LAST TIME . . . .
My nephew, Jeremy, had apparently overcome his drug problem; and, after working six months around our house, had accepted a greater challenge to help me teach mathematics to inner-city junior high school students.
He had bonded with these students more successfully, and deeply, than their classroom teacher, principal, assistant superintendent, or I had. He had earned their respect; and, in doing so, these students were responding with interest in a subject most had probably dismissed as irrelevant to their futures.
His success with these students arose primarily because he was able to take care of them in ways the rest of us could not well understand or implement.
WHAT JEREMY DID FOR ME . . . .
Our daily protocol, after the first week, became to enter the class at 10:15 dressed in sport coats, ties, slacks, and shined shoes. We would be carrying graded papers, quizzes, new worksheets, props (bottles of bleach, handkerchief boxes, one time even my motorcycle) long boards to be used as straightedges to draw nice looking figures on the board, our own white board markers in many colors, and a couple of fancy colored envelopes.
The lecture, usually scheduled for 30 minutes of our daily 90 minutes with these children, began immediately once the primary teacher turned the class over to us. Jeremy would sit in the audience, always in a different place, next to a different student.
We would usually begin with questions about the previous day’s ‘Class’ work. If there were questions, then I would write the problem out on the board, call for student thoughts on how to arrive at the answer, and have students whose responses showed insight come up to show their work.
When volunteers were hard to acquire, Jeremy would convince the students next to him to show him their work. If such work was correct, or nearly so, then he would encourage the budding mathematician to raise his or her hand.
After answering these questions for 10 minutes or so, I would turn the class over to Jeremy, requesting that he collect all ‘Class’ work from the previous day, and all ‘Home’ work from the previous night. We never accepted questions on the ‘Home’ work for reasons that may become apparent to the reader below.
Jeremy, while going from desk to desk, would collect these papers and give them a quick glance. Then the remarks would come: “Looks like good work!”. . or. . . “Did you struggle with Problem 6?” . . . . or. . . . "Next time make sure you do all the unit conversions before you attempt to calculate the final answer, OK?"
These remarks would invariably be respectful, benign, and always delivered in a positive, constructive, helpful, non-critical way. It was one of Jeremy’s many techniques designed to demonstrate his involvement with, and his care for, our students as well as to encourage student competition to garner the praise from him.
When the collections were finished, I would let Jeremy return control of the class to me, after he resumed his seat among the students. The class was quiet during this time. Collecting these papers became serious business; and students were expected to assume the "learning position" and take notes during the forthcoming lecture.
In fact, note taking quality was judged by the assistant superintendent of the district on several occasions; and a student's aggregate score in this area formed 10% of his or her final grade. The aggregate quiz grade of each student formed 40% of their final grade.
Each collected worksheet was graded by Jeremy or myself. The aggregate grade on the "Class" work assignments became 25% of the final grade for each student. The aggregate grade on the "Home" work assignments became 25% of the final grade for each student.
During the nine weeks we were there, we issued nearly 30 "Class" worksheets and nearly 30 "Home" worksheets to most of the 28 students. Jeremy and I graded over 1,500 assignments on top of nearly 200 quizzes. Every quiz, and every worksheet was several pages long; and our grading meant writing comments and showing students where they went wrong . . . . . I could not have done this alone.
Jeremy would not lecture, at least during the first six weeks with these students. Therefore, that task was initially left to me.
Actual lecturing would usually be limited to 20 minutes, but would sometimes be extended to insure understanding, accuracy and completeness. Only a small theoretical concept, or extension of the previous day’s topic, would be covered.
While I lectured, and played the straight man, Jeremy, among the students, would gently harass me from the audience in order to keep the monologue short and pitched on a level that the students understood. He would poke fun at any pretentious vocabulary. He would slow me if he believed I was covering topics too quickly and encourage me to move along if he believed I was covering them too slowly. He identified with these students so completely that this immediate feedback became an invaluable component of what little formal instruction we sought to inflict upon them.
Jeremy and I would work to make this as fun and as interesting as possible by using the props to illuminate examples, to help in communicating the concepts, and to connect the study of mathematics with its potential applications in our student’s lives and working careers. To end lectures, examples would be placed on the board to illustrate the use of the concept being taught. Students would be called up to the board to display the knowledge they possessed to solve these problems.
