Assigned Blog #2

Instructional Goals

During summer school, two of my objectives were as follows:
1)Students will multiply and divide exponential expressions and
2)Students will simplify square roots.
As per the assignment, one of these was met successfully and one less successfully. It does not take a genius to imagine which.
After a fairly short explanation, the students were quite capable of using exponent rules to perform multiplication and division. This process includes only one step and students have only a few things to consider in their minds before getting started. One reason we were more successful with this goal was simply that it was easier. Another, is that at least some of my students began to actually see why it has to be true. By expanding exponents and showing repeated multiplication, my students could look back at the definition of exponents and see that as long as they accepted this definition, the rules must be true. Maybe I ought to prove everything next year, and tell my kids they will have to reproduce certain proofs on the test. Because when you know that something must be true, you don't guess, you don't have to ask yourself whether you multiply or add, or whether your base multiplies too or just your exponent. You don't have to memorize anything, although you will. Also, using induction to allow students to discover these rules for themselves helped them to get a better grasp of what is going on.
Teaching students to simplify square roots was much more difficult and less successful. Partially, this is due to the increased complication of the task. There are more steps, and the process is less intuitive, but there are some obvious things I could have done differently that would have helped my students be more successful. I tried to rush through this lesson because of time constraints but if I did not have enough time to teach it well, I ought not to have taught it at all. What I should have done was illustrate why the process we were working on has to occur as it does, why root eight must equal two root two. Unfortunately, illuminating such connections requires me to spend more time talking, writing on the board, guiding through handouts, or something equally preachy. I have not yet been able to develop an inductive strategy to meet this objective, nor have I been able to find one on the internet. Working with decimal approximations on the calculator would be one way to tackle such a problem, but it would require the belief that the calculator is magical and always correct. I try very hard to dismantle the calculator myth in my classroom, so such an exercise would be highly counter-productive.

Differentiated learning in a classroom of three students just happens. It becomes obvious very quickly though informal assessment which students are not understanding the material, and the plans change accordingly. It is more difficult with more teachers, because each teacher might not see what the other teachers see, so communication is essential. Differentiation in the classroom took place in the form of assigning different students different problems, and also in questioning, when different students were asked questions relating to different depths of understanding.

In the future, to better address the learning needs of my students, I think it is important to seek out inductive strategies when possible, and to be patient and avoid rushing students. I need to be always committed to the vision of mathematics as a unified, interconnected web of knowledge and never forget that it cannot be understood piecemeal.

One of many

My Failure Story

One of Many

Preface:

When I began thinking about a “failure story,” I thought of Hank Bounds and his assertion that every child who is a behavior problem in your class is a result of a failure in your classroom management. In fact, he never said exactly those words but that was what I heard, at a time when I felt decidedly low about my classroom, the behaviors that I had allowed myself to tolerate, and the effects that my classroom management had on my students. I think he was right. Even the worst students I had, the absolute classroom terrors, the pregnant gang-banging girls, the bipolar ones, the sleepers, shouters, paper-throwers, and so on and so forth, each of them showed me on more than one occasion that they still carried within them a kernel of childhood, the desire to do well, to please, to succeed. They wanted to be successful, and at the times when they wanted it, I did not have the vision, the energy, or the clarity to show them a path to get where they wanted to be. Very few people would choose the lives that my kids are choosing for themselves every day, if they knew anything else, if they knew how to make that choice of something different, but they don’t know how to make that choice.

So what story do I settle on? Dominique, who I lost from day one? Ebony, who I lost from day two? Kendra, who I thought had gone for good only to return from alternative school just in time to disrupt final preparations for state testing. Tim Kelly, who cost himself his place in the tenth grade by cheating on his algebra final? Or should I choose my best students, whom I failed equally but in different ways. Keyera will still, if there is any justice in the world, go to college. Not community college, but a challenging, academic school. Millsapps? But if that girl does not get in to one of the elite educational institutions in the country in three years, I will have failed her too. I already did, by not challenging her enough, by not cutting through the mess and finding a way to teach her something stimulating. In the end, although I failed all of my students in one way or another, I can probably only write this story about Keith.

