Is Pre-Calculus Really Necessary?

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.

  1. 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.
  2. It is a 45 minute period.
  3. Every students has had me for at least one, if not two previous classes.
  4. I haven’t used a traditional lecture for the previous three years.
  5. There is no state or district wide exit exam or set standards for either the Pre-Calc or Calc class.
  6. 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.
  7. 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.

  1. 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.
  2. 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.
  3. 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.

  1. College is a near certainty for my students.
  2. Roughly have will be majoring in a STEM based field.
  3. 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)

  1. Verifying trigonometric identities. Especially my focus on having them justifying why                                    Cos(A-B)=CosA*CosB+SinA*SinB. (3-4 weeks)
  2. My unnatural obsession with the with the difference and sum of the distances between foci on conic sections. (3-4 weeks)
  3. 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.)
  4. 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.)
  5. 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.



On Poverty

**This will be my attempt at one of those writings where I just sit down and write. Start to finish, no breaks, minimal proof reading. I’ve seen it done before and I hope that it won’t ramble or repeat myself too much.**

Our school didn’t do so well on the latest round of state testing. Specifically, we struggled on the poverty subgroup. I guess we don’t get poor kids. So this summer we were given a book to read, A Framework for Understanding Poverty by Ruby K. Payne. There is a ton of criticism of this book, much of it deserved. I personally found it to be rather simplistic. The graphics are basic and not really enlightening, but maybe I was suspecting too much. The author has a Ph.D and the book claims to be research based. However, it relies heavily on patterns that teachers might notice about their students from different classes.

Did I say patterns? I really meant stereotypes.

The premise of the book rests on the idea that there is a shared culture among classes that supersedes ethnicity, gender, or nationality. For example, the book wants us to believe that the poor are loud, that the poor lack long-term planning, and lack proper social cues. It is even complete with a made up case studies of what might happen. Oh, and for an author that has a Ph.D, the notes are trash. The notes are’t so much citations of sources as they are a list of stuff she read. Kind of like the links in a blog post.

And there was another, more personal reason that I didn’t like the book. There is a connection between behavior and culture. When Ruby Payne connects poverty to culture, she is in essence saying that the behavior of people leads to poverty. If you come from a loud family that has a big screen TV you must be poor. If you value a relationship more than achievement, you must be poor. If you lack social tact, you must be poor. But I grew up in poverty, and I couldn’t relate to what she was writing. Don’t get me wrong, there were struggles. I have been employed since the 5th grade (paper routes, Burger King, YMCA, Burger King again, hotel house keeping, Target, teaching). I remember the subtle pressures and jealousy felt as my peers would take vacations, shopping trips, or attend camps I couldn’t. I remember what it would be like to not have a parent home at night because they were at work, and I’m not talking about an on-call doctor. I remember being worried about if we were going to lose our house. When my behavioral experience doesn’t match Ruby Payne’s description it’s like my experience in poverty has been disingenuous. If Ruby Payne had me as a child in class she might acknowledge that my family was poor, but I wasn’t in poverty.

That strikes at the biggest problem with Ruby Payne’s thinking. Being poor is just having a lack of money. That’s easy for society to fix. But the term poverty carries much more baggage (drugs, poor housing, low intelligence, etc.) than the term poverty. Being poor is a paper cut that requires a band-aid. Being in poverty is having a disease that must be eradicated. When Ruby Payne equates that loud, rambunctious student with poverty, we teachers look to cure the disease. That is dangerous. That is the type of thinking that will lead to racism, sexism, homophobia, xenophobia, and nearly every other kind of discrimination possible.

Okay, so I disliked the book, but I waited to write this post unit we had the in-person workshop with the presenter from Aha! Process. The presenter was much better than the book. By focusing on the lack of exposure people from poverty might have, he made poverty a experiential problem and not a behavioral problem. My growing up in poverty wasn’t based upon behavior, but was due to a lack of experience on the part of my parents. Even though I would say that I have moved from poverty to decidedly middle class, or lower middle class, there are still experiences that might have benefited me that I will never know about or have to learn myself.

While the presenter did fall into the trap of stereotyping occasionally, I felt that he did an exceptional job of maintaining the focus on experiences. What he was trying to get across was empathy. Our students come to us from many different backgrounds, and while some will have had the same experiences and then have similar mindsets and paradigms for interpreting the world, others might not. As teachers we need to make our expectations abundantly clear, especially for those little things we might take for granted. Most of our students aren’t trying to do wrong by us, and we need to not only understand that, but acknowledge that.

And if we can accept that as a maxim, those little things really aren’t differences after all.

Impending Doom: Or Why I Hate August

I hate August. I think it is the worst month of the year. All I can ever think about in August is school, but school hasn’t started yet. I dread the coming onslaught of school; the planning, the paperwork, the grind.

Now I want to clarify something, I don’t hate school. I mean, I’ve made it my profession. I actually love the place, but I cannot deny that it becomes an all consuming monster for about ten months of the year. Of those ten months, about nine are consumed with the grind. Everyone knows the grind. It’s that systematic repetition that occurs throughout the school year. The grind is the day-to-day activity that makes a school recognizable as a school.

I get a respite from that mind numbing monster for about two months.

September, October, November, December, January, February, March, April, and May. It’s all about the grind. I like the grind. I thrive in the grind. To me the grind is the beautiful cycle that happens when teachers and students spend time in synchronized learning. I have never been a good planner, but I have been a good adapter. I work best when I can do something, students respond, and then I adapt. It is a process that has made me incredibly flexible. However, there is an element of spontaneity that comes with being highly adaptable. The spontaneity that happens in my class makes it nearly impossible to produce a detailed plan, especially when I do not know my students yet.

My flexibility and spontaneity is highly dependent upon having students with which to interact. Those students give me immediate feedback about my effectiveness as a teacher, more so than any written evaluation system ever could.

The whole process becomes mentally taxing. It pushes me to my cognitive and emotional limits during the year, and why school becomes so consuming.

And that’s why I hate August. I know the storm is coming, but there is nothing I can do about it. I know the grind of the school year is coming, but without my students there is nothing I can do to prepare in a manner that works best for me. So here I sit, consumed with school, the potential classes, the activities, reworking tests. Maybe I will even take the time to work on some of those things, but it will ultimately feel like wasted time without my students to tell me how I am doing. I am missing that integral part of my feedback cycle.

I have three weeks left of my break to enjoy, but the thought of schools looms and I don’t have my students, meaning those weeks are ….