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Research Documents

Journal Documents

This page is dedicated to various works of mine. They include research and focus papers about education, as well as personal journals and thoughts while working in the MAT program at Colgate. Below is a focus paper based on my observations and interactions with students. At the bottom of the page is a collection of various works that are available for download and viewing.

My Work

Focus Papers:

(Example)

Community vs. Community

    Today the students had just returned from a week and a day of snow days. There was no bell work and the room quickly filled with random chatter about the days events. Today was a unique day, because the students had been working in groups, and were preparing to teach the rest of the class the topics they were learning about. The students quickly got together to discuss what they were teaching the rest of the class. I eagerly sat in my chair waiting for the presentations to begin. Talking seemed fairly brief as the students got out their notes and were silent after about 5 minutes. Topics ranged from subjects such as irrational numbers, greatest common factors, and in particular scientific notation. The group that presented scientific had a group of three students. Two of the students actively participated, while one student remained silent until the teacher asked him questions about the subject.

Teacher: Ok, the next group is presenting

Student A: We had scientific notation.

Teacher interrupts: Make sure you guys are taking notes.

Student A: When you have a number like 1,230, you move the decimal over three places so that you have a single digit number with a decimal like this. (Writes 1,230, and then moves the decimal over three places to get 1.230). How many decimals you move over is the number over the ten. (The student writes 1.230 * 10, and then places the number 3 over the 10). So now, you have 1.230 times 10 to the third power. If you had a number like 34,256, then you would move the decimal over by four places to get 3.4256 times 10 to the fourth power.

Student B: If you have a number that is already a decimal, then you still need to make the number a single number with a decimal. (Writes down the number .0012). If you have this number then you need to move the decimal so that you get the number 1.2. I moved the decimal over 3 places, but when you have a decimal and you are making it a single digit number with a decimal then how many places you move it over you put a negative number. So I moved it over three times, so it becomes 1.2 times 10 to the negative third power.

Jeff stands in the background and remains silent.

Teacher: Can you give an example of scientific notation Jeff?

Jeff: I don’t know……No, I don’t know how to do it.

Teacher: Can you explain what scientific notation is?

Jeff: (stutters for a second and shrugs shoulders as if he doesn’t really care)…. I don’t know what it is.

    It is put into question whether a community has developed, or if a math community has been developed. At the introduction of every class, the students come in full of energy and chatter amongst themselves about their day, random jokes, as well as extra curricular activities. Often, the teacher has to get them organized and ready for the lesson, by assigning them work to do at the beginning of class, or by attracting their attention. They have developed interpersonal relationships with one another, yet does this necessarily mean that they have developed a math community. When I state math community, I am suggesting an environment where interactions and learning are driven not only by the relationships formed with peers and the teacher, but I am also talking about an environment where learning is motivated and driven by math. Are the students in an environment where they can learn from each other, as well as from themselves, and is it being done effectively?

    A classroom community consists of a variety of contexts blended together. There are complex interactions between individuals in the classroom based on rules, guidelines, and expectations set (McCabe, 5). Jeff’s sense of community can be analyzed based on Ryan’s and Stiller’s three psychological needs that a student must have in a classroom. A student should have a sense of autonomy, competence, as well as a sense of belonging (McCabe, 11). It appears that Jeff may be struggling in all of these areas, which may be affecting his learning. At times, he does not know the answers in class, so he chooses not to raise his hand, and if often takes him a little bit longer to understand as well as complete in-class work. He may be lacking a sense of autonomy or control, because of the fact that it takes him a little longer to comprehend the material, and amongst his peers, he may have a declining self-confidence, as well as not have a sense of belonging because of his new perception of his self-confidence. This will lead to him being withdrawn from the classroom, as shown in his example when participating with the group. So Jeff may feel like a friend amongst his classmates, yet when it comes to learning math as well as participating in the classroom it seems he withdraws himself, possibly because he feels he lacks understanding and/or control in the classroom.

