I Used to Teach Algebra I

I used to teach Algebra I. Over time I had developed some eccentricities that matched my personality, and made my classroom fairly efficient. My current seniors are the last students that had me for Algebra I, and when they talk about it, often they will mention the movies they got to watch. HOLY LABEL MAKER BATMAN! I don’t want to give the impression that all we did was watch movies though. When most people recollect their math class experience the imagine, something like this.

And that’s what my class was like, for the majority of time. It started with some sort of homework review, introduction of new material, and then I would release the students to work on their assignment with roughly 10 to 20 minutes of class left, very much following the, “I do, we do, you do.” This wasn’t everyday, but it was the vast majority of them.

The last time I taught Algebra I though, it was different. I would simply start class by presenting the students with a question that would be familiar to them. Either something from the previous day or something that they had been taught the previous year. I had them show me their work on whiteboards right there so that I could give them feedback right there, instead of waiting until the next day.

This worked for me because of two reasons.

The first, and most important was consistency. The last time I taught Algebra I it was my fifth consecutive year teaching the class. With the exception of open enroll students, the pipeline was from the same teacher, so I knew what to expect in terms of prerequisite capabilities. The standards were the same, the state testing was the same. Teacher evaluations were the same. Utilization of special education resources were the same. All of the consistency meant that I taught using my schema, allowing me to devote every ounce of my working memory and fluid intelligence to provide feedback for my students. I think it takes me five years of teaching consistency to be a good teacher with a curriculum. It really makes a cycle; master curriculum to teach (this is different that getting answers to tests); find a good sequence of topics; properly pace the topics to align with state testing; analyze assessment choices; and then finally be an effective teacher.

Now I said there were two reasons that allowed me to teach Algebra I the way I wanted and I’ve already talked about the consistency of a schedule. The second reason was because of the degree of autonomy I was allowed. Basically, I was told to go teach math, and that was it. As long as math was taught, the how I taught wasn’t nearly that important. So I decided to make my class fit my personality. I dumped activities that seemed to represent more of an obedience (sorry, “on task”) component. I made a promise to my students that I would not have them do any activities that I felt were there solely for busy work. I stopped feeling guilty about providing my students with downtime. Every now and then I found myself mentally fried by the curriculum, especially that first year teaching Pre-Calculus, so I couldn’t imagine how it would be affecting the students, and I didn’t feel guilt acknowledging that I was stressed too.

That manifested itself in that first Pre-Calculus class in a manner where there were several discussions about learning and mastery in general because my students were stuck with a teacher who only a survivor when it came to his math background. Much of the math class was dedicated to trying to understand why things work because I was trying understand why they worked myself. Since I was so comfortable with Algebra I, I would look at student feedback and decide I was happy with where they were for the day, and occasionally notice that there was 10 to 15 minutes of class left. Remembering that I promised that I wouldn’t spend their time with busy work, I used the time to build relationships and share aspects of my life that I found important, and yes, that might manifest itself as movies. As my relationships with my students improved I noticed that learning became more natural, and more productive.

Then, rather suddenly it all changed. First, my schedule was altered, Algebra I, the class that I was so good with, was taken away going into my sixth year at my current school. This is what my schedule has been since then.

Year 1 – Algebra I, Geometry, Calculus I, 6th Grade math aide, junior high lunch duty, senior class adivisor

Year 2 – Algebra I, Geometry, Calculus I, junior high lunch duty

Year 3 – Algebra I, World History, Calculus I, Economics, Geography

Year 4 – Algebra I, World History, Economics, Geography, Pre-Calculus

Year 5 – Algebra I, Algbera II, Pre-Calculus, Calculus I, Math Intervention, Personal Business and Finance Math, senior class adivisor

Year 6 – Algebra II, Pre-Calculus, Personal Business and Finance Math, Statistics

Year 7 – Algebra II, Pre-Calculus, Statistics, junior high study hall/math intervention

Year 8 – 8th Grade Math, Geometry, combined Pre-Calc/Calc I

I was still excited to teach because I felt comfortable teaching how I wanted to, I still had that autonomy.  So I showed up the first day during year 6 with a stack of whiteboards, enthusiastic about how having the students work in class impacted the outcomes, only to be crushed when I shared that philosophy with the administration and that’s not how you should teach. I was pressed to defend myself (in writing) and referred to the experts at the local educational service center. I was even questioned about going out of order in the textbook.