Keith

Keith sat in the second row. He survived the exodus to pre-algebra, and remained in my class when nearly half my students were sent elsewhere for a remedial course in adding integers. His hair was always, well, rather unkempt, or else done in an entirely ridiculous manner. There was very little that was serious about Keith, but the pink beads hanging down from the beads, or the ridiculous halfro that he often sported were especially absurd. But they always managed, along with the rainbow headband and extra small female jacket, to get someone’s attention, and that was enough to light up his entire face with that equally absurd grin, so absurd that I struggled to keep my own smile encased within stern, teacher lips. That was all the boy ever needed, was attention.

Keith thought everything was funny, and would disrupt class in most ways he could, if he wasn’t asleep. One incident stands out, in which I take the blame. As the class was commenting about my the ever-present wrinkles in my pants, Keith, upon waking from a nap, uttered something to another student, disguised by his habitual, yet sleep-enhanced mumbling. Apparently, as he told me later, he said something about someone’s Dickies. You can imagine what I heard, and I pulled out the referral. As I began to realize my mistake, it was much too late, and Keith had already huffed and puffed himself up into a storm. I said, Keith, if you did not say what I think you said, tell me what it is you did say and we’ll discuss it after class. No, you think you heard me say something, you go on and write it down there and send me outta here. I want to go down to the office. Give me some days at the house, I don’t need to be back here no more. And so on, so off he went.

Hope

Keith’s expertise was slope. He could graph a line better than any student in my fourth block, finding the intercept, using the rise and the run, and making great lines. He was actually quite good at transforming equations into slope-intercept form as well as calculating the slope from a graph. He showed the entire class how to do it. There were plenty of concepts he struggled with, and some that he didn’t even bother to struggle with. I remember when he stayed after school, for an entire week. One day I called him to the board to explain something the class was struggling with, and heard the following conversation:

Keith, how you be knowin how to do all that stuff.

We did it after school the other day.

You be stayin after school? Who else be stayin up in here.

Just me and Mr. G. It be crunk though.

I took him home, to the little house on the end of central street, squat and square and very yellow. As we drove down the road towards his house, I thought I smelled a whiff of marijuana. You smell that, Keith asked. That’s my antie’s house. She always be smokin up in there. Sure enough, as we eased toward the white house on the left, the aroma became stronger and then faded as we moved on, bumping past the potholes and over the train tracks. His dad, all 300 pound of him, was sitting on the porch, or rather the concrete area under a small awning in front of the little yellow house, that performed all the functions of a porch. He sat, paper-bagged bottle in hand, waiting. As his son clambered out of the truck and past him, into the house, it became obvious that he was waiting not for his son, but for something much more elusive. He had been waiting a long time, and six months later, when I stopped by to check on Keith, long after he had dropped out of school, his father was still on the porch, still waiting.

Gone

Keith dropped out in October. He had already been suspended three times. He was still failing my class, but getting closer. During my first block class (Keith belonged in my fourth block) he knocked on my classroom door. I saw him standing there, his sheepish grin somehow absent as he held out his textbook and his withdrawal slip. He did not say anything. I took the book, and signed the slip. Made sure that he had my number, in case he needed anything, in case he needed help with the GED he has insisted so many times he was going to embark upon. I took a moment to collect myself before I re-entered the chaos of first block, and had to wipe away a stray tear. I never should have signed that slip.

What could I have done for Keith? I failed Keith in the same way I failed too many of my students, by not creating a classroom environment designed for success. I failed Keith with inconsistencies. I could have given him more progress reports, so he could see the huge improvements that I saw him making. I could have called his mother more, coerced him to stay after school more often. I could have done so much for Keith, he was crying out for attention, for love, for anyone to help him do right. He never wanted the eternal waiting of his father.

Epilogue – Touched down in the land of the delta blues

It was fantastic to be home for Christmas. After seven lonely months in Mississippi, I never appreciated more the love and support that I have from so many people at home. Without any understanding of god, I still felt blessed, for if there has ever been anything to be supernaturally thankful for, it is a plentiful group of people who love each other.

When my flight touched down in Memphis, I turned on my cell phone, a ritual that is still new to me. A few moments later I heard the text message chimes, and wondered who could be texting me. Since this story is all about Keith, the answer must be obvious.

