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Jeremy Gibbs

Junior Observation

Containing the appropriate level of the subject matter being taught is absolutely essential for teaching. The teacher must have the knowledge appropriate to be able to teach the students. Not only must the teacher know the material, but also must have a mastery of the topics that he or she can convey the lessons in a simplified way on the students’ level of understanding. The teacher must also be able to anticipate and answer any questions that may come up involving the subject matter. I was able to learn, observe, and demonstrate my knowledge of the discipline, ability to present the material in various ways, using students’ prior knowledge as the basis for constructing "new" knowledge, engaging students in methods of inquiry used in my discipline, and creating interdisciplinary learning.

Knowledge of the discipline is necessary for teaching. Not only is it essential to have mastery some subjects, but mastery of the entire discipline is required for a masterful teacher. I was amazed to see the knowledge of my cooperating teacher, Mr. Kern. In his Pre-Calculus class, he conveyed his knowledge of vectors by slowly stepping through what they are, how are noted, and how they are used. During this class, I was also able to demonstrate my knowledge of the material. During the time when the students were to work quietly at their seats, I walked around answering questions. The thing about this that I was most fascinated with was the fact that I had just learned about vectors in-depth in my last semester’s class, Linear Algebra. Thus, I had absolute knowledge of the subject and could answer any questions. Even though I had not reviewed the subject or the way it was going to be taught beforehand, I still could answer the questions. That is one of the things I learned from this observation; you have to be willing to review to remind yourself of how to do the problems and to be able to convey the topics in simple ways. As you progress through the various mathematical classes, little lessons are lost, but are helpful in reaching the big step and thus should be used in the teaching process.

In Mr. Kern’s Algebra I classes, when introducing the topic of proportions, not only demonstrated his own knowledge level of the subject, but also the student’s knowledge level, which they did not realize. In his speech, he showed several examples, showing how the use of proportions are all around us, even if we don’t realize it. In this class as well, I was able to answer questions during discussion time.

It was also this class that I taught. This allowed me to extensively demonstrate my own ability of the subject matter. I lectured about using the least common denominator to be able to add fractions without the same denominator for the first half of the class. During this time, I came out and told them plainly that "Today’s material was simply combing the concept of adding fractions along with the algebraic concept of finding unknown variables." This not only helped reassure the student’s that they truly did already know this material, but also made them more interested. I find, in all of the teaching that I have done, that if the math teacher can make the math seem like steps that the student’s just continue to build upon, then math anxiety is greatly reduced. So often students feel they can’t do something because the teacher teaches it as if it is some vastly new item the student’s have never seen, even though there may be a way of showing that the students have performed similar operations in the past. This makes the lesser ability students have more confidence in the lesson. In this manner, I was able to build on students’ prior knowledge to create "new" knowledge.

After taking a break in the lecturing, I allowed the students to work alone to make sure they understood what I had covered so far. This allowed them to get started on their homework and to ask me any questions that they may not have wanted to ask me in front of the whole class. Several students took advantage of this and caught me as I made my way around the room. This allowed me to present the material in a slightly new manner, one that would be more appropriate to the individual student.

During the second part of class, I lectured about word problems. Almost every student, upon hearing this topic, cringes. This is usually a tough subject for students. However, as I explained, it is simply changing words into mathematical symbols. I went through two examples stopping and circling words that needed to be defined. I explained that the first matter that needed to be defined was "the number." The questions asked that you "find the number" in an algebraic type of problem. So, upon prodding them, we agreed to call ‘x’ "the number." I went through the entire problems underlining certain parts of the question that we could define and asking them to do so.

One of the more interesting classes I sat in was Consumer Mathematics. This class was taught by Mr. Weber, the division chair at the school. The subject about which the students were learning was buying a car, financing a car, getting insurance for the car, maintaining the car, and other related topics. What I found most interesting about this class was the teacher’s knowledge of the subject. On one day, he talked about the different options about financing the car. On another day, he discussed the various types of insurance. Not only was this very informative to the students, but I also learned things. What this also did was to create an interest in mathematics in students who are at the lower end of the mathematical ability spectrum and to whom mathematics is usually of no interest. This showed to the students the various types of methods needed in order to solve the mathematical problems. For the insurance problems, one would have consider what coverage one would receive and how much the payments would be. Also, the class creates an interdisciplinary learning environment as the students must use various skills such as writing, reading, an of course mathematics.