Then came the day, during the first week of school, when I lost one of my Algebra II classes to a fundraiser meeting that came with no notice. I decided to take the opportunity to spend some significant time with the other Algebra II class not working on math, but building relationships that would make the rest of the year more productive and efficient. Of course, that would be the day that I got a walk through, my first experience with a “gotcha” moment, and was proceeded to be lectured about wasted time. I was told that this wasn’t an official walk through, but just checking to make sure I am using my time wisely.

In my Personal Business and Finance Math, another class that I was new to, I showed a video to the students about rationalization, and it just didn’t sink in. YouTube made the recommendation to show this Berenstain Bears video, so I tried it. It went perfect, the kids embraced the dorkiness of being high school students watching kids cartoons, and they seemed to grasp the concept of rationalization. But one of those educational service center experts walked by and I was later lectured on the inappropriateness of showing a cartoon, and then had to provide a written rationale for my choice.

Then came the day I gave a problem in Pre-Calculus that got me in trouble. We had spent weeks working on trig functions, especially transformations of trig graphs. I gave the students a problem in a worksheet that asked them to do the reverse, given a set of points, find a trig function. I was called down to the office and was lectured about how students aren’t capable to performing this task without being explicitly being shown how to do it first. It just goes on and on.

Novice learners were timed on problems to see how fast they could complete them.

I give out too many A’s.

No one learns anything in your class.

Students told me they didn’t care, they’re going to get a B.

There needs to be more ways to succeed in your classroom.

It is impossible to learn anything in your class.

You let the students do nothing.

More people would be complaining if the grades were lower.

Students will lie to defend you.

I want to tell them to shut it and punch them in the face.

If I were a student I don’t know what I would be learning.

There needs to be more grades in your class.

I’m not going to do it since it’s not graded.

On top of all those messages I have been receiving, the state has changed the end of year test. We have new standards to deal with. I’ve had to adapt to becoming a full inclusion classroom that doesn’t track students, meaning I have had classrooms with students with IQs in the 80’s have been in classes with gifted students. Now students are being pressured more than ever to get college credits while still in high school. Students and teachers are feeling intense pressure to get the most amount of academic achievement at an ever earlier age.

When we give students messages over and over and over again that they are dumb they start to internalize it and it becomes a self-fulling prophecy. The messages I’ve received the past three years, that my students are lie to me, that all they do is take advantage of me, that all they do is walk all over me, well, I start to internalize that too. So when they come to my class exhausted and stressed, then do not respond to my prodding questions with thought, quit from fatigue during complex tasks, I no longer meet them with sympathy. I just keep going because, well fuck them, I won’t let them take advantage of me anymore. If they are tuning me out it must be because they have already mastered the content. They can fail, their grades aren’t my problem. That’s the teacher I am now.

And here’s the bottom line, in this current environment, I am not the teacher anyone needs. I tried desperately to hold on to a few of my values, but slowly selling out one little piece at a time, bowing to the pressure from administration, students, parents, tests, has made me a bad teacher. I am a bad teacher because I got sucked into the spiral of my own paranoia. Instead of meeting my students fatigue, exhaustion, and confusion with sympathy and grace, I coldly pressed on. As it just became more confusing for them, more of them decided to just quit and I don’t blame them. Why should they stress out over math they won’t need other than to jump through some hoop to get a college degree? They have no incentive to master the topic. As long as they are getting a B or C, they’re good.

As I write this, I keep staring at the information about conic sections on my board that I used in Pre-Calc and thinking over and over to myself, this is not how it should be done. The more I look at it, the more appalled I am. It dumbs down our students and it dumbs down the math. It’s a result of me trying to hold on to three years ago, adapting to my new pressures, but producing an abomination.

