I teach math part time at a university and full time at a high school. I listen closely to my university counterparts. At the freshman level failure rates are very high. I hear concerns such as students are not well prepared, or students simply are not mature enough for college level work. At the high school level, we begin with the premise that learning can take place only from where the students are with respect to their current knowledge. In short, we determine where the students are in their learning, then, with specific course goals in mind, we develop a plan to achieve those goals.
At the college level, the premise seems to be that students who enter a class already have the prerequisite knowledge needed to help increase the odds of success or to at least survive the class. Therefore the instructor can begin immediately teaching new skills. If students lack prerequisite skills, it is the student's responsibility to get up to speed. To be fair, there are tutorial services and other resources available. I ask other university instructors if they make strategic decisions about the pace and direction of the class based upon data from assessments. The answer is no. They do not have specific information like that. I also ask what there goals for the class are. To be specific, I might ask if they could think of, say, three of four main concepts that students should take away from a course such as college algebra, that would help students in subsequent math classes. The results are mixed. I am searching through these questions if there is a sense of vertical a! lignment, always keeping in mind where the students are going.
How are instructors able to develop effective strategies which increase learning, and hopefully, result in a lower fail rate without data concerning their incoming students' math skills? Fail rates of 60, 70, and even 80% are not uncommon. This issue must be addressed proactively, not re-actively.