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.

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.

On Poverty

**This will be my attempt at one of those writings where I just sit down and write. Start to finish, no breaks, minimal proof reading. I’ve seen it done before and I hope that it won’t ramble or repeat myself too much.**

Our school didn’t do so well on the latest round of state testing. Specifically, we struggled on the poverty subgroup. I guess we don’t get poor kids. So this summer we were given a book to read, A Framework for Understanding Poverty by Ruby K. Payne. There is a ton of criticism of this book, much of it deserved. I personally found it to be rather simplistic. The graphics are basic and not really enlightening, but maybe I was suspecting too much. The author has a Ph.D and the book claims to be research based. However, it relies heavily on patterns that teachers might notice about their students from different classes.

Did I say patterns? I really meant stereotypes.

The premise of the book rests on the idea that there is a shared culture among classes that supersedes ethnicity, gender, or nationality. For example, the book wants us to believe that the poor are loud, that the poor lack long-term planning, and lack proper social cues. It is even complete with a made up case studies of what might happen. Oh, and for an author that has a Ph.D, the notes are trash. The notes are’t so much citations of sources as they are a list of stuff she read. Kind of like the links in a blog post.

And there was another, more personal reason that I didn’t like the book. There is a connection between behavior and culture. When Ruby Payne connects poverty to culture, she is in essence saying that the behavior of people leads to poverty. If you come from a loud family that has a big screen TV you must be poor. If you value a relationship more than achievement, you must be poor. If you lack social tact, you must be poor. But I grew up in poverty, and I couldn’t relate to what she was writing. Don’t get me wrong, there were struggles. I have been employed since the 5th grade (paper routes, Burger King, YMCA, Burger King again, hotel house keeping, Target, teaching). I remember the subtle pressures and jealousy felt as my peers would take vacations, shopping trips, or attend camps I couldn’t. I remember what it would be like to not have a parent home at night because they were at work, and I’m not talking about an on-call doctor. I remember being worried about if we were going to lose our house. When my behavioral experience doesn’t match Ruby Payne’s description it’s like my experience in poverty has been disingenuous. If Ruby Payne had me as a child in class she might acknowledge that my family was poor, but I wasn’t in poverty.

That strikes at the biggest problem with Ruby Payne’s thinking. Being poor is just having a lack of money. That’s easy for society to fix. But the term poverty carries much more baggage (drugs, poor housing, low intelligence, etc.) than the term poverty. Being poor is a paper cut that requires a band-aid. Being in poverty is having a disease that must be eradicated. When Ruby Payne equates that loud, rambunctious student with poverty, we teachers look to cure the disease. That is dangerous. That is the type of thinking that will lead to racism, sexism, homophobia, xenophobia, and nearly every other kind of discrimination possible.

Okay, so I disliked the book, but I waited to write this post unit we had the in-person workshop with the presenter from Aha! Process. The presenter was much better than the book. By focusing on the lack of exposure people from poverty might have, he made poverty a experiential problem and not a behavioral problem. My growing up in poverty wasn’t based upon behavior, but was due to a lack of experience on the part of my parents. Even though I would say that I have moved from poverty to decidedly middle class, or lower middle class, there are still experiences that might have benefited me that I will never know about or have to learn myself.

While the presenter did fall into the trap of stereotyping occasionally, I felt that he did an exceptional job of maintaining the focus on experiences. What he was trying to get across was empathy. Our students come to us from many different backgrounds, and while some will have had the same experiences and then have similar mindsets and paradigms for interpreting the world, others might not. As teachers we need to make our expectations abundantly clear, especially for those little things we might take for granted. Most of our students aren’t trying to do wrong by us, and we need to not only understand that, but acknowledge that.

And if we can accept that as a maxim, those little things really aren’t differences after all.

I Started a Twitter, and Other Musings

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

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

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

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

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

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

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

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

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

 

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

Then Facebook.

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

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

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

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

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

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

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

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

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

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

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

I seemed to have gotten off topic.

So… I started a Twitter.

Bell Curving My Students

There have been several questions on my mind lately, but a general theme has occurred on four separate occasions during the past two weeks.

  1. A student just blatantly asked if I actually like my students, as if his interactions with his teachers has lead him to believe that we teachers hate students.
  2. A student admitted that she feels like all of her teachers don’t respect her.
  3. In a conversation with a student I admitted that I will miss her after graduation.
  4. While planning reward activities at my school I get the distinct impression that some teachers do not want to interact with students outside of their academic comfort zone.

I don’t think I want to address each of the last four statements individually, but I would like to address the concept that is at play here, which would be, “how I think about the student-teacher relationship.”

Before I go too far into the details, let me say that I have always considered myself a generalist (though I have been failing at that lately). What that means for me is that the well-being and flourishing of the student should always come first, with math being the tool that I have been given to use. With maybe that being said, maybe this next part will be a little more comprehensible.

Since I am a math teacher let me bell curve my interpretation of the student teacher relationship.

Standard_deviation_diagram.svg The students that sit out beyond -3σ, that 0.1%, those students are the ones that I find truly detestable. These students are so few and far between that in ten years of teaching I can count them on one hand.

The students that lie between -3σ and -1σ, or 15.7%, I am a tolerable polite with those students.

One standard deviation in either direction, or -1σ to 1σ, or the vast majority of my students I am genuinely interested in their lives. I want to know how other classes are going. Are they looking for work? I want to know how the basketball game went because of this middle 68.2%, but my relationship with these students is strictly defined around school activities. The only thing that separates them is the mean of zero, which to me defines whether I initiate contact with the student or just participate with them after they initiate.

