Math Class: A Haiku

Irately I pace
back and forth 'round the dazed class
shouting about numbers

Writing About Writing

        There is a lecture I give to my GED students as I prepare them for the essays they must write as a part of the exam. It begins, "There are three ways to write about someone else's writing." I go on to explain the concepts of paraphrasing, summarizing, and quoting. Today I've been asked to write about my own writing experience in the last 9 weeks.
        A summary, I explain to my classes, is an explanation of just the author's main ideas in your own words. It condenses a piece of text and gets straight to the point. I would sum up my writing in the last few weeks as a strong start with poor follow-through (how typical of me and my average student!) and more negative than I wanted it to be. When they asked me if I wanted to do the 9x9x25 challenge, I honestly thought it would be simple, not really a challenge at all. After all, I love to write, I already blog and I'm a storyteller by nature. It hasn't been the experience I expected, however. I have fallen short of my 9 posts because I got stuck good and deep in the seventh week. Somewhere 7 or 8 paragraphs into a blog post/rant, I came to the realization that my writing has been overwhelmingly whiny, a laundry list of complaints about the system- from testing, to former teachers, to other professors, to my students- and I didn't know how to dig myself out of that hole. Because that really isn't how I feel. I love teaching. It's not infrequent for me to leave class singing. My students energize me and infuse me and I invariably leave them in a better mood than I walked in with. So why the preachy passages each week?
        A quote, I go on to tell my students, is the author's ideas in the author's own words. However, I always warn, quotes should be used sparingly and only when the author's words are so beautiful, powerful, or vivid that you could not say it any better yourself. The latest blog began by explaining my long history of getting emotional about education like this, "When it comes to learning, I've always had what could best be described as an overdeveloped sense of self-righteous indignation." It went on to describe in detail incidents where I have lost my cool at various teachers over the years as a result of letting that indignation win out over my common sense and finally settled into my latest diatribe against a certain large publishing group's online learning program that my students were struggling to use. 
         I define a paraphrase as all the author's ideas in your own words, clarifying that since this method gives you roughly the same amount of text as the original, it's best suited to writing about short pieces of writing or for supporting details you'd like to use to back up your points. According to that probably never-to-be published post of mine, the mandatory pretests meant to assess students current levels were poorly designed; the content was organized and presented in such a way that is would only overwhelm and bore my students; and the body of material covered was unlike that which is tested on the actual GED. Because of all this, I went on to say, this program should not be mandated for use in our adult education program (which it is.)

       Can you see why I got stuck? I just had nowhere to go from there. For two weeks, long after the post was due, I kept coming back to that lengthy diatribe and rereading and editing what I had already written but couldn't seem to finish it on a positive note. Personally, I despise a whiner who complains and complains but has no better solution. Ask my students; I scold them for it. There I was, moaning about a problem, with no solution at all. Finally, I realized I needed to do something more productive about my problem than a blog rant.
        So, don't expect anymore posts from me for a while. If you need me, I'll be in my office, busily typing away. I'm working on a new project- YC GED classes in Canvas with my own assessments and my own content- an online class that actually aligns with the GED. And you can quote me on that!

