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Making the subject matter meaningful for students is a very important task. In mathematics, this task is made a little more difficult as the students progress in their knowledge of how to solve problems, but start to question of what use mathematics is. Mr. Moody was able, however, to make the subject matter meaningful for his students in all of the classes he taught.
His first class is Applied Statistics. This class consists mostly of seniors, with four or five juniors. For the most part, they are there because they want to be there. However, this subject has caused many to wonder, "Will I ever use this?" or "Of what good is this?" Yet, Mr. Moody was able to combine those questions and make it very meaningful. He devised a project for the end of the semester. He took them to the computer lab, so that they could use Claris Works. On the first day, he explained how to use the program to use test statistics, a concept that they had learned earlier in the semester. The whole project was designed to tie everything the students had learned in the semester together and make it meaningful to them. They had to make up their own survey questions, survey people, tally the answers, and by means of statistics, test to see if what they tallied backed up their hypothesis. Mr. Moody was able to combine his knowledge of statistics along with the help of the computer to make a project that proved to be fun for the students. I feel that by using some tool, such as a computer, he was able to convince the students that what they were doing was indeed useful. I hope to be able to use this concept in my teaching.
His next three hours were Algebra II classes. These students varied from Sophemores to Seniors, with increasing numbers as the grade increases. These students basically had to take this class, so therefore, it was even more necessary to make the subject matter meaningful to them. Each day, before the lecture, he would place the necessary steps needed on the board. At the beginning of each lecture, he would always show a problem that was easy enough to solve, basically a review problem, only integers, without the variables. This allowed students to see that the steps they had to use with variables could also be used in the everyday world with integers. He was also able in various examples to show where material they had learned before, such as patterns they had had to memorize, came into play now. Though the students didn’t know why they had to memorize the patterns then, they now saw some real applications for them.
His last two classes were Pre-Algebra classes, consisting almost entirely of Freshmen. For these classes, it is not as necessary to make the subject matter meaningful for students. At this point in their development of math knowledge, the student do not seem to care much how the subject matter is applicable to their lives. Therefore, it is more necessary to keep them busy. However, despite the challenges presented him, Mr. Moody was able to make the matter meaningful to his students. For two days, he had them working in the computer lab, inputting data. Then, on the third day, back in the classroom he explained the significance of that exercise. They were to use some of the same principles that they had learned the week before in solving the problems over the data that they had put in. Later, after the Winter break, he gave them a worksheet in class that tied together all the things that they had been working on for the past few weeks such as order of operations, factoring, and other basic principles of mathematics.
Through various ways, Mr. Moody was able to make the subject matter meaningful to the students, whatever level it was. I think that I will incorporate many of his techniques of how to make the subject matter meaningful into my teaching style, as they seemed to work. I think it is of great significance to make the subject meaningful to the students, especially mathematics, a subject that most feel they have received enough of by their sixth grade year. That is why his examples are imperative to use.
Understanding and providing various means for developing all students is one of the vital concepts of education. This takes patience and incitefulness. In order to achieve this goal, a teacher must understand the overall basic level of the class and the different levels of students in the class with which he works.
One of the best examples of this is simply by helping all students. This can be done by making time out to make sure that all students learn. Mr. Moody was always available before school, willing to tutor students. He also made himself available after school as well. On five of the six days that I observed, when I came to school, he was already there helping a student or two students in either Algebra II or Statistics. This is the easiest and most effective way to see that all students develop. The thing that I found most fascinating about his tutor sessions was that he was helping a different student each day that I went in there. Usually, a couple of the C or B students will be motivated enough and feel comfortable enough in asking for the teacher’s help. However, he was willing and had good enough of a reputation with all the students that many different students were able to take advantage of his assistance. When I teach, I will definitely make myself available to the students before and after school. This works, giving the students a one-to-one session.
Throughout his lectures, particulary in Algebra II, he made sure to show examples that all students could understand and learn from. In one example, he kept the negative sign with the top number, knowing that many students would get confused if he decided to keep the negative sign with the original number as it went to the bottom. It was through examples like these that he was able to convey the lesson across, thus seeing a development of all students.
Another use of class time was that he was always willing to answer student’s questions as they arose. Frequently, he would ask if anyone had any questions and take the time to answer them thoroughly so that the student understood. This seemed to help all students better understand the concepts.
These two methods used in the lectures were very effective. I will try to incorporate these methods into my teaching style.
