of course the students had to have the necessary prerequisite math courses to take AP Calculus, but 40 percent of the senior class took AP Calculus AB or AP Calculus BC. This meant that some class members were weak math students, whose prognosis for success was not good. It was important to give these students confidence so that they would not become discouraged early in the course. The old adage "nothing succeeds like success" works, and I found it important to put problems that were very accessible to the students on the first few tests. The tests obviously had to test what was studied in class, but they would be based on homework and problems that were reviewed in class prior to the test. When students did well they were encouraged to go home and study some more, so they would do well the next time. I would write glowing (and sincere) comments on good papers, and the students would tell me that the paper would be attached to the refrigerator door all year.
I would give students the opportunity to "make up points." That is, students could make up half the point value of a missed question if they came to me within a week of the exam. I would give them a problem testing the same concept as the problem that they had missed, and ask them to solve it. I would ask them questions about the solution, and they would usually explain the solution using their graphing calculators. I never permitted the pronoun "it" in the explanation, so that students would have to talk about the function, the first derivative, the second derivative, and so on. This allowed the 60-percent students the potential to raise their grades to the 80-percent range. Students who prepared and understood the concept did raise their grades; students who did not prepare for the oral exam and did not understand did not raise their grades. A word of caution here: "Making up points" takes a lot of time before school, after school, and every free period. If you make the commitment, be prepared for long and busy days.
Sometimes I would give tests in pairs—let students take a test with a partner. Partners would be announced several days in advance to give them time to prepare together for the test. They would work on the problems and hand in one test paper at the end with both names on it. When test was graded, both partners would receive the same grade. Students who were absent put their partners in the position of having to take the test alone, so that few students were absent for the test. A plus side of this approach was that I had only half the normal number of tests to grade. A minus side was that each test had to be photocopied for the other partner before they could be returned. The best way to select partners is to allow students to choose whom they will work with. If there are an uneven number of students in the class, there is always one who does not mind working alone.
Assessment, as we all know, is a very important part of teaching and learning. The important thing is to keep students interested and successful. Later on in the year you can make the problems more challenging, because students will have built up the confidence to accept the challenge.