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"Give me my bunny!" [the Boy] said, "You mustnt say that. He isnt a toy. Hes REAL!"
When the little Rabbit heard that he was happy, for he knew that what the Skin Horse had said was true at last. The nursery magic had happened to him, and he was a toy no longer. He was Real. The Boy himself had said it.
Margery Williams, The Velveteen Rabbit
Mark teaches Grades 7 and 8 Math and Grade 8 Introduction to Algebra at a Christian school. This school has been in existence since the 1950s and is sponsored by a conference which is part of the Mennonite Church. The school first opened as a high school and later a middle school was added. Enrollment in the middle school is currently 70 students and is housed in a building separate from the high school though certain facilities such as the cafeteria, chapel, gym, library, computer lab, and guidance office are shared by both schools. The campus consists of 30 acres of land located at the edge of a city with a population of 25,000. The city is growing rapidly with an influx of minorities, and 10% of the students in Marks school represent minorities.
In the mid-1990s, community members expressed interest in adding a middle school. Careful planning by a group of educators, church leaders, and parents resulted in a middle school committed to providing developmentally
responsive education for students in Grades 6-8. Mark became aware of this
venture, made the decision to apply, and became one of three full-time teachers in the middle school. It was during Marks third year at this school that I had the opportunity to observe his classes and hear his story. The college professor who suggested I contact Marks principal about my study also specifically mentioned Marks name as an excellent, reflective teacher.
When I first spoke with Mark via telephone about participating in my study, he startled me by his willingness to make time in his already full schedule to tell me his story. He mentioned that he was eager to tell me about his journey from being a traditional classroom teacher to who he is today. This story, he added, would lend understanding to his classroom practices.
As I listened to Mark, watched his interactions with students, and contemplated his relationships with people in general, I was intrigued by the house his life created. At first glance it may appear commonplace, but once inside one becomes aware of how well integrated the furnishings and rooms of his house are. It is difficult to distinguish the purpose of each separate room. The furnishings were and continue to be carefully chosen to reflect this homes purpose--to provide for the needs of those who enter.
Mark grew up in Appalachia and appreciates his background. He recalled,
My dad grew up during the depression. He came from a family of 12 and started working when he was 12 [years old] for 10 cents an hour. . . . My dad is a very caring person. He would do anything to help somebody. I can remember him getting out of bed at 4:00 in the morning because someone called him on their way to the hospital. Their daughter was sick. They were wanting to get there in a hurry and their car broke down. [Dad] rushed out to help them get back on the road again. Im sure he didnt charge them anything for that. I appreciate that aspect of him. He didnt have a lot of [money] and I think part of that was . . . because of Dads generous heart and compassion for others. (Vol. IV, pp. 99-100)
In Marks small, elementary public school, Grades 1-3 had one teacher, Grades 4-6 had another teacher, and the principal taught Grades 7-8. One incident during his first years in school remains deeply etched in his mind:
I think back to my first- second- and third-grade teacher. . . .The memory is very vivid and I can probably tell you where I was sitting in the classroom and where the teacher was when it happened. . . . We had a first and a third grader who were brothers. Their family [life] was not a good situation and social services came to take them out of the home, but they did that at school and took them out of the classroom. Not [even] the teacher or anyone else was told and they came in and took the two boys out of the classroom. The teacher put her head down on her desk. We had three grades and probably seven [students] in each grade. . . . She had her head down for at least 10 minutes. No one said a word. She had her head on her desk and was crying. The rest of us werent rich either, but we certainly didnt have to come to school the way they came to school. For her to have that kind of caring stuck with me. (Vol. IV, p. 62)
Marks sixth-grade teacher was a first-year teacher who had just completed her college education. Mark also sees this teacher as having left a lasting legacy:
I got my first C . . . in her class; it was in conduct. . . . She had one of these paddles with a rubber band and a ball on it and I got swatted with that several times because of my misbehavior and . . . mischievousness. But as I look back, I had a different learning approach. . . . The thing I appreciate about her . . . is that in the midst of all this she never gave up on me even though Im sure I was a . . . problematic student in her classroom. . . . She asked me to go into a county-wide speech competition and I did. [I] presented and that gave me a real boost of confidence in myself. . . . I would not have done that without her encouragement and help. (Vol. IV, p. 94)
The principal/teacher Mark had for Grades 7 and 8 "was a very strict person, a very strict teacher," but Mark knew this teacher cared about students (Vol. IV, p. 95). Mark was somewhat afraid of him and thinks the teacher sometimes used this to his own advantage; however, Mark credits this teacher for teaching him fairness and consistency. Mark also recalled that this teacher helped students put a basketball hoop in a tree on the playground so they could play basketball.
Mark went to a very small high school where he again had "very caring teachers . . . who reached out and helped [him] with things [he] would never have done without their initiative" (Vol. IV, p. 95). Mark recalls,
I was not that outgoing. I am an introverted person by and large and I came from a family that was not really involved in social settings and events in school and education. Neither of my parents graduated from high school. My father only went to eighth grade. . . . College was not even in my thoughts until my junior year in high school. (Vol. IV, p. 95)
During his high school years, Marks friends played an important role in shaping his future. As a sophomore he developed close friendships with some seniors who played basketball with him, were in his 4-H Club, and were in the National Honor Society when Mark was inducted. After these friends graduated, they came back from college and encouraged Mark to also enroll in college.
The summer after Mark graduated from high school, some of his friends invited him to attend a Billy Graham Crusade. Mark said, "I accepted Christ on June 13, 1964. The thing I appreciated about Billy Graham is that he sent literature to you and encouraged you to get involved in a local church" (Vol. IV, p. 62). Mark began attending a Methodist church with his friends. Later in his life he became part of the Mennonite church and remains there today.
With the encouragement of his friends and the guidance counselor, Mark entered college:
Math was always one of my favorite subjects. . . . When I first started college, . . . I was going into accounting because I thought it was something I would enjoy. I actually got some experience with that because I dropped out [of college] after the first year so I could work before going back. I got a job at Good Year Tire and Rubber and I was the budget control coordinator. That gave me good experience working with spreadsheets and numbers.