Testing, Take Two

     I'm doing it again. Here I am in a peaceful and silent classroom administering a test. The only sound in the room is the hushed clacking of my fingers on the keyboard and the feathery whisper of turning pages. My attitude today, however, is much improved over our last little chat about testing. This week it's TABE post-test time. The majority of my GED class members have reached their State mandated 30 or 40 hours and must be re-assessed.
     Yesterday when I started this process with my Mon/Wed class, I was apologetic. "Sorry," I kept muttering to student after student as I passed out tests, "We're required to do this. We'll get back to learning tomorrow." One student remarked that they almost hadn't made it to class. "Now that you know we're taking tests today, I bet you wish you hadn't!" I quipped. Her retort surprised me. "I'm glad I came," she pronounced with a grin, "I want to see what I've learned." Of course, not every student reacted so positively: some were silent, others groaned or sighed, one even jokingly protested, "I can't believe you're doing this to me!"
       As soon as I started grading, though, my attitude began to change. There I was, in front of a productive and quiet classroom, answer sheets spread before me and purple pen in my hand, beaming. With each test I graded the urge to jump up and shout, "Hooray!" grew. Every time I pulled another learner out into the hall to share the results of her test with her, I had to make a conscious effort to keep my voice moderated so the rest of them, just inside the door, didn't hear her scores. The scores were beautiful! The progress was there, palpable for the students and for myself. Obvious. Self-evident. Crystal clear. These results could not be argued with. They were up a grade level in reading or two in language or even four in math. And the students' reactions were priceless! They were excited, pleased, proud and grateful for this bit of tangible validation.
       The average GED student hates tests and hates receiving test results. The average GED student left high school motivated, at least partially, by the dismal results of a few too many disappointing test scores. For once, an exam did not defeat these knowledge seekers. Instead, this week's test scores were a triumph! They directly addressed many of the lies that these students have bought into over the years about themselves and what they are capable of. The scores echoed what I have been telling them, "This isn't that hard; we can do this." They confirmed, "Your hard work is paying off." They shouted, "You, yes you, CAN learn." Today, for that gift to my class, I find myself thankful to those beautiful, blessed tests.
       And my students weren't the only ones receiving gifts. This morning in the hallway, as I shared the results with one young woman (up 2.5 grade level equivalents in math and 5 grade level equivalents in language, thank you very much!), she threw her arms out and hugged me in glee. O, what a test can do!
   

She: The Unreachable Student

       She sits in the far right corner of my classroom, arms folded over chest, hair falling over eyes. She never makes eye contact, she never asks for help, and she certainly doesn't talk to me or smile. When I walk around the class, as I do frequently, checking for understanding, she has the arm block perfected, body hunched over, arm curled around her workspace, a defeated embrace that prevents me from assessing her ability. At the end of class, she shoves all that work into her notebook and shuffles away, leaving me with no measure of her progress. She has been the one I simply cannot reach. I have made jokes, appealed, cajoled, smiled, begged, coddled, and scolded. Each of my attempts at reaching her and gaining her trust have been met with the same sullen wall of blank apathy.
       This is exactly the kind of student who shakes me to my core. I have prided myself on winning over the difficult ones, calming the anxious ones, and enlightening the befuddled ones. Am I not the teacher I thought I was? What am I doing wrong? Driving home each night, my stomach churns as I rerun the class, trying to decide if I lost her or I bore her. Perhaps I didn't explain the concept clearly enough and her attitude is just a front to mask confusion? Or is it that she knows all this material already and she's frustrated with the slow pace of a GED class? There's no telling really; she's not enlightening me no matter how I've questioned and I won't force the issue for fear of driving her away. If nothing else, her attendance is regular and she does what's asked of her even if she won't let me see the work.
       This has been our uncomfortable biweekly dance for the last 3 months until just this week, when a slight shift occurred. This week, as our final science lesson, I taught a lesson on ecosystems. As usual, her narrowed eyes fixed intently on the wall somewhere slightly to the right and above me as I taught. As usual, her face didn't flicker, her expression didn't change. When I divvied up the class into groups to work on creating food webs featuring different biomes, she participated. Slowly and sullenly, but obediently, she began the project, reading the packet on temperate deciduous forests that I assigned her group. Even when I made my offhand remark to the class, "If you aren't artists, that's fine. Just write the names of the organisms in your web. However, if any of you are blessed with any artistic talent, the walls of my office are pretty bare. I'd love to see some pictures," I didn't notice any shift in the atmosphere.
       Something happened as I was making my rounds, though. I worked my way through the classroom, quietly muttering things like, "the arrow points to the consumer," and, "are you sure manatees eat fish; I'm pretty sure they're herbivorous." I happened to catch a glimpse of a corner of her food web that had snuck out from underneath the wall of her arm. Oh! A deer! And what a beautiful deer it was. "You're so talented!" I exclaimed. Apparently, that wasn't the right thing to say either because she frowned and quickly hid even the corner of her page away from me again. A quarter of an hour later class was over and I collected the food webs, thanking those who had put illustrations in theirs and remarking how nice they would look on my office walls. The web she slid across the desk to me was beautiful. Each creature was drawn with remarkable skill and vivid personality: a squirrel, deer, a wolf, even an earthworm. It was such a work of art that I showed it off to the subsequent two GED classes who were doing the same project as an example of what they could attain to.
       The next class period, I thanked her again, telling her I had used her lovely web as an example for my other classes. If I thought that would melt her icy expression, I was wrong. She didn't say anything in return and she didn't appear to warm to me at all. And her attitude? Well, it didn't seem to change a bit either. Another 3 hour class went by just as all the others. At the end of the evening, as I wrapped up class and said my goodbyes and have-a-great-weekend's to everyone, she hung back in her corner, clutching her stack of books and avoiding my gaze. Finally, as the last of her chatting classmates trickled out through the door, she walked up to me, thrust a piece of paper into my hands and hurried out into the hall. In shock, I surveyed the sheet of scratch paper. Most of it was taken up with side work from solving 2-step equations with integers but on it were two drawings: an exquisitely detailed illustration of a proud dragon curled up in the right hand corner of the page and the head of an animated wolf in the opposite corner. For once, my drive home was joyous; what a relief! And do you know what I did yesterday? I hung a food web, a dragon, and a wolf on my office wall.