That’s not education. If that’s what I am producing it’s time for me to go. I thought I knew what my calling in life was, but if this is all the more I am capable of making, this passion has just turned into a burdensome job, which means I am no good for anybody right now. I’m not teaching. I’m torturing.

I hope that I actually made a difference for a couple students along the way, because right now I shouldn’t be here.



Having a Nervous Breakdown

During my second year of teaching Calculus I had a nervous breakdown in front of my students. I can’t remember exactly what topic I was trying to explain, I think it was the idea behind the Fundamental Theorem of Calculus, but I’m not sure. What I do remember was the feeling and how it started.

I was going over some procedure and explaining how to get the correct answer and one of the students asked me a simple question.

“Why did you do that?”

As soon as I thought about it I felt the sinking feeling of not knowing why. I hate that and have talked about it before. This time though, I didn’t respond with a command of just shut up and do the problem, and I did this for a couple of reasons. One, I was going through some graduate school classes that was completely rearranging my concept of knowledge. Two, the class consisted of only two students which had allowed me to develop more of a personal relationship than is typically involved in a classroom.

When I couldn’t explain the mathy stuff to my students beyond a just mimic me response, I stopped teaching. I literally stopped teaching and just sat there in class. After a few minutes I admitted that I had no idea what I was doing. It is blatantly obvious to most people that math that is used in school isn’t like math in reality, so if I can’t even explain what is happening, what’s the point of the entire endeavor?

I imagine that everyone has been in a class where they have thought to themselves, that the teacher has no clue what is going on, but I can’t imagine many people being in a class where the teacher came in on day one and said, “I don’t know what I’m doing…so, let’s get started.” While it wasn’t day one, that was essentially what I was doing in front of my students, admitting that I am clueless.

If I did that in class today I wonder how my students would respond? I fear they would use it as a justification to tune me out more than many of them already do. (He doesn’t know what’s going on why should I bother.) I fear that they would use it as a justification to complain about grades. (How can he give me a C when he doesn’t understand the stuff himself?) But when I admitted my cluelessness to these two Calculus students they didn’t pounce at the opportunity to take control of the class. I was met with empathy and sympathy, and it immediately transformed the class dynamic. No matter how comfortable I had felt with students in the past it was always centered around a me-them type relationship, but from my meltdown to the rest of the year, class took on a more of an us mentality. It was still a classroom, and I still had more mathematical knowledge than them, but I didn’t feel like the dispenser and controller of knowledge anymore. It felt more like I was talking with them rather than talking at them, as if we were exploring together.

What I learned from that moment on was that my classroom needs to be a place where vulnerability is acceptable, though I think I’ve lost that.  We finished out the rest of the year learning Calculus together. Some days were smooth, some days were messy, but it always felt as if it was together. Sometimes we talked about a concept for the entire period with no math written. Some days we worked on procedures from the book. Some days we did other non-math related stuff and embraced the human element of school. Looking back on the experience, it was probably the first time that I felt like authentic learning was occurring in my classroom and was finally finding a vision of what I want education to be.

That moment became the impetus that lead to what I consider the best two years of teaching in my life. Every class seemed to develop some sense of supportive community. I felt free to experiment with ideas and push the limits of my students. Unfortunately I have watched that environment whittle away that past three years. Why don’t I have that accepting, vulnerable, safe, welcoming classroom centered around togetherness? I’m not entirely sure, but I do know much has changed over the past three years. My schedule changed, students have changed, I have changed, administration has changed, technology has changed, testing has changed, all of this leaving me more disillusioned than I have been in a long time. Maybe I have to have one of those coming to Jesus type moments like I did way back in 2011 when I had a nervous breakdown. I don’t know.

All I know for certain is that right now, there are way more days that I leave work unfilled, like my presence at school has served no purpose. I was under no assumption that everyday would be a rewarding bed of roses when I started this profession, but I am tired of feeling like a piece of shit at the end of nearly every day.

