Is School Really About Education?

Today, and the next few days, I hope to be able to just talk to my students in one of my classes. I plan on using the timing of losing many students to senior class trip, along with having to do a mandated Ohio Means Jobs lesson. Many of the lessons are rather basic, or those that do require a little upper level math feel rather forced, kind of like they were copied straight out of the textbook. Yet somehow it has more career connections because it came from the state website instead of a textbook. But, like usual I need to digress before I start to ramble into something I really didn’t intend to talk about.

I have been using my blog to write about some of the more transformative experiences throughout my education and I spent a good chunk of last night rereading some of them. This wasn’t my first attempt at making a personal website, it just changed from what I originally thought it would be. Originally I was going to make a site to supplement my class, a resource for mathematical information. However, I am a unitasking teacher, so I really didn’t need a website to explain all the different methods I am using. Providing mathematical information was kind of pointless because there are hundreds of websites out there to do that, all of them better than anything I could produce. Why have I stuck with writing this time?

I used to consider myself an educator who happened to use math as my medium. To steal a line from my pastor, my purpose was to, “comfort the afflicted and afflict the comfortable.” My goal was to salvage education for those on the brink, the perennial discipline problems, the helpless, and to push the honor roll students to their limits. I felt like I accomplished this goal during a couple of years, and now I find myself constantly chasing that nostalgic moment.

Several years ago I stumbled across a blog that laid out in rather blunt terms the social contract that exists in most schools. (I didn’t bookmark it at the time and cannot find it again, but I want to make it clear that while I agree with the premise that will follow, I did not originate it.) It laid out a vision of school that really resonated with me after I had a nervous breakdown in front of a couple of students. Authentic learning is an inefficient, messy endeavor that is not conducive to a typical educational setting. A classroom inherently relies on efficiency to educate the masses. The problem is that this education resembles training more than education. To be effectively trained, quiet obedience is necessary, but in-depth thinking and analysis is not. A contract develops between teachers and students in this environment, one where the students agree to be obedient and complacent, and the teachers agree to not really make students think, but rather rely on memorization. Students are willing to sacrifice freedom and opinions in exchange for not being challenged.

School becomes a place where an encyclopedia of examples is memorized, and we denote the ability to memorize with grades.

After I had my nervous breakdown in Calculus I, I started teaching differently. Well, teaching in a traditional sense wouldn’t be the correct description. I talked with my students, explained everything in excruciating detail. Since it was more conversational in nature two things happened. One, it was easier to get off task. Two, the questions in class changed. It was less, “How do you…,” and more, “Why did that happen?” Every so often we would actually lose track of time and class would end with nothing resembling any sort of closure, and simply resume the next day. Instead of intro and hooks, we opened the book, picked a problem and started mathing. As a teacher, I absolutely loved it. Every statement or action I did was directly in response to something the students did, and every statement or action they did was in direct response to something I did.

There was only one problem with this set up. How do I grade an open-ended discussion? What if I abandoned my end of the social contract? No more grades.

It worked better than I could have hoped. No more grades, no more contract, no more complacency, actual thought.

The next year I decided to try it for a full year rather than a quarter with my next Calculus I class. Same result, but with an added bonus. I started to realize that there is a huge difference between productivity and learning. It was after one of our off task conversations, it could have been about college athletics, school rules, or whatever else, but it left me with an odd feeling. By any normal definition of a typical classroom it was a wasted day. But it didn’t feel like that. I felt like something was learned because my students engaged in some level of thinking. Don’t get me wrong, I still knew how to set my foot down and decide we needed to do some math, but I stopped feeling guilty if every second of class wasn’t devoted to math.

Unfortunately the following year I did not have a Calculus I class. Additionally I had a Pre-Calculus class, a topic I hadn’t visited since my sophomore and junior year of high school. I was teaching Pre-Calc in a relatively traditional way, cover previous assignment, introduce topic, go through examples, release students to work independently. One day though, I had assigned the following problem from this book. It’s #18 on page 163.

A car leaves Oak Corners at 11:33 AM traveling south at 70 kmh. At the same time, another car is 65 km west of Oak Corners traveling east at 90 kmh.

a) Express the distance between the cars as a function of the time after the first car left Oak Corners.

b) Show that the cars are closest to each other at noon.

