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.

 

 

What I Learned About Knowledge From Dropping Out of Grad School

After moving to Ohio I found myself without a full-time job. I even had a little difficulty getting substituting positions just because the system was so different from that in Minnesota, and I didn’t find the area schools very helpful, with the exception of the secretaries at Upper Sandusky High School. On a complete side note, ODE was not helpful at all with getting my license transferred. That’s not really important, but it does give me another reason to complain about ODE.

I decided that since I was just substitute teaching I would trying applying to a graduate school program. I ended up choosing the History program at BGSU because of it’s location and the timing of the classes. My first couple of times in a graduate seminar I was a little lost. It didn’t represent anything like I was used to. I could best describe the setting as almost like being in a book club. We had assigned reading, and then we discussed the reading.

Admittedly, I was lost, and also a little star-struck, since my first professor I had instantly recognized from History Detectives.

I had read the book, but the discussion didn’t have the recall questions I was used to answering. I kept waiting for the professor to ask questions that would allow me to demonstrate that I had read the book, that I could show my classmates my superior intellect. But it never happened. He only kept asking these, “Why did the author use this,” or “What did you think about this,” kind of questions. The only time I had ever answered opinion questions throughout my educational experience, it was always a, “Yes, I liked it,” type of question. I asked for advice from some of my classmates and was informed that as long as I speak up a couple of times during class it would be fine. That really didn’t help since I didn’t know how to voice a comment during class without the fear of sounding stupid.

Part of the class involved reading a book individually and then presenting it to the class. I had chosen this book about the Dust Bowl. As I began rambling through my summary of the book I felt all those typical feelings of anxiety that comes when having to present in front of an authority figure. I first noticed the ubiquitous amounts of head nods as my report of the book was heavy on the summary, but light on analysis. I then mentioned something about the failure of the Russians to adapt corn to their climate, and an ensuing drought there, but I worded it as a question. When I looked at my professor he hadn’t a clue what I was talking about. This made me feel uneasy, so I kind of stumbled through the conclusion of my presentation and mentioned the American ethos.

Then the questions began.

I don’t remember any of the specific questions, but I do remember feeling caught off guard, especially the questions from the professor. There are two types of teacher questions. The first type is the one almost everyone is familiar with, the checking for comprehension question, the rhetorical question. Teachers already know the answer to these questions, we are only asking students to see if they know the answer as well. The second type of question is what I call a legitimate question. A legitimate question acknowledges the limitations of the questioner, and transfers authority and power to those being asked, and that’s what made it so scary for me.

It seems to me that most students seek affirmation of their correctness from the teacher, without much thought as to why something is correct. I see this all the time students volunteer an answer to a question and want to know if it is correct, but cannot explain how they came to their conclusion. Many times they will answer questions with an upward inflection in their voice, as if their answer is a question itself. Usually to save time, teachers, including myself, will either confirm or deny the educated guess from the students. This is a problem because the students’ concept of knowledge and truth is based upon affirmation of the authority figure.

Which is why my professor threw me for a loop when he asked me a legitimate question about the American ethos. He wanted to know more about the American ethos that the author was discussing, but he wasn’t testing me to make sure I read the book, he really wanted to know and was dependent upon me to provide him with information. Suddenly, I was an authority figure over my professor controlling his access to Worster’s paradigm of American ethos. My struggle happened because I had never developed the executive function necessary to regulate my own concept of knowledge. My definition of knowledge was like so many of my students’, dependent upon the affirmation of the teacher.

As the year progressed in the graduate course, I became more comfortable and started to understand how authoritative knowledge is formed. It started to impact my concept of mathematics and my concept of teaching. I have written about my struggles in school, whether it be in the classroom or as a teacher, but this post is ultimately about how a History class changed how I think about knowledge and power.

I started successfully adapting to History class when I started justifying my statements in class. If I was going to offer a comment I made sure I had a passage from the book or some other source ready to provide evidence. That way, no matter how my professor or classmates might respond I could reply with the proof of my statement. When I started to reflect upon the math I was teaching I became appalled at how much of my mathematical knowledge rested not on proof of knowledge, but how much had simply been affirmed by authority figures. I had just memorized many correct answers and procedures. I knew I was right because I was told I was right, and it showed in my teaching.