. . . I worked with numbers day in and day out. Sometimes I worked until 3:00 in the morning making sure they balanced down to the penny. . . . It was probably one of the best jobs I ever had salary wise, but I didnt like working alone. In the meantime I had joined a church and started working with the youth group which I enjoyed very much. My former principal and junior high teacher encouraged me to go to another college and get into teaching. Id be working with people then. . . . I did go into education at that time and decided Id go with elementary [certification]. (Vol. IV, pp. 59-60)
Mark transferred to a smaller college and again found teachers who cared about him. One professor in particular exerted extra effort to keep Mark in school:
This one prof I had in American History was one of the best profs I had in college. His reputation as "motor mouth" was basically because he got so excited about the topic. . . . He had the reputation for being a very, very hard prof to get good grades from. I was convinced that I was going to make an A in that class. I studied really hard. Class participation was part of his grading system, and I was not participating in class. . . . I talked with him and he said, "Well, you have a presentation to make." We had to pick an American character and do a 15 minute report. He said, "If you can speak for 15 minutes and not use a note, it will be good enough for your class participation." I had Andrew Carnegies life memorized from birth to death and in between and I got an A out of that class. The next semester I wasnt going to go back because I had to work to make money. . . . And he called me and said, "I hope you dont mind. I talked with your roommate when I didnt see your name on the roster and wondered why you didnt come back. [Your roommate] said it was because of finances." I said, "Yeah, but Ill be back next fall." And he said, "I hope you dont mind, but I also took the initiative to go to the financial aid director. . . . I think theres a package that might enable you to continue if you want to go down and look at it." (Vol. IV, p. 96)
The financial aid package Mark received allowed him to continue as a full-time student. He ended up becoming very involved in campus activities such as being a resident assistant, Student Body President, joined the College Christian Association, belonged to a fraternity, and held offices within the fraternity. He elaborated on his fraternity association:
They had no physical hazing in terms of the pledging program. They had study tables. They had the highest GPA on campus. . . . The Greek organizations certainly dont fit into who I am, but it was a great experience. (Vol. IV, p. 97)
When Mark graduated from college, he went to his American History professor to tell him that he could in no way repay him for what he had done by helping Mark find a way to stay in college. Mark recalls the professors response,
He said, "You dont owe me a thing. When you get out there, there are going to be a number of other people who need a helping hand and assistance. Do the same for them." That has always been in the back of my mind. (Vol. IV, p. 97)
For his first teaching job, Mark returned to Appalachia. Marks student teaching had been in Grade 1 and he was hoping to find a position in the primary grades. That did not work out, however. Mark explained:
The County Superintendent called and asked if I would consider a possible opening at one of the county schools. Out of respect for the fact that he called me and was interested in my teaching, I said "Yes, I [will] do that." I had a very good interview and they also gave me a really nice position. . . . I started teaching seventh and eighth grades. (Vol. IV, p. 5)
This position included teaching science, health, physical education, and coaching.
This school consolidated and Mark was uncertain about his future. In the meantime, his alma mater contacted him about joining the college as their Director of Financial Aid. Mark accepted this position, but after a few years he "realized that [he] wanted to continue with and [stay] in teaching" (Vol. IV, p. 5). With the exception of working for 5 years in student development at another college, Marks experiences in education have been in the middle grades. These included another position in Appalachia, an administrative position in a school connected with the Mennonite church, a teaching position in Vermont, and now his current assignment.
The changes in Marks teaching positions were at times connected to events in the lives of others. These incidents point to the priority Mark places on relationships. Marks second teaching stint in Appalachia came about because of his dads retirement: "I moved back to . . . help my dad along in that transition in his life and got another job in a small county-like system" (Vol. IV, p. 6). This decision to relocate and provide support for his dad had a significant impact on their relationship. Mark reminisced:
I was in ROTC when I first went to college and enjoyed it. My dad was a [veteran] and very enthusiastic [about the military]. . . . I was encouraged to join the National Guard so I had to go to [Officer Training School]. It would give me military background once I graduated from college and I could be an officer. It was ideal. [However], through my own study and reading of the Scripture I began wondering if I could really take someone elses life. Should I have that right to end someones life that God created? . . . Am I my brothers keeper? (Vol. IV, p. 62)
Mark eventually concluded that he could not be part of the military because he did not want to take someone elses life. Having made that decision, Mark needed to follow his convictions:
It was hard for my family. My dad had served in World War II and wanted me to be in the military. I knew it would be hard for him to hear about my convictions. My mother reinforced that when she said that telling my dad would be like putting a gun to his head. It took a number of years for us to work through that. That was tough. (Vol. IV, p. 63)
Teaching in Appalachia during this important transition for his dad was essential in reestablishing a close relationship with his father. Mark said,
I moved back to be with him when he retired. We had never talked about [my decision to leave the military]. . . . One night [Dad and I] sat down and talked until 4:00 in the morning and he told me things about his time in the service. Hed never talked about it before. (Vol. IV, p. 63)
Currently Mark characterizes his relationship with his father as "better than [he] could have scripted it, better than [he] could have written up" (Vol. IV, p. 99). Mark also observed, "[My dad] is very trusting of me. . . . The relationship is very good and I will miss my dad a lot [when he passes away]" (Vol. IV, p. 100).
Another change in teaching assignment connected with a relationship involved the woman who is now Marks wife. Mark met Rochelle through church activities about 10 years before they married each other. By the time they decided to get married, Rochelle had already accepted a position to pastor a church in Vermont. Mark decided to move to Vermont--even though he knew it meant that he would not be teaching for a year--instead of asking Rochelle to go through the entire process of candidating for another position. Both Mark and Rochelle were in their 40s and knew "that might take some adjustment in itself" (Vol. IV, p. 6). Mark also recalls:
I [had never] been a pastors husband . . . so I decided that I would just take a year and be with her at conferences and meetings, just to know what shes doing and support her in that. And I worked as a carpenter. . . . After a year, I decided I would start looking for a teaching position. I discovered that a [teaching job] was not easy to come by because of the number of years [I had taught] along with having my masters [degree]. (Vol. IV, p. 6)
Marks search for a job stretched into a second year. Then one Sunday he received a phone call from a principal asking if he would be willing to come for an interview on Monday. By Thursday of that week, Mark had been hired to teach math for Grades 5-8 in a small K-8 school with 125 students. Marks describes his teaching approach:
I was teaching using a Silver Burdett and Ginn textbook I taught from [earlier]. I would go through the chapters and have the students do the introduction to different concepts that were in the book and maybe a thing or two on the side, but mostly I used that kind of approach. (Vol. IV, p. 6)
One of Marks colleagues, the Language Arts teacher for Grades 7 and 8, approached Mark about attending a class taught through the Vermont State Department of Education called "Problem Solving and Writing." She had signed up for this week-long class but was unable to attend. Their school had already paid the tuition, and she thought Mark would be interested in the problem-solving aspect of the course because of his interest and expertise in math. Mark agreed to go "just to kind of brush up and do something different" (Vol. IV, p. 7). He describes his experience:
[The class] was being taught by teachers . . . that came out of the classroom. . . . I walked in and here were all these experiential things. They had manipulatives to work with. [They had posters like] I have [on my walls], listing Problem Solving 1, Problem Solving 2, Problem Solving 3, and Problem Solving 4. Then Communication 1, Communication 2 and 3. [The teacher] started going down through . . . Problem Solving 1. [She talked about] looking at approach and reasoning and trying to get the students to understand the strategy theyre using, why theyre using the strategy, what they do with them, and then having them reason that through and explain it. By Wednesday I looked at [the teacher] and said, "This is just mind boggling. Im kind of losing it. Im not sure if I can follow all of it." She said, "Hang in there with it, I think youll see it. Itll come through to you." (Vol. IV, p. 7)
By the end of the week, Mark felt that "things were coming around a little bit" (Vol. IV, p. 7). The instructor encouraged Mark to call her about questions he may have about this problem-solving approach. Mark did keep in touch with her and another teacher who taught nearby and found this contact invaluable:
It was that kind of networking that proved to be really crucial for me to maintain what seemed to be a really different style of teaching and instructing, but yet it seemed fascinating. . . . We were all collaborating in finding ways that we could do this. The collaboration helped because it wasnt me just taking time to think of problems. We were piggy backing off of each other. (Vol. IV, p. 7-8)
During the fall after Marks summer class, his instructor contacted him about serving on an assessment committee for the State of Vermont. She was also on this committee along with seven or eight other teachers. Their assignment included designing an assessment format to use, defining benchmarks for students completing problem-solving tasks, and developing a rubric to score students work.