The 1σ to 2σ group, the 13.6% of my students, are the reason that I go to basketball games, musicals, concerts, etc. They are the reason that my date nights with my wife so often involve other people’s kids. Though I view my relationship with these students is still defined by a school environment, I view my compassion and caring through the lens of being a fellow human being more than that of a teacher and student.

Those students in the last two groups, the 2σ and beyond, the 2.1% and the 0.1%, those students are the ones that I want to become involved in their lives. I want to know where they want to go to college and how I can help them succeed. I want to know where they are five years after they have graduated. These are the students that I feel that I can wash away the line that demarcates the teacher-student relationship, to the point that I don’t have to worry about censoring myself. Being so connected to these is what allows me to be precisely the most effective teacher I can be.  These are the students that I will genuinely miss seeing them on a daily basis. These are the students that actually make me look forward to class. These are the students that I look back on with regret, thinking that I could have done more to push them to reach and surpass their potential.

But that last group the 3σ, once again a group that I could count on one hand over ten years of teaching, that represents the students that I miss or will miss the most. Those are the group that make me question the teacher-student relationship because that small group represents the group that I wish I could call friends, if not for the societal stigma of a teacher and student being friends.

So, after all that, back to the original list.

  1. Yes, I do like the vast majority of my students. It’s also the reason why I wish they would take more classes with me.
  2. I feel so empathetic to this student. It is precisely this empathy that usually starts to bridge a connectedness that makes the student teacher relationship so much more effective. I just don’t know how to address it in the middle of class.
  3. Well, I guess this student could figure out where she ranks in my hierarchy of students.
  4. This is why I like planning reward activities. It gives me a chance to hopefully interact with my students on a personal level, especially depending on which ones sign up.

Well, that’s how I think about my students. I just wish I was allowed the freedom to interact with them in a more humane manner instead of treating school like a gigantic information transfer.

 

The Life of a Self-loathing Math Teacher

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

But anyway….

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fun with Numbers

Time for fun with numbers. Also, time to practice math speak and poor reasoning skills.

Assume that we take a sample of 100 students at my high school. The following statistically will likely be their future.

  1. 97 of the students will graduate, based upon the past four year trend.
  2. 67 of the students will go to college, 44 entering a four year institution and 23 entering a two year school based upon Bureau of Labor and Statistics data.
  3. Of the 44 only 26 will graduate and of the 23 only 7 will graduate (with two year degree), ever according to National Center for Education Statistics.
  4. Of the 23 that start at a two year school, only 5 will transfer to a four year school, but 4 of the 5 will graduate according to Inside Higher Education.
  5. Between two year and four year degrees, there will be 37 graduates, but 17 will be underemployed and 2 will be unemployed according to Federal Reserve research.
  6. Therefore, 18 of the 100 students who were students at my high school will finish some sort of post-secondary education and be employed in a career that requires a post-secondary education. However, that does not account for the credential inflation among those 18. Aspiring Certified Public Accountants need 5 years of college rather than 4 years, or 2 years like it was ages ago.

Why do I care about this? It is because the educational experience of these students will shape the messages they send their children. Of my grandparents generation, those going to high school in the 1920s through 1940s, only 25 to 35 percent took Algebra I and only 1 to 2 percent attempted Pre-Calculus/Trigonometry. By the late 1970s about one third of high school students would complete Algebra II as the highest math course and Pre-Calculus/Trigonometry had crept up to 10 percent. Even when I was in high school (2001 graduate), Algebra II was suggested and strongly encouraged, but not required. I was placed in the gifted track in Junior High School and my first introduction to a variable occurred in the 7th grade.

Now, Algebra II is a graduation requirement and is suggested to be taken during the junior year. Anything below an Algebra I level cannot count for high school credit. Variables and algebraic equations are now standard fair in upper elementary. I rarely encounter a parent that can help their high school student with math homework. I more often encounter a student who is helping a parent returning to school with math homework.

But inevitably, that frustrated and jaded student, will ask Mom and Dad, “Why do I have to learn math?” As the students become older and older this question is harder and harder to answer. Because of the ever increasing academic requirements most parents cannot relate to the requirements their children face. Increasingly abstract math creeps to lower grades, making math seem more and more like a subject from Hogwarts. And just like Harry Potter, abstract math can be entertaining to some, annoying and frustrating to others, and virtually worthless when it comes to paying the bills or any other “real life” scenario.

Eventually the parent, or the teacher, starts to run out of answers for the, “Why do I have to learn math?” The reply becomes, “Because you have to take math to graduate/get into college/whatever.” Remember the list at the top. Let’s reexamine it for a moment.

  1. 30 of the 100 students never attempted college, which means their children will have to take more math just to get the same high school diploma. They will tell their children that they have to learn the math to graduate.
  2. 30 of the 67 who attempted college never finished, jading them to the educational experience. They will tell their children that college isn’t worth it so don’t push yourself to try, or they might encourage their children to go to college unlike themselves and that they have to learn the math to get into college.
  3. 19 of the 37 who graduate will end up at a job that they could have had right out of high school. What kind of message do you think they will send about math
  4. Of the 18 who graduated and work in a field that requires a college degree only 4 will routinely use math at a level of Algebra I or higher. 14 of those 18 will tell their children that college is important, but the math is just something you have to do.

Only 4 of the future parents, only 4 of the current 100 students have any hope of finding the math I am trying to teach relevant. The other 96, 96% of future parents, of current students do the math because they “have to.” Sadly though, that’s what I think school is about. We tell students you “have to” take this class, you “have to” fill out this form, you “have to” wear these clothes. From where I sit it seems like society has said to schools, “You ‘have to’ create obedient students.”

We use measure success in education by numbers and awards. GPAs, ACT scores, honor roll, all these awards are supposed to measure academic achievement, but all they really measure is complacency and obedience.

Did George Orwell create public schools?