Being able to understand and identify diverse learners is another key aspect of teaching. Some of this ties into the fact of trying to develop all students.
One of the ways that Mr. Moody demonstrated that he identified diverse learners was the fact that he was readily available for tutoring before and after school. Since he knew that not all students would be able to grasp the techniques for solving the mathematical equations from his lecture, he made sure to be available to tutor students on a one-to-one basis before and after school. This technique proved to be very effective as those students who were struggling in his classes were able to better understand the concepts. This is a technique that I will try to incorporate into my teaching style.
Another area where Mr. Moody demonstrated that he understood that students were diverse in learning was found in his lectures. In one particular case, his Pre-Algebra class was to meet in the computer lab. Realizing that not everyone knew computers well, he explained how to get into the hard drive and was available to help those who needed help on the computer concepts the entire hour. Several times, he made sure to answer individual questions. Always in his Statistics class, he made sure to walk around the room, making himself available for students. He was also willing to answer questions while he lectured, realizing that if one person was brave enough to ask the question, then probably another had the same problem understanding the concepts as well. He answered all of the students’ questions in the middle of class. In one of his Pre-Algebra classes, after being asked how to do some problem, he asked the student, "How do we find averages?" This was a review, which after some prodding the student was able to remember. This demonstrates that he knew how the student would respond, thus making it effective.
Another area where diverse learners came into effect was in classroom management. He knew that he had to deal with various student problems differently depending on the student. In one case, he said to a group of three guys, "Hey idiots, sit down, and get to work." This sounded harsh at first. However, they understood what he meant and did sit down and started working. The rest of the class found it funny, but understood that he was serious about it. The group of guys seemed to take the ‘idiot’ part as a joke, but the rest as reality.
When I worked with him on planning my lesson, he made sure that I would write down every step in the problem as I worked through it. This would allow slower students to see what I was doing. Also, after I taught my first hour, he told me to make sure that I slowed down a little from one step to the next, allowing students who normally would not say anything to get it down on their paper and hopefully understand what is being done.
These concepts worked effectively. I will try to use them in my classroom. It takes practice to get to know the students and realize what level they are on and how they will respond. This is a concept that Mr. Moody has mastered, and I hope to as well.
4. Long-Range Planning
It is important for teachers to realize that they will have to plan for the future. This is necessary in order to get through the material required by the state and school district, while going at a speed most profitable for the class. If a concept seems difficult, a teacher who has planned ahead will realize how much time that he or she can spend on that concept, and still be able to make it through the required material. This concept was demonstrated many times by Mr. Moody.
On the first day of my observation, Mr. Moody showed me a calendar for his Algebra II class. On it, he had put when each section would be taught, when the tests would be held, when the class would be in the computer lab, and when breaks were. He had planned ahead. This also allowed plenty of time for review in preparation of the semester final. He had this planned for all of his classes.
He had planned two days in the computer lab for his Pre-Algebra class before break. He told them before this. This was meant to allow students who don’t normally have fun with math to see the benefits of using math and that math can be fun.
On the first day after the Winter break, he told each class what would be happening the rest of the semester and what would be expected from them. For example, in his Algebra II classes, he said that he would be teaching today (Thursday), I would be teaching tomorrow (Friday), and then he would teach the last section Monday. He told them they would have a review day Tuesday, test Wednesday, then for the last four days review for the final in which they would have to complete a review packet. This gave the students plenty of time to prepare for the test and final, if they so desired.
This is one concept that I feel very confident on. I always try to plan ahead. After seeing the results of Mr. Moody’s planning, I realize how effective it can be. The students knew what was coming and could prepare accordingly. The teacher knew what was coming and could adjust the course if need be.
Many different strategies can be used when teaching. The key is to try to find those that work best to get the children to understand what is being taught. I noticed a few of Mr. Moody’s techniques.
One of the best ways to get students to believe that what is being taught in mathematics is really just adding on to what they already know. By starting off with a review problem, this allows the students to see that the new concept for the day all ties into what they have already mastered. In Algebra II, that is what Mr. Moody did every day. He would have about three to four example problems ready. They were arranged in increasingly difficult order. The first example would always be one with just integers. These problems students could already do. He tried to show that the steps they would have to use would also work with problems they already knew how to solve. At one point, one girl said, "We did this in second grade," referring to one of the example problems that he was doing. That was the intent; to show students that they could build on what they already knew.