My teaching during the first four years of my career could be summed up as regurgitation. In more uncouth terms, it was like I was telling my students, “Here is the shit I had to learn in school, now it’s your turn.” Okay, maybe I hid behind some platitudes about critical thinking, or 21st century skills, but my whole concept of school had nothing to do with knowledge.

That’s how dropping out of grad school educated me. (I couldn’t handle the work load of full-time work, becoming a parent, and watching other areas of my life go to crap.) It enlightened me to the idea that knowledge and truth is not something that is owned by teachers. They try to make sense of the world and then share their understanding with us, but they do not  create and control knowledge. Yes, teachers are usually more of an expert in their fields than their students, but they control truth. Real power comes from being able to make sense of the knowledge around you independent of any other people. It made me feel like so much of my formal education was a waste.

School as we know it, isn’t set up to achieve knowledge. Authentic learning comes in fits and spurts, and is not easily confined to weekly assessments and standardized testing. Grades and test scores do not necessarily accompany knowledge. One of the proudest moments I have ever felt as a teacher was when a student remarked that he achieved a 96 on an economics test at the local community college. (I had taught economics to him in high school, a class I didn’t feel qualified to teach.) The grade wasn’t what made me proud, but what he said next, “I know it is a good grade, but I don’t feel like I really know anything. I would rather have an 80, but actual know something.” After years of classes with me it was finally clicking for him. Grades can make us delusional to our own abilities.

I was delusional. I graduated with honors from both high school and college, but struggled to explain Algebra I concepts. I essentially was exactly the same person that I was in junior high. I had never learned or mastered any academic subject. The only thing I had ever mastered was how to put down the right answers on tests to appease my teachers. And I didn’t realize this until I was 26.

Are high school students capable of mastering knowledge? I believe the answer is yes, but it is a near impossibility under the lock step current system we have. The only time I feel like I have had success convincing students the merits of mastery, rather than the merits of grades, have been in small homogeneous classes, or in regular after school sessions. Mastery of knowledge will lead to confidence.

Grade motivated students will eventually be exposed, one way or another. When smart students become motivated by grades they become complacent. Complacent students become stressed when pressed about their knowledge. Complacency breeds the anxiety that will eventually breed perpetual underachievement.

We preach creativity and mastery, but our actions tell students that all we really want from them is the right answers. We are so wrong.

Deficit Thinking

I’ve been meaning to write about my experience at Center for Training and Careers (CTC), a contract alternative school that operated with the Minneapolis and Richfield school districts in Minnesota. The name is a bit misleading, as we weren’t a vocationally oriented school, but rather a school that offered a different setting than the traditional public school, but the curriculum was largely the same. We housed students that had been expelled from other schools, members of rival gangs at the regular public school, students that were working full time, and some whose home life just wasn’t conducive to a typical school day. I thought I was going to write about how difficult life was for some of these students, but I realized that struggle is all relative.

Some of the students at CTC had a remarkably positive outlook despite the obstacles that were placed in front of them. The problem with that thought is I would be trivializing any obstacles that my students face. It’s like I would be saying, “You think you got problems, let me tell you about problems,” without accounting for the relativity associated with problem perception. So I decided to scrap that idea.

My mind then wandered then to an idea of purpose, making sure I’m doing what my students need me to do. But I didn’t like the outcome with that draft.

This is my third attempt at writing about CTC. Each time I come back to the idea, I keep thinking about one conversation with my supervisor during my first year, during the first semester. The school year was not going good. Almost none of the students were doing homework, scores were miserable because of a horrid lack of prerequisite skills, and note taking was non-existent. I was looking at my grades, which were bad at best, and griping to my supervisor about all of the problems that I was facing. He interrupted me and asked me to think about why my students were at this school. He talked to me about all the ways that these students aren’t like students we find in normal school. He talked to me about making sure that we keep sight of what these students need.

