Stupid

“This is stupid.”

That seems to be a common way that students will vent their frustrations with academics. Okay, maybe it isn’t verbatim, but every time that a subject’s legitimacy is questioned with a dumb, stupid, or pointless, the sentiment is always the same. It’s what leads my students to write poetry like this.

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I don’t mind this, and I actually like the creativity behind it. Even now I have days where the last thing I want to do is go stand in front of 15-20 adolescences and talk about math. Usually though, the, “this is stupid,” sentiment comes from an incomplete understanding of the mathematical concepts being taught. Students know that the classes are important to their long term goals, but they realize that the math in the class is not important to their long term goal. Consequently, students become more obsessed with getting the correct answers, which leads them to ask, “how to do…” rather than the all important why. They want to get through class with the highest possible grade with the least amount of effort because the math itself isn’t important.

(My wife has a Doctorate of Chiropractic and has diagnosed some really cool stuff that I wouldn’t expect from chiropractors. But a few nights ago she couldn’t remember the formula for circumference of a circle. Yet she has a college transcript that shows she has successfully completed Calculus I. Needed the class to get into grad school, but not the math. She thinks math is stupid.)

Why this behavior manifests is a discussion I would love to have, but will do so in a different post. What I want to talk about in this one is what is class is like when everything is “stupid.” When my students experience this frustrations, I am more than empathetic to them because I have been in their place.

I enjoyed school throughout high school, but that enjoyment was based upon my success. When I started to struggle with school the enjoyment diminished. That mindset started to create a correlation, so the more I struggled, the more stupid I thought school was. Sometimes I would spend class time thinking about other assignments that needed to be completed, or about an upcoming work shift, or just spent time lost in my own contempt for all the students who seemed to get everything. The nice thing in college is that attendance is rarely required and majors can be changed. In high school though our students are stuck in that environment, they need Geometry, Algebra II, and maybe even Pre-Calculus just to gain the economic stability that comes with a high school diploma.

Looking back on my educational experience, I have noticed that my classes seemed to segregate based upon our attitudes towards school. There was me and the other future math teachers who would constantly complain about why we had to take classes we would never use, complained about the homework we couldn’t do, and looked upon our classmates that could engage with the professors with a mix of disdain and wonderment. Sure we were all math majors, but we weren’t a unified group. I never went to their study session, and mine, when they would exist usually turned into general venting sessions. Now that I am the teacher, I see this behavior manifest itself in my classes to some extent. We like to trumpet the positives of heterogeneity, but ultimately even our students know that homogeneity creates better learning conditions. All of my classes had an element of heterogeneity which allowed me to find the other students who also thought, “this is stupid.”

The first time I ever entered a classroom environment where true homogeneity existed was when I was 26, and entering grad school. The class was grueling work, especially with working full-time, buying a house, and starting a family. A typical workload was at least 1 book (non-fiction, dense, historical reading) that would be discussed each week, 1 book to present and discuss with the class about every three or four weeks, and 2-3 papers of original research during the semester. I don’t think I had read 5000 pages cumulative during my lifetime, let alone academic reading, in three and a half months. Then showing up once a week and discussing this for three plus hours, it was just too much.

But, as I quickly found out, I was the only one who felt like that.

That got real lonely, real quick. Instead of dropping out though, I slowly mimicked and embraced that behaviors that lead me to actually understand knowledge rather than just memorize answers. I started to speak up with original ideas, finding out even if they were dismissed I was not ridiculed. I began to ask questions in discussions and then participating in discussions. By the end of the class I was fully immersed in the subject matter, picking up the behaviors of my fellow classmates for which the subject was a real thing, and not just something stupid that is meant to be survived.

