¶ … teaching strengths for the content area (secondary school mathematics or science) you plan to teach. I have decided that I will teach mathematics at the secondary school level which is a subject I performed well at when I was in high school myself. I was always at the top of my classes when it came to math and I enjoyed all of the classes that I took in the subject. So, I think it has to be the right area in which I should pursue a teaching degree.

I can think of two strengths that I have, with regard to this subject, apart from the facts that I enjoy the study and was able to perform well at the secondary level. First, on a personal level, I do not try to act like I know more than other people, even though I may have a more perfect knowledge of the subject than they have. I realize that people are gifted with different types of intelligence (Plummer & Peterson, 2009), and I have a more logical mind than a lot of people are blessed with. I can see a mathematical concept and quickly, with a little study, understand it. This gift could lead me into a lot of different occupations, but I chose teaching because I am also gifted with being able to help people understand the subject.

There are certain subjects which students are forced to take so that they can complete their secondary education and receive a diploma. Most states require that a person take two or three math courses (Stiggins, 1999), even if the individual is not naturally gifted at mathematical concepts and does not intend to pursue a career that has anything to do with math (van Es & Conroy, 2009). Since this is a fact, these students are probably in need of a teacher who understands how to explain the topics without making them feel that they do not understand (van Es & Conroy, 2009) because they are in some way stupid.

When I was in high school, I was able to tutor several students who had these difficulties. I was able to do so using both of the strengths that I list. I was able to talk to them about the subject without making them feel inferior and also explain the problems in a way that they could translate into an understanding of the subject matter (Plummer & Peterson, 2009).

I have to admit that I am not sure which is the most valuable attribute. Do students want to understand the material more than they want to make sure that they do not look foolish? I do not know, but I know personally that high school was hard enough as it was with people judging everything you did and trying to find ways to make you feel that you were somehow dumb. So, I think that the most important quality of the two is to make sure that I do not make students feel inferior, and that I control the class in such a way that no student tries to make others feel inferior (Scott, Park, Swain-Bradway, & Landers, 2007).

When tutoring students I was also able to mentor some of them and make them take a different view of mathematics as a subject (Plummer & Peterson, 2009). The students stopped feeling bad about the subject, and when that occurred they were able to grasp the subject in a way that they would never thought was possible before (Peterson & Plummer, 2009).

So, it seems that watching myself and making sure that I do not make students feel bad about their lack of understanding, and making sure that their fellow students do not do it either is a valuable skill. As I said before, it may be one of the best tools to help students learn and it is definitely good for classroom management.

4. Describe the components of an outstanding secondary school mathematics or science lesson.

Math and science are difficult subjects for many people, so ensuring that the lesson follows a specific plan, to ensure understanding is essential (Stiggins, 1999). The perfect class period would be one in which every student was able to see a specific type of problem, and have the time and method to understand that lesson. Even if it takes several class periods to explain a system or method, there should be understanding by all of the students before the next one is introduced (Fontana, Scruggs & Matropieri, 2007). With that in mind, I have devised the three components necessary for an outstanding secondary school mathematics...

They are explanation, practice and assessment.
Every lesson has to be clearly explained first of all. That means that the teacher has to have a firm grasp of the subject before they can teach it to someone else. Of course that comes with setting up the lesson days ahead of time, and going over he material to refresh it. When it comes to the class, the necessary steps and algorithms that accompany that particular lesson must be explained with clarity and accuracy. The teacher should gage the level of understanding in the class and make changes to the lesson plan if the subject is an especially difficult one. Sometimes it is necessary to make sure that a lesson is broken up into several parts before an entire concept can be explained. It may be good for the teacher to teach it to some test subjects (family, or friends) before leading a class. The second part of teaching the subject is that it should be demonstrated by the teacher. The examples should be able to be simply grasped and repeated by the members of the class (Fontana, Scruggs & Matropieri, 2007). Stopping often and making sure that there are no question among the class members is essential.

A good lesson plan has two parts also. In this portion of the lesson plan the teacher should give the students some in-class problems that they can perform. These should be the type of problems that they will see in their homework, so that they will be able to perform those extra practice problems. The teacher should be circulating around the room to make sure that all of the students are doing the problems (a good classroom management technique), and ensuring that they are performing the functions correctly. As the teacher goes around to the different desks, he or she needs to ask the students if they understand what they are doing. Encouragement from the teacher could go a long way toward making sure that the students are actually "getting" the procedure and that they are confident in their ability to reproduce the results on their own (Stiggins, 1999). Confidence is a major part of being able to perform in mathematics or science, so the teacher should give as much of that out as possible.

The final component of making sure that students understand the material is that there has to be an assessment of their understanding. This is done in two ways: graded homework and quizzes/examinations. The homework should again not be so difficult that the student is not able to complete it. These are practice problems that enable the student to gain more confidence in the types of problems that they are going to need to demonstrate proficiency in later. The problems should also be reinforced with periodic quizzes or examinations that test a wider range of knowledge (van Es & Conroy, 2009). It may be better to have more frequent small quizzes and then larger exams, but that it is up to the preference of the individual teacher. Everything is designed to increase the confidence of the student with regard to the instruction (Stiggins, 1999).

5. How would you develop a lesson you have to teach in your secondary school mathematics or scientific classroom? Note the tasks, plans, background information, or knowledge you will consider in developing the lesson.

The first thing that I want to make sure of is that I know the material that I am teaching. If I am not engaged enough in the subject to study, how can I expect my students to be? Of course, I should first prepare by learning the material while I am in college (Plummer & Peterson, 2009; van Es & Conroy, 2009), but when it comes to an actual classroom experience, I should study enough beforehand that I am able to easily recall any facet of any type of problem that relates to the lesson.

Next, I should set objectives for the lesson plan. What do I hope to accomplish with this lesson? What can the students possibly get out of the subject that I have not previously thought about? I would ask myself these and other questions to make sure that I have covered all of my bases and have written objectives that will actually help people learn the intended subject. My motto is "Keep it simple."

After writing the objectives and filling out an outline for the lesson, I would want to come…