A student in class called me over to help her get started and another student joined in on the conversation. I became momentarily lost in the problem, probably a couple minutes elapsed, but when I looked up to talk to these two students I noticed every other single student had come over to observe. Right there it told me something wasn’t working. My students weren’t making the connections between the concepts I was teaching and the exercises that are supposed to enlighten those concepts. I immediately thought of my previous Calc class where I didn’t separate the concepts from the procedures and quickly sent out this poorly worded email.

I am looking for feedback on how I taught Calc I last year. Bascially, did the method of doing work in a small group and working through problems one at a time help or hinder your prepartation for whatever math, or attitude towards math, that you are encountering outside of high school? I ask because I have been burdened with trying to teach precalculus this year and I feel that my classes are creeping ever closer to the model that I used last year and the year before, just on a larger scale. If you guys feel that it actually helped your preparation I think I will try and do the same group work/pacing that we did with Calc. If it didn’t, I will stick with a more traditional model.

I know the sample size is tiny, but I received rather positive feedback. The closest to negative feedback I received was a student telling me he was on par with his classmates in the honors program where the students came from AP and IB classes. So I tried it with the larger group, and it worked surprisingly well. I had buy in from 12 of 14 students on a regular basis.

From these three years of experience I became comfortable admitting my own shortcomings in front of my students and learning with them at times. I accepted that I will never be able to embrace bell to bell productivity and always call it learning. I realized that the best learning is extremely difficult to pigeon hole into letter grades. Sometimes I would take a day off from math, but it never felt wasted because there is so much more to learn than what can be enlightened by mathematical procedures.

The next year I dropped many of the conventions found in the social contract of school. If the actions we were doing in class didn’t help enlighten mathematical knowledge, then I decided that that action was really about obedience. I stopped homework. I showed movies, played games, or just talked with my freshmen in Algebra I after they had mastered a set amount of material, which served the dual purpose of extrinsic motivation and allowed me to start to build personal connections. I completely eliminated the concept of a grade with my upper level electives and made the classes more about claiming authority over knowledge, rather than going over many different derivative rules.

There are things I can’t control in school, but for the first time I felt like I was actually teaching and the majority of my students were actually learning, instead of the usual dance around the burden of obedience. I had a purpose as an educator.

However,…

I no longer feel like I have a purpose as an educator who uses mathematics, but that I am now expected to be a provider of mathematical information, which makes be dependent on obedience. I’ve been told that students are liars (“they will just lie to protect you”). I’ve been told that students are not smart enough to engage with material (“they can’t be expected to push themselves like that”). I’ve been told that students are nothing but disrespectful and rude (“punch them in the face and tell them to shut it”). I could keep going, but I hope the picture is becoming clear. For the past three years, I feel like my work environment has been one that distrusts its most important stakeholders, its students, and places a premium on obedience and complacency.

That’s why I keep writing this time, because I’ve lost the autonomy to have these conversations about obedience with my students. If this was three years ago, I don’t think this blog would exist because it’s contents would exist between me and my students.

Why do We Forget Everything that We do in Class?

My fourth year of teaching I really began to reflect upon the purpose of my educational experiences. Specifically, the purpose of taking so many college courses to become a teacher. (How does having Abstract Algebra help me teach Algebra I?) It was after I admitted that I really didn’t know the math I was teaching I began to question the whole purpose of school as we know it.

As educators, we like to toss around rhetorical statements about mastery of material, but the reality is that the vast majority of the students we see will quickly forget the material we taught them. I don’t mean kind of forgetting and becoming rusty with the material, but completely forgetting it, so that if they were to encounter the material in several years it will be as if it never happened. I had this happen at my in-laws over Christmas break a few years ago. I had given my Algebra I class a worksheet where they were asked to find solutions to systems of linear equations by graphing. I was in the basement correcting, and as a joke I decided to give it my brother-in-law who had never passed College Algebra. (He is a college grad because he ended up using a Statistics class for the math requirement, which prevented him from becoming a history teacher, which make any sense to me.) He couldn’t do anything on the worksheet. As the rest of the family made fun of him he offered to let them try. My in-laws have six members in the immediate family, five of the six are college grads of typical four year universities. Only one of the six could come even close so correctly solving a systems of equations, and it was the one member who only graduated high school.