What I learned about myself was that I was part of that 80% of students who could achieve something (made me look back on my undergrad with regret), but could also become abject failures. I figured out that I was a product of my environment. If I was around highly motivated, inquisitive students, I became like those students, and if I was surrounded by students who wanted the grade, I became that grade motivated student who thinks classes are stupid. When I went back to the classroom I figured out that I am still part of that 80%, even though I am now a teacher. Essentially that means that a student will get out of me what they want. I don’t know if that is a good or bad thing, but it is reality.

One of the perks of working in a small school is that I get to see most of my students year after year and I know some of my students fall victim to me being unable to influence the environment inside my own classroom. I have watched some of the most inquisitive, creative minds stumble into a complacent stupor when surrounded by peers who just want the right answers and don’t really care why. I have also been surprised by watching some of the most indoctrinated students blossom, also when surrounded by the motivated knowledge driven students. I can try to influence students, but ultimately I am at the mercy of the dominant students in my classes, even if they are unaware they are the dominant influence.

I am empathetic to my students who are just trying to graduate. I just wish they could surround themselves with students who cared.

 

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.

Let Me Explain Something…

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A Disciplined School

Lately on my twitter feed there have been some stories about centralized detentions, classroom management, and low-level disruption. This seemingly is coming mostly out of England, but I have seen posts about it in the U.S. Most articles I read from public school teachers have been lamenting the support to fix low-level disruption, while those coming from schools of choice point out the improved environment under strict discipline.

I would say that most teachers believe that the majority of their students are good people and capable of some measure of success. Sometimes I have heard this broken down into a 10-80-10 rule, where 10% of the students are highly motivated, 10% are unreachable, and the other 80% could be swayed either way. Those teachers in schools of choice rarely, if ever, encounter that unreachable 10%, so when they write about strict discipline and teachers being free from the pressures of engaging lessons, it has a tinge of delusion for me. When students go to a private school, boarding school, or charter school, there is an element of choice that a traditional public school doesn’t have.

After I read another post about a school where teachers are free from the pressure of engaging lessons, where learning is the responsibility of students, I sometimes find myself envious. Just imagining working in a school where every student comes prepared to learn, where the slightest disruption is met with removal, makes me giddy at times. I suffer from flights of fancy where I dream about just being able to tell some of my students to simply go away. But I work in a public school, where if a student is removed from class it is my fault. My fault that the material wasn’t interesting. My fault that I haven’t made it accessible to students who still count on fingers. My fault that I didn’t call home enough to discuss the behavior of 17 year olds.

In a public school, we don’t get to choose our students, and the students don’t get to choose if they come to school. Standards are different when choice is involved, and choice seems to be a hot topic in education lately, especially considering who the new Secretary of Education is. I don’t think anyone would have a problem with the idea of giving parents freedom to choose where their children are educated, but when the outcomes are essentially the same what are the parents and students really trying to accomplish?

The harsh reality is that most parents that choose to take their students out of a school, do so to escape the unreachable 10% that cause school to be a living nightmare for some students. If the school is large enough, students usually have the option to be tracked away from their struggling peers. This was my experience in high school. I was able to take accelerated math classes or AP classes, which created a very homogeneous classroom environment for me. Some of my peers who I shared a practice field with, that I got along great with in the hallways, I think would have driven me insane in a classroom.

This past Thursday we cancelled school because of icy roads and I found myself watching Ellen. On the program was a story about a charter school that was achieving amazing results with undeserved children. I don’t doubt the result, but the bravdo comes at the expense of acknowledging the reality that charter schools don’t serve all students.

For example, let me use the numbers from this KIPP study and compare it to the 100 students I have under my watch this year. First, all 100 of my students would have to want to be here, so before they set foot in my classroom, every single one of the 100 has a family that wants them to be here. Using admissions criteria I would be able to eliminate about two thirds of the IEP students that I currently have. Of those 100 students that wanted to be here I would be able to get rid of 15 during the first year and then 15 the next by designing policies that some students can’t follow. Once I’ve done all that I could present a successful school. Get rid of 30 students, who were motivated to show up in the first place, and then I can claim success.