Through Marks work on this committee, he became involved with Opportunity to Perform, sponsored by the Vermont Institute of Science, Math, and Technology. Opportunity to Perform promoted teachers teaching teachers how to use a problem-solving approach in the classroom and how to learn in new ways. Mark became an instructor for Opportunity to Perform and taught three or four institutes over several summers. Eventually these institutes were offered through the math departments of two universities in Vermont which meant that Mark worked with the professors, used their facilities, and had them as a resource. Mark recalls one professor admitting, "Were going to have to change our instruction at the college level because of whats happening in the schools" (Vol. IV, p. 8).
As Mark was leaving Vermont to assume his current responsibilities, he and his committee were putting the final touches on their assessment rubric for scoring students responses to open-ended mathematics tasks. They also developed a matrix using the National Council for Teachers of Mathematics (NCTM) Standards so both students and teachers could keep a record of standards they are meeting. This matrix is part of a booklet which they also developed as a guide for teachers to use.
It was apparent to me that Marks professional opportunities in Vermont were a source of great satisfaction. In his voice I heard his delight at being able to network with other educators. He spoke with pride and excitement about the academic results he saw in his middle school students. During this time his comfort level was stretched and a whole new world of possibilities in teaching and learning were opened.
What, I wondered, prompted Mark to leave Vermont and the work he so obviously enjoyed to move to Michiana for his current position? Mark explained:
I was at [a Mennonite school earlier in my career] and I enjoyed being in one of our church schools. . . . Ever since I started this [problem-solving approach in Vermont] I thought, "Wow, this is what our church schools should be doing. Learning in cooperative groups and working together just reinforces our theology." That was probably one of the incentives in my coming. (Vol. IV, p. 9)
The middle school where Mark teaches is housed in a large, dark-brown building which has been remodeled for active, energetic middle schoolers and their teachers. A large wood-shop area remains on the first floor and is used for both middle and high school woodworking classes. The middle school classrooms are on the second story and are reached by a lengthy climb up creaking, wooden stairs.
The students tables and chairs claim a significant area in Marks classroom. Instead of individual student desks, there are 12 tables with two chairs at each table. Around the walls are a teachers desk, two computers, filing cabinets, shelves and crates for storing materials and students work, a spot for the overhead projector, and an unusually large sink. Even without students, the room seems full with all of its furnishings.
Hanging on the walls are various items typically considered part of a school room. Mark has white boards which I have never seen totally empty, there is a place for announcements and a school schedule beside one of the two classroom doors, one bulletin board displays a calendar, and the other bulletin board says "Welcome to a Great Year" along with various small inspirational posters. Other posters and banners help brighten up what could be a rather dark, dreary room with its dark-brown paneling and limited window space. Though my visits to Marks classroom spread over the period of 6 months, with the exception of a few posters, the decor in his classroom remained the same.
Three separate displays of posters and banners in Marks room give clues as to what kind of teaching and learning occurs in his classroom. Two groups of displays proclaim that Mark teaches mathematics. There is a set of small computer printouts stating ways of tackling problem solving. On the wall above the sink, Mark has four handwritten posters made of poster board. These posters remind students of Marks rubric for problem solving: Approach and Reasoning, Connections, Solution, and Communication. Each topic is also broken down into three or four different levels. A third display is a group of posters entitled Group Procedures: 1) Take responsibility for oneself. 2) Be respectful of one another. 3) Be willing to share and be helpful. 4) Be certain that everyone in the group understands all of the group work. (Underlining on original poster.)
The driving force for Marks curriculum and instruction stems back to his involvement with the Vermont State Assessment Committee and the Opportunity to Perform program. The teachers he worked with believed that teachers need to help students learn by their own thinking, not with the teachers thinking. Mark explained what motivates him:
I do not want to teach [students] the way I was taught. I want to teach them the skills they need to take them into the next century. . . . The fact that they get engaged in the activities excites me. I think that has helped me get more of a passion for what I do. The other thing that motives me is that I know what they are processing, how they are processing, and what they are coming up with. This is not just beneficial for mathematics, but for other disciplines as well. They are more apt to think about it, draw conclusions, and ask the question "What if?" That is a needed component in our educational process rather than [having teachers] feed students information for them to regurgitate. It empowers them. . . . They are not doing it for a grade; it is a learning experience. (Vol. IV, p. 56)
Though Mark has a textbook for his students to use, it is used only sporadically. He showed me different materials from various states and companies that he either uses or was considering for use. When I asked him what criteria he employs in choosing materials for his classroom, he replied that he relies heavily on the NCTM curriculum standards and refers to the rubric he helped develop in Vermont.
It is important to Mark that he have his curriculum organized and written down. Mark likened his written curriculum to a human skeleton. Just as humans have the same basic skeleton, each year he follows the same basic outline for his classes. However, just as people look very different on the outside, so the way his curriculum is "really played out [is] going to take different forms and shapes" (Vol. IV, p. 101).