Another class in which I demonstrated my knowledge level was in Mr. Kern’s Calculus class. In one class, Mr. Kern was feeling sick and not able to think clearly. He got stuck on one of his examples and was unable to explain how to work it. After he sat down, I was able to look at the problem and show him how it should be solved. In another example, he asked me to grade papers for the class without a key. It was on simple integrals so I could grade them simply by looking at one paper and using that as my key.

Knowledge of the subject matter is extremely valuable for teaching. What I found out in the observation was that the teacher not only must have an understanding of how to work the problems, but more importantly such an understanding and ease at solving the problems that it is not necessary for him or her to look at his or her own work when trying to explain how to solve the problems. This allows for more eye contact and thus more attention on the part of the listener and in turn a better level of understanding.

Even a more important skill concerning the excellence of teaching is being able to adapt the instruction for individual needs. If one cannot master such a skill, then one will be known as a really smart teacher, but unable to teach because he or she always talks above the students’ heads. To be able to do this, one needs to identify the prior experiences, learning styles, strengths and needs of students. All of these are of great importance in being able to adapt the instruction to meet the needs of the students. Also, one needs to be able to use individualized instruction based on prior experiences, learning styles, strengths and needs of the students involved. Another important aspect of this concept is being able to access specialized services to meet students’ needs. And finally, an excellent teacher needs to be able to connect teaching to students’ prior experience and family, culture, and community.

The first class I observed in which I saw demonstration of this skill was Mr. Kern’s Pre-Calculus class. In this class, when he was introducing the concept of vectors, he explained some of the more common uses of vectors such as in Physics and other examples, taking the concept out of the abstract and making it real to the students. This also interested them since some of them were in a Physics class.

Another way that Mr. Kern made the concept meet their needs was when he put the students’ names into the examples. In one particular example, he had one male student able to pull with great force while another could only pull with little force. This peaked the students’ interest as they saw practical use of the concept and they were in the examples.

One of the ways I noticed and demonstrated that ability was when I taught the two different Algebra classes. The third hour class is much more behaved and thus can move quicker with material than the fifth hour class. Mr. Kern pointed this out to me before he had taught the classes. I noticed that when he taught them, he had to monitor much more closely the fifth hour class than the third hour class. Thus, when I taught, I also noticed that it took longer to go through the examples and explain the material with the fifth hour class and had to cut out a few problems from my assignment due to the fact I was unable to explain the complete material to them. I noticed a similar result in Mr. Kern’s instruction. On one particular day, he had to spend thirty minutes explaining the material and working examples for fifth hour, whereas in third hour he only spent twenty minutes covering the exact same examples and material.

On another day of these two classes, after seeing third hour struggle to convert centimeters to meters and kilometers to meters, he wrote the formulas on the board when it was time for the students to work on their assignment.

Another class of Mr. Kern’s was Calculus. This class consisted of all very bright seniors. Thus, Mr. Kern could adjust his teaching to meet their particular needs. One way he did this was with examples. With this class, rather than encouraging them to walk him through the steps to keep them on task, he would step back of the room and allow some time for all students to work the problems. This could not be done in a lower mathematics class, such as Algebra, because most of the students would not be motivated to finish the problem on their own. However, with an advanced class like this Calculus class, all of the students had a desire to be the one to get the correct answer. It worked extremely well.

Another class to the extreme end of learning ability the other way was Mr. Weber’s Consumer Mathematics class. All of these students were slower math students and thus presented an individual case to the instructor. Rather than spending all of the time on the subject of mathematics, which almost all of the students didn’t care about, he would discuss other practical topics. When first introducing the idea of buying a car, he first asked, "What do we need to know when buying a car?" He encouraged them to participate in the discussion providing whatever answer they felt would possibly be important. This definitely eased the minds of the students who weren’t particularly fond of mathematics in the first place. From that discussion, he slowly worked in the math concepts.