So I started doing a little thought experiment, what would my classes be like if I could remove 30 students? Which students would I want gone? Maybe it was a day that seemed to be plagued with the, “when will we ever need this,” mantras, or maybe it was a day that I just couldn’t get the kids to stay focused and work, on those days it seems relatively easy to think of 30 students that I don’t want anymore. The days that it is such a struggle to teach makes me nostalgic for those classes where it never was. (But that was with different students and different admin, and I don’t know if it will ever come again.)

Over time I’ve learned to embrace the struggle though, not to simply push it out and pretend it doesn’t exist. Those students who struggle the most are the ones that need to be met with the most empathy. My first year teaching was spent at an alternative school with a student body that consisted predominantly of those who had been kicked out of traditional schools. I spent most of my first year blaming the students because as students, they weren’t like me. There were two events that I think had a lasting impact that potentially saved me from becoming yet another teacher burnout casualty. First, I was fortunate to work under a wonderful mentor, and one dinner conversation about what students really need keeps coming to mind. The second was a couple of sermons delivered by my pastor that have stuck around as well. Both had a similar message, empathy, and the sermon also had the message of discomfort.

I didn’t know how to relate to my students and the impetus to find empathy for them made me uncomfortable. I found it hard to find empathy for behavior that I thought was incomprehensible. It would have been so much easier to just write off the students as lazy, unmotivated, poor decision makers who have no view of the future. To start fixing that though, all I had to do was listen. When I listened I started to view my students struggles as ones of circumstance and not of behavior. At first it was having sympathy for the gang members that felt trapped. Then it was for the girl who couldn’t get a job because she didn’t have papers. Then it was the kids just trying to survive class. Next it was for the student who just doodled the entire class period. And it just kept growing and growing. I can’t deny the role that faith has served in this part of my life. Each time I had empathy for a student it made me uncomfortable with my own preconceptions and values, which kept sending me back to the sermon about being comfortable with the uncomfortable. To think that students don’t drive me nuts at times would be a lie, but these habits have become so ingrained that it has manifested itself in my relationship to my students.

This year I lost a student at the semester. She moved into another district. This isn’t the first time this has happened, nor will it probably be the last.  The student that left wasn’t an honor roll student. She wasn’t a highly motivated student. In fact, on any given day she could make my life miserable. During my first year I would have thought good riddance, but now all I can think about is how much I wish I still had that student in class, how I miss seeing some of her artwork, how I miss some of the YouTube videos she would tell me to watch, or, when I could get her to work, how I missed the challenge of trying to make her see that she was more intelligent than she believed.

I feel sympathetic to those that choose charter schools. Sometimes there are just too many competing interests in a class, students whose prerequisite knowledge isn’t there, students who are only motivated by honor roll, students who are preoccupied with a test in another class, students who have an intrinsic love of the subject, and students who just have to be there. Many days it can feel like madness trying to motivate and engage all those groups and I wish we had a system that allowed more leeway. So from the perspective of a student or a parent, choosing a different school allows me to find a homogeneous environment.

But what I saw on Thursday was just wrong. When Ron Clark, KIPP, AUSL, Betsy DeVos, or any other successful charter school seems to have a solution to the problems in public schools, it always rings a little hollow to me. Operating a school of choice is inherently admitting that not all students are worth your time. When administrators, teachers,  and policy makers lament the failures of those of us who accept the least among us, while boasting of success by expelling the neediest, seems like…qualification to be Secretary of Education.

 

I Wanted to Write a Math Post…I Really Did

Here’s a scenario for you MTBoS, can I rotate a point on the coordinate plane 53 degrees without the aid of a protractor or some sort of technology beyond a scientific calculator? I had been wondering since the day I told my classes that they wouldn’t have to worry about knowing anything beyond a multiple of 90 degrees. On my drive home I started to visualize ways that trig functions could do the rotation of any angle and have been wanting to try it out during class.