Combined, my in-laws have at least 18 credits of college level math completed, yet were clueless when it came to something that was standard fare for 9th grade students at the time. That experience, combined with my own struggles with teaching mathematics, made me question the whole purpose of education as we know it. I often hear math being defended as a subject worthy of study because it teaches critical thinking and problem solving skills. But critical thinking skills cannot be taught outside of a context, and if the context is impermanent has anything really been learned? No content retained, no thinking retained, nothing learned. I started to view my college diploma not as an accomplishment, but as a receipt for time spent avoiding the realities of life.

I am enough a pragmatist to admit that not every student can be reached. I know that there will inevitably some students who slip through the cracks no matter what opportunities are presented to them. I also know that there are some students that will achieve tremendous things in spite of everything obstacle placed in their way. I know that there is a group of students who have their destiny already determined and are just surviving the hoops placed in front of them. But there is a group of students who need school to be something more. This group needs school to be a place where knowledge is gained and retained, and it will be used to push their limits. There is this group that needs to be broken out of the complacency of unquestioned honor rolls and 4.0s.

That group of students will never be served until we can unequivocally answer the question, “Why do we forget everything we learn in school?”

My epiphany occurred when I was teaching Algebra I in 2010. There was one problem the class wanted me to go over from the homework assignment. I asked for volunteers, which there were none. Probably yet another assignment that was either incomplete, copied, or just mindlessly filled in hopes of a completion grade, I thought to myself. The question came from this book, and was found on page 422. It’s number #47

In your chemistry class you have a bottle of 5% boric acid and a bottle of 2% boric acid solution. You need 60 milliliters of 3% boric acid solution for an experiment. How much of each solution do you need to mix together?

I couldn’t do it, couldn’t figure out the answer. I gave the answer that was in the teacher’s edition, but I didn’t have the worked out solutions manual and I had no clue how to get the answer. I have a BA in mathematics, taken courses such as Calculus I, II, and III, Ordinary Differential Equations, Elementary Statistics, Linear Algebra, Abstract Algebra, Physics I and II. I took three rounds of Chemistry classes for my science requirements. I graduated Cum Laude. I ….couldn’t do 9th grade math. That’s kind of humiliating, especially in front of freshmen.

At first I took the rust route of blame, “It’s been years since I’ve seen a problem like this.” That was my scapegoat for my struggles in Calculus I also. It kind of falls in line with that old cliche, “if you don’t use it, you lose it.” As I thought about that more and more, it just didn’t resonate very well with me. Instead of wondering why we forget everything we learned in school, I started a little thought experiment with myself.

What if that’s the point. What if we are supposed to forget everything we learn in school, unless we are explicitly using it. If we are supposed to forget, then what is the purpose of any class in the first place? The only logical conclusion I could reach was as some sort of gate keeping mechanism. Basically, as a society, we are finding out how much a person can temporarily withstand in pursuit of obtaining a long term goal. Once the goal has been achieved, the path to get there can be forgotten.

Want to be a doctor? Well, you’ll need to pass at least Calculus I. Why? Because I want to find out how bad you want to be a doctor. Once you’ve become a doctor, you can forget all that calc crap anyway. (I would venture that this a rather common sentiment, though I am basing it on my personal anecdotal evidence.) The only reason academics would exist then is to torture students, as a way of weeding out the weak.  Ghoulish images of evil old men devising ways to make students confused. “Quadratic Formula…Muwahahaha…”

Solely because of my principles, I refuse to believe that all of math was created as a means of inflicting pain on students. That might be the very real world outcome, but that can’t be the reason for the existence of academic subjects. This was a turning point for me, I either had to accept that the whole premise of school was to make students suffer through some kind of sorting mechanism, or I need to find a purpose behind the math I am teaching. Not only did there need to be a purpose for the math, I needed to find out why do we seemed doomed to forget everything we learn in school. Over the course of the past six years, here is what I believe causes us to seemingly forget so much of what we learn in school.

There are two large elephants that hang over public education that I don’t believe gets the level of discussion they deserve. One is determined largely upon genetics, and the other would require a massive change in society. This means that we should acknowledge them, but realize that they probably won’t change.