Since Mark teaches both seventh- and eighth-grade math, he is working to ensure that his program fits in with the scope and sequence of both sixth-grade math and with what the high school math teachers are doing. Mark sees the high school math teachers as having been very helpful in providing input for his curriculum.
Mark also looks to his past students when it comes to designing his curriculum. One day he told his students that he met with a group of freshmen to get feedback from them concerning the math they learned in eighth grade. He wanted to know what things they wish he would have stressed more and what things could be stressed less. Mark informed the eighth graders that the freshmen believed one of the most beneficial things for them was writing daily reflections on their homework.
The fact that Marks curriculum is challenging quickly became apparent to me. Though I do not consider myself an accomplished mathematician, I did well during my 4 years of high school math, the math I took as an undergraduate, and in my statistics classes as a graduate student. Even so, there were times in Marks class that I struggled to understand the concepts his students were learning. Mark was careful to scaffold, or build on students prior knowledge, before presenting them with problem-solving tasks. During this entire process, he always asked the students to think and reason their way through the concepts they were learning. A typical response from Mark when a student asked him a question was, "What do you think?" (Vol. IV, p. 19) or "See if it works" (Vol. IV, p. 47).
Asking questions is standard procedure in Marks classes. One time he asked the class to look for similarities and differences in equations they had graphed, telling them to set their own parameters for making the comparisons. After giving them time to discuss this assignment in their groups, Mark chose a name randomly and asked a group to share their observations. When it became clear that this group had not formed any observations, Mark said, "Let me draw some out of you" (Vol. IV, p. 32) to the entire class. He then proceeded to ask a series of questions about their work: "What did you do to graph this one? What kind of table did you use? How would you know from looking at the equation that they have the same y-intercept? What would make these lines intercept?" (Vol. IV, p. 32).
Not only did Mark use this questioning strategy with the entire class, he also used it when groups or individuals were struggling to understand a concept or task. Mark recognizes that his problem-solving approach to mathematics challenges students, but he said, "I think it is a challenge that is an asset to them. It is helpful and does not distract from their learning process" (Vol. IV, p. 57).
Mark expects his students to help each other out. His classroom is a place where it is safe to think, to question, and to admit that one does not know an answer. When Patti, a student with learning disabilities, struggled to understand a computational problem, Beth, another member of her group, began breaking the problem down further and further until Patti was able to understand how to solve it. As I watched the process, I was amazed at Beths commitment to helping Patti understand the problem and her expertise in breaking the problem into pieces until Patti understood what to do.
Since Mark groups students randomly, the possibility of having students who struggle most with math in one group is always present. When this occurs, Mark explained that he "stays close to that group, gives them more help, and tries to bring them along. In most cases there is always someone in a group who understands it and can help the others along" (Vol. IV, p. 55). Mark added,
I am just amazed as I walk around and listen to some of them talking to students who . . . struggle with learning. I feel good that they are saying, "Do you see this?" "Do you understand this?" "This is what I did." . . . They are getting different perspectives and that is enriching. (Vol. IV, p. 55)
I was impressed with the vocabulary I heard students using in Marks classroom. They used with understanding words and phrases such as analyze, observations, extra input, intercept, parabola, functions, factor, quadratic, exponential, symmetrical, motaire, independent and dependent variables, Fibonaccis sequence, permutations, and Pascals triangle. Once I did hear a few students use the words "thingy" and "curvy" in connection with the slope of the equation they had graphed (Vol. IV, p. 34); however, this was the exception, not the rule.
Using mathematical language is a phrase on Marks math rubric so I asked him why this is an important aspect of his math program. He replied,
It is part of students being able to articulate what they are doing and how they are doing it at higher levels of thinking. I want them to use the appropriate mathematical language to coincide with [their thinking] so they are not talking about some rather sophisticated, complex concepts using very basic language. This is an important part of the NCTM standards. Later on in high school and college, it will be helpful for them to have the language and terminology that goes with the math they are doing. (Vol. IV, p. 58)
I will now describe what occurs in Marks classes.
Mark begins each math class by asking students to write reflections on their homework. He also shares the agenda for their time together, and there is a mixture of individual and group activities. As students busily work on writing their reflections, Mark walks around the room and quietly speaks with individual students.
After giving students a few minutes to reflect on their homework, Mark asked a student to draw a name from an envelope. As the first student read the name he had drawn, I heard a "Yeah!" and was amazed to observe that the student whose name was called was genuinely eager to read what she had written. After the first student finished reading her reflections, Mark asked the class if someone has written something different they want to share. A number of students explained how their reflections differed, and one student even included an example from his homework.
The second activity on Marks agenda is to move students into groups to correct homework. To form random groups, Mark asked students to draw three names from the envelope and read them for the class. These three students became group members for the day and in some cases 2 days if their project lasted more than one class session. After identifying the groups, students arrange themselves around the tables so that, for the most part, they are face-to-face in their groups.
The first thing students did in groups was correct their homework. One student in each group began reading his or her answers. Each individual was responsible for checking the accuracy of his or her answers. If students disagreed over an answer, they discussed the problem in the group. Students who had not understood the homework or missed a number of problems were immediately given explanations by their peers.
During this time I again observed Mark moving around the classroom, talking with various groups, and helping students resolve differences. One student remained at a table working by herself. She explained to me that she had not completed her homework so she needed to work on it while her group members corrected their work.
Mark dealt with the issue of giving credit of homework completed in various ways. Sometimes he asks students to report their grades orally while he recorded them. Other times when he had several different assignments for students to turn in for his review, Mark asked them to record points earned on the paper itself.
After correcting homework, the class next turned to their learning activities for the day. Though the concepts and experiences varied, I noticed similar threads running through each class Mark planned and taught. Sometimes, when time moved more quickly than problem solving, the class debriefed about work done the previous day. Each day I observed, students were given some type of open-ended problem to solve utilizing mathematical, reasoning, and communication skills. Sometimes these problems were found in students textbooks and other times they were on papers Mark passed out in class.
Debriefing is a time of reporting what students accomplished, extending and refining their understanding, making connections, and an opportunity to share ones perspective on the problem-solving process. To get started on debriefing, Mark asked someone to draw a name from his envelope and read his or her explanation of the work completed. Students perspectives are valued and affirmed.
Students work during debriefing was sometimes extended. One day Mark asked students to determine ways the trees in their problem could have been planted other than in the stair-step fashion illustrated thus far. In their groups they were to draw a diagram of their ideas including the varying heights of the trees. Students generated and illustrated a wide variety of answers to Marks question. They spoke eagerly and someone said, "I have a cool idea!" (Vol. IV, p. 19) which was then shared with the class. After sharing a number of ideas, Mark moved on to the next class activity he had planned.