After getting a student to come to the board, I would retreat to the back of the classroom to allow the student at the board be the ‘star’. This was our segue to turning the teaching over to the students.
I would continually pace while waving my arms around and asking the “And, what would be the next step in arriving at the requested answer?” questions, while encouraging students in the audience to respond. My pacing among them, coupled with Jeremy’s serene presence at one of their tables, kept us both in close proximity to each child in the classroom in an effort to insure that they all remained alert and engaged in the learning process. Jeremy was invaluable in not allowing any student’s mind to go into neutral.
When the students were stumped, Jeremy would come in with the “Well, what if you did this?”. . . . or . . . . . . "Is this a place where the multiplicative identity might help?" hints. The class was never stumped for long with Jeremy's encouragement.
Jeremy would also help me award the $1 prize and the $5 prize each day during this period from the colored envelopes to the ‘uniquely correct’ and the ‘most inspired’ responses from students, respectively. This was a program that we called ‘bribing for answers’ – a tremendous hit with these children, even though at most $6 was awarded during any one day and often only the $1 prize was awarded. We did our best to spread this money around evenly among the children who competed for it.
Jeremy was always a reminder that we were never to yield to the temptation simply to teach just the ‘process’ of narrow mathematical applications or proficiency objectives. While our curriculum was guided both in pace and in content by what would appear on their State standardized tests in April, we never taught with the objective that our students would simply learn the ‘steps’ to solve each of the various problem types that would likely appear on it. Instead, we taught the theory from which we expected them to deduce the processes necessary to solve the problems we presented.
After the lecture and the examples, the class would be given a break to get water and go to the bathroom. Upon their return, the class would be instructed to break up into their work groups.
When the students where in the seats associated with their work groups, new ‘Class’ worksheets would be distributed by Jeremy and me. The rules during this part of their classroom schedule were that individuals within each group were to work together to solve the problems on these sheets.
Our job during this last hour of the class was to keep the students focused on their work and not on each other. They could talk to members of their group about mathematics all they wanted. They could learn from each other how to do the problems associated with the new material. They could help each other so long as they each did, and understood, the work on each problem. Members of one group were not allowed to communicate with members of another group.
Jeremy and I would go to each group that requested help. We would guide their thinking into deducing the mechanics of solving the problems.
In the end, we were certain that most of the mathematical education that took place in our classroom occurred peer-to-peer in these work groups and not teacher-to-student during either lecturing or through grading feedback. Students communicated far better with each other on these matters than an adult could; and this hour of the day was the part that Jeremy clearly liked best because he understood better than any other adult, including me, what was happening.
Five minutes before their scheduled dismissal to lunch, the students would be asked to return to their individual seats. During this chaos, Jeremy would hand out the ‘Home’ work, which they were expected to do on their own that evening, outside of school hours.
Concepts on the ‘Home’ work were always those presented earlier in the curriculum than concepts on the ‘Class’ work. Consequently, "Home" work was the retention/mastery component of the educational process, while 'Class' work was the learning component.
Each Friday was a ‘Quiz’ day and generally a marker after which new concepts on the previous week’s ‘Class’ worksheets would migrate as review concepts on the next week’s ‘Home’ worksheets. Scheduling this way usually prevented us from assigning ‘Class’ or ‘Home’ work for the weekend – a happenstance much appreciated by the students.
One of our best policies was not to allow student progress into new material until most of the class demonstrated at least five times a proficiency of 85%, or better, on each concept covered in the prerequisite material. The benefit of this policy is a diversified classroom, which better provides the opportunity to identify and to address individual needs; but the difficulty of this policy arises in trying to accommodate students who naturally learn at different rates.
In the middle of March, it became clear that we had three distinct classifications of math students. Upon Jeremy’s suggestion, the assistant superintendent interviewed each student in our class in advance of dividing the class into three sections.
The first section would learn more advanced math theory. The second section would spend the rest of our time together reinforcing their knowledge of the topics that had already been covered. The third section would use the educational software at the school for additional remediation in order to learn those topics we had already endeavored to teach.