Cognitive Ability

The longer I have taught the more I believe that people get equal opportunity and equal outcomes confused. (If you’re not sure what I mean, the movie Ratatouille is a good example). There is such a stigma surrounding cognitive ability that I don’t know if we could ever design an education system that actually meets the needs of everyone involved. If I want to actually bring up cognitive ability in designing a curriculum or class schedule, I am at best written off as being an elitist or worse, thought of as being an inhumanely, cruel, dream crusher. Why? Because I don’t believe I can change someone’s cognitive ability any more than a basketball coach can change someone’s height. So when I am told another story about everyone achieving amazing results, it makes me think of every basket ball player dunking on a 7 foot hoop. Unfortunately, I believe that we have sacrificed so much of our students’ potential at the alter of equality. When we think and act like everyone is the same we decide we know what’s best, which leads me to…

Compulsion

We force students into school to take subjects they may or may not want to. We take this very heterogeneous group, force them into the meat grinder that is academia, and expect uniform results. There are countless analogies written about how school is like a prison, which to some extent are accurate. The problem with compulsion is that it forces people to do an activity, and when an activity is forced it will ultimately be of poor quality, whether or not that activity was enjoyed at one point. And if it wasn’t enough that we force students to go to school, we force them to take subjects that many in society view as largely useless. Then when we find students’ math skills lacking, we force them to take more, so they will be better prepared. It really is a vicious cycle.

I don’t think anything can be done to solve the problems posed by cognitive ability and compulsion, but at least acknowledging them would allow us to try and design an appropriate curriculum and structure, rather than the insanity we have now. But forcing students to do something they don’t want to is really going to impact…

Motivation

Yes, they are forced to go to school, but what do they get out of class? Are they just trying to graduate? Do they need an ‘A’? Maybe they want to graduate with honors. It doesn’t matter, all of these are extrinsic motivators and are doomed to fail. Maybe the student will be fine in the long run, for example, the doctor who can’t remember linear relationships are modeled by y=mx+b, but nothing will remain in long term memory if extrinsic motivation was the reason. That’s because extrinsic motivation doesn’t produce results, just the opposite, they hinder results. Intrinsic motivation is the way to go. If students want to understand that tangent lines are perpendicular to radii of circles, they simply want to have to know WHY. The questions and problems have to be motivating enough, they need to be an end to themselves, not a means to an end. I might be able to convince a student that mathematics might provide a pathway to becoming an engineer, but I cannot make a student value mathematics for itself. I might be able to force compliance, but I just can’t make a student want to learn anything. And when students aren’t motivated to learn, they fall victim to…

Distraction

If you are motivated, you are hard to distract. No motivation, easily distracted. The problem in a classroom is that distraction is not just limited to cell phones. If students are thinking about an upcoming Physics test, they are distracted, even though they might appear compliant. Overcoming distraction takes difficult, self-aware, personal work, and the ability to admit that multi-tasking doesn’t work. I will freely admit, that as a teacher that I do not try an eliminate all distractions for a couple of reasons. First, I firmly believe that limiting distractions is a personal endeavor and is best achieved through intrinsic means, not extrinsic. When students think, rather than rely on memory, distraction is difficult. Ironically, if students are thinking, distracting noises can actually be beneficial, as long as it’s not above typical human conversation, like sitting in a restaurant. When students are trying to memorize information for recall any sort of background noise can be distracting and detrimental. Which leads perfectly to…

Learned Helplessness

“I need help.”

“I don’t get it.”

“Is this right?”

As a teacher I have to acknowledge that I am somewhat an accomplice in this behavior. Students can only be told they are wrong so many times before they just start to assume anything they do will be wrong.  At that point math, or any subject, becomes some arbitrary set of rules to memorize, so students no longer have the capability of understanding their own work, which makes them reliant on the teacher for validation. When students encounter a problem many will start to try and recall previous examples. If they cannot find one similar enough to duplicate in their memory, they quit. They are helpless. They are helpless because students don’t actually like to think.

I don’t want to give the impression that all the responsibility is placed upon the students. Teachers have their role in memory retention also, which I feed into by…

Pseudoteaching

This isn’t a scientifically researched topic as far as I know, but this post about pseudoteaching is one of the most influential I have ever read. I used to be a much more traditional teacher in format. I would spend several minutes going over previous homework, then I would spend several minutes going over new material, and finally give students several minutes to start their own assignment. The problem was that for the majority of the class it was only me doing any thinking, and then it wasn’t much. Even when I would present new material, I made sure to provide examples of everything that might appear on the homework, explicitly saying, “on this section you will see….” Pseudoteaching isn’t about methods, style or entertainment. It occurs when the teacher is the only one doing any thinking and the students nod along in agreement. They nod along because everything the teacher does makes sense. Then they try the homework or take a test and go, “What?!” So my goal is to try to create some controlled confusion, hopefully to make students uncomfortable. If students can embrace being uncomfortable, and differentiate their discomfort from being loss, then they are in the right environment for learning to occur. One thing I can do to try and cause some discomfort is to use…