One day when I visited Marks class, students were asked to determine the approximate ages of living trees. The following excerpts are taken from the textbook, Interactive Mathematics: Activities and Investigations (1995).
[A] method of finding the age of a tree is to measure the circumference of its trunk at a height of 5 feet above the ground. The measure of the circumference in inches is about the same as the number of years in its age. Most trees in temperate regions add an extra inch to their circumference each year. Some trees, like redwoods, firs, and eucalyptuses grow more than this in a year, while yews, limes, and horse chestnuts grow less. Palm trees tend to grow taller without the trunks growing any fatter.
l A passage in The Swiss Family Robinson reads as follows. "I gave Jack some twine, and, scrambling up one of the curious open-air roots, he succeeded in measuring round the trunk itself, and made it out to be about eighteen yards." Calculate the approximate age of the tree.
l Find the approximate circumference and diameter of trees that were started in: the year you were born, 1900, 1776, and 1492.
l Write an equation that you could use to determine the approximate age of a tree. Let the independent variable represent the trees diameter, given in feet.
l Use your equation to determine the ages of five trees in your neighborhood. Make a chart that includes the type of tree, its circumference of diameter, and its age. (Foster et al., 1995, p. 120)
Since this was an in-class, group assignment, Mark asked students to find the ages of two trees in the school yard instead of having them calculate the ages of trees in their neighborhood. There was snow on the ground at the time of this assignment, and Mark had shoveled paths to these two trees for students to walk on instead of asking them to wade through snow. Another teacher was assisting Mark that day, and she monitored students outside work while Mark remained indoors.
Mark constantly circulated among the groups of students as they tackled their assignment, encouraging them to think through the questions. He made comments such as, "Think about the independent and dependent variables to find the formula." "Good question. Very good question." "Well, what do you think?" (Vol. IV, p. 19). At one point Mark stopped the entire class because a number of the groups were struggling to recall how to find the circumference of a circle. He reminded them of an activity they had done last year when they measured lids to find the relationship between the circumference and diameter of a circle. The class was then able to recall the formula and move on with their project.
As the period drew to a close, Mark walked around the room to take stock of students progress. He murmured comments to various groups, "Good job!" and "Nice job!" (Vol. IV, p. 20). Mark then commented to the entire class that they had not been able to accomplish all he had planned for that period, but he was pleased with the work they had done.
Students were given the following homework assignment:
The largest living thing on Earth is a sequoia tree named the General Sherman, standing 274.9 feet tall, in the Sequoia National Park in California. In 1989, the circumference of the tree was 82.3 feet at 4.5 feet above the ground. A sequoia tree seed weighs only 1/6,000 of an ounce. If a mature sequoia tree weighs 1,300,000,000,000 times as much, how much does the average mature sequoia weigh?
Extension: How old would you predict that the General Sherman is? (Foster et al., 1995, p. 142)
Mark added these directions to students homework, "Show and explain all your work. What mathematical concepts did you use to get the regular problem and the extension?" (Vol. IV, p. 18).
Introduction to Algebra
The majority of my observations in Marks classroom occurred during eighth-grade math class; however, when I heard that he teaches Introduction to Algebra using manipulatives, I also wanted to see what this class was like. I was surprised to learn that all eighth graders take this course during the second semester. Mark explained that he uses the same problem-solving approach with algebra as in the regular math classes. Since students are well-acquainted with this approach and with his use of manipulatives, he does not think that algebra should be classified as using higher-level math skills. In his experience with this approach, students with a wide range of academic abilities can understand and use algebraic concepts. He then told me that Patti, a student with learning disabilities, commented to her mother that she is concerned because she can actually understand algebra.
Many practices and routines in Marks algebra classes are the same as his general eighth-grade math classes. He began by asking students to reflect on their homework; they checked their homework in groups, addressed challenging problems that students struggled with, and were given algebraic problems to solve.
During parts of two classes, I watched students struggle with and eventually become successful in finding the perimeter of four figures. Each successive figure became more challenging. The first figure Mark put on the overhead looked like this:
Mark asked students to find the perimeter, which they quickly determined was 20 because there are five squares on each side.
The next figure Mark flipped on the overhead was this one:
Students were again asked to find the perimeter of the figure. This task was more challenging than the previous one had been, but I saw the same look on students faces I had seen before. They first looked stumped, then thoughtful as they began talking with group members about what the solution might be. Instead of giving up because they find a task challenging, these students try different ways of answering the question.
After a brief interlude of discussion, one group reported that the perimeter is 2y + 10 and another group said they got 10 + y + y. Mark acknowledged that both groups were correct but did not explain why. Students did not appear confused and it appeared to be common knowledge that one group had combined like terms and the other one had not. Mark then asked students to simplify the equation by saying, "Is there another way to write 2y + 10?" (Vol. IV, p. 77). The groups eventually responded with 2(y + 5) in answer to Marks question.
The third figure Mark put on the overhead was this one:
I found myself wondering what the students knew that I did not which would enable them to find the perimeter. Mark let the students work on this task without offering much assistance. After they appeared unsuccessful, he suggested they use their algebra blocks to figure it out. These manipulatives are called Algebra Log Gear and come in white muslin bags with a drawstring top. Students got their blocks and began working again.
One student, without having used the blocks, asked Mark if they had found the perimeter. Mark replied, "Why dont you get one of those [blocks] and show me. It may not help you, but it will help me" (Vol. IV, p. 86). The student started explaining his thinking using the blocks. He had not found the correct answer so Mark kept asking him questions to guide him into figuring out for himself what the answer was. Students eventually found the perimeter, 2y + 12. During the class discussion of how to find the perimeter, one group commented, "That is not how we did it" (Vol. IV, p. 86) though they had found the same answer. Mark immediately responded with, "Good!" (Vol. IV, p. 86), asked them to explain their thinking, and validated their efforts.
The fourth and final figure Mark gave to students was this one:
Some groups were able to quite quickly find the perimeter while others who had not understood clearly how to find the third figure struggled much more. In the end, however, they were successful and Mark gave them a follow-up activity to do in their groups using the algebra blocks.
Since Mark teaches at a Christian school, I was not surprised to see chapel as part of the schools master schedule. I would have been more surprised to learn that no part of the day or week was given to some type of religious activity. Mark also has devotions with the seventh and eighth graders during their first class meeting of the day.