Let Me Explain Something…

The vast majority of my followers on social media are my students. Not my readers here, but as long as it’s only 140 characters there might be a chance they read it. In preparation for another school day, I was overcome with the usual sense of frustration and dred, imagining another course of IDK’s and IDC’s. So I impulsively sent out this.

It probably was the first time I fell into the trap of sending a subtweet.

Previously, I have talked about the amount of interaction and the relationships that can form between teachers and students in a small school. With all the schedule changes this year, I am fortunate enough to have one class where I have been around all the students for at least one previous class, while most of the students have had me twice, and a couple three times. (Figured out who I am talking about yet?) So, I entered this year with high hopes in anticipation of working with all these students that I have had before. I wouldn’t have that typical feeling out period where students and teachers kind get to know each other. We could just jump in and start to math. But then I saw the schedule. Not only was this class nearly twice as big as it ever had been, I had two different classes lumped together. I thought it would be okay though, I had built up a relationship with these kids.

Reality was a let down though. I am modifying my curriculum on the fly, which is never good. Because the class is twice as large the negative behavior has reached a critical mass where it can drag down all but the most motivated. I have students in class who wouldn’t be there except for the relatively new fourth year math requirement. The pressure for college credits has increased drastically even in the last three years. I fear that the majority of students in my class are there because they believe they are SUPPOSED to be there, not because they WANT to be there.

That’s just the student influences though, I haven’t even begun to talk about my own actions. I need to make sure that I had weekly grades. I need to vary my grades, of which I don’t. I need to make sure I am providing enough opportunities. There is too much down time. I need to vary my presentation. I give out too many A’s and B’s. Students don’t know how to improve grades. I don’t provide enough resources. Instruction needs to be bell to bell. Everyday is an academic day. If students say they are learning in my room, they are just lying to protect me because I am likable. Students can’t be expected to do math without examples. Students shouldn’t take more than 2 minutes to solve a math problem. I haven’t asked students what their preferred learning style is. I should contemplate if a high school is really the place for me, because sometimes people just need a career change. Essentially, nothing is ever learned in my classroom, my students just look at social media, and if anyone ever did want to learn something, they would have to find another teacher. This has been my environment for the past three years.

All that has influenced me in ways I really don’t like. I don’t have patience like I used to. I don’t have empathy like I used to. For example, today I covered a topic that should have been largely review from the previous class. I had a quiz planned for tomorrow because it was a review topic, so if everything went smoothly I would assess tomorrow. If the students struggled, I would keep teaching, they would keep learning and I would assess at a later date. But one student I think slept through class, another studied lines for the upcoming musical, a couple did a few questions then studied physics formulas, three were consistently on their phone, and I had to almost constantly talk over four. The 10 or so who did problems consistently seemed to know what was going on until we got to linear and angular speed and then the questions and confusion just got weird. (Figured out who I am talking about yet?)

Should I assess tomorrow? I think yes, because those students who had time to ignore me and focus on physics, or whatever else they were doing, must understand what is going perfectly. If they didn’t understand what was going on why else would they possibly choose to ignore me.

I hate that I think like that. It’s like school is making me hate students who I normally like. It’s kind of like Ghostbusters II. Watch from about 3:40 to the end.

It’s like school is the river of slime, especially true with a description like, “pure, concentrated evil.” This class that I am talking about, I really like them, I really do, but when I have to meet them in the river of slime that I call school, now I hate them. That whole vindictive process ultimately delegitimizes both the teacher and the students.

Several years ago I wouldn’t have handled it like that. First we would have been in one large group, 13 or 14 tops. The structure can alter the class dynamic drastically. I would have found time for us, and I mean all of us, to discuss the upcoming musical. I would have found time to talk about physics, whether that be studying the formulas for the class, talking about the formulas, or the purpose of memorizing the formulas. I would have talked about the stresses of work and how to deal with fatigue. I would have worked in a discussion of multitasking and the impossibility of multitasking and learning. With whatever time was left we would have discussed the math topic for the day. Those discussions about physics, the musical, or multitasking, would have all probably centered around the idea of how we learn and why we learn. So even if math didn’t dominate the day, I would still have felt like it was a productive day.