I found an opportunity after school today to attempt my rotation frustration with a student. She took a different approach then I would have. She established where a 90 degree rotation would have been and then did proportions to figure out the new point. For example, we used (3,4) rotating to (-4,3) and since 53/90 became about 58%, she used 58% of 7 (the distance between 3 and -4), and found the rotated x value to be about -1.1.  As we took time to accurately graph what she was doing, we noticed that what she had created was a right triangle with legs of 7 and 1 and she was finding a specific position along the hypotenuse of the right triangle. This was different than what I had found using trig functions to rotate the original triangle formed by (3,4). In contrast to her, I had formed an arc, not a line. This led us to contemplate what is actually meant by rotation, of which we didn’t draw any firm conclusion. It has also lead me wondering if there is a way to make our answers match, can I extend her hypotenuse point out to meet my arc?

It’s discussions like the one above that I live for as a teacher. I think it is the goal of many math teachers to make their students think like that. I think it is the desire for OCTM, NCTM, and even CCS to get students to that point. The problem is that it is really hard to grade that dialogue. It was a dialogue without a designated answer, in which no firm conclusion was drawn, yet so much learning occurred. But it was so wonderful that I dream of the day that I can get a class where that is the norm for 179 days. I have that dream because I have had that class in the past and I know that is how school can have some sort of lasting impact. Those wonderful dialogues are part of a mechanism that can help change and challenge a student’s emotional intelligence.

A couple of years ago I had fortune to have a math textbook with a misprint in the answer key. We dubbed it the impossible problem from the blizzard bag. It was a problem that required the use of logarithms. I gave it to a couple of students to attempt throughout the day, and two of them perfectly illustrate my understanding of emotional intelligence. One student was in his fourth class with me. He had bore the brunt of the harassment I call teaching in at least two of his four classes. When he was presented with the impossible problem, he solved it correctly, saw the answer in the book, and then explained why the book answer was impossible. The other student also solved the problem correctly, but when she didn’t get the answer the book had, she redid the problem two more times. At that point she gave up, frustrated that she couldn’t figure out what she was doing wrong.

The first student, I don’t think he ever held the stereotype of being a genius (sorry if you read this and figure out who you are, I really do think highly of you), but he had embraced the challenges that I had thrown at him about justifying everything, about making sure stuff made sense, and when the time came to claim his authority, he did. The second student, who probably has a higher IQ, never learned to explain and justify her answers. She never learned to claim authority over knowledge always relying on some external force to reaffirm truth. Students like this are ultimately subservient to the textbook or the teacher. I realize that maybe it’s just math for some of these students, but it is frequent enough it does make me worry.

It’s hard to imagine students who come into class and demand to be complacent and feeble minded. Why would anyone want that? It’s not that students want to lack authority, but they are making an economic decision. They are smart enough to know that their worth is measured by two numbers, their GPA and their ACT (or SAT) scores. They want to go to college, and they know that colleges just plug those numbers into a matrix that will then tie a dollar value to the student. The numbers themselves have more value than the knowledge that those numbers represent.  That is why students will ask me, “Is this going to be on the test?” Or my personal favorite, “Do I need to know this,” implying that much of what I teach is actually worthless.

The student with whom I was working on rotations was not there for that purpose. She had come into work on ACT math, of which three problems stand out.

  1. Sequences – She caught on quick, it was the notation holding her up. That is entirely my fault for not showing the notation in her previous classes.
  2. Matrix Multiplication – I haven’t done matrix multiplication since college and wasn’t introduced to it until my junior year in college, in a Linear Algebra class. Why is this on the ACT?
  3. Graphing on the Complex Plane – I have never done this, ever, at any level.

All three of those topics are very specific and can be memorized with very little understanding. Memorizing enough of those has thousands of dollars worth of value. What she did with the rotations, while fascinating and enlightening for me to watch how her mind works, has no immediate impact. Why do we seem shocked by students who like plug and chug math?

