Winging It

I hate how time dictates the school day. I hate how we expect drastically different students to learn the same material, at the same age, at the same time of day, and even at the same pace. Sure some have drank the differentiation Kool-aid, but we haven’t yet differentiated high school as a whole. Same graduation requirements, same times, everything is the same.

From my experience, the majority of teaching takes the form of presentation of material, followed by some guided structure with the teacher, and then some independent time for the students to practice. This is the typical I do, We do, You do approach to education. When I prepared for this approach I would carefully think out my presentations. They wouldn’t be flashy, but I would take a substantial time to think about how I was going to talk about something, what I wanted students to notice, and what examples I want students to use. My goal wasn’t to entertain, but it was my goal to make the information clear. Though there are supporters of the entertainment aspect of education.

Are you not entertained?! When I used to show that to students they would remark that the class looks fun, that he makes the subject matter exciting. However, at the end of his courses, the attendance rates and failure rates were similar to other classes. So if the results were the same, what is the point of all that prep work to make the presentations exciting?

Maybe my presentations weren’t nearly as entertaining, but at least I was being clear on what I want accomplished. I started class telling the students what we’re going to do today. I wrote up clear definitions and gave clear examples with multiple steps shown. But the goal of education should be to create students with the ability to think, which involves a whole host of issues. Part of the problem with using clearly stated goals is that novice learners will only focus on the goals, most likely bypassing interesting and important connections along the way. Yes, I know that that study is talking about reading, but from my experience students do that with just about everything they do.

To put it another way, when I was presenting mathematical information I was covering information that is part of a complex tapestry of mathematics. However, my students only take in minor details, basically ignoring as much of my voice as they could, grasping for the bare minimum structure to be memorized so that they can correctly answer test questions. This picture eloquently summarizes what I think is going on in the journey from my mind to their minds, even though it really is about rubrics.

It is a visual representation of why so many of my students seem to think math is just a disjointed collection of random facts and procedures. When I thoroughly thought out my presentations, I made sure to highlight those red dots of importance, but in my mind those dots are just part of the whole picture. My students just pick up on the red dots though, which I often referred to them Charlie Browning me. My voice was the blue, my examples were the red, they copied the examples and heard this.

My good compliant complacent students were Charlie Brown. The had the appearance of listening, but really were just quietly searching out those red dots, those examples and steps to let them solve the next math question. My favorite are the students like Patty though. At least they weren’t pretending to care, yet an alarming amount of them are on the honor roll. They have internalized the process of hunting out those red dots, be it from examples in books, notes, online, or asking their friends, “How to do this?” They are obsessed with the how’s, but not the why’s?

To help try and combat this I changed my presentations. Instead of carefully planning out every individual step with concise, clear objectives, I started to wing it in class. It didn’t mean I wouldn’t lesson plan, it just means that my plans were a rough outline, a framework, that was then filled by the organic discussion in class. My goal was to make sure the students wouldn’t become fixated on the red dots. When I would be planning my presentations I would pick a topic, think of how it connected to the previous topics, and then try and use student questions and ideas to drive most of the presentation. When I know my students and my content I find this to be an enlightening experience. They start to finally see some of that blue background behind the red dots.

However, it does have a couple large drawbacks. It did give class a more organic feel, but students crave the conditioning that they have been experiencing for years and years. Charlie Browning is most prevalent in my honor roll students because it has allowed them to get success in the past, at least in terms of grades, with the least amount of mental effort. For most of my students, it takes a significant amount of time to overcome that conditioning, and some, unfortunately, never will.

It also gives the appearance that I am unprepared, but for me, it changed the hierarchy of my teaching prep. When I plan, I start with content from a teaching viewpoint, then worry about presentation and pacing, then worry about assessments, then worry about supporting activities, then worry about individual students. My ever changing schedule the past eight years has meant that I feel like I am perpetually stuck in my first hierarchy of teacher needs, focusing on content.

I guess I forever will be a rookie.

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.

I Almost Quit Teaching…

Classroom management.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It all makes me feel like I am weird.

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

Generating a Genuine Mathematical Discussion

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

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

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

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

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

“Umm….no. What happened?”

“He failed his Calc quiz.”

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

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

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

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

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

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

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

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

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

I don’t know what to do.

Projects Make Me Question My Ability

When I first discovered that there was a math blogosphere it was because I had become frustrated with my students. Specifically the condition that occurs in education where students seem to approach almost every task as if they are helpless. At first I read blogs that vented  about the frustrations of being a teacher and then progressed into finding blogs that devoted themselves to pedagogy, educational philosophy, psychology, policy, and eventually math tasks. It’s the last group that makes me feel inadequate as a teacher though.