During one devotional time, Mark told the class they would be reading from John, chap. 8. He had a large Bible in his hand and asked for student volunteers to read the passage. After a number of students raised their hands, Mark asked another student to draw a name from the envelope they use for random calls during math class. He wanted to see if the name pulled randomly matched any of the students who volunteered to read. Loris name was read, and since she was also a volunteer Mark gave her the Bible. Some of the other students commented on the fact that Lori had just recently read the Scripture passage in class. Mark commented that it is just "the luck of the draw" that she was chosen to read again (Vol. IV, p. 71).
Lori began reading the designated verses, and the other students sat quietly. Some of them were doodling on papers or folders, but most of them just sat in their chairs staring into space or at some object in the room. It was impossible to tell from their behavior whether or not they were listening to the Scripture reading or exactly what was going through their minds.
Mark retrieved the Bible after Lori completed the reading, got out a pair of half-glasses, and picked up a devotional book. He pointed out the phrase "what if" in the Scripture passage and focused on it. He told students that one of the items on their math rubric which he uses to score their projects once had the phrase "what if" in it. Asking "what if," Mark pointed out, leads to deeper, more thoughtful reflections. Mark then stressed the importance of not only asking "what if" in academic pursuits, but to also ask it in our personal lives: What if I go to the party? What if there is drinking there? What if I follow through on the teachings of Jesus Christ? Mark indicated that this last question was presented to Jesus disciples and still confronts people today. He read from the devotional book and challenged students to think carefully about walking like Jesus did in their interactions with others.
The students were then given an opportunity to comment on the Scripture reading and Marks comments, and to share prayer requests or praises. No students chose to comment on Marks challenge, but many of them used the next 15 minutes to share items for prayer and/or praise. I heard items like prayer for the upcoming middle school play, prayer for a cousin getting married next month, prayer for a father who is traveling, praise that a students soccer team did well over the weekend, praise that a students ankle is healed and she no longer needs to use crutches, and prayer for a sister who is blind and wanting to find the right college to attend. Mark recorded each of the students items and occasionally asked questions to clarify what was said. He also reminded students to pray about an international conflict in Eastern Europe and the refugees involved, especially the children. Mark then prayed about each of the items students had mentioned to the class. After this interlude of focusing on spiritual issues, the class resumed its usual routine of learning about mathematical concepts.
Mark chooses devotional topics based on what is happening in the classroom and in the world at large. A recent school shooting in the United States prompted Mark to discuss issues with his students related to this tragedy. If the class members are experiencing challenges in getting along with each other, Mark makes this a devotional topic.
My first impression of Mark led me to assume that he is a mild-mannered person who rarely asserts himself. I wondered about his classroom management style and who actually controls the classroom, he or his students. I also knew that the majority of Marks students come from middle-class homes where church attendance and participation are valued, and that many of his students, no matter what school they attended, would never be labeled at-risk students. These students parents for the most part are involved in their childrens lives and value education. I felt confident that the type of and degree of discipline problems Mark would face are minimal compared to a stereotypical middle school in the United States.
Marks success in managing his classroom is built on the relationships he cultivates with his students. Since he teaches in a small middle school, he knows most of the students and their parents well. Some of them attend the same church he does, are involved in a youth group he helps lead, and the majority of them are part of the larger Mennonite community surrounding the school which has family ties, church connections, and spiritual bonds ingrained into the very fabric of the community. Though Mark did not grow up in this community or even in the Mennonite church, he has become an accepted part of it through his personal beliefs and involvement in the school. It is in this context that Mark both meets and develops relationships with his students.
Expected behavior is actively taught at the beginning of each school year. While talking with students, Mark stumbles over his own feet. He ignores it and continues with the discussion. He stumbles again and again, but each time he pretends to ignore his clumsiness and the students follow his lead. Finally, he trips over his own feet yet again, but this time he chooses to laugh about it and the students respond by laughing with him. He then uses this example to drive home to students the difference between laughing at and with others. It is important to him that they learn to take cues from each other and never laugh unless the person who made a faux pas leads the way by laughing at him or herself.
Mark expects his students to learn how to work with others successfully regardless of personal likes and dislikes. At the beginning of the year he and his students spend time talking about the reason most employees lose their jobs. Students often suggest reasons such as "people are incompetent, they do not like what they are doing, and they miss a lot of work" (Vol. IV, p. 55). Mark, however, tells them that "the number one reason people get pink slips is because of their inability to work with coworkers . . . and [stresses the] need to learn how to work with one another" (Vol. IV, p. 55). Because of this, Mark chooses to use random groups in his classroom. If there are students who are not getting along for whatever reason, Mark tells them, "We are in a job. You have an assignment. You need to put all that stuff behind you and leave it outside the classroom. Make the best of it" (Vol. IV, p. 55).
Another issue related to group work that Mark addresses at the beginning of the school year is the importance of making sure that every student in the group understands what the group is doing. He sets the stage by sending one student out of the room on an errand. While he or she is gone, Mark presents information to the rest of the class. After the student returns from the errand, Mark asks students if everyone understands the information he covered while the student was absent. He stresses that it is essential for everyone to understand this information, and if they do not, they need to let him know. At this point the student sent on the errand will usually raise his or her hand admitting a lack of understanding. Mark then uses this as a springboard to stress the need for all group members to be knowledgeable of what the group is doing. They are responsible for each other.
An essential element in Marks classroom management is empowering students. He does this by frequently giving them choices and taking seriously their thoughts and input in his classes. Though it is not always easy for him to give up control, Mark believes
[students] are co-participants. It is not that I am empowering them by who I am or what I am. It is because of who they are. I model [giving up control]. . . . It is important to give [students] ownership. If students have an understanding that they have a part in [the classroom], it is easier to discipline than if it is seen as something I hand down. (Vol. IV, p. 61)
Marks students are real middle schoolers and as such will on occasion challenge him or choose to be less than cooperative. One day in the midst of a challenging algebra lesson, I suddenly heard Mark say, "[Rick] and [Jim], this is where it becomes very critical. Maybe you understand it and can explain it to the rest of us. Can you explain it to us?" (Vol. IV, p. 86). The two boys acknowledged that they did not understand the concept and could not explain it to the class; Mark then moved on as though nothing out of the ordinary had happened.
Marks deep respect for his students is returned to him. His students spoke of their respect for him and appreciation of the way he treats them. They pointed out to me that they like him because he is personable; interested in their lives, not just in how they are doing academically; he lives his personal beliefs in the classroom; and he even takes time to do things like going to a recreation center with them outside of school hours.
