Learning Isn’t Easy

One thing I learned the hard way is that grades do not reflect an level of actual knowledge. In my eyes many grades measure how many tasks a student successfully completed. I am not trying to be dismissive of hard work. I have numerous students that work really, really, hard, some that I think work way too much and are on the verge of breakdown. I even experienced the struggle with this myself when I nearly flunked out of college.

But hard work isn’t enough to actually master a subject. Doing hard work means just that, you’ve worked really hard. Learning will always come from struggle, but struggle by itself doesn’t produce learning. I experience this for myself several years ago in graduate school, and watch it on so many of my students regularly.

Learning, real authentic learning that leads to mastery of something that is actually usable, comes in fits and spurts, in flashes of brilliance at inopportune times. We can’t schedule learning. We can schedule training, we can schedule task completion, but if our goal in education is to have students learn anything in any sort of meaningful manner, the schedule inherently works against us. No matter what questions I ask, resources I use, if a student comes into class obsessed about the recently failed Spanish test or whatever, no learning will occur. I might be able to get compliance and task completion out of a student, but unless if that student’s mind is clear and ready, learning will not happen. We think we can multi-task, but in reality all we are doing is switching between tasks, and if learning is the goal, then switching between tasks is detrimental.

I can think of one example that recently happened. While teaching rotations in Geometry this year I have been relying on the coordinate plane. I was showing the students how the x and y value of coordinates move when rotated 90 degrees, or multiples of 90 degrees. When I was asked about rotations that weren’t 90 degrees, I told them that they wouldn’t have to worry about them. Why would I do that? We had already talked about trigonometric ratios, so, with the benefit of hindsight, I realized that we could have done them. I thought it through a couple of days later and came away slightly miffed that I hadn’t thought of it earlier. Probably just dismissed it because the book didn’t have any examples.

That bothered me though. It bothered me because it should be possible to rotate something that wasn’t a multiple of 90 degrees, and fortunately I was able to figure out how to do that. I had the opportunity to quiz my former students on the subject, so I decided to let them take a stab at the non-90 degree rotation. First I showed them what I had covered in Geometry, how rotating 90 degrees is like moving legs on an ‘L’.

Then I showed them what I wanted.

A student came up with the idea of using the 53 degree rotation as a percentage of the known 90 degree rotation, then using the corresponding percentages to change the x and y values.

Which produced the following result.

Now the point A (3,4) includes an angle of approximately 53 degrees, so a rotation of 53 degrees is a total angle of 106 degrees, or a reference angle of 74 degrees in quadrant 2. Well, I checked the trig using the proportioned A prime, and came up with slightly less than 72 degrees.

Well, that’s not 74 degrees, nor is that anywhere near the realm of rounding error in this case. But the method seemingly made sense, if the percentage of the angle should be the percentage of the sides of the triangle. Why wasn’t it forming the same angle? Later I made a little table to investigate what was going on.

Clearly, when I was using percentages of the sides I wasn’t getting the same percentage of the 90 degree angle. The more I thought about it though, I started to realize that at zero percent the length is 8, but then at 100 percent the length would be 6. That doesn’t make sense. Later, I took one more crack at trying to figure out why the percentages were creating a different angle than a rotation and created this picture.

That’s when I finally saw it. A rotation implies a circular motion.  Moving the point as a percentage of the x and y distance changes the distance from the center of the circular rotation. The bottom line of the right triangle is not broken into equal partitions because it is changing distance from the point of rotation. Using percentages the same percentages from taking 53 of the 90 degrees conflicts with taking the same percentages on a straight line distance of 7 units. The differences in the answers is because of the nature of the definition of rotation.

What did I learn from all this? About myself, I learned that my geometry skill is sorely lacking and very rusty. I also learned that I no longer have the trust to learn with the student in front of the students.

It also reinforced that the nature of school is not always conducive to learning. The students I were working with were capable of thinking of the answers. They even came up with a reasonable idea, but when they didn’t get the same answer as me they dropped the idea, writing it off to rounding error or just being wrong. This has nothing to do with capability. To learn is to devote every mental resource to a subject, to think, analyze, justify, and simply ponder. Our students are just simply too busy, they have to worry about 5 or more subjects, extracurriculars, college applications, part-time jobs, and any other myriad of activities. They just don’t have the time/interest/focus to clear their mind of all the other clutter to actually engage with math.

What the students want from me is clear, straight-forward, methods to find clear, straight-forward answers. They don’t have the time to think about open ended possibilities, there’s too much to do. But to really learn something, that’s what is needed, those open-ended, no solution, what do you notice type of questions that can spur a dialogue. How do I create that when all my audience really wants are the answers?

Why I Hate College…in High School

The push for college has grown to epic proportions, even since the 15 years it has been since I have been in high school. We inundate our students with message after message about going to college. We show statistic after statistic about how much college degree holders earn. At the same time we hear more and more stories about unemployed and underemployed college graduates. When a student will take the step to be forthcoming and tell us what path through college they want to take we often will respond with, “what are you going to do with that?”

We tell our students anecdotal stories about how pointless general education courses are in college. Why should I have to take X if I am going to do Y? We also hear how some of the general education courses can cause students who are capable of becoming productive members of a profession to drop out of college altogether. The only logical reason for general education courses for many students is to rationalize them as a sort of categorizer. We rationalize that the purpose of general education courses is to weed out the weak minded.

Some communities apply pressure to their children to get into the right school. They are worried about the brand that is attached to a degree.

Students in my community are under a different kind of pressure, cost.