That’s why I thought this was going to be about purpose, about realizing what my students need. In reality though, much of the purpose of my class is out of my control. The state dictates the content taught, OTES guides my practices and pedagogy, and stigma and traditions influence my behavior. So if that moment wasn’t about defining purpose, what was it really about?

I’ve come to the conclusion that my meeting with my supervisor was more about me than anything that goes on in my classroom. The problem I was experiencing was justifying my status as a teacher. To me my students were lazy, they didn’t care about school, or they weren’t prepared. I thought they didn’t have the support at home that they needed. I thought that their priorities were misplaced, that they were too concerned with social status and not enough with academics.

When my supervisor directed to think about my students he was actually forcing me to abandon my deficit perspective of them. I had to stop thinking about everything that was preventing them for having success in the classroom and focus on the ways I was preventing them from having success. It was difficult to drop it at first, because losing a deficit perspective means I take blame for my students failures. But as I gradually began to accept my part in my students struggles and failures I became a much more content teacher.

**An example of  my understanding of a deficit perspective would be the restriction of bathroom privileges in school. I should limit the number of times students use the bathroom because if I don’t, they will leave class constantly to go to the bathroom when they really don’t need to. The first time I catch a student wandering the halls instead of using the bathroom my deficit thinking is confirmed. In response, I limit bathroom privileges for all students because I don’t trust students.**

I am by no means perfect. I still find myself stumbling and placing the blame on students on occasion. I still catch myself in a conversation where I say, “I did my part, they didn’t pay attention.” But now I feel guilt every time I fall back into that mentality. It has become ingrained in me as part of who I am as a teacher. Lately, it’s been more of a struggle than it has been in the past (thanks OTES), and I have found myself leaning on faith more than I had used to. The temptation is there though, to just go back to the way things were. I don’t want to, and luckily very few of my students know that side of me.

I sometimes wonder if I would be the same teacher, or even the same person, if my first years of experience would have been in a more traditional school.

 

How Do I Get an “A” in Your Class?… Or How Failing Made Me a Better Teacher

It’s happened again. I have been accused of not teaching, by a student. It’s not that this particular student blatantly raised a voice during class and shouted, “You never teach us anything,” but it started with a couple of innocent statements.

“I think it would be better if you gave us notes.”

“Can you go over an example of an ‘A’ questions?”

“How do I get an ‘A’ in your class?”

The problem I have with all of these statements, no matter what the circumstances are surrounding them, is that they come from a mindset that I believe has infected education on far too many levels. Students come into my class operating on a training, recall, example laden mentality. The expectation from these students is that I will present the material as it will appear on assessments, and it is their responsibility to memorize the material presented, and the material will be identical. There is a subset of students, parents, administrators, and even the general public, that believe this is what education should be.

How does that happen? How did we get to a place in society where it is thought that education is the same as memorizing tasks?

Schools, both high schools and colleges, are under tremendous pressure to ensure students graduate. Graduation rates affect funding levels for schools. The higher percentage of students that pass the more money a school receives, or is less likely to lose.  If the graduation rate falls at my school, it will be endanger of losing funding. In addition, standards for graduation keep increasing, creating a perfect milieu for grade inflation.

Ahhh….grade inflation. That concept is not new. It has been the bane of education since the existence of grades. As long as there has been no standard definition of an “A” people have blamed others for inflating grades. But the idea of an inflated grade wouldn’t exist without someone finding out that the student who had that inflated “A” really wasn’t that smart. For that, we can blame employers, admissions departments, scholarships, and even teachers.

When people in authority use generic measurements, a GPA or transcript for example, as a gauge of intelligence it invites sympathetic teachers to inflate grades. We are to the point in society that if I were to truly hold a student accountable for mastery of a concept such as parabolic functions, it could represent that student’s ability to obtain a low skill job in the service industry. To me, that represents my incentive to make my class as easy as possible to pass, because I don’t want to be the person who tries to say with a straight face, “I’m sorry, but you can’t have a job bagging groceries because you cannot complete the square to find the vertex of a quadratic function in standard form.” (This is not meant to be an insult to grocery baggers of which I really appreciate the good ones. The statement was  there to try and point out the futility of connecting arbitrary education with work preparedness.) Every employer that has said a job applicant has had to have a high school diploma, without a thought as to what that student was subjected to learning, using a high school diploma as a rudimentary haphazard sorting device, causes an increase of grade inflation. It is because employers like that exist that my class is easy to pass.