    At one point in time, Jeff was on the verge of understanding the material he was learning. The topic of the day was recognizing patterns and developing equations that represent those patterns. With the assistance of my fellow tutor, he was beginning to recognize the number patterns, and from there he was able to create equations that matched those patterns. From his response, he seemed delighted that he had learned something, and he wanted to show his classmates as well as his teacher. At this point, he did something outside of the usual. He openly attempted to participate. When reviewing the in-class work, he raised his hand to answer a question; something that he rarely, if ever, does. The teacher, however, called on one of the “more-able” students to answer the question. Since then, I have not seen him raise his hand to participate in class. In a way, I feel that he has developed the idea that “if the teacher doesn’t call on my when I raise my hand, then there’s no reason to participate.” Though this is an isolated incident, it can have a serious impact upon individual’s perception of themselves in the classroom. They may feel isolated by the fact that they wanted to participate but weren’t called on to do so. I can call on my previous days of education, when I wanted to participate, yet was never called on, so I merely withdrew myself from the class, because I felt my opinion was significant enough to deserve class time.

    Jeff may also see the material that he is learning as something that is not meaningful or applicable outside of the classroom. If this is the case, along with the additional factors of him withdrawing himself from the classroom, he will be even more unwilling to participate and engage himself in the classroom. The group work, although an attempt to get the students to learn from one another, as well as developed relationships within the classroom, was not effective in this context for Jeff. He stood silently as the other two students led the presentation, and when asked about what was being presented he simply stated that he did not know.

    To ensure effective group work, placing an emphasis on the concepts presented, instead of simply whether or not the group got the right answer, and although the teacher asks the students about their understanding, it is not done as effectively as hoped (Webb, 16). Webb suggests not only that should teachers place more of an emphasis on the understanding of concepts, but also teachers should be active monitors in group work. This means that teachers should make sure that students are doing their work, but should also ask questions to evaluate a student’s understanding and redirect them towards the correct or more appropriate response (Webb, 16-17). A teacher is somewhat like a compass in this matter by pointing the students in the right direction, but not necessarily telling them how far they can go or what restraints there are. In order to get Jeff engaged in the classroom, I suggest that there should be a focus on building stronger bonds between what assistance Jeff is receiving, as well as his response to the assistance he is receiving. Either he isn’t getting enough help, or he may not be responding to the help that he is getting, which may in turn be a result of his level of motivation in the classroom. Another way to get Jeff more involved in the classroom, group work could be presented in a way that encourages the equal participation of all students, and students should be made aware that each individual has their own strengths and each person can bring something different towards group work (Webb, 19). If this were the case in Jeff’s group work experience, Jeff may have engaged himself more, relating the topic to what he knew, and material may have been presented in a different fashion relating to what each student knew and did not know.

Influencing Motivation

    Today was another day that was “unique.” The teacher was now implementing punishments for those students who failed to complete their homework. Punishments ranged from doing work during free periods, doing work after school, missing extracurricular activities, and calls home to parents. Today seemed to be a fairly unusual day, because many of the students did not do their homework. However, it seemed that Jeff was pointed out in particular for not completing the homework assignment.

Teacher: Where’s your homework?

Jeff: I didn’t finish it.

Teacher: Should I call your mom, or should you?

Jeff: I don’t know, I can’t. I don’t have time to.

Teacher: Does your mom care if you do your homework?

Jeff: No, I don’t know.

Teacher: You do know

Jeff: No, I don’t

Teacher: (Now standing in front of the class to write something on the board) The last time I called she, even though you said she wouldn’t be there and that she wouldn’t care, she actually did care, and she was pretty upset that you didn’t do your homework. So, should I call home, or are you going to call your mom and tell her that you didn’t do your homework.

Jeff: (says under his breath) I’ll call my mom.

