Hollenbeck Dissertation Draft
Productive Disposition
Instantiating a Productive Disposition
In my experiences instantiating a multiple solution norm, I have found that the beginning of the school year is a critical period for establishing management related routines and norms for social and mathematical behavior. My prior experience with eighth grade Algebra and Geometry classes is that the first few days of school are a time when students are particularly attentive and compliant as they enter their new environment with a mix of excitement and apprehension. The first day with the students is an opportune time to clearly communicate expectations and goals for the year. During this important class, I attempt to identify a non-routine task whose solution is accessible to the students in multiple ways. As students work on the problem, I explicitly explain what I am expecting from them, and offer guidance regarding how they should be working with other students they are grouped with. Similarly, in whole class discussion of solution methods, I clearly point out my expectations for student behavior. All the while, I make a conscious effort to have a strong affective focus and be sensitive to students who are uncomfortable with their role in the class. I carefully and continually monitor the classroom environment and promptly recognize occurrences that are consistent with my goals for social and mathematical behavior, and purposefully address any incidents that are undesirable.
Unfortunately, on the first day of the pre-Algebra class, I was not afforded the luxury of working with quiet, attentive, and compliant students. Part of my journal entry from this first day addressed the uniqueness of the group:
As the students started to enter the room, it was obvious that they were not like my other classes. They clearly were not intimidated by my presence at all. They were talkative and loud, they complained about my seating arrangements, and I had to plea for their attention. As I tried to explain my expectations and goals for the year, I was interrupted multiple times by their off-task chatter. [Personal Journal Entry, August 28, 2006]
The task I had planned for this first day was:
Find a four digit number so that:
1. All four digits are different.
2. The number is even.
3. The sum of the digits is 20.
4. The hundreds digit is twice the ones digit.
My frustration in trying to engage the students in meaningful mathematical activity is highlighted in my journal entry that day:
When I asked them to come up with their four-digit number, Cedric and Erika were completely disengaged. Erika tried to withdraw from the group by sliding her chair several feet away from the table. When I asked her to join the group, she only moved an inch or two. The other students answered the problem in a matter of seconds [only Chris’s number met all four criteria] and quickly started talking and joking around. Chris in particular, kept making jokes. When I asked if they could come up with a different four-digit number, they again answered the problem too quickly, with almost no reflection. Most of their numbers did not meet all the criteria. When I pointed this out, students pressed me to tell them if their number was correct. . . . When I tried to publicly compare their solutions, I couldn’t keep the focus on one of their numbers long enough to have any meaningful discussion. Jamaal, Chris, Alan, and Jordan seemed interested in the problem, but they only wanted to discuss their number and kept pressing me to tell them if they were right. [Personal Journal Entry, August 28, 2006]
My construct of a multiple solution norm was predicated on having students demonstrate high levels of task engagement, effort, and persistence when challenged with a non-routine problem. Sadly, my students did not approach a mathematical task with a desire to significantly engage in the problem. Moreover, it was not uncommon for my students to actively avoid an academic task and engage in a range of maladaptive behaviors. The following quote from Holt (1964/1982) captures my interpretation of how the pre-Algebra students thought of a mathematical task during the beginning of the school year.
For children, the central business of school is not learning, whatever this vague word means; it is getting these daily tasks done, or at least out of the way, with a minimum of effort and unpleasantness. Each task is an end in itself. The children don’t care how they dispose of it. If they can get it out of the way by doing it, they will do it; if experience has taught them that this does not work very well, they will turn to other means, illegitimate means that wholly defeat whatever purpose the task given may have had in mind (pp. 37 – 39).
Perhaps the most significant obstacle in establishing a classroom culture predicated on the cooperation of students to engage in meaningful academic work was overcoming the tendency of my students to abruptly lose focus on a mathematical task and become occupied in mathematically pointless chatter. After an observation in September, I asked Sandy what she viewed as some of my biggest challenges. Her response was, “The management of the students. You can tell they have a hard time staying seated for any length of time and they cannot avoid talking to each other.” More than the quantity of off-task behavior, Sandy noted the challenge of creating an environment where the focus would remain on mathematics. After a November observation, Sandy stated, “Students had periods of working with periods of not working, and it is hard to maintain continuity across that.”
