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.

Feeling Nostalgic Tonight

Two interesting things happened a few days ago. In one class, as I was trying to push some students with “why” type questions, a student pointed out that I seem to have disagreements with the American education system. In the next class, a student mentioned that she wasn’t sure where she was going to college. Well, I felt like a failure right then and there, but why? I am just a math teacher, my responsibility is to teach math, everything else is the responsibility of the student, right?

After the class of 2013 graduated, I decided the answer was no. The class of 2013 was the first group of freshman I had at my current job. I had many of them for three years of classes, and several for four. In a way I kind of grew up in my teaching along with them. Growing up with them meant that I formed countless inside jokes and built a level of comfort so that I could try and push their boundaries. In return, they pushed my boundaries as a teacher as well. This was the group that got to watch me experiment with different formats and styles. It was towards the end of their time with me that I began to regret that I didn’t demand more.

When I say demand more, I am not talking about academics. I have mentioned previously about how grad school affected my concept of knowledge, but it also made me realize that many more students are capable of achieving goals they never believed if put in the right environment. There was a segment of that graduating class that reminded me of myself. It was a group of students whose cognitive ability would allow them to pursue nearly anything they wanted, but they seemed to be going through the motions.

There was no subject or activity that invoked some sort of passion. If something did create a spark of interest, they were overwhelmed with worries about future career prospects. The cost of college frightened several to the point of not even trying.

They reminded me of myself because I was that student that was doing what I supposed to do. I had the good grades and test scores that got me the scholarships, but I didn’t have any real sort of passion. When I went to college I chose a major not based upon some sort of calling or desire, but on future career prospects. I chose my college largely based upon how much it would cost.

When I graduated I found myself wondering, now what? Six years into my career I found myself wondering, is this it? I felt like I had done everything society ever had told me to do, I got good grades, I was respectful, I stayed out of trouble, I participated in voluntary activities, I held down a part time job in school, got married, bought a house, had kids, and at 27 I felt like it was a big let down. Where’s my stability? Why don’t I have the enjoyable career? All that work for just a paycheck. Then I started to worry that I would take it out on my kids, literally and figuratively.

I don’t know what the future holds for the class of 2013, but there is a handful of students that come to mind that I wish I would have pushed more. I think I did an adequate job getting most ready for college math, or at least no worse than any other teacher, but I have this nagging feeling that I should be responsible for more than just an ACT score. My job should be to guide students down a path towards a rewarding livelihood, whether that be changing their current path or encouraging them on the one they are on. If that isn’t my job I should be replaced with an automated math program, like Khan Academy.

The next year I decided to make some changes. In a conversation with a coworker I mentioned that I decided to do what I thought was right. In earlier years I had learned that I cannot impact a student’s cognitive abilities any more than I can impact a student’s height. But I had learned that I can impact a student’s EQ. I had the most efficient, productive, fun, off-task Algebra I class I ever had to that point. I was fortunate to have a small group of dedicated seniors that let me push their limits (I cannot emphasize how much it was pushed), and I don’t solely mean academic. I proof read essays and talked about college with them. I got them to question assignments instead of just complying with the assignment. Seriously, coloring as as a senior? Not everyday was about math, but everyday felt productive.

I hope that when they left that something stuck, and I’m not necessarily talking about math rules. I hope that they developed a perseverance they didn’t have before. I hope that they developed an understanding of what it means to know something. I hope that when they left me, they learned not to be content with complacency. I know that sounds kind of hippieish, but I do consider myself an idealist at times. To me though, that’s what school should be about, not power-reduction rules.

So when that student said she didn’t know where she was going to college, my heart sank. I have known this student for four years. I have had a few opportunities to push her in the past, but this should have been the year that I had her, and a couple of other potential filled students, in a small group that would have allowed me to shift the focus of education away from math. It pains me because it is reminiscent of the class of 2013 all over again. They told me their plans, or lack of them, and kept my mouth shut. I’m back at that regret all over again. Things change and the good times can’t last forever, but there has to be some way for me to get at least closer to what I had. When I reminisce about those years I don’t know if I made a difference in those student’s lives, but I know I’m not making a difference now.

