Parting Thoughts

This Wednesday I ended my tenure as a high school mathematics teacher for the algebra II program that lasted five weeks. I feel that it was the most fun that I have had in a job so far and also the most rewarding. The students mathematical improvement from the pre-assessment to the post-assessment was astronomical and my co-teacher, a veteran of many years, said that he had never seen such an improvement. We had a bright group of kids and I like to believe that I helped them reach their potential in the classroom.

Hopefully they take their newfound math knowledge to the classroom during the regular school year and I know that this experience as a teacher has not only shaped my introductory experience to the profession but has also made me a better learner. I know how to dissect topics more in-depth which gives me an opportunity to create a more fundamental and powerful understanding of the material.

I do not foresee this experience being the last time I involve myself in secondary education. These students are our future and I hope to lend a hand to help guide them in the right direction as I pursue a career of my own. Thanks again to everybody who has read these posts and feel free to voice your opinions, comments, or general thoughts!

- Elijah

(Very) Quick Thoughts

Nothing too big today since it was an old 8am – 8pm day today because of preparation and attendance of my first parent night. Just wanted to give a quick thank you shout out to those of you who have been following this blog! Teaching for me has always been about bringing people up as a community and the more the knowledge is spread, the better. Tomorrow is the last day for me…one of the students today asked how I felt about it being the final day and I definitely said that I was sad. It’s been such a blast and an affirmation that teaching and youth education and empowerment is truly a passion that makes getting up early in the mornings to a relatively underpaid job no problem.

One thing that I will say that was reiterated often during the initial meeting was the sense that this program is a family. I definitely got that sense and felt that here. Without a doubt, it makes learning and education much more enjoyable.

And this might also be the shortest post I’ve ever done ever on the internet so enjoy because don’t count on it again J

Grading high school math students' papers

Grading papers…the bane of every teacher’s existence. My students have two big project assignments during this five-week program, and I was responsible for grading the final project this weekend. I dreaded it because I had never been in this position before—analyzing the grade that someone deserves rather than the other way around.

First, I established a rubric of sorts. Using the prompt that the students had to follow, I created my point allocation. Although it was a projectile motion math problem, the process and instructions had students follow a four-section science-type template. As a biology major and someone accustomed to this format, I found it refreshing to see it presented outside of the science classroom. Even though the problem has physics implications, the problem was catered to parabolic and algebra II-prepared students like mine. I initially intended to grade one section at a time (ie section I for student 1, student 2…then section II for student 1, student 2…etc.). After realizing that I wanted to be able to judge each students work from a holistic approach, I decided that grading an individual completely before moving on was the way I wanted to go.

Common mistakes were prevalent and there was incomplete work that disappointed me. Despite giving the students ample time in class, there were still those who said that they just couldn’t figure some part(s) out. Out of 10 total points, passing (as determined by the program’s administrators) is a score of 7. Only four or five students did not pass, so they will be turning in rewrites shortly.

I was happy with my consistency as established by the prompt and felt that my justifications were appropriate. No students complained about grades which was a good sign, too. Although I would have modified the rubric because I didn’t feel the prompt allocated points the way that I liked, I felt that deviating too much would not have been fair to the students. As a student myself, anything that is not explicitly asked for is not fun to deal with. (Maybe that’s why I prefer hard sciences to social sciences…) So even though my co-teacher mentioned that I had flexibility and leeway to grade however I chose, I wasn’t comfortable modifying the rubric from what I interpreted the prompt asked for.

More students passed than I felt earned a passing grade. However, now the end of the program is less than 48 hours away, so I didn’t harp on my qualms. The discrepancy between my preferred grading and the way I interpreted the prompt was there, but at least I got a taste of the struggles and time consumption that grading papers takes.

Honestly, I found it a bit fun after feeling I buckled down on my consistency. Some of the answers were amusing… “well, I don’t believe there can be any other answers, unless there are other answers. In that case, I’m not sure.” Sounds like some unintentional life advice from a 14-year-old.

Student demographics and teaching

As a white male coming into a job with exposure to a diverse population in my undergraduate career at University of California, Berkeley, as a student and as a tutor, I expected Oakland to be much of the same. Although Berkeley has a predominantly white and Asian population, I loved being exposed to more than the largely biracial community that I grew up in (white and Latino). Growing out of my comfort zone and “bubble” as a kid was a great entrance into the adult world. 

Walking into the assembly room to greet all of the students on Day 1 of this teaching program, I could not see a single white student. And out of maybe 20 staff, there were only two other white teachers. The vast majority of the population was Latino/a. At that point, I wondered if this would be a different experience than I was mentally preparing for.