This is a Test- This is Only a Test

       It's another Saturday morning and here I am in a quiet library doing it yet again: administering a test. As usual, I shook a new tutoring student's hand, sat her down, had her fill out form after form, then slid an answer sheet across the table to her and started the timer. This time it's a GED practice exam. It could have been reading fluency, a driver's permit practice test, or basic math skills. They're important, these assessments, I know that. They give me a starting point to launch from; an idea of where this individual has been, academically speaking; and a measure of how far we have to go together to accomplish their goals. Most importantly, they give me a baseline to report to my students' counselors, my real bosses, to which they can compare future scores. After all, they need some way to measure if our tutoring sessions are worth the pretty penny that the state is dishing out for them.
     This same tutoring client also joined my GED preparation class this week at Yavapai College. What was the first thing we did together in the classroom? Again, mounds of paperwork and then 8 tests all in a row, this time the TABE. The first three class hours I spent with her consisted of this one-sided conversation and the sounds of pencil scratches and page turning: "You have twelve minutes, please begin....You have 5 minutes, please begin.....You have 8 minutes, please begin....You have 12 minutes, please begin....You have 25 minutes please begin....You have 15 minutes, please begin...You have 25 minutes, please begin....You have 25 minutes, please begin." By the end I was apologizing to her, "I'm sorry. This is the worst day, I swear. Class will get better." I let her go wondering if she would come back. Would you?
      I didn't even have the heart to tell her she's not done yet. Chances are good that she might have to retest in one or more of the subject areas. The way the TABE is designed, the first four tests are "locators," meant to narrow down what general level a student performs at in each subject so that you can give them more tests at their ability level and further pinpoint their grade level equivalents. That's how those locator tests are supposed to work anyway. Frequently though, the student doesn't end up with a final score in the range that they should based on their locator. In that case, the score is deemed out of range, and we are required to retest them as soon as possible. Almost half my class needed at least one retake at the beginning of the school year. I'm not the only one; the instructor I share an office with has been bemoaning the fact that many of her retests were still out of range and those students needed to be RE-retested. Additionally, once the student has hit 30 or 40 hours of instructional time, depending on their level, I'm expected to get another round of TABE testing out of them to obtain that all important data. Eighty percent of them have got to show progress in their weakest area after 30-40 hours of instruction. It makes sense, it does. After all, our program is funded by tax dollars. The State needs data, The Federal Government needs data. How else would we get standardized, objective, quantifiable data?
       How else, indeed? I began this blog last week Saturday and I've been pondering this question since then trying to come up with a moral to my tale, a positive take-away. If not all the tests, what? I still don't have an answer and my midnight on Sunday writing deadline looms. However, there are a few things I do know. "Because it's on the test" is not enough relevancy to make a concept matter to my students. Some of them may never finish 25 math computations in 25 minutes but that doesn't mean they can't learn the concepts.  Most importantly perhaps, test scores only reflect one aspect of their classroom progress. There are so many valuable and important lessons that I watch my students struggle with and finally grasp that cannot be measured by any test score. There are students who realize they are capable of things they never thought they could do, like algebra. Students fall in love with poetry or develop a passion for numbers. Others who once rolled their eyes and sat with their arms folded begin leaning forward and listening, curiosity sparked.  Students who originally trembled when asked to introduce themselves begin participating in conversations. I have no way to report this data but that doesn't make it any less valuable. Not all learning is quantifiable.
   