I Started a Twitter, and Other Musings

I started a Twitter. I started a Twitter because I wanted to jump on the #MTBoS bandwagon. Since joining, I have used it to get ideas for class, reflected on my practices, engaged in a conversation about the purpose of high school, communicate project ideas to my students over the weekend, and even had a student bring in supplies to keep a project going for class. Unfortunately, the following I have developed has been mostly, okay, almost exclusively students.

One student asked me, “So all you do is tweet about boring teacher stuff?”

Boring? Teacher stuff? I was incredulous. This is my work, this is my life’s passion. Are we really to the point that our students think that all I do is clock in, clock out, assign some homework, grade some tests? Do I really give off the vibe that all I think of teaching is that it is just another job?

I used to think like that, but that was when I was first decided to become a teacher after listening to the advice of my guidance counselors. I followed the dogmas of, “do what you like,” and, “do what your’e good at.” I liked school and was good at school, so I should be a teacher. Problem solved. But the problem was that I was nothing but a soul crushing teacher. There was no purpose behind my teaching other than to generate work for good little obedient students, and I thought I was a great. Even my evaluations and test scores said I was great. In reality though, all I was doing was training students for a life of drudgery working menial jobs.

I managed to change though, or at least I think I did. Sure, to many students I am still just another soul crushing teacher, but I am not that to ALL my students. So here’s what happened.

First I was taking graduate courses in History at Bowling Green State University, which did two things for me. It made me reevaluate the formulation of knowledge, making me keenly aware that knowledge, truth and power, is not defined by any person. It is why the Allegory of the Cave speaks to me as more than something read in literature class. I also learned the power of the herd effect. When I was surrounded by individuals who have a very compliant view of school in undergrad, I became just like them. I did what I needed to do to get good grades, without questioning what I was doing. Being in an environment where everyone, and I mean everyone, was authentically engaged made me become engaged with learning for the first time in my life. Since those years I have never need a GPA, ACT, Praxis, or GRE score to define my worth.

Second, I had a melt down in Calculus during the 2010-2011 school year. I had been struggling to teach the subject blaming it on the “rust” that developed since I hadn’t been exposed to the subject since 2002. Eventually it became to much. I couldn’t keep justifying why things happen in math with the reasoning, “because that’s they way they are,” or, “that’s how I was taught.” I realized that I didn’t actually know Calculus, or really much other math for that matter. I had a BA in the subject, but couldn’t apply the math in anyway outside of a textbook problem, and even struggled with some textbook problems. Combined with what I was learning about knowledge in grad classes, I realized that they way I was teaching math was to make it nothing more that some torture device thought up by some people in a room somewhere to categorize students. It had absolutely no meaning. And I had this existential crisis in a single moment, in front of students.

Luckily for me they were very understanding. It was then that I decided that I needed to either leave teaching or redefine my teaching. I tried to make sure everything in math had a purpose, a reason for the way it was. Everything didn’t need to have “real-life” applications, but I started to use the term “math-world.” I wanted students to be able to at least apply what they were learning in an abstract math sense. At the time I didn’t know it, but I was trying to force my students to activate prior knowledge with the hopes that by doing so would increase retention and comprehension. Things had to at least make sense. What this means is that my classroom really became more about how to acquire knowledge more than any particular math topic.

It also made me hate the student I was during high school and college. It made me keenly aware of the horrible teacher I was early in my career.

 

I had found a purpose in my teaching. I want my student to find a purpose because a purpose is what keeps me up at 2:28 AM writing and reflecting on my profession, searching for ways I could be better. Purpose is what makes a career rewarding. My purpose is explaining math to students in comprehensible ways.

Then Facebook.

Facebook is a great way to stalk former high school classmates. Perusing through the ones I could find off the top of my head I found, four doctors, one lawyer, two dentists, one optometrist, one lawyer, three psychologists, two university professors, several business owners, multiple accountants, three engineers, and so on. I also noticed several who had bounced from career to career or who could have been considered to under achieve. I would count myself as that underachieving group.