I found this important when I taught this class. I opened the class by asking, "What do we need to concern ourselves with maintaining or keeping up?" This opened up the airwaves and made the class more free.

In fact, the entire way he ran the class was designed to meet the needs of that particular type of student. He was very laid-back in allowing free speech, knowing that any kind of authoritative figure, if he comes on too strong, is automatically thought of bad by these type of students who also experience behavior problems many times. Yet, he also had very strict rules and expectations laid down from the start. The rules were tight while the lecture was loose.

Another class for which this concept was used greatly was a self-paced class. This class was taught by Pauline Johnson along with a special educator. The class was Consumer Mathematics and consisted of a class within a class situation. The students could pick the units they wanted to work on and had packets for each of them. The results were astonishing. The difference from first quarter to second quarter, when they implemented the plan, was dramatic. Of fifteen students, all but two saw an increase of a letter grade in their scores. Surprisingly, this format worked very well. The students didn’t have trouble staying on task at all. Each night, the teachers would check the packets to see how far they were and assign them to get done with the next page of the packet usually.

Seeing the importance of adapting the instruction to the various types of students was very helpful to me. It is of great importance to receive maximum results that this is done. Whether the students are advanced or at-risk, the teacher must have individual plans to meet their needs.

One of the components of teaching of vital interest to creating the proper learning environment involves classroom motivation and management skills. Both of these skills are necessary to foster in order to obtain maximum results in the students.

Several theories of motivation exists. The way in which one views motivation affects these strategies. The four most common approaches include humanistic, cognitive, social, and external motivation. Whichever of these schools of thought are used affects how one views motivation. The humanistic point of view believes that the student naturally wants to learn and is intrinsically motivated. Thus, the environment affects him little. The cognitive view assumes that the motivation is affected by the stimulation of the brain. Thus, the learning is desired by the students in order to stimulate their own brains. The social school believes that the environment affects the students’ motivation. Thus, if the community values the learning and education, then the student will also have the same values and be motivated to learn. That last school of thought is the behavioral psychology. This school of thought believes that the student needs a reward for learning.

In Mr. Kern’s first hour class of Pre-Calculus, he tended to reflect the social view. Not only is education encouraged at home and in school, but also in the classroom among the students’ peers. He would encourage the students to participate in the learning by taking data from them and using it in the problems. That students would naturally be motivated to be able to complete the problem in order not to look dumb in front of their peers. These students were mostly seniors, with a few juniors. They had achieved high levels of mathematics already and felt that learning was important.

Another way in which Mr. Kern motivated his students was found in his Algebra classes. In beginning the lecture, he would gently remind them that this was all stuff they had seen before and thus could be able to do it. This motivated them to participate and try the example problems. I also used a similar approach when I taught the classes and found it to be effective. During the lecture, both he and I encouraged the students to participate in the discussion to foster the motivation among the class.

Another method used for motivation involved extra credit. I found it very interesting the mode that Mr. Kern used regarding this. In his Calculus class, upon introducing the concept of integrals, he gave out an extra credit assignment in which the students would try to approximate the area under the curve, which the integral will find, by using a concept of limits and approximation. What I found to be most remarkable about the assignment was the fact that it motivated the students to discover the relationship of the definition of the integral in order to receive a few extra points. He also required them to make it be poster like so that he could put them on his wall, which he had done with previous extra credit assignments.

One example of ineffective motivation was found in Mr. Takahashi’s ACT class. The class was to prepare the college bound students to take the ACT. It was his custom to ask the students for the answers to the questions and for an explanation. That seemed like a good idea, as he would call randomly on students. However, what I found interesting was that he would take ‘I don’t know’ as an answer. The problem with this was that a lot of these students didn’t always want to participate and thus, allowing them to get out of doing any work or thinking simply by saying ‘I don’t know’ encouraged many of them not to take chances if they weren’t sure of the answer. I don’t think it was the best method to motivate the students.