But it’s not just low skill service jobs that use GPAs and transcripts as lazy sorting devices. Colleges and scholarships do so as well. Maybe they look beyond just obtaining a high school diploma and focus on certain classes and certain grades, but the concept is the same. When I have a student who is very capable of being a nurse, but they are encouraged to take Pre-Calculus because that is what is required of the college’s nursing program, I am incentivezed to make getting a decent grade relatively easy. I wonder how many doctors, not to mention nurses, could tell me what a conic section is, let alone describe the relationship of the sum and difference between foci that generates the different conic sections. The college won’t really care what she knows in regards to Pre-Calculus, only that the class shows up on her transcript with a certain grade by it.  As long as I have her prepared to take her one math class in college from the professor who is under pressure to make sure she passes, I feel like I have done my job. These students know the game of gatekeeping that is goes on at the different levels of education. It is why I try to make it relatively easy to get a “B” in my class. It might take dedication and work, but it is achievable by nearly all students who have a mediocre grasp of concepts learned in previous classes.

I make sure that “B” is achievable because anything less than a “B” must be justified. No one wants their child be the student that struggles, but I cannot assign a grade below a “B” without being able to document the behavior the student demonstrated that led to the low grade. I have to document how I tried to correct those behaviors. I have document all the interventions I tried for the student. I have never, NEVER, been asked to justify why a student has an “A.” By making a “B” relatively easy, I can defend my low grades with simple work ethic defenses and lack of prerequisite knowledge statements. (Those are legitimate issues, it just makes the administration of my class easier to have most students around a “B”.)

So far I have mentioned the money involved in education through the application of graduation rates  impacting a schools’ funding. I have also discussed the societal pressures to obtain a high school diploma or take certain class only for the label, without any regard to the content of those classes. These lead me, and probably other teachers, to ultimately reduce the rigor of their classes.

However, there is one other influence that shapes education into memorization. In my education classes about assessment in college we covered the concept of test validity. We were taught that for a test to be valid the material on the test must be explicitly taught. If the test material is not explicitly taught then the test is invalid. This was then interpreted as meaning teach what is on the test, though never said in that manner.  In class we provide students with every example they might see, with all the information that might be around, we provide study guides and review sheets, we play review games, and then we give a test. When students do well we congratulate ourselves and think our students are all above average. When they do poorly we point out all the places in the study guides or homework examples where the information was located. Even though we so often trumpet the mantra of, “don’t teach to the test,” we don’t listen to ourselves.

This is what my education was. When I entered college back in the fall of 2001, I had every indication that I should be successful. I had tested into the gifted program in elementary, I was accelerated in math in junior high, I had never placed below the 93rd percentile on any standardized test (Iowa Basics, ASVAB, PSAT, ACT), I took AP classes in high school for weighted grades and finished with above a 4.0 GPA. I finished my freshman year of college with nearly a 4.0 GPA, with a little struggle in the spring semester that I simply attributed to college being more difficult.

My sophomore year it all fell apart. I was failing classes. I dropped classes in a desperate attempt to salvage my grades in the remaining classes. I let the funk infect every aspect of my life. It ruined friendships and jobs. To this day I am not comfortable talking about my failure. Sure, I can mention it happened, but mentioning that failing happened is very different that coming to grips with the reality that my self-identity was a complete and utter lie. I visited depths of personal hell that I wouldn’t wish upon anyone. (Here is a link that describes it better than I can.)

I can remember sitting in classes, trying to take a test, and feeling like it was gibberish on the page in front of me. It’s the first time I can ever recall thinking, “He never taught this!”

Slowly, I started to develop the work ethic necessary to pass during the second semester of my sophomore year, but it was still an emotional period of my life. I still remember one of my moments of clarity during my embitterment. I went to pick up a quiz from our Quantitative Analysis professor. I had worked so hard for this quiz, I had put in so much effort trying to understand the examples and making sure the extra homework problems were correct and figuring out ways to evaluate them myself, but I still lacked confidence and was nervous. I got the quiz back and was ecstatic that it was a good grade. As I examined the work, I noticed one of the problems that I got correct was one that he had never covered in class. I let out a very loud, audible, “I got this right and he never even taught us this!” in front of his office door.