So MTBoS, we preach mathematical thinking, growth mindsets, grit, and any number of ideological approaches that hopefully will create enlightened problem solvers, but our students live in a world where they are valued upon correct answers, not original thought. Math as I know it, is essentially useless to many of my students, but the right answers have thousands of dollars worth of value. How do we show them empathy for their plight, but get them to embrace our ideals? I ask you MTBoS because I am losing my students.

All My Students Are Special

Apparently I work in Lake Wobegon. We were given a sheet with a grade breakdown from the first semester. Removing all the “fluff” electives left slightly over 1500 grades that were given. Of those grades, 733 were between an A- and an A+, and another 535 were between a B+ and B-. In core classes, I work at a school where 82% of the students are above average.

I decided to compare it to my own grades from the first semester. I learned that I am part of the problem, if it is a problem. While I gave out many more B’s than A’s, overall, 79% of my students are above average.

But why give out the summary of grades in the first place? Are they too high? Are we going to be dictated to bell curve the students? There was a statement about making sure we are asking rich questions that align to new standards. So I assume this was directed at the idea that we have average test scores and college placement, but our grades are extremely high. How does this happen? I can think of a couple of possibilities.

These will be skewed in a secondary school direction because that is where I teach.

First, maybe our teachers just don’t have adequate content knowledge. If I have substandard mathematical knowledge, I would have no basis to make judgement decisions on whether students have mastered the subject. I probably would struggle to make meaningful assessments. In spite of what students might think, I don’t really subscribe to this idea. It’s been awhile since I have met a teacher who I think just doesn’t know the subject.

Second, maybe our teachers match their criteria for success based upon personal experience. Maybe the experience of our teachers have taught them valuable lessons about work ethic, consequently the criteria for success in their classes, possibly made subconsciously, has consisted largely of assessments that allow students to demonstrate work ethic. Maybe our students have above average work ethic. This is somewhat true for me, but I actually have set up a system that only implicitly rewards work ethic. Work, on it’s own doesn’t get rewarded, however, if that work improves understanding and comprehension, then there will be a reward.

Third, and I hate to think how much it influences me, is the pressure to make sure there are equal outcomes. Right now, if a student fails my class and then complains, it isn’t the student that has to prove that the teacher made a mistake by demonstrating mastery of content. If a student fails, I have to justify the grade. When students get good grades though, A’s and B’s, and even C’s occasionally, no questions are asked. When that “A” student comes back with an ACT score of 16 we just write it off as test anxiety, which apparently has almost reached epidemic proportions. That ultimately stems from the pressure to make sure that learning opportunities are accessible to all.

But at some point accessible to all somehow morphed into everyone gets the same grade. Equal opportunity, which I don’t think anyone would ever be against, simply means everyone gets a chance, it doesn’t ensure everyone will succeed. It all sounds great until it is you or your kid that fails. Maybe the material wasn’t presented correctly. Maybe the teacher didn’t provide the right resources. Maybe there is some sort of disability that prevented content going to long-term memory. The point is this, when a student comes home with a report card, we ask what’s on it and if it’s A’s and B’s we congratulate the student and move on with our lives. If that report card has poor grades, the inquisition begins, with everyone looking to blame someone, teachers blame students and parents, parents blame students and teachers, students blame everyone.

Considering how utterly useless my subject is to most people, I find it easier to devise a grading criteria that will keep everyone happy. Students get the grades that will keep them scholarship eligible and parents off their backs. I get to set a standard that makes an “A” a token achievement of mathematical understanding, yet passing my class takes minimal effort. Sure, this is a very cynical take on grades, but it is an accurate description. I could make my grades really be reflective of mathematical knowledge, but I don’t think students would want that, nor would parents and administrators want the outcomes that would ensue.

Besides, if I really was concerned with mathematical knowledge, grades are a terrible motivator.

Best to keep living “A” lie and move on with our lives.