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.

Why Do So Many Students Take Remedial Classes in College?

My first year of teaching at my current school I was given a Calculus I course. I was scared to death. Calculus! It had been six years since I had done any math above an Algebra I level, and I had never taught anything above an Algebra I course.

The Calculus class is entirely elective at my school, so all the students that were in my class all wanted to be there to some extent. They should therefore represent some of the most academically driven students we have. We also offer dual enrollment options through the area schools. One day one of the students in my first Calculus class asked me for some help with some of his college math homework. As I was helping him I asked him what class he was taking at the community college because the math questions seemed lower than the topics we were working on in Calculus. He responded that he was working on a College Algebra class.

I was shocked. Here was this student who had passed Algebra I, Geometry, Algebra II, Pre-Calculus, currently in Calculus I, maintaining a good GPA, staying on honor roll, and would eventually graduate near the top of his class, but he was struggling in College Algebra at community college. While he was my first personal experience with this phenomenon I started asking around and found out that it was kind of common for a college bound students to be placed into remediation.

I started to hypothesize why this was happening and came up with some possibilities.

It’s all a conspiracy for colleges to make more money.

Think about it. We tell students they get free college. Colleges get extra state funding that would normally be sent to public schools. Incentive exists to have a placement test that forces students to start at remedial classes. That way high school students would have to take at least two math classes at the college before receiving even credit for one college level math class, which means more money for the college. The colleges can hide their greed behind the placement test scores and deflect blame to the bad high school teachers.

While I think there is an element of plausibility to the idea of a conspiracy, I have too much faith in educators at any level to be driven by greed.

The students just don’t test well.

Anxiety is a very, very real issue. But, ugh, come on.

If I am writing off the idea of anxiety as a reason for remediation. how is it possible that a student appears to be excelling in my class, but struggling with the same topic in another setting?

It’s my fault. I suck at teaching.

If it’s not the student and it’s not about greed, then it must be my fault. At least I am not alone in being a crappy teacher though. Roughly 20% of all college freshmen will take some sort of remedial class, and of those in the remedial classes, 4 out of 5 had GPA’s above 3.0. Since the early 2000s colleges have turned increasingly to placement tests like the Accuplacer, or standardized tests scores, like the ACT, to determine if students are academically ready for college level work. Colleges just want to make sure that students are prepared for the work they will encounter. I thought my students were doing well, colleges didn’t, therefore I suck.

 

It was during that year that I realized that there was something wrong with the way I had experienced education. I was 26, in my first year at my current job, and had never previously questioned the whole system. Sure, I had the sympathetic talks about schools being like prison, or generic work ethic or critical thinking dialogues with students, but I had always believed in the piety of the enterprise. That year started me on a journey that I have never abandoned.

Is Pre-Calculus Really Necessary?

I have a dilemma. This year I have two classes in the same period. Those two classes are Pre-Calculus and Calculus I, and I am not sure how to effectively teach both at the same time.

But first, some background information about the school, class, and teacher.

  1. I teach at a small school, so a class of 23 is large. 20 students are enrolled in Pre-Calc and 3 are enrolled in Calc. I traditionally have had about 10 in Pre-Calc with a max of 15 one year. I have never had more than 3 in Calc.
  2. It is a 45 minute period.
  3. Every students has had me for at least one, if not two previous classes.
  4. I haven’t used a traditional lecture for the previous three years.
  5. There is no state or district wide exit exam or set standards for either the Pre-Calc or Calc class.
  6. Because of the small number of students and my familiarity with them I had previously done some significant college work with the. Proof-reading essays, applications, scholarships, etc.
  7. It is not a college credit bearing class.

I should have had four or more Calc students, but several didn’t sign up for the class and some decided to switch to the College Credit Plus (CCP) classes that we offered. If I teach the same Pre-Calc I taught last year my three Calc students will range from bored to annoyed, not to mention that it wouldn’t sit well with me to have my name associated with teaching them two different classes on their transcripts, but in reality it was exactly the same thing. It would feel like cheating.

After I kind of exposed some people to my temper-tantrums of frustrations I began to try and think of ways I could make this work. I thought about  #5 and #7 from my list and thought about the topics I covered in Pre-Calc.  I started to think I could make this work.

But before I continue, let me provide a couple of beliefs that I hold as a teacher that greatly influence how I make educational decisions.

  1. We’ve gone too far with pushing math advanced math down on our students. Then society expects all students to master the complex math, which is measured through state level testing. Then funding and job security is tied to those tests and we wonder why so many students show up to college with glowing transcripts, but substandard grasps of basic concepts.
  2. Economic stability is difficult to achieve with just a bachelors degree from college, let alone nearly impossible for those with just a high school diploma. Hence I try to make my classes relatively easy to pass. I can’t justify judging a student’ potential to hold down a steady job based upon how well he or she could explain the subtle differences between ellipses and hyperbolas.
  3. I think it is of utmost importance that I prepare students for the math they will encounter in college. However, I believe that much of the math that is encountered in college will only be used as a gatekeeper to weed out students that are thought to be weak. This isn’t true of all college majors, but I think it is true of many, even some in the STEM fields. (When was the last time your dentist had to use Calculus?)

I found myself at a crossroads. The vast majority of my students won’t need advanced mathematics in their jobs, but they will NEED advanced math to get their jobs. With that thought I decided to give my students a survey to decide what topics I really should be teaching them. Here is a brief summary of their answers.

  1. College is a near certainty for my students.
  2. Roughly have will be majoring in a STEM based field.
  3. No one plans on majoring in pure mathematics.

To challenge my Pre-Calculus students, but still keep my Calc students engaged I am proposing dropping or extremely scaling back the following topics from my Pre-Calculus class. (rough time length follows)

  1. Verifying trigonometric identities. Especially my focus on having them justifying why                                    Cos(A-B)=CosA*CosB+SinA*SinB. (3-4 weeks)
  2. My unnatural obsession with the with the difference and sum of the distances between foci on conic sections. (3-4 weeks)
  3. Scale back the graphing of trig functions. (Used to go over many transformations, all six trig functions, inverses, etc. spending about 4 weeks or more. I think I could scale this back.)
  4. Since the class is so much larger than I had in previous years I don’t think I will lose critical mass as often as I did in the past. It didn’t happen often, but it is difficult to move forward with new material when over 50% to 60% or more of the class is gone. (1-2 weeks.)
  5. I would also stop some of the in-class college discussion that normally took place. (1-2 weeks)

All in all this would save myself 10 to 14 weeks of instruction. Ideally I would replace the missing topics with limits, derivatives, integrals of polynomials. I think I would have to sacrifice some of the specific topics from Calc, such as derivatives and integrals of trig functions, but I am not sure. Since most of the students leaving my class would start off in college someplace between College Algebra and Calculus I, I don’t think I would be doing any long-term educational harm. The more I think about the drastic restructuring I think it might actually be more beneficial to our student population than covering some of the specific topics in detail that I had in the past.

I never had tried it before, so ultimately I need advice. Has anyone tried this? Is this a good idea? Is a basic introduction to derivatives more beneficial than in depth instruction on trigonometric identities. I don’t know.

Help?!