Another strategy that Mr. Moody used was to encourage students to participate in solving the problems. He had already established earlier in the year that they were supposed to say answers when he asked for them. He would work a problem and several students would tell him what the next step was going to be. This helped Mr. Moody know that the students were understanding what they were doing. It also gave the students a sense of accomplishment. Several times he would even ask about a problem. For example, at one point he said, "What multiplies by twenty-one to make sixty-three." After pausing several seconds with no one saying an answer, he said, "Somebody, please say three." And then a student would do just that.
Another and probably the key of the components was his frequent review. On the first day after the winter break, he did a quick review for the students on how to find the lowest common denominator. This refreshed the students’ memories and allowed him to proceed with the next lesson. He seemed to understand what the students would know and what they would need help with. He didn’t review basic concepts, but if a concept came up that they had not used for a week or two, he would go over it again without waiting for students to ask. This allowed the quiet students to review the concept, whereas they might not have had the opportunity if a student who usually talks was asked if the class remembered the concept.
These all seemed to be very useful and helpful strategies. I definitely see that review and refreshing the students’ thoughts are the keys. These are strategies I will use.
Yet another important part of teaching is creating a learning environment. This means not only keeping the noise level down so that students can learn, but also establishing a principle from the beginning that learning is going to be done.
The latter concept was established mostly at the beginning of the year. However, it has to be reestablished every day, especially with the Pre-Algebra classes. On the first day that the Statistics class was in the computer lab, he had everyone look up at his monitor so that he could explain how to use the program to find the test statistic. This established from the start that they were to get actual work done while they were in the lab, and not to make it a free hour.
Another class where he had to establish a learning environment daily was in Pre-Algebra. On the last day that they were in the computer lab, they were supposed to complete a worksheet unless they had not quite completed the computer assignment from the last two days. All but three had completed the assignment. Therefore, he went around and made sure that everyone was working on the worksheet and not playing on the computer. This helped establish the learning environment necessary.
The primary concept in establishing a learning environment is to try to keep the class quiet. Mr. Moody did an exceptional job in this area. After lecturing in Algebra II, he would yell at those not working. This would sometimes mean the whole class, sometimes a large group, or perhaps just one person. This helped establish what was expected for all students, not just those acting up at the time. A few times, he would have the one person not working to be quiet or come sit by him or pass out already graded papers so that those wanting to do the homework in the time allotted in class were able to. With respect to two other teachers I observed during this time, Mr. Moody was far more effective in keeping his classes quiet. This probably arises from his great height and overwhelming presence.
I will hopefully try to implement a program with the same effectiveness. Realizing how important it is to keep the classes at a quiet level and trying to establish that learning will be done every day, I would hope to implement these programs customized around me. I would hope to have my presence create similar results.
One of the purposes of this early field experience was to see different techniques used by teachers and to see which ones were effective, and which were not. This required modeling of effective verbal, nonverbal, and media communication techniques. I observed these watching Mr. Moody teach.
Verbal techniques vary greatly. One of the areas of concern was how the teacher talks to the students. This requires a knowledge and understanding of the students and some goals which the teacher would like to see the student achieve. Several times, Mr. Moody encouraged the students to participate in his lecture by asking, "Now, what will we get?" This worked, since many students were eager to participate and be the one who said the right answer. In another class, the statistics class, when asked a question about how to use the data, he allowed his students to come up with an answer on their own, which they eventually remembered. This seems to be better than just telling them. This requires that the student remembers for themselves. This will carry over and allow them to remember it longer. A different kind of verbal technique was used when he had to deal with disruptions in class. He asked a group of male students, who were goofing off, "Guys, do you have a mental defect in following directions?" This worked effectively as the boys stopped talking and got to work. They seemed to respect him a little more because he used terms that they used. Yet another verbal technique had to be used when he called the student’s parents. He made sure to call all of the parents of the students with F’s or low D’s, thus warning them that their child would not be allowed to be in the class unless he or she passed the first semester. Though he was extremely nice to all of the parents that he talked to, many parents blamed the students’ difficulties on the teacher and the curriculum. In reality, it was the students not coming to class or not turning in assignments that created the problem.
All of these verbal techniques seemed effective. I learned that you have to talk to different people differently depending on the situation. I believe that his methods proved to be quite successful. I will try to implement them into my routine.
Other techniques I observed were nonverbal. This was demonstrated in his appearance and in his actions. His appearance alone, since his is a very large man, required that the students listened to him. He also was able to convey that message in looks he gave the students. They knew when to be quiet and not talk to him. However, they also knew that when he was smiling that they could joke around with him a little bit. These messages came through quite clearly.