    Jeff rarely completes his homework on time, and when asked about it he either responds by saying he forgot about it, or that his mother does not really care if he does or does not complete his homework even when the teacher states that his mother does care. The use of a punishment, such as a call home, or staying after school to do work, takes a behaviorist approach towards learning. If a student does not do “x”, then they are punished with “y.” Some of the students have adjusted towards it well, but other students such as Jeff, have not been phased by it. Even by getting his mother involved, he seems unmotivated to finish his homework assignments on time. At this point, it seems that his motivation for learning math is primarily extrinsic, in that he is motivated only by outside factors, and as a means to get to the end of class (Eggen, 299). Yet he is barely motivated at all, and it appears that not all these forces of extrinsic motivation are working. The call home discussions seem to attract the attention of the class to the individuals who did not do their homework, which “puts them on the spot” where they are not only judged by their teacher, but by their peers as well. I can also see how this affects a student’s performance in class, because although Jeff said that his mother would not care, in the back of his mind he is thinking about how he has to call his mother throughout the entire class period. This can also distract him from engaging and learning about the material in the classroom, when he is focused on how his mother is going to respond.

    All of these factors can shape Jeff’s motivation in the classroom. From the looks of things, it seems that Jeff’s sense of belonging is at risk, which in turn affects his self-esteem as well as his intellectual achievement. This can be related in terms of Maslow’s hierarchy of needs. If a students’ sense of belonging is put at risk, then their self-esteem will also be impacted. Due to this, a student cannot reach their growth needs of intellectual achievement, because they are focused on maintaining their sense of belonging as well as their self-esteem (Eggen, 303). To relate it to Jeff, it simply suggests that Jeff will be unable to learn in the classroom, unless he feels comfortable with the people around him, as well as himself, and the way he perceives himself in the classroom.

    To balance off the use of punishments in the classroom, rewards could be used as well to help develop student’s motivation in the classroom. Simple things such as compliments or “nice job” can go a long way with these students, and even the use of rewards such as extra credit, or some type of small reward can go a huge distance in helping students develop motivation. This can help improve Jeff’s self-efficacy in the classroom. Compliments, such as “great job,” make students feel competent about what they are learning; they develop a sense of “I finally get it.” When students feel they can understand as well as feel they are in control of their own capabilities, they are more likely to be motivated in the classroom (Eggen, 325). In Jeff’s case, simply setting goals can go a huge distance. This means clearly setting goals, such as what ideas you want your student to learn and how they are applicable. By using the goal theory of motivation, a student knows what is expected of them, and are guided along the way towards achieving that goal of intellectual understanding. All of the students are given schedulers, which are an attempt to help the students develop goals and learn to organize their assignments, but Jeff needs more individual attention, because a simple scheduler is not enough. Encouraging him to develop self-determination would also benefit his learning experience. If he is given the opportunity in class where he feels like he has a sense of control he will be more willing to participate, and although he may not know the correct answers, hopefully he will have the courage to now ask questions to what he does not understand. If his “needs for competence, control, and relatedness” are addressed, then he will be more willing to participate in class as well as complete his homework assignments (Eggen, 325). If the process can be done, then his once extrinsic motivation will begin develop as intrinsic motivation as long as he feels what he is learning is applicable and has a purpose.

Does He Get It/ How to Help Him Get It

    At this point, I can honestly say that Jeff does not get it. He does not fully understand the material that is being presented to him, and because his lack of understanding, it seems he is not motivated or pushed enough to understand it. It seems as if he is been labeled as the student who does not know the answers, or the student who does not complete his homework assignments on time. Those expectations are affecting his achievement. Once he has been labeled, it is often very difficult to break the mold. The only time that Jeff was able to “get it” was when he recognized the relationship between number patterns, and creating equations from those number patterns. You could tell that he got it, because of his willingness to participate in class. However, when he wasn’t called on, he was not able to apply it, so by now the importance and meaning of number patterns may be gone for him. Before and after that moment, he has seemed to be withdrawn from the classroom, and although he sits in the front to help encourage his participation and focus in the classroom, he remains silent.

    The only way to help encourage Jeff to “get it” is to get him more engaged in with the material he is learning. This can be done in multiple ways. In terms of group work, this can be done by getting him equally engaged with the material along side his peers. Promoting equal participation whether it is during a presentation of group work or the creation of group work should be emphasized. This means not only monitoring if the students are getting the right answers, but if they understand the answers they are getting. This will help develop relationships with his peers, and hopefully help develop his self-determination and self-efficacy so that he feels like an equal amongst his classmates. In order to motivate Jeff, punishments may be implemented, but perhaps not in front of the class so he feels isolated and possibly violated or threatened. Rewards can be used as well, but more importantly, I am beginning to realize the time constraints this presents in the classroom.