Then when I walked into my classroom, I found that only about 4 of the students were boys.

But you know what? Despite the observation that I was the only white person (and one of a handful of males) in the classroom, I felt at home with the kids. Aside from the fact that I really need to become fluent in Spanish—three years of it in high school can only get me so far—I have appreciated and loved the opportunity to have such a new experience. And I felt like my colleagues in the classroom (co-teacher and tutor) were friends. One observer said today after spending time in our classroom that it felt like a comfortable/warm environment.

One of the white staff members did not feel the same way as I did. This person said something to the effect of he/she felt it necessary to walk on egg shells with minority students because they did not want to cross any boundaries. I said, “wait, really? I don’t think that’s true at all.” At this point, I had taught maybe a week but he/she had been teaching for years. I continued: kids are kids. As long as we provide them all the equal opportunity and respect and show that we care, why treat people that look different from you differently...especially in the classroom? Wasn’t that the root of the problem in the beginning anyway?

I did graduate on the 60th anniversary of Brown v. Board of Education.

My main point was this: come down hard on anybody who needs it. As long as they know that it’s out of love, they should respect and take your comments to heart. I’ve found that philosophy has treated me well so far…but there will be a moment of truth tomorrow to see if the students that I came down on today come through. 

I believe that they will.

Dealing with difficult students

I want to preface this post by saying that I recognize that my class of students has not been insanely difficult. Maybe it’s my approach or tolerance, because other teachers have complained, but I have felt I am in a great situation. The classroom management that I had to deal with was nothing insane. I mentioned it in one previous post, but there was one student that I had to give a referral to the program’s associate director. This student was ignoring instructions repeatedly and it became a last resort situation because I did not want the class to get out of hand. Anyway, she came back later that day and everything was fine. The worst problem that I have had is two girls who have a teenage sassiness about them that is unlike anything that I have really seen.

These students “misbehaving” comes in the form of lack of responsiveness to questions. They hardly engage in activities and actively seek to ignore requests from me, in particular. I do not appreciate this and really could not understand where it was coming from. I repeatedly sought to help them out during problems sets in one-on-one situations and it was just as bad, if not worse, than classroom lecture situations. “So, how are you doing?” I would start off, innocently and openly. One huge sigh, a binder slammed shut later, and looking away from my direction, I got the idea of how they felt. My co-teacher repeatedly said to not take these things personally. I tried and tried, but I did feel it was personal and really did not understand the root of the behavior. Had I said something? Why was it two friends doing this? And why would they sometimes actively seek me out for help while most of the time ignoring me?

Earlier this week, I was grading one of the girls’ classroom journal entries. (We have the students spend the last 5-10 minutes of class writing about a topic of the day, to give them a chance to express themselves other than the mathematical equations that they’ve been solving all day.) The topic was “who would you go back in history and talk to?” She chose her mother. When she was young, her parents were divorced and she spent her childhood with little exposure to her father. This was something that she clearly resented. In her journal, she talked about asking her (younger) mother why she made all the mistakes that she did. I found it a brutally honest openness from a young girl who, as my co-teacher said, must have clearly thought about this previously. Her lack of candor in words was more clearly expressed on paper.

You really never know what’s going on inside of a kid’s head. I know that I will look at her with a renewed respect and acknowledge that what she has gone through must not have been easy. Even if she and her friend still ignore me, I know there are probably some more deeply seeded problems that I can’t really scratch the surface of in the position that I am. She’s a smart kid in the classroom so I’ll take my worries about how she treats me to this internet space. In the classroom, I’ll do what I can to help where I can, and let her be her. 

Learning as a teacher

I have learned a ton in these short four weeks as a math teacher. More than I could have thought I would, which has made coming to work every day constantly exciting. Since my time in the classroom is wrapping up soon (next week), I thought I’d share a few lessons that stuck out.

To be a good teacher, you have to be a good listener. It seems somewhat counter-intuitive…why would someone teaching a subject need to listen? You’re instructing, after all. What I’ve found is that planning is really only a small part of teaching. Of course, to be a good teacher, you need to know the material and be able to present it in a logical fashion. But it’s the improvisation of answering students questions that is what makes a really good teacher. 

It’s prodding students with endless “why?” questions to see if they really understand the material and are not simply regurgitating it. It’s walking around and seeing their work, finding not only specific struggles for students but also general trends. One other prospective teacher asked "what if they ask X?" and a veteran teacher said, "what if that happens? You can't prepare for everything now." Use what you know and what the students know to fill in the gaps.