All those pressures about grades, bell to bell, every day an instructional day, I didn’t have those several years ago. I could teach in a manner that would align with my perceptions of the purpose of school. In my lower levels that meant I could dangle free time and movies as incentive for work. I didn’t fear being called down to the office to explain my lack of resources, which freed me to harass/encourage students, rather than just ignore them like I do now. In my upper levels we spent time talking about zones of proximal development and theories of how we learn, purpose of college, school in Brazil, or even the TARDIS. When we did math it was done collectively, which was fine because grades were more or less a fabrication and students were more or less on the honor system whether they learned. It wasn’t just math, but it was also while I was teaching a class that became dubbed epicnomics, where the exam was a report on UHF. I was able to run a project based Geography, full of down time, but full of great presentations. Ever contemplate the geography of nothing?

That leeway in class allowed me to branch out and pressure students to move beyond their comfort zones. It started with simply trying to get a student to think about a homework assignment (why are you coloring as a senior?), morphed into proofreading papers to try and instill a mindset that a good grade isn’t enough (“I got a 95, but don’t feel like I know what I’m doing.”), and culminating when I got tired of excuses from one of the smartest students I have ever met, set my computer and credit card in from of them and told them to register for the ACT.  Those are some of my best memories from several years ago, even though they have nothing to do with math. Math was still taught and learned, but it was incidental to why that slimy school should exist.

It was a different climate though. I felt as though I had some autonomy to define success. OTES didn’t exist. I had different classes. I had different administration. I had different students. I’m different too.

When I say I need a break from school, I’m not talking about a vacation. I still want to learn something.  I just want to leave the river of slime behind.

I Almost Quit Teaching…

Classroom management.

That is a popular term on the Google. One of the most common gripes with new teachers is that college never really taught them anything about classroom management. I couldn’t agree more. I also really HATE that term because classroom management is really code for how to make kids behave. (Maybe there are some amazing examples out there but the ones I have experience generally center around behavior modification, whether that be through positive or negative influences.)

When I was in school I was a good pupil. I still am to some extent. Students will tune me out in class, but truthfully, I really don’t care. I understand the plight of many of them, being forced to take a class they don’t want to. I have sat through many a professional development sessions, college classes, and even high school classes and felt the same way. Sometimes I would just go through the motions and sometimes I would completely disengage. For me, disengagement meant daydreaming or doodling, not rebellion. I had been in classrooms where students had acted out, but because I was tracked it didn’t happen often.

My 7th through 12th grade experience was marked mostly by being surrounded by good, complacent students. Though I knew acts of disobedience and rebellion did occur, I rarely witnessed them, let alone participated in them. I can only recall one time where I was openly defiant and that was during football, not in the classroom.

So the first time I took control of a classroom as a student teacher I was lost. My mathematics student teaching was in an Algebra I classroom in a school that tracked students, and I wasn’t with the good, obedient students.

I started presenting material, and a couple of students started talking over me. I made verbal corrections like I had witnessed my teachers do before, but I also began wondering, “Why do they do this to me, but not the other teacher?” Honestly, I still wonder this sometimes. I kept teaching like this for a couple of days. At first students would respond to my corrections, but eventually they stopped all together. I then moved to the next phase that I had witnessed in my schooling, the hallway chat. I took the worst offender into the hallway and discussed the behavior with the student. Finally, I reached the point where I started handing out detentions.

But it still wasn’t enough. There were still disruptions, still students being defiant. At last a couple of students spoke up, wondering aloud why that student was being disciplined, but not another student. Rather than end the discussion I engaged in a dialogue that was ultimately a power struggle between me and the students. Then a day or two later, it happened again. This time though, I lost it and cussed out the class. And when it started to happen again a few days later I took a couple of students out of the class that I was working with, told the cooperating teacher I was leaving and going to work with the students that wanted to learn. When I came back, my cooperating teacher told me that the kids were worried that I had quit on them. I was told to stay away from a parent teacher conference.