Students chasing brand schools sacrifice happiness, and even health, in an effort to obtain that label. They want to be able to say, ” I am a Harvard graduate.” They want that elite label without having to be concerned without embracing the qualities that made that institution elite in the first place. Money isn’t the object here, it’s status.

I get the distinct impression that at my school students aren’t chasing the brand so much as the label of being a college graduate. They seek out the path of least resistance, usually in terms of lowest cost. Best case scenarios would be a path that would allow for the lowest cost and lowest effort. Our society has created an economy that has credentialed out many middle income professions to high school graduates. As more students enroll in college to gain access to decent paying jobs a gap in academic skills was noticed, which then led to the ever increasing push to have ever increasing academic standards since good jobs required college.

Those standards increased to the point where we as society felt that wide swath of high school students are adequately prepared for college and that spending extra time in high school doing busy work was unfair, hence the rise of College Credit Plus (CCP). CCP allows students to obtain for college classes which are taught on campus, online, or at the high school by qualified teachers. I see many detriments to CCP. The main selling point behind CCP is that students will save money when they eventually enroll in a four-year university because of all the general education courses they have taken. While I will freely admit there are students who would benefit from this program, I feel that there are far too many variables involved to broadly advertise CCP to the entire 7-12 student population.

As a teacher, since I am not qualified to teach CCP, I feel pressured to become qualified so that students would could take more math classes at the high school rather than taking them online or on campus at the local community college. Right now my schedule includes teaching upper level math, math that would normally be college level in content, but because I can’t offer college credit to students, they might choose to take their advanced math at the community college and get the credit. No one has ever directly stated that I need to go get CCP qualified, but when students are encouraged to take math else where that means that there are fewer math students for me. And if my classes can’t be filled I become unnecessary and can be let go.

In my upper level classes, Common Core provides leeway on what specific topics get covered. Because the upper level maths don’t have a state mandated end of course exam, I have the freedom to widely adapt the pacing to my students abilities. When it comes to the process of teaching I have to worry about local evaluations and OTES, but I have been allotted professional discretion when determining the content of my class. If I were to become CCP qualified I would lose the last vestige of my control, the content. My cooperating college would determine the pacing and assessments. As much as I want to the job security of CCP, I don’t know if I am willing to sacrifice my autonomy for it.

What really bothers me though doesn’t have to do with CCP, it is about the students. Every time students chooses CCP over my class they are essentially telling me that I have nothing left to offer them. Best case scenario, a student that takes CCP over my class is telling me that they are willing to sacrifice my class to potentially save about $600. In other words, students that sacrifice the college credit are telling me that whatever it is that I offer, it is more meaningful than $600.

I know not every student is going to like me or want to take class with me. That should be a given understanding of anyone who takes up the teaching profession. I do not have an issue with a student who wants to take math someplace else simply because of a personality conflict.

Where CCP is concerned, it forces students to make an economic decision regarding my value as an educator.I am worth about $600. My identity as an educator is being prostituted. As the deadline for my CCP application draws near I feel like I am caught in some horrible sting operation.

I feel so dirty.

My Goal: Make Myself Unessecary

In a three part series, I had laid out my brief journey of how I define my purpose as a teacher. In part three, I stated that my main goal, the one that keeps me coming back day after day, year after year, is to create free and independent thinkers.

Another purpose of maintaining a blog was to document interesting phenomenon as it occurred. I have several years of bound up frustration that I want to share with the world, but I want to record events as they happen, while they are fresh in my mind.

Recently I had one of those class periods where several students were out for a field trip at the end of an already grueling week, making for a period that the remaining students were pretty lackluster in their desire for mental exertion. We did a little review and then began talking. We started talking physics and one of the girls in class chimed in that she felt like she was only able to do the examples in class, that she need formulas to be able to accomplish the exercises. Here is roughly how our exchange went.

Me: “Why don’t you make up some problems?”

Another Student: “That’s what I did.”

Her: “I don’t know how.”


I go to the board draw a little scenario. We start messing around with the problem. One of the students puts up a formula involving the square of final velocity and gravity. We are hung up on the use of acceleration due to gravity and how it would affect projectile motion. Bell rings, but I am still intrigued by the problem. Luckily, she usually stays in my room during the next class and I keep going back to the problem every so often. Eventually I come to the conclusion that the acceleration due to gravity is unnecessary.

Her: “I said that a long time ago.”

She was right, she did, but we had discounted it at the time. That, and she didn’t state that gravity was not needed she ASKED if gravity was needed. When she asked she is admitting that she wasn’t sure. She is admitting that she doesn’t want to support her idea. She is looking for me to support her idea because if I do it she can remember that she is right and never has to find a reason why her idea was right. She is granting me the power and authority of knowledge and admitting weakness.

I dismissed her because I didn’t know better. She stopped because I didn’t affirm her. What should have happened was that she would have challenged my dismissal and forced me to see how her idea was correct. She is acting as a microcosm of how school functions for many of our students. Too many of our students seek the approval of their ideas from an external source (teachers) rather than reason out the correctness of their ideas for themselves.

That’s my goal though, to rectify that scenario. Every time a student leaves my care answering every question with a question, seeking that approval, I feel like I have failed. Every time a student leaves my class feeling good about their grade, but not sure of what they know, I feel like I have failed. I want my students to be able to confidently answer questions, to reason the answers for themselves. My students should eventually view me as a resource, but not a necessity.

Maybe this isn’t such a good goal.  Is it really a great idea to make myself unnecessary?