That’s the moment I considered a turning point in my college education. (I managed to finish with a 3.43 GPA after a semester on academic probation.) It’s when I realized the amount of work authentic learning requires. But it’s not the quantity of work learning takes, but the quality of the work that leads to success. I learned that I needed to generalize better.

When I was in high school I bore the label of being one of the smart students. Now, with the benefit of hindsight, I realize that it wasn’t that my GPA was any higher than my peers, it was that I had to work less than them to achieve it. My education amounted to me watching my teacher do some examples, easily memorizing them, and regurgitating them on a test. I was doing an academic binge and purge. Eventually it caught up to me. I never learned how to effectively learn, all I had ever done was memorized and thought I was a good learner. I even identified myself as a quick learner on job application when I should have been saying, “I am a really good at memorizing repetitive tasks, so I will be the perfect employee for Burger King.” Since I have become a teacher I have started to notice that several of my students share that mindset.

Unfortunately I feel and obligation to ensure that my students don’t feel that false sense of security. I don’t want a student to go through what I did. I can’t live with the thought of students who would leave my class thinking it would be easy, then fail their next math class. And that motivation, probably one of the earliest I ever adopted, has shaped my class in two distinct ways.

The first way my failure impacted my classes is that I have jumped on the teach less bandwagon. Teach less, be less helpful, productive struggle, productive stupidity, there are a plethora of blog posts, editorials, and even a few journal articles about the concept. Basically, it boils down to the idea that if I teach every possible example I have done all the thinking for my students. This is bad because then students never learn to think for themselves. From a progressive standpoint, I would say my students are discovering, and from a traditionalist view I probably have just gotten good scaffolding. But the point is the same, I lead kids, I prompt kids, but I never explain explicitly every step.

The second way that my failure impacted my class is on my assessments. Several of my students who are used to getting an “A” in class are undergoing a period of adjustment. They have trouble because they were me in high school, smart, but relying on the teachers to do all the thinking for them. I have modified my assessments so that questions that will warrant an “A” are never explicitly covered in class. I have covered concepts, but not specific examples. I am trying to use the training aspects of school to train my students to be prepared to answer unfamiliar questions.  I was working with a student after school last year on a quiz that she missed and the story almost perfectly illustrates the thinking that I am trying to avoid.

She was having trouble on the “A” question. “I don’t know what to do!”

I responded by saying, “Tell me what you’re thinking.”

“I’ve read the problem and it doesn’t look like any of the examples we’ve done in class. I tried to match the work to the problem like______(I forgot the one she mentioned, but it was about radians), but it doesn’t make any sense”

For years I had been trying to describe the point of not covering “A” questions in class, and now it made perfect sense. She read the problem on a surface level and scanned her memory for similar problems. She really didn’t comprehend that she needed to dissect the problem and pick out the concepts she knew and then apply those concepts to an unfamiliar question.

As I prompted her through the idea asking, “Do you know what this means?” over and over again, it finally seemed to click. She finally realized that she knew everything that was there.

I can’t prepare my students for every conceivable test question that might appear on an end of course exam, ACT, SAT, or whatever. So I purposely under prepare my students for my tests. When they grasp being under prepared, then they are really prepared for the tests they will have to take when I’m not around. When they embrace the mindset that comes with being under prepared, they will succeed in my class.

That’s how you get an “A” in my classroom.

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.

Is This Where You Want to Be?