Wat up mr. G this keith i was just textin to mess wit you since i aint heard from you in a min...3341234 this my number if you want to call in holla.

That was the first message. In the second, he explained that he would be joining up with the national guard in a few weeks. I called him the next day, and we tried to set up a time to get lunch, but it never worked out.

As the months passed, I did not hear from Keith, and the number he had given me, unsurprisingly, was soon disconnected, so that I had no way of getting in touch with him. I heard that he had not gone into the guard; rumors suggested that he had possibly joined job corps. So one day I went down to central street. Keith's father was still waiting one the porch, and was glad to see me. Remembered the truck. No, Keith had not joined the guard, no, he had not joined job corps. He was just trying to stay out of trouble. Was he succeeding, I asked. No, not really. He's looking for a job, but has not been looking too hard. Here's his cell phone number; I know he'd like to hear from you. On my way back to Leland, I thought I saw someone waving to me in an old Blazer when I stopped at the four-way. I wasn't sure, but the Blazer followed me through the two turns to my house, and as I got out of the truck, I realized it was Keith, with his absurd grin and do-rag covering his ridiculous hair, and my face lit up. I just stopped by your house. I know, my momma called and said you was there. I gotta go drop my sister off now. This where you stay? Yeah, this is where I stay. Aight, well, I'll holla at you some time. Ok Keith, I got your number, I'll give you a call. We still haven't managed to get lunch. But I have the number and if it changes, I always know where he lives. So I hope we'll get to sit down and talk, and maybe he can muster up some sort of initiative, some sort of drive. I just don't want to imagine that absurd smile extinguished behind a paper-bagged bottle, on a porch that isn't a porch, waiting for a future that has already come and gone.

Ready, Set...

Ben suggested that we should post about something we wished we had done before the school year started. I've got a long list, both of things I wished I had and had not done.

Organization - Clear, detailed procedures for my students and myself.
My most challanging problem last year was organization, which, based on the way I had made it through college, nevermind my own experiences as a student in high school, should not have been surprising. Before I started the year, I needed to have better procedures, that were much more thought out and thought through, both procedures for what the students would do and for what I would do. Where would I put the daily attendance list when it showed up at lunch, during 3rd or 4th block, or the next morning (that is, if it showed up at all)? What would I do with the do not admit list? How would I keep track of attendance in my own classroom? How would I record disciplinary infractions, and how would I inform students of consequences? How would I communicate grades with parents, and when would I have time to grade all the crap that I assigned? Would I grade at home or at school? Even simple things, like what I expected when I asked the class a question, were unclear. So I wish that before school started last year, I had set these ideas out very clearly, in writing, and played them through a few times in my head, then went to a second year and gone through all of them with the second year, just to get an idea of what is reasonable and what is not. A second year from my district would have been ideal, but since I was the first in my district, that was not possible.

My room
I wish I had taken more time to make my room an inviting place for students. I don't mean a circus, but I do mean clean, neat, bright colors. Encouraging slogans or posters. Lots of math. Things that I find exciting and interesting, so that if my students ask me about them, I can share some of my passion for other subjects, even if they are not math-related. In this regard, I would especially like to have some things posted that reflect the world outside of the town in which I taught. A world map. Posters of Russia, Africa, South America, anywhere but the delta, memphis, or chicago. College posters of both local and elite institutions. I have students who could go to Williams, Harvard, Standford, etc. Or at least Amherst. They need to know these places exist, and about the doors that they could open for a delta kid. This sounds extraordinarily elitist, maybe I am. But Delta State and Valley do not provide the kind of education my kids deserve. The fact that I was told by someone at Valley that I should teach there after I finish MTC illustrates exactly why my students deserve better than that. A continuation of the high school experience is not what they all need - although some of them certainly do. My room also needs to be neat, which means better organization, and also better procedures about leaving the room, eating, etc.

My Sanity
I wish that, before the year had started, I had set some limits for myself. Regarding, for example, grading. Next year, I plan to do all my grading at school. I have a 98 minute planning period. I am only going to allow myself to take home grading on days when, for one reason or another (covering another teacher's class, school pictures, the extravaganza, meetings, general chaos) I do not have a planning period. The sheer amount of grading I accumulated and did not deal with immediately terrified me as it piled up in my classroom, backpack, dining room, living room, and bedroom. It will all stay at school next year, organized in folders.