Why did I underachieve? Where some of my classmate just smarter than me? The more I think about it, the more I started to realize there usually was one key difference between us. My underachiever compatriots grew up in environments where our parents had jobs and not careers. Day in and day out we never witnessed our parents pursue a career with a passion. They had jobs, but it was just a mean to pay the bills. We were never exposed to the behaviors that would lead us to a great career. Or another possibility was that we achieved good grades and accolades in school, and that was enough. As long as we made honor roll we were told “good job” and left alone. All this did was breed habits that got good grades with the least amount of learning possible. I wasn’t necessarily dumber than my more successful peers, I had just made grades and test scores an ends rather than a means.

I feel as if my college and high school years were completely squandered. When a student says, “I get good grades, but I don’t feel like I am learning anything,” I know exactly what they mean. I am especially elated that they are realizing that while still in high school, while there is still time to right the ship, unlike me, who wasted years of educational opportunity.

During the 2012-2013 school year I realize that just teaching math wasn’t enough. I was a much better math teacher, but I wasn’t pushing the students to achieve. Looking around me I saw that all I really was doing was creating clones of what I was, setting students up to find environments where they will feel comfortable, but won’t be pushed. I started to question if I can consider myself a good teacher if all I can do is teach math. I didn’t want students to squander the opportunities I did.

After watching the Larry Smith video above, I started to think back to my high school and college days, searching for reasons why I squandered my opportunities. I enjoyed my time at Jamestown, but I started to realize I ended up at Jamestown out of fear. I was worried that engineering would have been too difficult. I was fearful of going as far away as Princeton. I was worried that I would be the dumb student at U of Chicago. I was terrified of playing sports at a school like South Dakota State or Valpo. I told myself that I was JUST going to be a teacher, so Jamestown would be good enough. It wasn’t that there was anything wrong with Jamestown, it was that I didn’t even explore my other options. I wrote them off, rationalized away my trepidation.

My school is infected by fear as well, but it is a different fear than the one I faced. My school is infected with a fear of money. So many of my students see education purely in terms of finance. They think about careers in terms of salaries and job placements. They think about schools in terms of tuition dollars only. They think about classes in terms of ease rather than knowledge. Deep down though, I think some of them realize that this process is wrong. I want to push those students, but I don’t, because I have found that I can push students to pursue knowledge and wisdom (in terms of the Cave) or I can teach math, but often I can’t do both.

So I search for that opening from students. Those students who aren’t just content saving money at the local community college or living at home. Those students who think they could find better things out there then what’s just sitting before them. Pushing into that fear can be painful.

I ask students what their plans are for after high school. Some will get defensive when I ask and I back off. I want to push my students, I want them to desire more than the lowest cost alternative, but I am afraid. I am fearful of a society that tells me that my job is to teach students math and nothing more. Often I feel like I am confronted with choosing between doing the right thing or doing the OTES thing.

How do I respond to this internal conflict? I ask, “What are you going to do with your life?”

What I really am saying is…”I have seen some sort of potential in you. Someplace along the years you made the mistake of showing me that you have a wonderful mind that is only begging to be tapped. But you have also shown me that you are not entirely sure how you want that potential to manifest itself. You have shown me that you are conflicted between what you really want to do and what your friends and parents are telling you to do. I want to help you. I want to push you, but I can’t in this setting, in this classroom.”

Every year I see a handful of the potential Will Huntings, maybe not geniuses, but those students who are smart enough to do anything, but are too afraid to. Every year I really, really, want to give them Ben Affleck’s speech. (Don’t watch if you offended by the F-Bomb.)

I seemed to have gotten off topic.

So… I started a Twitter.

Searching for a Purpose

I have been very unhappy with myself lately. While Googling ideas on ways to discuss leadership I came across an entry written by Morgan Guyton.  What he is describing is that vulnerability and leadership can go hand in hand. In a way, leadership can come from the weak and meek. As I read through more of his posts I realized that for the past two years I have been missing the solidarity that I used to have with my students on a regular basis. Every now and then I get a sense that solidarity has come back, but too often it feels like we are separate, like I am living and working in an “us”  and “them” kind of environment.

When I started blogging again I stated that it would be for my own benefit. The whole purpose was to be about reflection. And if OTES doesn’t think that writing about my teaching at 1:27 AM on April 13 doesn’t count as reflection, I don’t know what does.  As I sit here and reflect, I think I lost my sense of purpose. I feel like I have become a teacher I really never wanted to be. I know what I am doing (teaching math), I know how I do that (I use whiteboarding, but there are many different methods), but I feel like I have lost my reason for why. I teach math, the concepts and procedures, but at the end of the day it just feels so empty and shallow.