The Worked Example Effect

The worked example effect is one part of cognitive load theory. Worked examples are one of the most efficient ways to learn a new task, however they pose a slippery slope. The best way to master a new concept or task is through goal free, open ended questions. But those types of questions pose a problem, one of efficiency. To increase efficiency, worked examples are used to guide students. If too many are used, if the tasks to be mastered are too similar though, worked examples actually have the effect of killing thought and creativity, which is why students end up relying on memorizing rather than thinking. My goal in class then is to use some worked examples. I might only use a couple and then make sure the tasks to be completed differ from the examples, or I might start, but not finish the example, forcing the students to complete it. The tough part for me as a teacher is trying to find the delicate balance between efficiency and mastery. Provide too many worked examples and I am contributing to learned helplessness, don’t provide enough and there is no semblance of efficiency. Worked examples are the primary medium in which I invest, but I also need to know…

Other Cognitive Theories

I need to know about the spacing effect and how to use it. I need to know about the expertise reversal effect and how to avoid it. I need to know about ways to reduce cognitive load. I need to know that learning styles, though they sound nice, basically have no evidence for their existence. I need to find a way to convince my students to overlearn. All these things will help students move what is learned into long-term memory. The goal is to force new information into a schema, which are large, framework like memories that allow us to interpret and analyze new information. If I can accomplish all this, and I find students willing to embrace it, maybe, just maybe, some sort of knowledge might last beyond the semester exam.

 

Please notice that nowhere did I talk about making learning interesting or relevant. Those are nice if they are available, but the purpose of this post is to discuss why we seem to forget everything we learn in school. Maybe that’s our destiny as a society, and until we stop using education certificates as economic gate keeping mechanisms, we will be stuck with an ever forgetting society. It kind of makes me sick that our education system is that, but it is what it is.

 

A Summary of Why We Forget What We Learned

Students come are forced to come to school and teachers are forced to teach certain topics. We both need to get over it. If we can’t let coercion component go, our motivation will always suffer. When we rely on punishment and rewards to motivate us, we never really do any action to the benefit of knowledge. All we ever do is try to avoid detentions and get stickers on our diplomas, the knowledge is actually pretty irrelevant. If we don’t care about the knowledge, we will turn our attention to something we actually care about, like Snapchat stories. Between our distracted attention and our willful ignorance of cognitive differences, we condition ourselves to dislike thinking, or at least thinking about academics. When we avoid thinking, we rely on memory because it is so much easier. Teachers provide step by step examples and students memorize them, meaning their knowledge is only, at best, an encyclopedia of examples, devoid of all meaning and context. It allows all students to succeed as defined by grades, but leaves us in the unfortunate position of creating a definition of book smart, which apparently doesn’t have anything to do with actual intelligence. When school is about book smarts, we are acknowledging the irrelevance of academic knowledge. We only perform tasks to get the grade, the test score, the scholarship, the degree, the paycheck, or the promotion. Once we get what we want, we don’t care. The memory is gone, poof, vanished.

This won’t change until we learn how to make ourselves care. It’s not about technology, movies, rewards, grades, tickets, 3 acts, projects, discovery, or anything else. It is about you. You control your care, and when you figure out how to care, you will see that you won’t forget.

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.

Grades and Empathy

My students are just finishing their last rounds of state-mandated testing. Many of them are burnt and fried. It’s just too much testing all at once, especially for the sophomores at my school. For my tests the results are mixed.

I fall under the auspices of something called Student Learning Objectives (SLO) under the Ohio Teacher Evaluation System (OTES). I have to create a test that is to represent a years worth of material and administer a pre-test and post-test to show growth. Since the test is practically identical, much of the material is new to the students. To encourage students to take the tests seriously, we are allowed in our district to use the SLO as an exam grade.

Without the threat looming of exam grades, the only consequence SLOs had was teacher evaluations. To put it another way, the test wasn’t necessarily a measure of student ability, but of teacher quality, or in the case of most SLOs, teacher test writing ability.