Discipline
I wish I had known something about my school's discipline policy before I started. I also wish that the school offered school-wide, supervised detention. But that won't happen.

Planning
I wish that I had planned ahead more. Actually, as I recall, I did plan ahead, but was completely shocked by incompetent my students were at basic mathematical operations. Few of them were actually unintelligent, but fluidity in mathematical operations was somethinng that alluded them, so I had to throw out all my planning on the first day, since it assumed that my students could add and subtract fractions, and integers. Assume nothing.

Like anything you do the first time, there are still a million other things I think I could have done better, but that's why I'm glad it's a two year program. Just a year here and I would feel completely unsatisfied.

Summer School Goals

What can I possibly teach this group of students tomorrow / next week / next month? This question has been one that troubled me throughout the year, and all too often I found myself asking about tomorrow rather than thinking as far ahead as I would like, but with summer school, things have been a little easier.

I have four students this summer. Some failed pre-algebra, some failed transitions to algebra. Luckily for me, and unluckily for the students, the pre-algebra and transitions are in fact the same course. So is eighth grade math. And seventh grade math. Most of sixth grade is devoted to the same concepts as well, which are then re-taught throughout the high school math sequence.

This is not just a rant about the absurdity of the system (though such absurdity is significant). If affects the goals that I choose for my students. These are not always the objectives I write on my lesson plan and on the board. I do that because I get observed. The goals that I have been trying to chose for my students involve deeper levels of learning, connectivity and understanding than most of the objectives in the frameworks target.

These goals are much more appropriate for my students (in terms of development, past mathematical experiences, and student needs). Recognize patterns. See mathematics as something that stems from fundamental truths about the way that numbers interact, and begin to see that the rules governing these interactions are not arbitrary, that in fact numbers could come together no other way. Build confidence. Create a framework of language that will allow each student to process thoughts about math in logical ways. My students have been "taught" the tricks of math so many times. They've been told that when they multiply exponents they add the exponents, and other equally nonsensical things, but they do not see the connections, they do not see the why, and so the rules all get jumbled when there are no reasons supporting them.

My instructional strategies so far have been very different than they were last summer, and throughout last year. Last year, my goal was to survive. This year, I have loftier ambitions. I have a vision of math as I want them to see it. To that end, I have changed the way that I speak and give instructions. I pay very close attention to the language that I use, defining and re-defining math terminology, and making my instructions much clearer and more specific. I try to provide more definite structure to my lessons, and place enormous stress on the continuity of ideas, the connectivity of concepts, and the multiple paths to solutions. I stopped saying the word "answer" so that I can always be sure that both I and the students know what it is we are talking about. We are never trying to find the answer to a math problem, we are always trying to find something, and if we cannot name that thing for which we are searching, we may never recognize it when we find it.

One inductive strategy that I created this summer was used to introduce exponent rules. I gave students several products and quotients of exponential expressions to simplify, without mentioning the exponents rules, and offered them "clues" from a clue jar to help them solve the problems. The clues showed similar products and quotients that had been simplified correctly, and the students were left to deduce the rules for themselves. The activity was appropriate in that it forced all my students to think and will help them remember the exponent rules much better in the future. However, it did not do enough to make these rules more than simply rules, even though they may be more memorable since they discovered them themselves. I followed the activity up with a formal definition of the rules and an explanation of the symbolic language used in the definition, then a lecture and discussion about why the rules, especially the multiplication rule, must be true as long as we understand the definition of exponents. At that point, it was obvious that the definition of exponents had not completely sunk in yet, but I think that may be something I'll have to keep plugging away at.

Although not exactly relevant to the assignment, I feel I ought to mention confidence. Confidence in a summer school class is bound to be low. Everyone failed regular class. Yet confidence is essential to learning, and I feel that it is my responsibility as a teacher to build the confidence of my students back up, and so I've made that one of my goals. We're on the right track on that one, but it comes slowly, and I hope that our first round of quizzes will not crush that.

I haven't yet spoken much about how to assess these goals, mostly because that is a question that I am still struggling with. But I'm working on it.