I feel that as teachers, we continually hear and use rhetoric about the actions we take in school are “in the best interest” of the students. But what always bothered me was that rarely were the students consulted about their “best interest.” It always felt like that “best interest” was just an empty justification thrown around by teachers, administrators, and parents. I am not trying to portray the people behind Common Core, or any other educational fad as self-serving, maniacal, ego-maniacs, but no matter how sincere the belief behind “best interest,” it really isn’t. Our students are unique in so many ways and when they get aggregatized to the extent of most “best interest” initiatives, they lose their uniqueness, leaving many involved on the front lines of education feeling jaded. When our new initiatives don’t work, we then blame the students.

That’s where I am right now.  A couple of years ago I felt much more accomplished as a teacher. It’s not that my methods have drastically changed, they haven’t. Grades and test scores are pretty similar. But now when I go home at the end of the day I don’t feel like I have accomplished anything. Right now I don’t know why I am here. I know I teach math, but why? Right now, I feel like I am an employee at a prison. Right now, I feel like I have otherized my students. Right now, I feel like I have made them a “them.” As long as I am not “them” I am free to blame “them” for the shortcomings of the classroom.

Right now I’ve made my classroom about my methods, my philosophies, and my math. When I started the process of changing my methods and philosophies a couple of years ago, it wasn’t because they were special, but it was because I decided to make a couple of students my priority. This revelation occurred because for the first time I made myself vulnerable to my students. I made myself emotionally vulnerable to my students. I stopped being the arrogant, pompous, self-righteous, sanctimonious, authority teacher I was and confessed that all I really am was a lost asshole of a human being.

When I admitted that to my class, albeit a class of two, I was met with grace, sympathy, and understanding. If the two guys in class had every opportunity to crush my spirit and destroy it, but instead met me with a feeling of solidarity. I slowly began morphing my teaching to improve the learning in my class and over the course of two and a half years. I would be the first to admit that there are aspects of my class that are entirely unconventional. My purpose had shifted from teaching math to being more student focused. I wanted to become the teacher that inspires students to free themselves of the shackles of intellectual servitude that is often experienced in school. I know I can complete this purpose, I have in the past. (Beyond my intuition, I keep a thank you that a student wrote me a couple of years ago. I read it when I need an emotional lift after a rough day.)

I know I can accomplish my goal, but I think that my priorities were misplaced. Changing my methods didn’t change my outcomes, it was changing my mindset. When I made myself vulnerable I felt a solidarity with my students that I think I have lost. I have become an asshole again. My teaching isn’t really about them, it’s about me. I need to reclaim that solidarity because when there is genuine solidarity in a classroom it can be like a sanctuary of grace during a hectic day.

The Life of a Self-loathing Math Teacher

I’ve had a problem lately. In my mind I have this clear image of a rant I want to post, but each and every time I try to write a post about said rant it turns into a rambling mess. Maybe that’s okay, maybe that is just what a rant is, but there will be no effectiveness. And if the post really wasn’t effective at anything, what was the purpose in the first place.

But anyway….

What, exactly am I supposed to be teaching? No, seriously….

Well, I teach math, but what, exactly is math? No, seriously….

Math is a beautiful exploration into the discovery of the structures that explain the universe. Or something like that. The point is, for me, math has intrinsic value. A few days ago, after school, I spent 45 minutes just playing with the idea of the sum of distances compared to the distance between foci and the triangle it forms in conic sections. There was no set answer, no goal. There was no “real life” purpose. The only purpose was because I wanted to. The explanation in the textbook felt too formulaic, too cookbook. I think what I did was what Paul Lockhart describes in A Mathematician’s Lament. I explored and inquired into the recesses of my mind. I created knowledge that is not beholden to any other authority. It can’t be taken away by another teacher or a different textbook. I can’t be told I’m wrong. I can be proven wrong, but I can’t be told I am wrong. And that is math in its most basic form. When math is authentic, it contains a simplistic elegance at it’s core. It is amazing and awe inspiring.