I went to the doctor and was diagnosed with strep throat. I don’t think I had it, but I was able to harass him into giving me a prescription and a note so that I wouldn’t have to go back until the next week. I wasn’t sure if teaching was for me, but I wasn’t sure what I was going to do. I walked out of a class in the middle of the day. (Coincidentally this is how I obtained my first, semi-permanent job.)

Obviously I didn’t quit and am still teaching after 11 years. How did I manage to last that long?

This past Thursday we had a guest speaker come to talk to our students, of which many spoke highly. He did a brief presentation to the teachers before school during which he made the following claim.

“If you lie to a student and are caught, it is over.”

Yup, that perfectly summed up my student teaching experience. When I tried to discipline my students they challenged me, and deep down, I knew they were right. I claimed that one student was a distraction, but then insisted another one wasn’t. If I acknowledged the correctness of their argument, it would represent that I had lost control of my classroom, and I had been taught that was unacceptable.

My experience forced me to question the idea of authenticity. Across three different states and with numerous veteran teachers, I have heard a variation of the line, “You’ve got to take control, be the one in charge,” or in the case of female teachers, “Sometimes, you’ve just got to be a bitch.”

I am then left with the choice of either authentically acknowledging that I lied to my students and  not caring that they will view me as a liar, including all the spite and contempt that comes with that position, or acknowledging that I am a mean spirited person. I really, really don’t like either of the those propositions.

While my positions on behavior and classroom management have evolved the longer I have been a teacher, I can pinpoint the moment that I think I actually started to realize that I would make it. After my meltdown, I slowly worked my back to being in front of a class. The first time I went in front to lecture, a kid in the front row, covered in crank bugs, looks up and says, “F*** YOU!”

The class was silent, waiting for me to react. They were probably expecting me to explode and kick the kid out of class. But instead of doing what I had seen other teachers do, I decided to do what came naturally to me. I looked the kid in the eye and replied in a dull, monotone voice, “Awesome.” I turned around and kept presenting material. I know many of my coworkers would be appalled that I would let something like that happen, but the students that have had me for years probably wouldn’t be shocked.

Over the course of the next couple of weeks I started to let myself come through in my teaching more. I would joke around with the kids a little more while at the same time asking more questions and demanding more work. I would share stories from school or be sympathetic to their frustrations incomprehensible rules while probing their minds about linear relationships. To act as if I got a glowing review from my cooperating teacher would be disingenuous, but at least I could live with myself.

Now I do the things that come naturally to me. My classes are loud and blanketed with chit-chat because that’s what my personality invites. This doesn’t mean that my classroom is unproductive. I like to get side tracked on conversations with students. This doesn’t mean that they are disrupted. To me it is normal to be referencing Back to the Future, discussing Carol of the Bells parodies, and teaching about angle relationships created by transversals; at the same time. My classroom is pretty barren and depressing, but I do have a buffalo head. cam00102 Why? BECAUSE I HAVE A BUFFALO HEAD! What other reason would I need? I like to joke around with students. I like to throw around insults, that are meant in the most supportive way possible. I like to go to their musicals and athletic events. All those things build their trust. Once I have their trust I can do what I really want to do, which is push them to their limit, to their breaking point.

I still feel the pressure to conform, to have hooks, give out detentions, assign homeworkticket-in, have students sit in rows, keep them busy. I feel the pressure to be like other teachers, to use feedback devices like a ticket system, even though I believe they are pedantic. I feel pressure to hand out detentions or use reward days, even though I believe they are just extrinsic motivations at best or coercion at worst, never addressing any real issues. I feel pressure to give and grade homework assignments even though I believe that graded homework does not actually correlate with comprehension. I feel pressure to make sure my students are on task 100 percent of the time, even though I don’t believe that being on task does not automatically mean something is being learned. I believe that sometimes being off task, whether that means addressing other issues facing students or simply taking a break, is more beneficial to the long-term productivity of the class than making sure 100 percent of the time is used for academic activities.

It all makes me feel like I am weird.

Sometimes I  wonder when it all will end, when that day will come where I am told that I am just too weird to belong here.