The other aspect of this category involves management skills. Keeping the classroom in a somewhat orderly fashion is necessary in order to reach maximum learning goals. Different methods may be used from simply a quiet reminder to sending the student directly to the principal’s office.

Mr. Kern, for the most part, simply used a gentle reminder. Any time the students were out of line or up out of their seats, he would just remind them of the policy and they would always respond kindly to him. I am not sure exactly what he did at the beginning of the year in order to lay down the law, but apparently he did something very effective. He has been teaching for twenty-seven years, so he has found what works best for him and his students.

One of the classes where classroom management is most necessary was in Mr. Weber’s Consumer Mathematics class. His classroom was strict in rules, as far as where students needed to be, but loose in lectures. He encouraged discussion of all kinds, even if the students had a desire to talk about something else totally off the subject. He felt that that was necessary in order to maintain the students’ interest and motivation. One time a student was in the teacher’s seat, where he should not be. Mr. Weber didn’t overreact, but rather, while working with someone on their problems, talked out loud how he hoped that no one was in the wrong seat. It worked, as the student proceeded back to his own seat.

One of the ways that the school of Wentzville High School found effective in management involved student passes. Rather than writing out passes on slips of paper, which ended up costing the district a lot of money going through so many of them, they started writing the passes to the bathroom, nurse, etc. in the students’ individual planners. Each student, at the beginning of the year, was given a planner indicating the upcoming school events. Not only did this save money on the passes, but also allowed the teachers in later hours to see if it was a common reoccurrence for the student to leave class. For example, if twice already the student had been to the bathroom or nurse, then the next teacher would have those records in front of him or her and could respond appropriately. This management method seemed to work extremely well.

Another important aspect regarding successful teaching is the planning time. It is important for the teacher to have proper planning times and to use them wisely. One of the aspects of teaching not generally noticed is how much time it takes to teach the class. The lesson must be mastered, knowing every example and type of problem needed to present. Possible questions must be thought of, so that the teacher can be able to answer them thoroughly, anticipating what the students may ask. Tests, worksheets, and other assignments must be well thought out and considered in order for the students to reach appropriate mastery of the subject. In planning the lessons, the individual students must be accounted for. The teacher needs to be able to have a general idea of where the students are coming from, their current level of mastery, the resources of the classroom and possible resources needed, and the overall curriculum goals of the school.

The first planning session I had with Mr. Kern occurred during his first hour Pre-Calculus class. He showed me his file, consisting of six or so worksheets which he had prepared over the holiday break. These worksheets were completed with the idea of being able to learn vectors. Not only did he prepare the entire unit with worksheets supplementing his lectures, but he also had prepared the test and quizzes for the unit. Thus, I realized that it takes a lot of time to prepare for the teaching. However, as was shown here, it is much better to be prepared well in advance so that proper adjustments may be made later, if need be.

During his Algebra class, we discussed possible lessons for me to teach. We came to a conclusion that I would teach a section the next time his classes had class. (It was a block schedule, so every other day they would have the same classes.) The next day we went over the lessons that I had prepared. He said that he liked my lesson plans, thought my relating the least common denominator to proportions, which they had learned about the day before, was a great idea and offered some tips. He told me since this would be such a difficult lesson for the students, make sure to spend a lot of time going through the example problems step by step. Also, allow them to work problems themselves to arrive at understanding before moving on.

The next planning session I had was with Mr. Weber. After deciding to take the maintenance costs section from the chapter, he explained to me his goal for the class. Knowing that these students were the brightest math student and in fact probably didn’t care much about mathematics, and knowing that these students, for the most part, were coming from low middle class, possibly divorced, families, the goal of the class was to make real-life situations and not to get caught up in the drudgery of algebra. He wanted to, if he could find a way to reduce the paper work, to give the students jobs and make them pay for things. I thought that would be an excellent way of teaching this subject. He also went over with me the different ideas of presenting the material. We went over the advantages and disadvantages of the chalk board versus the overhead projector. I just decided to use the chalk board for what I was doing.