Well, to me math is amazing, but to many other people this is art. Beauty is in the eye of beholder and I am certainly glad I wasn’t coerced into taking up drip painting. That’s the catch, coercion. Intrinsic appreciation is achieved through an intrinsic fulfillment of an intrinsic purpose. Coercion frequently masquerades around as different forms of extrinsic motivation, movie days, pizza parties, grades, scholarships, detentions, suspensions, etc. The problem is extrinsic motivation doesn’t really work, especially in a setting like education.

Ever since I started teaching, which is 10 years ago, I feel that  there has been an increase to push more students into more advanced math. I have an intuitive feeling that the push for creating new standards (Common Core), for standards in the first place, for the push against rote learning, is all stemming from a desire to create the type of mathematician that Lockhart describes.

How do we know do we know, as educators, if we have been successful? How do universities and employers know what kind of mathematicians schools are creating? Are these good future academics or employees?

Assessments, projects, PARCCs, MAPs, ASVABs, PSATs, ACTs, any number of devices we create as educators to quantify a student’s qualitative abilities as a number or letter, that’s how we know. I try to design assessments that can’t be coached or trained, but ultimately I realize that I don’t know if it is truly possible to make an unbiased, reliable, valid assessment that is perfectly uncoachable. The problem is that the students who have learned math through rote, by turning out exercise problems full of procedures but devoid of concepts, take the same assessments as those students who have internalized math. When I look at an ACT score of a student how do I know if that student just memorized a plethora of examples or is really a great mathematical mind that is just lacking experience?

I propose that the intrinsic motivation is necessary to comprehend math at the level that I feel pressured to create is an impossibility to extrinsically create.  This would be acceptable as long as math is entirely voluntary. Conflict arises when the math students are coerced into learning has no relation to their desired outcome. It is difficult, if not impossible, to internalize something when the process itself serves no purpose. Most high school students I encounter are acute pragmatists. They might realize that to be a pharmacist they will have to take a Calculus course or two, but from their perspective those courses are only necessary because a university has set Calculus as a prerequisite. Students realize that the label of Calculus is much more valuable in society than actually comprehending Calculus.

The list of prerequisites keeps growing for my students and I feel pressure to ensure students keep getting past the barriers that are placed in front of them. I feel that my job is becoming less about teaching math and more about making sure my students obtain certain ACT scores, have certain GPAs, and have impeccable transcripts. I don’t feel pressure to teach Calculus, I feel pressure to teach how to get good grades in a Calculus class. We have created a labor supply that is hardwired to hoop jump. We have created a labor supply that is all accepting of school functioning as nothing more than a gatekeeper, but the gate is really the colander used to drain the bag of tortilla chips before I serve them for a snack.

Do tortilla chips really need to be drained in a colander? Of course not, but is a universal math requirement really  the best way to determine the competence of a student? There is a movement out there to completely change the paradigm of education, but I think it is too fringe to go mainstream. For most of us we live in the cruel reality of that chip colander that consists of prerequisites, test scores, and GPAs.

And our reality has some harsh consequences. Books like Academically Adrift  are written. Employers complain about college grads lacking workplace skills. The reality of our school system is that it is full of students who don’t really learn, yet have Pavlovian responses to terms like “honor roll.”  That is the reality of school and I am the problem.

I wish I could inspire my students to love math and see the subject the way I do. I empathize with Lockhart. Every so often that passionate mathematician surfaces in class, which really gives my class a bipolar atmosphere some days. But as much as I have developed a passion for math, I have humanistic tendencies that dictate much of my behavior in class.

When I started writing this rant I had intended for it to be a indictment of the state of mathematics education in our schools. I wanted this post to be about how I want to teach pure mathematics, and how I can’t. I could teach math from a more stringent standpoint, but I couldn’t live with the self-image I was creating. I can’t sacrifice the economic futures of my students so that I can go grind my own personal vendettas about how I feel the educational system is failing. As much as I enjoy a good mathematical discussion and how some days I veer off topic into more theoretical mathematical explanations, the reality of my classroom is that the core is procedural drill. As much as I would be thrilled if I could inspire a student to take up research mathematics, I am proud that many of my students score high enough on the ACTs to avoid college remediation. I am happy when I hear from former students that they felt that their general education math requirement was relatively easy and that they felt ready for the class. I like to hear students who normally struggle with math say that they like my class because they feel successful.