    It is difficult for a teacher to do all these things for an individual student while teaching and maintaining the entire class. I propose that it is our (my) role as tutors, as mentors, to help develop Jeff’s motivation as well as comfort level in the classroom. This includes understanding his attitudes and feelings about the class, as well as helping him make connections between what he is learning and its practical use in everyday life. We serve as guides and role models, and instead of constantly correcting the students, we should guide them along, while giving suggestions and advice. The goal is to hopefully develop a relationship with the student so that they willingly come to us if they have questions and concerns. If they know we care, and are willing to listen to their problems, they will not only look towards us for advice, they will begin their path towards participating in the classroom. If they can open to us, the will soon open up to others, including their classmates and teacher if they have questions. It may also be helpful to help Jeff solve his problems aloud, so that he hears what he is saying, and it may provide for a way for him to interpret what he is learning better. Allowing him to solve his problems aloud will not only work on his math skills, but it will help his presentation of his opinions and ideas (Gourgey). It is also crucial to recognize that learners learn differently, and as Gardner states, have multiple intelligences. A more varied curriculum could both engage the learner, as well as help the learner address his or her own learning strategies and how to perceive different problems. As tutors, it is important that we try and recognize that students will have different points of view, and it is our job to put ourselves in their perspective in order to help them (Ball). To help Jeff learn mathematics, we have to promote two of the functions for a classroom setting. This will be promoting the pleasure and enjoyment of learning as well as intellectual growth in the classroom (Weinstein). If Jeff sees math as something that is fun and we can get him engaged in the material, he will develop an intrinsic motivation to learn and complete his homework assignments, because he sees them as worthwhile.

    Since Jeff does not understand and get what he is learning right now, the only way to access if he is getting it in what little time we have is to see if he increases his participation in the class. If he does, then this may mean that he is engaging himself in the material about asking questions to things he does not know. Of course, we can also tell if he is understanding if he is presenting the correct answers, and is able to explain his answers, but I feel that he will best benefit from the material if he is an active participant in the classroom, but this possibly requires reshaping parts of the classroom community, as well as the use of different strategies of motivation.

Work Cited

    Ball, Deborah Loewenberg. “Mathematics in the 21^st Century: What Mathematical Knowledge   is Needed for Teaching Mathematics?” 10pp.

    Eggen, Paul, Don Kauchak. Educational Psychology: Windows on Classrooms Seventh Edition. Pearson Merill Prentice Hall. 2007.

    Gourgey, Annette F. “Tutoring Developmental Mathematics: Overcoming Anxiety and Fostering Indpendent Learning.” Journal of Developmental Education. 4 pp.

    McCabe, David S. “The Role of Teacher In The Classroom Community.” 35pp. April 2001.

    Webb, Noreen M., Sydney H. Farivar, Ann M. Mastergeorge. “Productive Helping in Cooperative Groups. CSE Technical Report.” December 2001. 27pp.

    Weinstein, Carol Simon. Secondary Classroom Management: Lessons from Research and Practice. The McGraw-Hill Companies, Inc. 1996.

 

Research Documents for Download

          My Portrait of a Child

          Optimal Foraging Patterns in Mice

          Pollinator Constancy and Preference

Delinquency and Social Identity in Adolescence

Methods for Teaching Science, and Sciences’ Connections to Literacy

Teaching Students with Disabilities and Motivating Students to Learn in the Science

Building a Community

What Have I Learned: A Capstone Essay

Capstone Essay Music Track

Personal Journals for Download

Journals Part One

Journals Part Two

          Teaching of Palmer Reflection

          My Failed Lesson Plan

          How Do I Learn?

          Qualities of Teaching Response

          Misconceptions In The Classroom Reflection

          IRI Anaylsis