For example, I taught a lesson today on graphing y = 1/x. From a class poll, the students had not seen it before. We went to a t-table and plotted (my carefully chosen) x-values with their tabulated y-values. But I noticed that many students wrote that 1 divided by 0 was either 0 or 1. Instead of just telling them “no, that’s wrong.” I wanted to get them to understand why it was undefined. To do that, I needed to come up with an on-the-spot analogy that would makes sense. So I asked, what’s 6 divided by 2? Everybody shouted out the answer. Why, though? I ask. Because 3 times 2 is 6! So the sky is blue because blue is the color of the sky? And so on. 

After considerable prodding, we got to the root of what division really means and why there is no combination of groups of zero that can give you six. A follow-up was why is division the same as multiplying by the reciprocal? At a certain point, we all take these facts to be just facts. Even I found myself starting out with some things thinking “well, that’s just how you do it.” But listening more acutely allowed me to fine tune my teaching and hopefully give students a deeper understanding of what they were doing.

Getting the answer, even in math, is not enough. Comprehensive understanding and a curious mind are what will help students succeed in subjects more than just math.

(Part II, with more lessons learned, will be soon.)

Perfecting pacing

I had no idea what to expect of the students abilities on Day 1. Sure, this is an Algebra 2 class, and yes, I know the students are generally somewhere in the middle of the pack in terms of ability. But to a new teacher what does that really mean? I recalled the Algebra 2 material when going through teacher training, but trying to decipher the students’ background mathematically worried me initially. To complicate matters, these rising tenth graders came from more than a couple high schools. As we all know, that adds even more variability to the equation. As a tutor, I never had this worry because I could tailor my teaching to one student. Using the Socratic method, I could probe students and find out exactly what they knew and where the gaps in knowledge were. I could spend time creating brief examples to illustrate how to approach homework problems that they struggled with. In a classroom setting, that is often not feasible.

The pre-test that we gave the students on Day 1 was not very helpful. Few could recall how to solve systems of equations or graph non-linear equations. My co-teacher re-assured me that this was normal and it just means that we hit on the necessary topics to build the summer around. We designed the entire curriculum from scratch. So when I got up in front of the class for the first time, I had no idea if I would be talking to students thinking “oh my, this guy thinks that we are kindergarten students” or on the other end of the spectrum thinking “is this dude speaking English?”

I started off with a slow pace. Explain as much as possible without detailing the basic arithmetic. I found it made things run smoothly for the majority of the class. There is one student in particular that I am concerned about, but other than that, I have been impressed.

That positive impression gave me the feeling that I needed to speed up. My co-teacher sat in the back of the room after one lesson where I really picked up the pace and confirmed what I surmised. Based on the blank stares I received while delivering the lesson, I went too fast. Slow down, ask the students questions, keep them engaged, and double-check that the material makes sense.

There is a happy medium to pacing. I talked about this with a teacher who has been in education longer than I have been alive and he said even he still struggles to hit that sweet spot. Those were reassuring words. I’ve returned back to a pace that the students seem comfortable with but it’s a constant fine tuning process. And I’m enjoying every minute of it.

Effective group work in math

Math is not generally thought of as a collaborative activity. A teacher gives a lesson, students ask questions, and complete assignments and tests individually. The strong movement toward group work has only really begun in the last couple years. Particularly with the Common Core, American mathematics is being pushed in a positive direction. The Khan Academy has been another important tool in assisting a change from the traditional lecture-homework style of learning. Khan Academy has even embraced the Common Core within their own program, which should help promote the standards country-wide.

I implement collaborative activities in my own classroom in the form of activities and group work. Whether it’s using “angry birds” to model parabolic motion or getting them to work together on problem sets, I’ve been incredibly impressed to see how they work together. My co-teacher taught me this great “fishbowl” activity, where students observe a group of their peers—usually three or four students—who work on a (doable) math problem. The observers are instructed to take notes not on the correctness of the math being performed but rather the group dynamics. This includes the brainstorming of approaches to solve the problem, the creation of a poster to present the problem and solution to the class, and the actual presentation itself. I believe that this helps instill self-awareness in the students. After this activity, they can think “oh, do I step back and not do much during group work?” or “do I tend to dominate a group?” It just so happened that the most recent group that we randomly selected worked together nearly perfectly. The group dynamic was textbook with equitable contributions.

Creating a good group of three in any situation does not have to mean putting a top student with an average student with a below-average student. My co-teacher and I generally do not match students based strictly on ability. I have found that often the case may be that the top student simply does all the work if only ability is considered.