Mathematical Reasoning Cannot be Taught: A Cautionary Tale

       "How idiotic to require education students to take this class!" spat professor Guerzhoy, "This type of reasoning cannot be taught. Either you are a mathematician or you aren't." The four other education majors in the class seemed to shrink further into themselves, a pitiful island of students huddled against the far left wall of the classroom. I tried not to blink. I always sat in a neutral space mid-room, straddling the fence between the education students and the math Master's students who filled the right. Between that and the fact that I occasionally got glimpses of understanding regarding the abstract algebra Professor Guerzhoy scrawled across the board with his nicotine stained fingers, I figured I still had him fooled. He hadn't figured out that I was just a wanna-be high school math teacher and not a real mathematician. Not yet anyway.
       Even when I utilized his office hours to bring him my incomplete proofs, pages of my desperate attempts at explaining concepts I only partially understood in a language of signs and symbols not my native tongue, I never let on. He would dart his eyes back and forth from my proofs to my face, peering darkly at me, and muttering things like, "Unconventional...not at all what I would have.....and yet...," then grunt and affirm that what I had written was indeed true and to keep thinking about the problem. Each office session would end in a barrage of at-least-you-can-think-logically-not-like-those-education-majors and mathematical-reasoning-can't-be-taught. I still never let on. I let Dr. Guerzhoy assume what he wanted to assume. Yet all the while, I felt dirty, like I was betraying the other education majors, like I was living a lie.
       Finally, about a month into the course, and after another bitter classroom tirade in his almost unintelligible Russian accent about the general stupidity pervading the left hand side of the classroom, I lost my cool and decided to do something. Something had to be done! I was going to be a teacher; did I or did I not believe that math could be taught? I decided that I did believe it, with all of my heart. So, after class I ducked out quickly to lurk in the hall, waiting for that humbled group of education majors. When they heard my proposal, they seemed stunned. I don't know if they even realized I was one of them before that point, but they all assented to my plan. "Meet me in the cafeteria after class and I will teach you. I will read that book, I will figure it out, and I will teach you!" O, and it worked. I have always understood things best as I tried to explain them. Just the process of trying to simplify and organize a concept well enough in order to teach it solidifies the information in my mind like nothing else. We would sit there in the cafeteria after class working through proofs and discussing abstract algebra and I felt like a teacher. A teacher! Then one day, as we sat there, I happened to glance up, and there, a few tables away stood Professor Guerzhoy, mouth agape and eyebrows knitted. He caught my eyes and his expression shouted disapproval and worse, betrayal. He had thought I was one of his. He had believed me to be a math major. My little charade was up. He never spoke directly to me again, in or out of class, and I never bothered to drag myself into his dark little office for help again either.
      