When I talk to other teachers about my school compared to theirs I often end up saying that I am so glad that I teach at a small school (30 to 40 kids per grade). Don’t get me wrong, there are perks to a big school. When I scan the #MTBoS, I see really cool things happening, but many times those take place  in larger schools. Usually at larger schools classes are more homogeneous when it comes to academic abilities. It allows the environment to cater towards a somewhat standard mindset. There are times when I dream about having a class of 20 some students who would willingly geek out and fully engage on math with me. I would even like teaching in an environment where students are simply ritualistically compliant, acknowledging the advance math they are learning will have no bearing beyond graduating high school. Unfortunately at a small school we often don’t have the opportunities to homogenize like that. I have had classroom of 11 students where one student had a tested IQ in the low 80’s and another had tested as cognitively gifted (IQ of at least 130 in our district). The unfortunate consequence of this is that I believe that I end up developing far too many strategically compliant students, and I personally detest the mindset of the strategically compliant, mostly because I was one. I personally have witnessed the hell that many of those students will go through, but perhaps I am engaging in one of humanities greatest follies, projecting my own image onto others. I think we do that far too often and I want to confront people when I see them do that, but I don’t because I am way to introverted and don’t feel comfortable without the protection and distance of a computer screen.

But I digress….

Why then do I stay at a small school when there appears to be positives to a larger school environment? It’s because of my introvertism. I fit in a small school environment much better because of my personality, whereas if I would succeed at a larger school it would be in spite of my personality. I once was told, “I get the impression that what happens behind closed doors is different than what I see,” by one of my past administrators. Ummmm…..yup, I don’t think there could be a truer statement. Here’s the thing, I interact with my administrators in a classroom environment for anywhere from 70 minutes to 190 minutes during the year, and because of our current revolving door with the administration it has maxed out at 300 minutes for an entire career. I interact with the majority of my students for a minimum of 16410 minutes, with a few of the students having interaction times as high as 40275 minutes.  I know that my administrators hold my job security in their hands, but I value the opinion of the students more. I really believe that they should have a larger say in the learning environment than the admin and legislatures.

Reflecting on my experiences in high school, I remember not feeling much respect towards the teachers  that treated us like children. When I began college I told myself I would start to think of high school kids differently. When I found myself working with high school students at the local YMCA in college I told myself I would think of them differently once I was student teaching. When I was student teaching I told myself I would think of my high school students in a different light once I graduated and obtained a full-time job. When I obtained a full-time job I told myself that I would think of high school kids differently when I had my own children. Now that I have been a parent for almost six years I have given up. I can’t think of my high school kids differently than I think of my coworkers, and I happened across some research to back that up.

Everyday that I enter a classroom I can’t help but see my students as equals. As long as we are talking about math I probably am superior, but that’s because of my experience with the subject. My authority is dictated by two things: one, my knowledge of the subject I teach, and two, my position as a teacher. The power I derive from knowledge is only confined to the realm of mathematics. When I discuss another topic with my students, they get the opportunity to claim power. But the power I derive from being a teacher is all based upon accepted societal pretense. Which is why I love teaching at a small school. In the thousands upon thousands of minutes I will spend with my students it is almost inevitable that the false power that the pretense of the student-teacher relationship is built upon will be obliterated. Once that power structure of a student-teacher relationship is gone I can truly get to work of education. Students will learn much more from me when they view me as an expert because of my knowledge and not because of my title.

Removing the power structure of the classroom also allows my students and I to separate math ability from character traits. We are able to acknowledge the IQ bridge that might exist between us that hinders instruction, but can guide learning anyway. (I really wished we lived in a society were we could rationally discuss the impact of IQ without shaming.) Obliterating the student-teacher power structure paves the way for students to form an opinion of me as a person aside from their opinion of the subject I teach. It allows me, as a teacher, to do the same for the student. It is why I want students in my class, even though it might not make the most sense for a particular student. It is why I want certain students in my class, even if math isn’t their strength. It is why I feel badly when I say scornful things in class. It is why I have students for whom I feel like I should have done more than teach trig functions of any angle. It is why I think I can have a long term impact on students. It is why I conflicted emotions about taking extracurricular duties. It is what allows me to describe my students as more than grades.

I once had a conversation where I was asked if this is the place I thought I should be.

Does the math instruction suffer in a small school environment under my watch? Probably, sometimes, maybe.

Do I get to have a bigger impact on the kind of person that leaves my classroom compared to a big school? Yes, definitely.

Am I happy here?

I couldn’t imagine it any other way.

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?