In my calculus I class, 50%-75% of my students do not do well on one particular integration problem that requires basic rules of exponents and fraction knowledge.
The need is due to having high failure on this problem which utilizes foundational math concepts students should know before entering MAT22X.
For 10 years, I have implemented several things to address this ONE problem - Review prior knowledge at the beginning of semester; drill and kill during class; collect homework specific to the problem; group work; board work; daily quizzes; journaling; telling them flat out that this problem will be on the exam; Khan Academy; review throughout the semester; detailed feedback; a mix of all of these, etc.
I see no pattern of anything truly helping. This semester, I still had 19 of 30 students not be able to do simple algebra in a calculus class. I am at a loss. They did well on the "harder" integration problems, so why can't they do algebraic integration? This semester, I incorporated so many different techniques with students in hopes of them doing well. I think this goes back to the core concept students struggle with - fractions.
Clear communication and collaboration between faculty is so important to make sure our curriculum lines up throughout the sequence of math courses. WIth developmental education gone, faculty teaching college level classes will need to incorporate review of basic concepts within their courses. Open dialogue and collaboration with instructors are always important. We need to make sure our courses are in alignment with each other.
Please note: From speaking with faculty in the prerequisite coureses, they are incorporating reviews of rules of exponents and fractions. But, at what detail and how, I am unsure. Hopefully with the creation of SLOs and having Guided Pathways, we can come up with some activities and best practices as a group to help students understand these two concepts better. I am not happy with the idea of just accepting that students will not be able to integrate a fractional problem that requires rules of exponents. There has to be something out there to help our students be successful with this. See attached for a sample problem that I am refering to.