As discussed in the previous section, I had significantly underestimated the challenge of simply maintaining on-task behavior and creating a culture where students would be willing to do mathematical work. By May, much progress had been made; students were willing to engage in a mathematical task and persist in solving non-routine problems; moments of unproductive behavior, although still present, were more easily managed and redirected. An examination of the data suggests that the following six interrelated factors were influential in shaping student behavior and my students’ willingness to do mathematics: (1) creating a supportive environment with strong teacher-student relationships; (2) selecting and/or designing an appropriate task; (3) students’ attitudes and beliefs; (4) external influences; (5) informal organization of the classroom; (6) instructional decisions
Teacher-student relationships
In addressing classroom situations characterized by a lack of student discipline and an apparent apathy toward academics, a common refrain from my school’s principal was, “Many students don’t care to learn, unless they learn you care.” Right away, I recognized the importance of building positive teacher-student relationships as an important component of classroom management to counteract unproductive patterns of student behavior. On August 30, after the third class meeting, I wrote in my journal, “I think by building strong relationships, their willingness to do some of the things I’m asking will improve.” In some ways, it seems trivial suggesting that a constructive teacher-student relationship can positively impact a student’s willingness to engage in a mathematics problem and persist when challenged. Nonetheless, unlike my other classes, the successful building of relationships with my pre-Algebra students was a necessary condition in my efforts to constitute an environment where, minimally, students would not partake in disruptive, off-task behaviors. At the end of the first week of school, I believed I needed to approach the pre-Algebra students differently than students in my other classes:
I know building relationships is key, but Amy [School’s Psychologist] only echoed that today. I want them to see me more than just a teacher. I suspended some of the mathematical work for the day in order to answer their questions about my age, background, and family. I shared pictures of my wife and daughter, and Keisha and Erika seemed real interested in these. I also asked them questions about their families and what some of their interests are. This was a good investment in time, as they seemed to focus a bit better today. These are things that I haven’t done with my other classes. In my Algebra and Geometry classes, it seems like the students, as a whole, have intrinsic respect for me. As long as I prevent any feelings of negativity toward the class, or myself then these students should continue to respond in positive ways. But for this class, it is more difficult than that. Not only do they show less respect for me, there seems to be some distrust. I need to earn their respect and confidence. I think it will be important for them to like me. [Personal Journal Entry, August 31, 2006]
Because I felt it was important for students to like me, I was reluctant to discipline students; however, due to the pervasiveness of their off-task conduct, I ultimately felt compelled to follow some of the traditional consequences for disruptive behavior. After growing frustrated by my students’ lack of attention during a class on the second day of school, I warned them about behaviors that would receive infractions:
I know you are all aware that we have these things called infractions, and that there are consequences for getting these. You will be assigned lunch detention, we will have a conference with your parents, and you if you get, more than six combined, that means six total from all your teachers, I think, you will either get a Friday school or a suspension, and you will not be able to take part in our end-of-quarter activity. You probably won’t be allowed to go on any field trips. These are not things that you want to get, you don’t like getting them, and personally, I don’t like to give infractions. I don’t think there should be a need. I know that each of you know how to behave, and more importantly I know that each of you are good kids. But if you keep interrupting with things that have nothing to do with math, then I will have no choice than to give you an infraction. So try to keep us both happy, and when I ask you to stop talking, or singing, or anything like that, that you respect me enough to listen and do the right thing and stop. [Classroom Transcript, August 29, 2006]
Despite this expressed reluctance, I, nonetheless, by the end of the second week of school, had written numerous infractions, and assigned lunch detentions to all students except for Keisha. Each infraction was for continued off-task behavior. For Erika, Chris, and Alan, who received more than one during the first two weeks, I made calls to their parents or guardians. Admittedly, it was difficult to differentiate student conduct that would be singled out to receive an infraction. There was no well-defined action in which an infraction was issued. The students did not act out violently, or speak to me in an insubordinate way. When I explicitly addressed a student to stop talking, the student frequently would apologize, and temporarily suspend the behavior I singled out. However, in a given moment, even with repeated individual warnings, any member of the class might be engaged in an off-task conversation. The threat of issuing infractions seemed to offer little deterrence or prevent the continuance of the disruptive behaviors in the classroom. Further, if a student received an infraction, they seemed to perceive, correctly, that I would be hesitant to write a second one during the same period.
With the exception of Chris’s Mother and Alan’s older Sister, I did not sense that efforts to contact a parent or guardian had positive effects regarding the conduct of the students. Although the level of parental backing improved throughout the year, I did not feel well supported when I made contact to a parent or guardian during the first several weeks of school. In a September 5 journal entry, I recorded some of my perceptions after calling Erika’s Mother:
At lunch, I called Erika’s Mom at work to discuss my concerns with how she’d been behaving, and to let her know that Erika had been given two infractions for being off-task. Unfortunately, I couldn’t articulate very well to her why I had given Erika infractions. Her Mom kept questioning me about what was wrong with Erika’s actions and seemed very suspicious of my decision to issue these infractions. I felt like I was being put on the defensive to justify why I had disciplined Erika. [Personal Teaching Journal, September 5, 2006]
As I noted in the following journal entry at the start of the fourth week of school, my role as a teacher, a supposed position of authority, provided minimal influence in my attempts to persuade students to behave in desired ways. I believed creating a positive rapport with students was instrumental in any success I had experienced in changing the culture in the classroom:
It is still humbling to realize that my authority over them is limited. Today, Kyle and Chris lingered at the start of class, and Chris blatantly carried on a conversation, and was laughing while I was right there with him, trying to get his attention to start class. I asked him if he had any respect for me at all. He said that he did respect me, and finally moved to his seat. Relationships and respect are how I am most effective getting them to put forth effort. [Personal Teaching Journal, September 18, 2006]
Sue also shared this perspective. After observing a class on October 26, Sue was particularly impressed by the nature of student work and behavior. When I asked her why she thought the students did so well, Sue said, “You bring a personableness to the room, and they want to please you, they want you to like them. When you talk to them, you kneel down so that they can look you in the eye, and that really means something to them.”