All lives are touched by pain and heartbreak at some time, and Marks students are no different. During one of my visits, Mark warned me that he had to tell his students about a death in the school family, a woman whose daughter was in the high school connected to the middle school. Many of the students and faculty knew this woman well. She had been active in the Mennonite church, having been a pastor and at the time of her death held an office at the conference level.
Mark started by telling the students that this was not an easy announcement for him to make; his voice was quiet, but steady as he spoke. After telling students of the death, a few of them gasped, then silence pervaded the room followed by a few students tears. Mark reminded them how they had prayed for the woman and her family that very morning, and though they did not realize it then, it was close to the time she died. He then asked the students if they would like to take some time to pray about the situation. Immediately one student said, "Yes." The entire class then moved into a circle and joined hands as Mark prayed aloud. After prayer a few of the students were crying and giving each other hugs. I realized that these students not only support each other academically, but also emotionally.
In Marks classroom, I was much more of a participant observer (Yin, 1994) than in the other classrooms I visited. Mark encouraged me to help in the classroom by answering students questions. When I told him of my fear that I would not be able to help students because of my lack of mathematical background, he told me to just ask questions. This allowed me to interact with the students during my visits.
I was surprised with the students polite manners. Their seemingly small gestures helped make me feel valued in their school community. This ranged from holding the door open for me when I arrived to excusing themselves when they walked in front of me. I was slightly amused when I accidentally tripped over the legs of one students chair. He had been leaning forward so the legs stuck out farther than I expected. He immediately apologized and told me he thought he had gotten over the habit of leaning forward in his chair.
In a brief conversation I had with some students, they talked about the fact that Marks classes are challenging. They said Mark "stretches" them and makes them think (Vol. IV, p. 85). One student mentioned that she likes the way he expects them to find answers to their own questions because it makes her feel good when she is able to solve a problem.
Students objective was not merely to find an answer, but to understand concepts. One day a group of students was trying to simplify this quadratic equation: 2n2 + 2n + 6. I recognized immediately that they could factor out the 2, but struggled to communicate it to the students. Though I helped them find the correct answer, they appeared unsettled because they did not understand what happened when we simplified the equation. Later I noticed Mark conversing with this group, using manipulatives. They were attempting to simplify the same equation using algebra blocks, and this is what I saw:
Mark asked students what each term had in common. The students responded by indicating the two smaller squares. Mark asked them to divide each term by the two squares, using rulers for parentheses, and pencils for the addition sign. Students ended up with this:
As I left the group, I noticed the students were smiling and nodding because they understood how to simplify the equation. Their body language expressed a sense of relief because they understood what happened to the equation when they simplified it.
I struggled to identify specific beliefs emerging in Marks professional and personal life because I kept coming back to one belief from which it appeared that all the others stemmed: His commitment to living out his religious beliefs. The more I understood what he identifies as core religious beliefs, the more I realized how integrated these beliefs are to his very being. This personal integration is one of Marks uniquenesses and is part of making him Real. I am choosing to discuss Marks commitment to living out his faith as one of five separate beliefs though it is foundational to the other beliefs. Other beliefs I want to discuss are valuing others, compassion for others, community, and preparing students for the future.
The other issue I want to address in connection with my efforts to articulate Marks beliefs is my own experience in the Mennonite church. I was raised in a Mennonite church, and I am familiar with the tenets of Mennonite theology. Mark personally adopted a Mennonite theology before joining a Mennonite church, and I, though I was taught this theology, have since left the Mennonite church. It has been a number of years since I have been part of a Mennonite church, so while I was familiar with Marks religious beliefs, our journeys and experiences differ greatly. My past experiences, however, provided an understanding of the unique aspects of Mennonite theology to which Mark referred.
From my first to my last conversation with Mark, he frequently referred to his faith or religious beliefs. As I learned more about the core beliefs which compose his faith, I discovered that Mark does not merely talk about his faith, but he is intentionally and thoughtfully living out his faith. It composes the very core of who he is and is integrated into the fabric of his entire life, including his educational philosophy.
When Mark began going through the change process in Vermont, he remembers thinking, "Wow, this is what our church schools should be doing. . . . It just kind of reinforces our theology. I thought [using this approach in a Mennonite school] would be great" (Vol. IV, p. 9). It was a difficult decision for Mark to leave his position in Vermont; however, his desire to again teach in a Mennonite school pulled him to the Michiana area. Though the move meant loss of prestige as an educator and a lower salary, Mark chose to teach in a school whose religious beliefs mirror his.
I asked Mark how much of his teaching philosophy is influenced by his religious affiliation. Without hesitation he replied,
I think it parallels closely. The Anabaptist, Mennonite understanding of community, shared responsibilities, and valuing everyone equally is very much a part of who I am. The process of problem-solving and using a variety of strategies to approach situations brings together teaching and my faith. This comes out of being a Mennonite. (Vol. IV, pp. 61-62)
The capacity to change and take risks Mark attributes to his faith. When I asked him if he considers himself a risk taker, Mark replied,
[I am] a cautious risk taker. My dad is not a risk taker. I think that my faith has enabled me to take risks. [I] do some things not knowing how theyre going to turn out, but I know God is with me. I dont think I would have done that without my faith in God. . . . I would probably have been more like my dad, getting into a routine and going with that. . . . I like when things are predictable. Taking risks is not easy for me. (Vol. IV, p. 100)
Mark sought to live out his faith not only in the classroom, but also in his relationship with me. His repeated encouragement that I become a participant observer in his classroom told me he valued my input in his classroom community. I sensed his efforts to make me, an outsider, feel part of this community of learners through reminding the students of my name and involving me in the class routines. Mark also asked for my input in the organization of his curriculum, which gave me an opportunity to share in his responsibilities.
Marks religious beliefs motivate him to value human beings highly. This is seen in his convictions that he could no longer be part of the military lest he be forced to take someones life. When considering the issue of whether or not he could kill someone, Mark recalls thinking, "Am I my brothers keeper? Were brothers and sisters in the world" (Vol. IV, p. 62). Mark concluded that he valued his brothers and sisters too much to take their lives and ended his career with the military.
Valuing human beings is lived out in Marks classroom by both himself and his students. This begins with Mark; he models it and teaches his students to value each other. The very structure of Marks classroom shouts the message that students ideas and input are valued. Beginning each math class with students writing and verbally sharing reflections on their homework demonstrates the importance of individual thoughts and ideas. Mark repeatedly gives students an opportunity to express their own unique ways of solving a given problem.