Most of my SLOs are completed and the grades are mixed. Overall though, I feel that they are too low to use as an exam score that would accurately reflect what was accomplished during the year. So why are the scores so low? I think there are three factors in play.

First, students just flat out forget a large quantity of the information they are presented with throughout the year. I have read psychology research, cognitive load theory, and numerous other theories as to why this occurs. I believe there appears to be debate about whether instructional practices or student attitudes account for this phenomenon, but either way it exists. Our students just forget so much stuff.

Second, so much of math instruction is perceived to be this, whether it actually is or not.

What happens is that students freak out and have borderline panic attacks when problems don’t match the memorized examples from class. Students who normally volunteer information and come up with some of the best ideas in class shut down when the assessed problems don’t match their memorized examples.

Third, my usual assessment format does not require to students to be as attentive to precision as they should be. The multiple choice format SLO I gave requires precision regarding negative signs and arithmetic. My usual assessment rewards creativity at the expense of precision.

So why are the scores so poor? The first problem, students just forgetting, I think that is something that is only minimally impacted by teachers. I can encourage, I can try and provoke, but if students won’t authentically engage with the material learning will not last. The second problem I think I usually do rather well with, or at least with the grade obsessed students. My reading through pseudoteaching has really changed the approach I use to the presentation of my lessons. I have adopted a less is more approach in my lesson presentations, emphasizing that the work done in class only illustrates concepts and that can be applied in many different scenarios. And I am pretty happy with aspect of my assessments as my students have become more flexible and adaptable in new mathematical situations.

But the third reason why I think the grades are low, the precision, is something I need to change. In the multiple choice section of the SLO, I noticed that many students had the concept down, they were just making procedural errors. That means, to some extent that the low scores are my fault. Every year I keep saying I will, but because my open ended assessment reward creativity more than precision, it is ultimately empty rhetoric. I don’t want to just dump my current assessment as I am happy with the outcomes. I was able to use the students attachment to grades to make them be more mathematically creative. I think I can do the same by using some multiple answer assessments throughout the year. It would force the students to become more accustomed to mathematical accuracy and lingo.

Now back to the original purpose of this post, curving grades. I have never felt the urge to curve grades like I have this year. I also never realized there were different ways to curve grades. In past years I have felt that the exam scores accurately represented my students knowledge of math. As I have interacted with these students over the course of one to three years I have a pretty accurate representation of their mathematical potential regardless of their specific exam score. This year I had a couple of students perform much more poorly than I expected and much of that performance is based upon my not training them well enough to handle the precision of a multiple choice exam, hence my urge to curve the grades. So here is a list of all the questions and dilemmas running through my head.

  • While I have sympathy for those students who engaged fully throughout the year and want to take blame for their poor performance, I have a handful of students that have so effectively tuned me out that I really don’t feel the need to curve their grades. In a way I want those students to suffer the consequence of lacking authentic engagement, which in this case would be a drop of a letter grade or possibly two. For clarification, none of them would be in danger of failing, just GPA reduction.
  • I thought about applying the curve to only those students who have shown effort throughout the year, but I revolt at that for two reasons. One, I despise effort grades. Two, if I pick and choose which grades to inflate it ultimately renders the concept of an exam mute.
  • I realize that much of my desire or lack of desire to curve is based upon which math class students are in. I have more sympathy in my required courses (Algebra 2) and less sympathy in our elective courses (Pre-Calc).
  • I have a couple of curve breakers whose scores are high enough that it renders the curve pointless for my low scoring students.
  • I really don’t want to put my students through another exam. I don’t want to take the time to make another exam. It rewards those students who didn’t take the SLO seriously enough the first time around knowing that there is potential for another exam.
  • If I give another exam it punishes the students who did well on the SLO.
  • If I let the students just keep the higher of the two scores, why stop at just two? Why not give the students three, four, or even more opportunities? And if I give them endless opportunities isn’t it really just like me determining their grades subjectively?
  • At the end of the day my students did well enough to help ensure my job security (met SLO growth targets). Well, most of them. I think there were a couple that really want to get me fired. Is it wrong that I want to somehow manipulate the grades in a way that either rewards, or at least doesn’t harm my students grades?
  • I really, really want their input. However, I want their input in a manner that takes into account more than their individual grade, which I feel most  are capable of doing. I do fear the implicit pressure placed upon me to “control” my class and that requesting feedback from students is empowering them too much.

Isn’t it nice that grading is so simple.