A more effective way of making smaller student groups keeps in mind the personalities of the students. Pairing an outgoing and talkative top student with a shy and unconfident student will only exacerbate the shy student who might need more time to think about the problem. Taking into account factors like this is really critical to creating effective groups. While eventually group work cannot be this highly specified in a classroom setting or otherwise, at a high school level, I think this is important to consider. I have been impressed with how the students work together if not just ability but also personalities are considered.

When college rolls around for these kids, studying in groups is a critical tool to have in the toolbox. Some students may prefer it while others may not, but ample opportunity in their K-12 education gives them the chance to see through trial and error for themselves.

Mathematics and the age old boys vs. girls debate

Previous generations of Americans saw tremendous disparities in the number of boys and girls that excelled in math classes. Women would either be discouraged from or discriminated against achieving on the level of men in math and sciences. However, my own personal (and more recent) experience in the American public school system has seen a much different angle. In my childhood, I saw that the other high achievers were as likely to be women as men. It was probably relatively close to a 50-50 balance in my AP classes, a far cry from the male bias of previous decades.

I see a more visible, perhaps even counterintuitive, disparity as a teacher: the girls in my class far outnumber the boys. I was shocked to see an approximate 3:1 ratio of women-to-men in my classroom. Talking with my co-teacher and the program’s director/principal, I learned that a larger trend is also apparent program-wide. When the students come into the program in middle school, the gender split is fairly equitable. As they grow up, the boys drop out at a far faster rate than the girls…and you end up with advanced high school math classes, like mine, with a student body largely composed of girls.

The ubiquitous studies on the gender gap in math show that as an entire population that males generally score higher than females. I have yet to come across studies that analyze the lower-income communities, though, like the ones that my students come from. And personally, I have yet to come to a satisfactory reasoning myself as to why this may be the case. Former Secretary of Labor, Robert Reich, once mentioned in my lectures that the current school system favors females because males have a harder time sitting around longer. Could this thought be exacerbated as the males feel more pressure from their social environment? What other factors, maybe even confounding ones, nuance this discussion?

We often focus on the high achievers who may skew our understanding of the overall achievement of our society. As you can read in my about page and see in the header, I am new to teaching. I am striving to understand and work on not just the microscopic level of teaching for students’ success but also gaining a broader perspective on the American education system. Particularly as to how it relates to mathematics. I’m very curious to see what the future hold for American male and female students in terms of math education and STEM-related careers. 

Teaching students to love math

I love math. My parents spent hours on a near-daily basis with me doing math before even kindergarten, so I came into school knowing multiplication when most kids were learning how to count. It became something I was good at, too, which also helped immensely. Some combination of parental enthusiasm, early exposure, and a stress-free environment helped me succeed in mathematics. That is certainly not the norm though. Lack of exposure, poor teaching, mathophobia, and any number of factors (algebra 2 joke intended) lead to a lack of enthusiasm by the vast majority of students when it comes to math. The collective result is the United States math scores falling below the top-25 nations in the world.

My goal coming into this teaching experience was to pass my love for the logic and beauty of math onto my students. One of my personal friends asked the natural follow-up question: so how do you plan on getting them to love math? My short answer had four components, the first being to show excitement and be upbeat myself. People, and especially kids, are very attuned to the energy that someone gives off. If I’m visibly dragging through the day and the lessons, they are going to do the same. While I’m not the rah-rah cheerleader like the tour guide for our class’ recent college campus tour, my general positive energy in tutoring has helped me achieve this goal previously, so I aim to stick with that. These students noticed the tour guide’s enthusiasm when asked, so even if they don’t directly articulate it, they at least subconsciously notice their teacher’s energy.

Complementing students and giving them an opportunity to “show off” to the class if they do get the right answer are two more cruxes to helping associate math with enjoyment. Confidence is critical to success in anything. Math in particular can get difficult and annoying when someone does not understand it and loses confidence. It gets even worse when they start to fall behind. Recognizing students’ small achievements and patting them on the back is important.

If a student does fall behind, that’s where the final component of my strategy, one-on-one attention, comes in. Struggling is tough, and struggling alone is miserable. It’s a vicious cycle that can only be broken by showing the student that you care. Walking around the class after assigning problem sets is crucial to assessing and addressing individuals who are slower to pick up the material. Then, by giving one-on-one attention to someone, I can show that I care about their personal well-being and their achievement, I believe that will help students begin to love math. It can be an enjoyable struggle. Learning isn’t easy, I like to say. If it was easy, are you really learning something?

