I have a dilemma. This year I have two classes in the same period. Those two classes are Pre-Calculus and Calculus I, and I am not sure how to effectively teach both at the same time.
But first, some background information about the school, class, and teacher.
- I teach at a small school, so a class of 23 is large. 20 students are enrolled in Pre-Calc and 3 are enrolled in Calc. I traditionally have had about 10 in Pre-Calc with a max of 15 one year. I have never had more than 3 in Calc.
- It is a 45 minute period.
- Every students has had me for at least one, if not two previous classes.
- I haven’t used a traditional lecture for the previous three years.
- There is no state or district wide exit exam or set standards for either the Pre-Calc or Calc class.
- Because of the small number of students and my familiarity with them I had previously done some significant college work with the. Proof-reading essays, applications, scholarships, etc.
- It is not a college credit bearing class.
I should have had four or more Calc students, but several didn’t sign up for the class and some decided to switch to the College Credit Plus (CCP) classes that we offered. If I teach the same Pre-Calc I taught last year my three Calc students will range from bored to annoyed, not to mention that it wouldn’t sit well with me to have my name associated with teaching them two different classes on their transcripts, but in reality it was exactly the same thing. It would feel like cheating.
After I kind of exposed some people to my temper-tantrums of frustrations I began to try and think of ways I could make this work. I thought about #5 and #7 from my list and thought about the topics I covered in Pre-Calc. I started to think I could make this work.
But before I continue, let me provide a couple of beliefs that I hold as a teacher that greatly influence how I make educational decisions.
- We’ve gone too far with pushing math advanced math down on our students. Then society expects all students to master the complex math, which is measured through state level testing. Then funding and job security is tied to those tests and we wonder why so many students show up to college with glowing transcripts, but substandard grasps of basic concepts.
- Economic stability is difficult to achieve with just a bachelors degree from college, let alone nearly impossible for those with just a high school diploma. Hence I try to make my classes relatively easy to pass. I can’t justify judging a student’ potential to hold down a steady job based upon how well he or she could explain the subtle differences between ellipses and hyperbolas.
- I think it is of utmost importance that I prepare students for the math they will encounter in college. However, I believe that much of the math that is encountered in college will only be used as a gatekeeper to weed out students that are thought to be weak. This isn’t true of all college majors, but I think it is true of many, even some in the STEM fields. (When was the last time your dentist had to use Calculus?)
I found myself at a crossroads. The vast majority of my students won’t need advanced mathematics in their jobs, but they will NEED advanced math to get their jobs. With that thought I decided to give my students a survey to decide what topics I really should be teaching them. Here is a brief summary of their answers.
- College is a near certainty for my students.
- Roughly have will be majoring in a STEM based field.
- No one plans on majoring in pure mathematics.
To challenge my Pre-Calculus students, but still keep my Calc students engaged I am proposing dropping or extremely scaling back the following topics from my Pre-Calculus class. (rough time length follows)
- Verifying trigonometric identities. Especially my focus on having them justifying why Cos(A-B)=CosA*CosB+SinA*SinB. (3-4 weeks)
- My unnatural obsession with the with the difference and sum of the distances between foci on conic sections. (3-4 weeks)
- Scale back the graphing of trig functions. (Used to go over many transformations, all six trig functions, inverses, etc. spending about 4 weeks or more. I think I could scale this back.)
- Since the class is so much larger than I had in previous years I don’t think I will lose critical mass as often as I did in the past. It didn’t happen often, but it is difficult to move forward with new material when over 50% to 60% or more of the class is gone. (1-2 weeks.)
- I would also stop some of the in-class college discussion that normally took place. (1-2 weeks)
All in all this would save myself 10 to 14 weeks of instruction. Ideally I would replace the missing topics with limits, derivatives, integrals of polynomials. I think I would have to sacrifice some of the specific topics from Calc, such as derivatives and integrals of trig functions, but I am not sure. Since most of the students leaving my class would start off in college someplace between College Algebra and Calculus I, I don’t think I would be doing any long-term educational harm. The more I think about the drastic restructuring I think it might actually be more beneficial to our student population than covering some of the specific topics in detail that I had in the past.
I never had tried it before, so ultimately I need advice. Has anyone tried this? Is this a good idea? Is a basic introduction to derivatives more beneficial than in depth instruction on trigonometric identities. I don’t know.