Generating a Genuine Mathematical Discussion

One of the most difficult tasks of a math teacher is fostering an authentic discussion about math. Every now and then it comes back momentarily in small groups, but I have trouble generating a real math discussion. I know there ideas out there in the internet ether, but I have found that as long as students are given prompting worksheets, think-pair-shares, they will always want to know what answers to put down so that they get the highest grade. When I ask a class to discuss for the sake of discussion, most of students will give me, at best, lip service, since the discussion won’t have any immediate impact on their grades.

I want my students to discuss math. I want them to discuss math because it is the most effective form of mathematical learning that I have encountered. In math teacher land there is often debate about finding the right balance between practicing procedural fluency and developing conceptual understanding. The procedural fluency camp usually follows a dogma of basic skills and will lament the “fuzzy” math of the 1980s and 1990s. The conceptualists worry about cookbook math and creating math zombies. Myself, I lean towards the conceptualist. However, I do rely on a lot of drill and kill during class. Procedures are great for immediate impact, but if I want long-term, flexible learning, I need to have high quality discussions.

In the past I have had one class where discussion has flourished. That has been my Caclulus I class. My Calc classes have always been small and have always been with students that I have had in previous classes. Because of this familiarity, I was able to make a bargain with my Calc I students. I would give up my power, in the form of grades, if they would give up their expectation of the reliance on examples. It worked beautifully for three years. There was absolutely no structure to the learning. When we would learn, we would just open the book and start reading and working. Some days math didn’t happen because, well, we didn’t want to. Some days we talked about other stuff, like college essays or homework assignments from other classes. Instead of viewing me as the authoritarian, or even authoritative teacher, my Calc students started to view me as more of first among equals, as more of a peer with extra experience. So, when we decided to math we did it because we wanted to, not because we had to.

Anything that was learned in that environment I really feel is more impactful, more powerful, and more portable than what is learned in a regular classroom. There is one story that I can think of that perfectly illustrates what I mean.

A student in Pre-Calc asks me, “Did you hear about Alex?” (Former Calc I student, name changed, who was then a freshman in college.)

“Umm….no. What happened?”

“He failed his Calc quiz.”

“Okay.” (I really think this student wanted me to make some sort scene in class, but I didn’t. Inside though, I was screaming WTF?!!!)

While my Calc I class is not for college credit or an AP class, I feel that I do enough that Calc I should be mostly review for my students when they get to college. Fortunately I ran into Alex around Christmas break and I felt compelled to ask about the failed quiz.

“So, I hear you failed one of your first quizzes.”

“Yeah, that was stupid. The quiz was about finding derivatives using the limit process, but I just used the power reduction rule.”

“Okay, whew. I was worried that I had really screwed up, but really it is about your inability to read directions.”

“Yeah. I met with the professor during his office hours and talked to him. I explained what happened and then talked to him about what I should be doing.”

It was reassuring to hear that he didn’t ask for extra credit, to redo the quiz, or fix his mistakes. He felt comfortable enough with the math I had taught him to go discuss it with his professor. Not only did he feel comfortable enough with math to discuss math, and not just demonstrate procedures, he felt that his knowledge granted him the authority to approach the professor. (I have wondered if this is a skill I was implicitly teaching during Calc and does it apply to subjects outside of math.)

That is what I want out of my Calc class, but this year my Calc and Pre-Calc classes are combined. I have figured out how to approach the topics so that I can teach both groups without giving too much subject material up, but I wasn’t sure how I was going to grade my Calc students compared to the Pre-Calc students. My Calc students know what my Calc classes in the past were like and have been wondering if they would get the grading leniency that I have shown in the past. I kept telling them I wasn’t sure, since they will be covering the same material as the Pre-Calc students.

This past Friday I gave my first quiz. I have already noticed a couple of interactions with my Calc I students that make them different than most of the Pre-Calc kids, but when the quiz was given they were the last ones working. Their approach to the problems were different than all but a few of the Pre-Calc students. Everything about how Friday went tells me that they are ready for how I run Calc I, but I know I can’t run my Pre-Calc class of 23 like I have run my Calc classes in the past.

I don’t know what to do.

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.