Lesson+Plan+3+Reflection

This review is for the lesson taught on 17 November 2008. The lesson was taught in a Precalculus class of 18 students. This lesson was the beginning of a new chapter and allowed for the introduction of new materials. The class had completed a test the previous class period and they were eager to move on to new materials and to put the problems of the previous chapter behind them. The general flow of this lesson went amazingly well. The new chapter is dealing with polynomial functions in general and begins with the basic linear and quadratic forms of these functions. The purpose and drive of this lesson was to specifically define what a polynomial function is and what forms it can take on. The lesson progressed through the general outline that was provided in the lesson plan. The students were very attentive and participated well in the classroom discussions. The students seemed to grasp the new materials well and did not have the questions that I had anticipated. The lack of planned questions caused me to introduce items that did not appear to be on the minds of the students. This caused a little jump in the basic logic to be formed, but I tried to bridge the gap to integrate the materials without the students noticing. There were, however, questions that came up during the course of the lesson that I had not anticipated. In the discussion I asked what the order of a constant function is. The order of a function is the highest whole numbered power of the function attached to a variable. In a constant function there is no variable. One person correctly answered “0” but another asked “Why is that.” I had assumed that by the Precalculus level the idea of a zero power making anything be 1 would be in their minds. Another student stated the rule but this one young man asked for justification again. I gave a quick aside to explain in terms that they were familiar with. This was taken well and the justification was accepted. One other thing came up that actually worked well. The students were given two points and asked to write an equation to relate them. The students all arrived at the rate of change the same but they then took different paths to arrive at the final answer. As a class we explored both paths. When they asked which was the proper method I shared a story with them about Bill Gates wherein he stated the best computer operating system ever made was “the one you learned on” meaning that there is no best way. It all comes down to familiarity. I told them that I have no right to tell them that the method they used was wrong. Perhaps the conclusion was wrong, or they were asked to attempt a specific method and they did not do that, but they should not be told that the method is wrong. They all appeared to enjoy this. This lesson did not require any special materials or supplies. The stories and examples that were used were very appropriate for the subject being discussed. Through the examples that were provided and the discussions that ensued there from we were able to cover the materials that were intended. There was even some extra time at the end of the hour for the students to work on their assignment. They were allowed to ask additional questions about the day’s materials. The lesson went well due to prior planning and knowledge of the students in the room. The lesson plan was followed very closely making it so that another teacher could have come in and used the materials provided to cover the lesson. The specific questions that came up during the lesson might have posed a problem to the other teacher, but they could have easily been handled. The stories and anecdotes that I shared were not the only ways to resolve the concerns and answer these questions. A person experienced in mathematics could have come up with proper solutions very easily. The lesson seemed to be student centered. The beginning was designed to incorporate the entire class by allowing for individual interpretations and then allowing for the justifications from their individual points of view. The way that each student was allowed to offer input into the progression of the lesson also allowed for a student centered feel to the day. The justification of solving for the proper function by individual students also permitted the students to have a greater say in the learning process than they are accustomed to in this classroom. One challenge that was present in this class and that is a constant struggle is the existence of three individuals that do not want to participate at all. Two sleep and one does nothing. To engage these students I do many different things. Today I attempted to call on them more often and to be in their immediate physical presence as often as I could. This helped them to stay focused on the discussion and material at hand and they were more engaged at the end of the hour than they have been for a long time. I will need to do more of this as the class progresses.


 * The evaluation of this lesson from Eastern's Department of Education can be found at this link: [|University Evaluation.pdf].
 * The evaluation of my Master Teacher can be found at this link: [|Lesson 3 Evaluation.pdf].