Part of the reason that I can create that successful environment is because I have created grading scale that casts a wide net. I am able to catch several students who would have normally slipped through the cracks. A couple of years ago I had a miserable time and a large portion of my students ended up taking summer school. Often summer school simply acts as a credit recovery process more than a learning opportunity. Because I was trying to make my class rigorous by common conceptions, many students were struggling. Before I began the next year I decided to change how I evaluated students because I really didn’t like the fact that the quadratic equation was standing in the way of students taking up electrician classes at the vocational school. I really didn’t like that it was my personal adherence to the quadratic equation that was keeping students from taking vocational classes. I really didn’t like families had to spend money on summer school because I placed the quadratic equation on a pedestal.

Though I am happy that my changes in pedagogy and grading has broadened the number of students that find success in class, there is a sacrifice that is made to create this environment. My safety net has the unattended consequence of lowering the standard for all students. Really my success story means I am just a grade inflator. I should feel awful about myself, but I don’t. I felt worse when students would fail my class, but I could claim an ethical and academic high ground. I still expect a basic level of competence, but my students won’t be graded on compliance and obedience. Sure I don’t have the ability to push the intrinsically motivated math students, but they will be fine. Because they are intrinsically motivated they will find success someplace, usually in college when they can finally group with other intrinsically motivated math students.

I started out by asking what exactly am I to be teaching. I wear the label of math teacher, but I don’t teach much of anything that Lockhart would probably recognize as mathematics. In cruel acceptance of reality I teach survival skills. I teach students skills that will hopefully help them navigate a world of prerequisites, Accuplacers, and ACTs. We practice those skills in class. I wish that I could create an intrinsic love of mathematics in my students, but I can’t. By teaching students how to survive the system of hoops and gates I am part of the cycle that creates hoops and gates.

I am the very thing that I wanted to rail against in education.

Mindsets of School

Over the past couple of months I have been following a discussion about math zombies. It originated in the comments on Dan Meyer’s blog. It has been expanded upon with examples in several other blogs such as here, here, or here. I had previously been thinking about different mindsets in math class; how different people could sit in on the same class and come away with drastically different experiences. Now what I will be discussing in this post is the mindset of the person who sits in on the class, not the engagement of the person with the material of the class. For the purpose of this argument I am defining a mindset as how a person thinks about the material at hand and engagement would be how a person articulates that mindset.

From my personal experience here is how I would classify the mindsets of the students that come into my class.

  1. Wizards – Have you ever met that person that seems to “get” everything, that everything seems to come so easily? Wizards are those students that can perform a task that would make others struggle, to the point that sometimes it seems like magic. This is the student that usually craves projects or might want to initiate discussion. Every time a teacher asks questions about concepts, those “why” questions, the wizard is usually the first to volunteer an answer. (I got the idea for this name when my five-year-old grabbed a copy of our Pre-Calculus textbook and called it his wizard book. I thought it was appropriate since for some people math does seem magical, or at least like witchcraft.) For another good description view the difference between a good mathematician and a great mathematician.
  2. Survivors – The survivors are the students that do what they have to do to get through the class. They see much of their academic experience as gate keeping procedures.  An example from my experience would be a student who was deciding what math he should take his senior year and couldn’t decide between Statistics and Pre-Calculus. As we looked at different math requirements at various colleges for his planned accounting degree we noticed that the requirement ranged from College Algebra to Statistics to Calculus I. All of the graduates can be qualified to take the CPA exam, so what is the difference in the specific math requirements? A survivor has realized that these courses function for the purpose of weeding out those students who will not put in the requisite work. As such, the course material itself is irrelevant, putting the student in the mindset of wanting to pass the course with the least amount of effort possible. Understanding is inconsequential since the material will not be needed for the end result.
  3. The Lost – Everyone has probably seen the lost before. These are the students who seem to randomly be guessing all the time. These are the students where a slight change from procedure can flummox them. These are the students who seem to have never mastered procedures from other classes, that cause the teacher to wonder, “how did they pass?” When they complete an assessment, they have no idea whether if the outcome will be good or bad.
  4. Delusionals – A delusional student has many of the characteristics of a survivor, except they are not aware of the superficial aspect of their learning. I often find these students will create an image of themselves based upon a grade and not on any sort of comprehension. They measure success upon GPA, class rank, and  ACT scores. When they struggle in class, these students are often the first to ask for extra credit or blame the teacher for their struggles. If they achieve low ACT scores, they blame test anxiety or say that test scores don’t matter/ A delusional student will be eager to expunge the value and importance of a class, but then be unable to actually apply material to any sort of context. A delusional student dreads word problems, and will ask to do “actual math,” which means manipulate equations. They lack the ability to apply “school” math to the real world.