Sadly, it often isn’t this simple. For whatever reason, a student just might not be able to "love math" in the allotted time that I can teach them. My co-teacher, who has years of experience in high schools, said one thing that has stuck with me: yes, our personal goal may be to get a student to love math. Sometimes it just will not happen, and it’s important to recognize that our ultimate goal is just to get them to pass. There should be a clear hierarchy then of my two-fold goals mentioned in this blog’s inaugural post: first, get them to succeed (or pass), and second, help them love it as a subject. I’m not sure this mindset will help produce more STEM college majors and math/science professionals, but it’s what I have to work with at this moment.

Adding humor in teaching

I take education quite seriously—as many people that know me can readily attest to. As someone so focused on the lesson material and the education, humor in the classroom was not something I naturally gravitated toward. My co-teacher and mentor opened the doors for that opportunity. Or more appropriately, he demolished them and opened the floodgates for humor. Even though students don’t laugh at all of the frequent jokes he makes or the people he pokes gentle fun at, the students do find his puns amusing. And it keep them on their toes.

At first, I wasn’t too sure about adding humor in my teaching. (I know, even that sentence sounds like a mathematical formula I’m plugging into my brain…does teaching + humor = success?) After all, shouldn’t education and the learning experience be taken very seriously? Throughout these past few weeks, I’ve noticed that laughter and humor in teaching is extremely valuable. For one, it helps relieve the pressure of learning material. When students see that their teacher is having a good time and challenging students in a humorous way, it helps keep the mood light and the students engaged.

Joking around adds a personality to a teacher. Students often have a hard time picturing their teacher as a human outside of math (or whatever subject that they teach), but humor gives a teacher a personality and ultimately relatability. This relatability is a valuable asset. It helps students listen to someone who would look more like a human than just a talking calculator.

Of course, there is a fine line that bridges humor with insensitivity. My co-teacher/mentor has shown, by example, the areas where to be funny and how to keep things light. Now, this is not to say that students cannot take a humorous teacher seriously. My co-teacher and I have both had serious discussions with the entire class about classroom management issues (something I will talk about in a later post) and each referred a student to the program’s director for disciplinary issues. This balancing act of being serious about learning but not too serious where you can’t have fun has been something I am working on learning.

Humor definitely may not come naturally to everybody. I know it does not come as naturally to me as it does to my co-teacher, but it’s something I feel I will continue to work on. Just like anything else, I feel that being funny takes practice. Don’t take students remarks too seriously—and for that matter, don’t take yourself too seriously…or at least that’s what I tell myself.

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Teaching for Students' Success

I came into the classroom for the first day as a teacher with my tutoring mindset. My goal was, and is, two-fold: 1) get the students to succeed mathematically and 2) help the students love math as a subject as much as I do (okay maybe as much as I do is unrealistic...but still, appreciation is a goal of mine).

The challenge arose with what I defined as classroom mathematical success. My desire to make about 20 students understand 100% of the material that I was teaching made Day 1 overwhelming. I came in confident in both my knowledge of the curriculum and my communicative abilities, but I wasn’t ready for the flood of different personalities and abilities. As a tutor, I worked with students who virtually all wanted to learn -- which is why they were seeking help. Obvious newsflash #1 to myself: not all high school students want or are able to sit in a classroom and learn mathematics. Their reasons could vary from simply the newfound raging hormones coursing through their veins to family and psychosocial issues.

After teaching a lesson, I walk around the classroom, glancing over students’ work on practice problems that I assign, trying to see if they understood what I had just taught. If I saw a student that did not understand, I’d kneel down or pull up a chair and guide them through the process. (I find it important to meet at eye level with the student and not literally look down on them.) The tutor in me wanted to spend the necessary time to give each student enough time to master every concept. I ignored the basic math that averaging 5-10 minutes per student times 18 students is going to translate to a very slow paced class -- and one that leaves the top 50 percent of the class occasionally bored. Even with two other adults in the classroom (a second co-teacher and a tutor), it was tiring and ultimately unrealistic to get 100% of the class at 100% comprehension.

Reconciling my desire for education with the reality of time constraints and students’ abilities (both inherently and based on previous education) has been my first true challenge. Being adept at explaining topics in multiple ways is critical, and presenting material in a digestible and logical manner is something that I expected would carry the load. Within this early stage, I’ve realized that isn’t the case. However, I am paired up with a great teacher who has taught high school math for many years. I’m ecstatic that he is my mentor as someone who will continue to be critical to my development as a teacher.

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