Unaccountably, these interviews were emotional events for the students. Perhaps students feared being separated from the groups to which they had become accustomed for six weeks. Perhaps they feared any change would hinder the progress they all apparently felt they were making. In the end, there were tears, more revealing stories of difficult student home life, and a general expression of gratitude from the children for what they were learning (amazing!).
Jeremy took the middle section and helped them every day in a separate classroom by lecturing some, but mostly by putting example problems on the board and having students come up to show their work in arriving at the answers. The primary teacher took the lower group each day to the computer lab, where they used the educational software to learn. I took the upper group; and we learned more math under the existing protocol in the same classroom where we began. However, I, and the students in this upper section, greatly missed Jeremy.
In the middle and upper sections, new work groups were formed, new peer-to-peer alliances were established. Progress was made in all three sections.
WHAT THE STUDENTS ACCOMPLISHED. . . .
This essay has gone on long enough to impart the nature and flavor of what Jeremy did for these children, and for me, over his concern for their welfare, and mine.
When we first came to these students, their average absentism rate during the first semester was nearly 6%. During the course of our time with them, this rate averaged slightly more than 3.5% for the third quarter.
Of course, we came to them in late January after a winter season of swine flu. It could well have been that they were simply more healthy during the spring than they were doing the fall and winter. However, I would like to believe that Jeremy's intersection with the lives of these students, formed part of the reason these students may have been more motivated to attend school.
Initially, there were clearly three or four students in this class who had mastered the elementary mathematics material that had been placed before them. These students were confident; they raised their hands often; they volunteered to come to the board often; and their monopoly of the interaction with the teacher meant the remainder could 'coast'.
With Jeremy's street wise help and with the respect he engendered in these students, these 'coasters' were awakened. No one escaped either his scruntiny or mine. Nor were they allowed to 'coast' by their peers in their work groups. This meant that all the children in this class started studying better, faster, and harder.
In the end, these students, who were stuggling with manual long division at the beginning of the third quarter of their junior high school years, scored better . . . . . statistically better. . . . . . . measurably better . . . . . . clearly better . . . . . on the Arizona State standardized mathematics test than their counterparts at the "performing plus" K-8 school in this district in the middle class neighborhood in the west end of town.
THE END . . . . .
When the scores were published, I was so proud of these students. I published an e-mail memorandum to the district administrators and my fellow governing board members announcing (naye, EMPHASIZING) the results and giving all the credit to these children.
By then, Jeremy had left my employment. He had found work as a heavy equipment operator, driving a scraper. That job lasted less than a week.
A series of other jobs followed for him, all short-lived, apparently. Then, a summons to court. . . another sentence imposed . . . . . now being served in a prison in Douglas, Arizona . . . . six months. . . . . Maybe I get to see him when he gets out in April. . . . I am not sure to this day that Jeremy knows how well his students did . . . . . . .
Unfortunately, the standardized test results are announced in Arizona well after most schools are dismissed for summer vacation. Therefore, Jeremy and I could not go back into our classroom and tell them how very, very proud we were of their accomplishments. We could not prove to them that they were capable of much more than they probably believed they were. We could not repeat again to them how honored we were to be allowed to be their teachers and what a great time we had with them.
We understood during our time with these students that they were trying hard and that they were progressing. In recognition of this, we held two pizza parties for them in the classroom. . . a violation of both school policy and State law, both of which forbid eating or drinking in such rooms.
We covered the narrow window slot in the door with cardboard to keep prying eyes from witnessing our criminal behavior. However, it could not have been hard to deduce what was going on simply by listening outside our room.
Jeremy and I did some entertaining during these parties. We did some magic tricks. We regaled them with the revelations that I was the Uncle and that he was my nephew. We told them stories of our exploits. We listened to stories of their sport successes.
When one asked loudly, "Mr. S______ how OLD are you?", I thought a little bit, smiled, and answered, "I am in the second year of my seventh decade." It was two days, and dozens of guesses, later that they figured out that I was 61.
Another student at one of these parties had heard that I could prove that 1 = 2. I showed the 'proof' at one of these parties . . . and then immediately tried to explain what was wrong with it. . . .
There is no more satisfying job than teaching well. It is extremely hard work, in my opinion.
While I paid Jeremy his regular wage during all of this, our efforts cost the school district nothing. However, I doubt there is a reward for what we might have done that would exceed the one that we have already received.