I read about Dan Meyer’s 3 Acts, the modeling instruction of Frank Nochese, the enriching tasks like those at Emergentmath, just to name a few, but I don’t know how to develop them or even properly implement them. Every time I try to, I feel like I am unable to correctly judge when to provide instruction and when to let the students struggle. I will give that my project creation skills are sub-par, but when a student will blurt out confusion without bothering to read the introduction is that my fault? My knee jerk reaction is to say no, but maybe I have created a climate where the students have been conditioned to bypass directions, so maybe it really is my fault. I tried to leave gaps where they could productively struggle, but most of them give up quickly. Is this a lack of motivation on their part, or have I conditioned them to think that all problems either have quick simple solutions or no solutions at all?

I am good at math. But my mindset of math is so different from the students that I will lose many of them if I try to teach math how I think about math. It’s not that I lose their attention because of lack of ability, but because of lack of interest. Most of my student are either lost in math or in a survival mode in math. Basically, to most of my students, math class is simply see problem, solve problem, get grade. I am completely empathetic to their plight, I realize that in their reality the math they learn in school is useless, and I try to compromise with my students by using grades. In my reality grades hinder learning, but they are of utmost importance to my students. So I offer a sort of compromise, I get to pose some very theoretical conceptual ideas to them of which several will embrace, but I get to do this as long as they get the extrinsic credit of a grade. Right or wrong, I am content with this set up and I think most of my students are.

My previous six years this worked out fine. My classes ran under more or less the same procedure until it was time for final exams. Exams worked as a nice natural conclusion to the course. The students got what they wanted and I got what I wanted. This year though my exams occurred early, with about three weeks of school left. I was able to use the SLO as an exam score. Since my students performed well on the SLO (in regards to my job security, not necessarily their grades) I thought it would be prudent to reward them by curving the grades and using it as an exam, especially after the effort several of them displayed on a test that didn’t have to count as a grade. However, I have conditioned myself to be finished after exams, so now I want to be done. I teach upper level courses and my students will pursue many different pathways, so I can’t really teach something that will prepare them for next year in any sort of uniform manner. I could just do my normal routine, but with exams done it feels self-centered to force new material, and for my grade motivated students three weeks of grades only have a marginal impact, which will lead to many of them tuning me out.

I found my solutions in projects, those really creative math demonstrations I find on  the internet all the time. As long as I make the math “real life” or “authentic” students will engage with the material. Well, that’s what I was taught and that’s what students tell me. Usually that means they want to know how to balance a checkbook, do taxes, or pay a mortgage. What they don’t want to do is learn how to use a bell curve to make an accurate budget, they don’t want to learn how tax tables are created or the philosophical discussions behind what is a deduction, nor do they want to deal with the geometric series to figure out how the bank calculates that fixed payment. Projects seem so difficult in my class because I haven’t found a way to get my students to authentically engage with mathematics. Because their motivation has never moved beyond the extrinsic, they have never been anything other than compliant students and compliant students don’t really learn anything except obedience.

I don’t know how to motivate a student to find intrinsic value in math. I encourage. I try to discuss. I offer to be flexible with grades, pacing, rules, whatever. But no matter what I do they won’t engage. So when I see and read about amazing projects, classrooms full of excited engaged students, all I ever realize is that my students can’t do that. I know them well enough that I realize it’s not them, it’s me. Many of them are immensely talented, but choose to display that talent in settings other than the math classroom and it reminds me that all I have done is created a bunch of obedient students. It reminds me that I am a failure. Projects prove to me that I am a terrible teacher.

Hit By a Student

I have a bruise on my arm right now. It is a small bruise, not very deep, barely any coloration. Probably will be gone in a day or two, but it is still there.

Why am I so excited about a bruise?

Because it was given to me by a student.

I am the kind of teacher that is happy that he was hit by a student. This blog started as a place to be reflective, and I think it finally has had that effect. My post from a couple of days ago lamented that I have lost the solidarity that I used to have in class with my students. Losing that solidarity made me a worse teacher. I vowed to try and get it back. Though it has only been a day, I believe I did a good job creating that solidarity today. How do I know?

I treated my students like human beings today. I relented some of my pressure and allowed them to dictate the pace of class to some extent. There was down time. There were moments where they were off task. There were moments where I was off task. There were moments where we were both engaged in learning. But for the first time in a long time, it felt like the engagement was authentic rather than some sort of complacency. I have difficulty describing the intricate details between authentic engagement and complacency, but I can vouch for the difference in feeling between the two.

And there’s that bruise. I received it when I made a disparaging comment about a student. Not a horribly mean, bullying comment, but the kind of good natured joking that can occur between friends, family, and acquaintances. You know, how human beings treat other human beings. I was then met with a human response, a swift slap in the arm. Instead of gasps and stunned silence, the rest of the class laughed. I need to work on cultivating that atmosphere again because that is what I had lost. My interaction today was not as teacher talking to students, but just as a person talking to other people on equal footing.

A student hit me today. It was best day I’ve had in a long time. How was your’s?