Mark valued and encouraged students questions and believed in their abilities to solve difficult problems. He creates a classroom where students feel safe to ask questions when they do not understand concepts. Instead of quickly answering students questions, Mark asks students to use their skills and reasoning abilities in order to answer their own questions. This was always done in a tone of voice which expressed confidence in students abilities in finding answers. Mark sought to challenge his students, but along with these challenges came provisions for success.
One of Marks Group Procedures in his classroom is "Be respectful of one another" (Vol. IV, p. 16). Mark consistently models this for his students by the respect he shows them. One day he interrupted a student who was speaking and immediately apologized for his action. When Mark and his students discussed ways to solve problems, he responded positively when someone had a unique idea and acknowledged times students methods were new to his thinking.
Part of valuing his students is celebrating their successes, and students have learned to celebrate their own and others success. Mark asked students to share observations with the class about a series of equations they had graphed. They were first to discuss these observations with group members then share them with the rest of the class. One male student was the spokesperson for his group and stated that all the equations were in the same quadrant and were positive. His tone of voice and the hesitation with which he spoke gave away the uncertainty he felt about his answer. When Mark commended the group for their insightfulness, the male turned to one of the female group members and they gave each other a high-five.
Valuing individuals logically leads to showing compassion for others, and this is another belief Mark holds and lives. One of Marks students, Patti, faces both physical and academic challenges. It is Marks policy that students who have not completed their homework are responsible to complete it alone while the rest check their work in groups. I noticed Patti working on homework one day while other students were correcting theirs; however, she soon joined her assigned group. When I asked her about it, she explained that Mark told her she could join the group even though they had not yet completed grading the homework. This allowed the group to work with Patti and explain the concepts to her. Though Mark has policies which he follows, he does make exceptions to rules when it is in students best interest.
Marks gentle way of telling students about the death of another students mother impressed me greatly. He recognized that it would be difficult for some of the students to hear this news and gave them time to process the information before they had to leave for their next class. The entire class pulled together and showed compassion to each other through their prayers and by embracing those students who were closest to the family.
Marks students share prayer requests with him and their classmates. This can become a lengthy process, but Mark shows his interest and concern about each request by recording them and then actually praying about each one specifically. Some of the requests appear almost trivial to adults, but Mark responded to each request with the same level of interest.
Modeling and teaching students to value each other and showing compassion are essential to creating a sense of community within the classroom. Mark actively teaches his students the importance of ensuring that all group members, or a small segment of the classroom community, understand what the group is doing. Students have learned this lesson well. I heard them asking each other if they understood what the group was doing and explaining concepts to each other until everyone felt comfortable with the direction in which the group was moving.
Though Mark is the leader in his classroom community, he is not a dictator; he is a fellow traveler. I noticed him constantly giving control to students in his classroom. When I asked him about this practice, he replied,
When I think of education, it is about empowering the students as co-participants. . . . Students need to be stretched; they need to expand their intellectual abilities. Its through their empowerment, through their processing of ideas and concepts that learning takes place. . . . Its also a good model for them to know that there isnt any one individual who has all the answers. As a teacher I dont know everything, but together we can find what we need to learn. (Vol. IV, p. 61)
Helping others and being willing to be helped is an essential characteristic of Marks life and is crucial to creating a community. When Mark looked at his own life, he observed,
I cannot give enough credit to the people that have helped me. As I look back, thats been my life. Ive received a lot of help from others. I know people talk about pulling yourself up by your own bootstraps and those kinds of things. Yes, we do need to have some of that, but we also need other people who stand alongside of us. Ive experienced that. (Vol. IV, 98)
Mark comes alongside his students and helps them grow in a safe community of learners, he stretches them to keep them from becoming stagnant and complacent, but all this is done within the context of a community committed to the success of all its members.
A number of times in our conversations, Mark mentioned his goal to adequately prepare students for their future, to be successful wherever life may lead them. Part of this emphasis on students future involves not only the academic, intellectual part of students lives, but also addresses other aspects of students being. Mark keeps one eye on what students need in the future while integrating these skills into their current lives.
One of the motivating factors for Marks problem-solving approach to math is wanting "to teach [students] the skills they need to take them into the next century" (Vol. IV, p. 56). He wants his students to feel confident in their reasoning abilities, to be problem solvers, and to be able to work independently or in collaborative settings. It is important to Mark that his students are willing to look to others when they need help and realize the power of synergy. Marks entire classroom structure and modus operandi not only support this belief but also develop these skills and attitudes in students lives.
Marks concern for his students spiritual and emotional growth and preparation for the future permeates all he does and is. When making plans for the devotions he has with students, Mark looks at current issues students are dealing with and discusses them. These topics are not just for students immediate needs, but are chosen based on what Mark hopes they will become in the future. He constantly seeks to view students in the future tense:
I always think about where [my students] will be, not where they are. I have to think that thats what [my] sixth-grade teacher thought about me. She probably thought, this is not who I am, where I am, it is where I am going to be. Thats how I try to view students. (Vol. IV, p. 98)
Students current situations, skills, and knowledge are bound together with their future needs in Marks classroom. Marks goal of preparing students for the next century does not make him blind to their current needs; he uses the immediate as a means to the end of developing students prepared to face an uncertain future.
Mark summarized his life for me in our last interview. After creating his life map and explaining various events, he said, "Its those kinds of experiences that have laid it out for me that my life is to be a life of giving. I think thats what has helped me get to where I am" (Vol. IV, p. 97). Mark gives unselfishly and humbly to those around him, his students, his colleagues, his church, and his family.
While giving to others and becoming part of their lives, Mark searches for ways to learn from them. Mark said,
There are things I need to learn. The people who have expertise . . . are the ones I want to learn from. It becomes reciprocal. I am not an island unto myself. Learning and teaching and doing [this] with important help from others only adds to the excellence of it. (Vol. IV, p. 60)
Marks students are an important part of his learning and growing. Because they are different each year, he is challenged to stretch himself to meet their needs. Mark is constantly seeking ways to better tailor his curriculum and instructional strategies to what his students tell him they need. He observed, "I think the students are really the ones that initiate some of [my curricular changes] too, the questions they ask, the things they want to do" (Vol. IV, p. 101). These keep Mark from growing stagnant. A lack of growth to Mark signals an indication that retirement is on the horizon,
I want to stay in teaching as long as [improvement] can continue. When I begin to feel everything Ive done, Im doing over again and there isnt anything better to do, then its probably time to retire. (Vol. IV, p. 101)
Marks ministry to his students grows out of a life that has been ministered to by others. He has grown through the unselfish service of others and his goal is to pass on what he has freely received in hopes that his students will continue the cycle by living a life of ministry by giving to the world around them.