The media communication techniques consisted largely of computer projects. In both his statistics class and his Pre-Algebra classes he had computer assignments for them to do. This seemed to make the students feel comfortable doing the assignment. He also used it to communicate with fellow colleagues.
Francis Howell School District set up a system where one can "quick-mail" another teacher either in that school or in another school in the district. He made use of this outlet. He also was able to use the internet. He had had the statistics class find the background for their surveys off of the internet. Though I was not there when he did this, it seemed like the students really enjoyed it. Since these techniques seemed to work, I will implement similar programs in my classroom.
Both types of assessment, formal and informal, are important in education. I observed both of these in various ways.
Formal assessment ranges from tests to quizzes to grading homework. It is through these two types of assessment that the student understands what is expected of him or her and can see what progress that he or she is making. Mr. Moody used this technique. He gave one test the Wednesday before Christmas break in his Algebra II classes and another test a week after break for the same classes. This allows the students a chance to see what they know, and what they need help on, especially since the semester final is so close. He also gave out ten to fifteen homework problems each day. The next day, he would collect it, and have different students grade them. This was another example of formal assessment, of which the students were able to know the results within that same class period, thus allowing them to chart their progress.
Informal assessment is also important. This motivates students to continue studying and doing homework. Mr. Moody demonstrated this mostly in while working example problems. He would ask how to find something and allow the students to answer. Then, when they were correct, he would offer praise, such as, "Good" or "Correct." He did this several times in each class.
Both types of assessment seem to be extremely important in the development of the students. I feel that the informal assessment that Mr. Moody used seems to motivate students to participate in class. However, the smart or shy students didn’t feel comfortable in this assessment, wanting to avoid being shunned by their fellow students. Thus, other informal techniques would have to be developed.
A teacher needs to reflect on what they did to be able to determine what worked and what didn’t, therefore providing the best possible education for the students. When I talked to Mr. Moody about this, after teaching my lesson, he told me that this is a concept he has to apply every day. He does this in between every Algebra II class, deciding which examples worked and where the difficulties arose. I noticed from watching that he would change the way he explained one particular example to each of the three Algebra II classes. He saw what the students had difficulty understanding and then focused more on explaining that part of the example. For example, on one particular problem they were asked to find the lowest common denominator out of (x^2 - 4) and (x - 2). The second-hour class seemed to misunderstand and said the wrong answer of (x - 2). So, for the next two classes he made sure to ask before he asked for the lowest common denominator, what does (x^2 - 4) factor into. The students were then able to understand what he meant, and were thus able to answer the question correctly.
I noticed how important reflection was, especially when I did my part of the teaching. I had four example problems prepared before class. After realizing that the second hour class understood the least common denominator concept better than I had anticipated, I decided not to use my first example problem. After teaching it to the second hour class, I decided to change a few things, such as terms I used for different parts of the equation. It seemed to improve each hour. This is definitely a concept that is beneficial for the students and therefore should be applied.
10. Relationships with school colleagues and educational partners
One of the important parts of being a teacher is to have a continual learning attitude. One of the best ways to accomplish this is by spending time with other educators in the school and parents in the community. These are the people who can help give new instruction ideas. On one hand the other educators have a different style and perhaps have a better way of teaching material. On the other side, the parents know their children and might be able to help explain how they learn. Then, the teacher can combine these two viewpoints with the teacher’s already developed style to create a better learning environment for the students.
Mr. Moody talked to various instructors at different times. He talked to the head of the department, who also taught a Pre-Algebra class almost daily to get an idea of what and how she was teaching the material. The course allows several days for each section, which causes the teachers to have "filler time," in which they have to provide worksheets or computer exercises to keep the students busily working. He also talked to various other teachers at lunch every day. The conversation ranged from sports to cars to home life. But, it also included some great discussion on how the district was handling the hiring of the teachers, particularly the coaches of the new high school that will be ready the next school year. Various opinions were expressed. On a few mornings, he discussed practice times with the other volleyball coach. This helps allow for the physical benefit of the students.
The other aspect of relationships with educational partners concerns the parents. Time and time again, Mr. Moody would call the parent’s of the students who were either flunking or close to it. It was through this experience that he learned different techniques to teach their children, some applicable, some were not.
It was through this experience that I learned how important it was to talk to other teachers and parents to come up with different education techniques. This helps the teacher from becoming out of date with the students of today.