When planning my lessons for the two classes, I realized the true desire of teachers. I found that it is not always clear cut the best way to present the material. Teaching is a constant search to find the most perfect way to teach the material to make the students understand. Each teacher, even Mr. Kern who has been teaching for twenty-seven years, is always in search of making their lessons a little bit better the next time. I found that he changed some of the things he did from third hour to fifth hour, in order to reach maximum results.

Being able to assess the students’ progress is absolutely vital to be able to most effectively plan the lessons to reach maximum learning. Several methods of assessment are used each and every day. Methods range from informal assessment, such as asking for questions, to more formal assessment methods, such as tests. It is also a good idea to report the students’ progress to the individual students. This way they can know how they are doing so far, what areas they need to improve on, and as a result be motivated to learn.

In Mr. Kern’s Pre-Calculus class, he had worksheets prepared for the students to complete. What this did was make it possible to make sure what he wanted emphasized would be emphasized in his own problems. This allowed him to effectively analyze and assess the students progress.

In his Algebra classes, as I have discussed, he would lecture for twenty or so minutes, then allow the students to work on part of the assignment. When I taught my lessons, I found this to be extremely helpful in order to make sure the students understand what I had taught so far. If they had not, which several of them in fifth hour did not, I knew that I could and did adjust my examples for the second part of the class to try to make them understand the subject.

I saw another effective method for assessing students’ progress in the block setting. I saw this working with Mr. Mace, a teacher at Canton High School. In order to make sure the students completely understood the material, he had them write in journals what they thought about the lesson and to work a couple of examples. I liked this method extremely well. Students would actually write in their journals either, "This was really easy. I know how to do this," or even, "I don’t understand this at all. Please help me." It was really neat to see. This allowed the teacher to assess their own teaching and see on what areas they need to spend a little bit more time. It also allowed the teacher as he roamed the room at the end reading the journals to work individually with those students who needed help. Concerning the students who didn’t need help, he could pass right by to make maximum use of his time with the class.

Another type of assessment that Mr. Kern used was a review day the day before the test. He would play a Jeopardy trivia game to get the entire class involved. He made the game a lot of fun for the students, with categories such as "I only come to school to see Mr. Kern" and "Mr. Kern is my favorite teacher" with algebra problems in each category. The students really liked it and Mr. Kern could access their progress from it.

The self-paced classroom allowed all kinds of assessment by the teachers. Since they were constantly walking around, they could assess their progress. They actually had to in the given system to assign the proper homework problems. Thus, it encouraged assessment.

The ACT class consisted of daily quizzes. The students knew these were coming and could anticipate. The quizzes were on different topics. He had a pre-quiz and then a later quiz to make sure the students would arrive at deep concentration of the subject. This seemed to work well in this class.

One area that Wentzville High School found to be very effective regarding student assessment was seminar. This was an entire period of study hall. Everyone in the entire school had this class at the same time. What this allowed was students to get any individual help from any teacher all over the school that they needed without having to worry about staying after school or coming to school early in the morning. This worked very well. It not only allowed the students to check their answers with the teacher edition if they simply wanted a little assurance, but it also gave the teachers assessment about what areas they need to spend more or less time on, depending on how many students came in to see them. Each seminar class consisted of a mixture of freshmen through seniors. This allowed some peer tutoring as well as new friends. The only members of faculty that really complained was the library, who usually was crowded. This also allowed the teachers to give more group assignments since they knew that they had this time to get together with their classmates. Thus, the concept of working in a group could be most effectively learned. The seminar was described by Mr. Kern as being "teacher friendly and student friendly."

Junior observation was very nice for me. I feel that I learned a whole lot this time. I think that since I had had two additional education classes, along with my methods of teaching mathematics class, that it was a lot easier for me to pick up things. It was also very different and nice to be in a high school other than the one I had gone to, other than the one I knew. Overall, the experience was magnificent. I feel that I learned a lot about teaching - what it takes and how to excel - about people - how to work with various types of people - and about different school districts and administration.