       That's the end of my sad little tale. Yet, it's not the end. Dr. Guerzhoy may be a striking example but he's not the only professional educator perpetuating the "it-can't-be taught" lie. He's not the only one of us buying into the easy out of "they-just-can't-learn-this." I have spent the last five years tutoring students with disabilities. They were mostly your students, professors. They were taking math 082,092 and 122. They've been enrolled in Psych classes, English classes, and Chemistry classes. They've been nursing students, machining students, and criminal justice majors. I've worked with hundreds of students with dozens of disabilities from hundreds of your classes. What's the one thing they all had in common? They are the students you couldn't or wouldn't teach. They are the ones you said "couldn't be taught."
       Now I realize that tutoring is a whole different world than classroom teaching. I understand that it's impossible to personalize your instruction for each student who walks into your classroom. Nobody understands that better than a GED instructor. We teach four years of material across four broad subjects over the course of a semester to a group of students whose test scores vary from a second grade equivalency to a twelfth. That's not what I'm talking about.
       I'm talking about the dedicated ex-con who I tutored through his GED. I helped him cope with the dyslexia that danced numbers across the page by uncovering one digit at a time to add fractions. He had to write out his 6, 7, 8 and 9's times tables before every test because he couldn't memorize them but he would not give up. He came back to me devastated after a meeting with an academic advisor who told him, "Based on your test scores, you aren't capable of college math. Perhaps you ought to consider airplane mechanics instead of criminal justice." That old sense of injustice kicked right in, and I told him he could do whatever he damned well please and that academic advisor had no idea what he was capable of. He went on to pass his college math classes and without any further tutoring, I might add.
      I'm talking about the culinary certificate seeking student with ADHD and LD who fell in love with math as we worked together on his 092 class and decided he wanted to change his degree to engineering. His counselor told him he had no aptitude and shouldn't pursue it. I assured him that no matter what the tests said, he had the spark, I had seen it. He's well on his way now to his Master's in biomedical engineering.
       I'm talking about the sweet, dedicated young woman with mild mental retardation and a passion for medicine who was told that the most she should ever aspire to was to be a home caregiver or a CNA. She doggedly applied and reapplied to, then finally completed her radiology program even though she had to take physics three times.
      I'm talking about the dozens of students who have come to me saying that they went to your offices during office hours and you couldn't or wouldn't help them. You told them you already explained it in class. You told them they were too far behind and they should just withdraw. You asked them to consider other career options and majors. I'm talking about the ones who reported that they couldn't ask questions during class anymore because you mocked them or belittled them. I'm talking about the ones who came to you with their accommodations and, despite the fact that you are legally obliged to grant them, you decided they either didn't really need them, were being lazy, or you just didn't have the time.
       I have made it my life's work to teach these students: the low ones, the slow ones, and the ones for whom it never comes easy. I will admit that they don't always do well with traditional teaching. I will admit that sometimes I have to explain the same concept 10 times in ten different ways before stumbling upon an explanation that makes sense to a student. I will admit that many of them don't succeed or give up too quickly. However, this is what I want you to know: they all can be taught. Every student. Any concept. I beg you, teach them. And to those of you, and I know there are many, who have gone home and rethought your teaching style, who have stopped in the middle of a lecture to reteach, who have spent countless office hours and personal hours working tirelessly with my students who often seem to show so little progress despite your best efforts, thank you. You are truly teachers.

Where do you Teach?

      "What do you do?" you often ask. It's a fair enough question, and one we Americans are fond of.  The answer to that question, at least, is easy. I am a teacher. From there, though, it tends to get complicated. For the last five years, whenever I have confessed this, you have asked (you always do, you know), "Where do you teach?" The very next question you posed was always, "What subject?" Then I've had to admit that I have no official classroom or subject, but I've taught virtually anything anywhere. I have taught nursing at the McDonald's on 35th and Union Hills, Astronomy at the Starbucks on Stapley and Baseline and 100 other subjects in hundreds of other fast food restaurants and coffee shops besides. I have taught reading at the Cholla library, statistics at the Scottsdale Civic Center, and commercial truck driving at the Red Mountain Library. I have schleped my over-sized bag of text books to Phoenix College Library for Intermediate Algebra, Gateway Community College's Gecko Cafe for Machining, and a deserted classroom at Mesa Community College for Biology. I have home-schooled my daughters in between these many classes, driving from one client to the next, spouting spur-of-the-moment American History, Literature, and Geometry lectures as I speed down the I17, I10, or Loop 202.
        Now, before you get too impressed, I'm no expert in any of these subjects. I've got a library of knowledge spilling out of the trunk of my car- a couple of milk crates overflowing with text books- and my best friend is Google. No, what I have really been is a translator. My native language is the written word and I'm fluent in explanation. There is great joy to be found in unlocking the puzzles found in text and simplifying and organizing them into consumable, understandable pieces. Teaching well is like cooking a feast for people, or singing them a song. Teaching well is laying your art at the feet of your students as an offering of love. It is a beautiful thing. Oh, and it has been beautiful these last five years, yes, but it has also been transient and hurried and harassed. Quite simply, my teaching has been homeless until this point and I've had no subject to claim as my own.
       Until now. Nowadays, when you ask me where and what I teach, I have an answer. I am a GED instructor at Yavapai College. I am a teacher with a home.