About the final exam in honors algebra 3-4...
I know that students taking honors algebra 3-4, and their parents, expect excellence and we do as well at DV, which is why the final exams for honors algebra 3-4 are challenging tests, even for honors students. Sometimes, students who generally understand the material well and have done well on tests during the semester score lower than expected on the final exam. I'd like to share with you my observations about why this sometimes happens:
1) The final exams in honors algebra 3-4 are quite difficult - This is a college level precalculus class, so the final should be expected to be difficult. For all students, the finals in this class will be the most difficult encountered so far in any math class, and possibly the most difficult tests they've taken so far in any subject. The material is complex, and there is much covered, so students must work quickly and accurately in order to score well.
2) No partial credit, so minor errors are amplified - On regular chapter tests during the semester, we grade using partial credit, so if a student has the concept of the problem correct in work shown but has done something like missed a negative sign, only part of the problem's credit is lost. On the final exam, since it is multiple choice, any error at all, no matter how small, results in no credit for that problem. This means that careless errors or minor slip-ups are more amplified on the final than on other tests, and this is unavoidable due to the multiple choice nature of the finals for our district.
3) Only 40 problems on the final means each problem missed significantly lowers the grade - With only 75 minutes to conduct the final exam, and an entire semester of challenging material to cover, the problems on the honors algebra 3-4 final are conceptually difficult, and take significant time to complete. There is time enough to include only 40 problems on the final exam. This means that missing only 4 problems (even for minor errors) lowers the score a full letter grade. The final is somewhat sensitive in this respect, but the alternatives (more problems that are each less difficult and therefore unable to test advanced concepts, or fewer problems by choosing to omit testing some portions of the curriculum) are not really acceptable, so this is just the nature of standardized final exams in challenging classes.
4) Long term vs. short term information retention - Some students are very adept at memorizing and retaining information in the short term (a few weeks, long enough to do very well on a chapter test) but have more difficulty at complete recall of the details of an entire semester's worth of information on a comprehensive test. Again, this is just the nature of semester-wide finals.
5) Nervousness due to the stressful environment of high stakes testing - Even though the final exam is only 20% of the overall semester grade, that is high enough that some students become very nervous while taking the final exam, even when they have fully prepared for the exam. The stress of the test itself, particularly for students in younger grades, can cause students to make more errors than they usually would.
Any or all of these reasons might explain why a student who does well during the semester receives a lower than expected score on the final exam. You may ask, why have a final exam if there are issues such as these with it? Here are my thoughts on the positive aspects of the final exam:
1) There should be some measure of overall understanding for the entire semester which contributes reasonably toward computing overall grade - I believe the district rule that 20% of the overall semester grade is determined by the final is about right. It is high enough that it is significant, but not so high that grades are drastically affected by a low result. Typically, the result on the final exam will result in no more than plus or minus one letter grade from the grade a student has going into the final exam.
2) District wide, standardized, final exams help maintain consistency in courses between schools - The district's goal is for students taking a class to have a similar experience regardless of the classroom or school in which the student is enrolled. Requiring all honors algebra 3-4 classes to take the same standardized final exam helps maintain this consistency.
3) Preparing for the final exam provides an excellent review of course material - The studying and reviewing we do in preparation for the final exam gives students an overview of the semester, helping to tie sections together, and solidifying their understanding of the material going forward.
4) The final is good preparation for high stakes testing in college - Students need to become adept at preparing for, and performing well during, high stakes testing. Students will need to face the SAT and similar entrance exams before college. Once in college, many classes base most, or sometimes all, of the course grade on one or two very high stakes tests, so it is important that students learn to perform well in these tests. Final exams at the high school level helps prepare students for testing environments they will encounter in college.
I hope these thoughts help to give some new perspectives on how to interpret scores on the final exam. Personally, I feel that final exams are a good thing to do, but I like that they make up only 20% of the semester grade, and I feel that the overall semester grade is a more accurate reflection of what a student knows about course material.