The problem with mindsets is that they are not easily measured. I find that I have to interact with my students to understand how they view math. The first thing I learned is that grades do not necessarily reflect a mindset. I have been fortunate enough to have been in every mindset on my list, albeit relying on the benefit of hindsight to come to that conclusion. I was delusional in high school, became lost during my sophomore year of college, slowly morphed into a survivor over the course of my junior year, and finally became a wizard after teaching for several years. This provides me the benefit to at least empathize with every student in my class to some extent.

Now as a teacher, I wonder how I could effectively reach each mindset. I wonder if I should be trying to encourage to students to change their mindset? I think of my presentation, am I modeling the type of mindset I want my students to have? What I have learned as a teacher is that I think heterogeneous classrooms strive for mediocrity. It’s not a numbers thing. I have had classes of two students and I have had classes of 25 students, and I have found that the most effective classrooms I have had the most homogeneous mindset. And I think that is because I can only effectively engage one mindset at a time, I can only teach from one perspective at a time. But homogeny ain’t cool, so what do I do?

Why I Teach (Part 3)

Why do I teach? A quick search of the internet provides a variety of reasons, one of the most frequent being that teaching is a way to change the world for the better. At this point in my career I truly believe that to be the case.

What exactly does that mean, though, to change the world for the better? My previous post referred to the sickening feeling that I got when I realized that my whole school career centered on authority and control. My teachers (authority) had the answers (knowledge) and used grades to reinforce certain behaviors (control). I don’t believe that they had malicious intent, but that they were a product of a system that produces this behavior.

I don’t want to be a part of it. I think it is the reason that we have students who can pass Algebra II, Calculus, and other college level math classes, but can’t manage to create and maintain a personal budget. I think it explains the phenomena of the student who is on honor roll, but is below average on the ACT and other standardized tests. I think it is the reason that there are phrases like, “He’s good at book learning, but has no common sense.” As a society, we have created a system that rewards obedience and complacency. Many of our students just become cogs in the giant mechanism. Remove the mechanism and they fail.

So, why do I teach?

  1. I am here to break the machine. I want to create students who are free and independent thinkers. I want to create students who question authority with the power of knowledge. This doesn’t mean that our schools can’t have the three R’s; rules, regulations, and rubrics. Everything in the lives of our students should have a purpose, and they should know that purpose. Nothing, absolutely nothing that we do in school should happen because, “it’s a rule,” or “because I am the authority.”

It is a struggle to turn students into free thinkers, but the rewards of the struggle are immense. That moment you realize you are not beholden to anyone for knowledge, that you have control over knowledge, you become empowered. And there are no words that can describe what living an empowered life is like. Unfortunately far too many students, far too many people, will never experience the empowerment that comes with knowledge.

  1. The second reason that I am a teacher is to have math make sense to my students. I want my students to move from a position of duplication and memorization to a place where they can reason through a problem. It’s a laudable goal, but I cannot emphasize the gulf that exists between #1 and #2 enough. Also, I hope it was noticed that there was nothing in #1 that specifically mentions math.
  2. I hope that students who go through my class and plan on attending college will at least avoid remedial classes.

As much as I hope that all my students will be in #1, I know that most are in the second and third reason that I teach, with a few not even in any. I care about all my students, I really do. I would never wish anything less than success for any of them. But for the few that fall into my first reason for being a teacher, you are the reason that I keep getting out of bed. You are the reason I keep coming back each year. You are what has kept teaching from becoming a “job.” The fact that I know at least a few of you exist will keep me coming back.