Precalculus courses take a variety of different appearances depending on the institution. From two semester Algebra- Trigonometry sequences, to one semester all in one sequence, to one semester function courses. For some students precalculus will be a terminal course and for others it is meant as preparation for calculus. The question for precalculus instructors becomes how to effectively teach to a range of abilities and outcomes? There are a range of ideas and tools that can be used to help you effectively help your students.
One tool that instructors use to help assess their class structure is a pre-class review test. A review test at the very start of the semester helps identify weak students that need immediate remediation. This knowledge helps you to target students early who may struggle with material later in the course. Review quizzes can also be helpful before starting new units as they identify areas prerequisite deficiencies that can impede learning.
Projects and labs are another way precalculus instructors are changing the classroom. At AMAYTC several talks focused on using labs, and interactive assignments to engage students. These types of assignments have the benefit of scaffolding for weaker students and creating interest and challenge for stronger students.
Precalculus also lends itself to a flipped the classroom model. By flipping the classroom, a general course structure can be in place for all students and additional specific assignments can be assigned for students who need remediation and for those who want more challenging work. In class group work helps students of all abilities by fostering discussion, deeper mathematical thinking, and retention of material.
To assess what might work best in your class, pick a day during the semester and try out a new idea or several. If you have other suggestions, let us know and we will post them here!