EDCI 602 BLOG # 2

Of the lessons that I taught this summer, my students were most successful at mastering the learning goal of utilizing the order of operations to simplify mathematical expressions. I think the students were able to master this objective for several reasons. First, this is an objective that the students have been introduced to numerous times. Therefore, the students were simply being refreshed on something they already knew. Secondly, when I reviewed the order of operations, I pointed out the typical mistakes that students make (for example, failing to perform operations from left to right when multiplication and division are consecutive operations, or when addition and subtraction are consecutive operations). I gave several examples containing the common student pitfalls, and therefore encouraged the students to be careful when those types of problems arise. Also, because the objective is a relatively simple one, I had ample time to allow the students to practice the concept by participating in a class activity.

The concept that I taught in which the students were least successful in mastering the learning goal was solving a system of equations by using elimination. I think that the students’ lack of success on this objective was due to the fact that solving a system of equations involves numerous steps. Typically, the more steps it takes to solve a problem, the more likely it is that a student will either forget the steps, or make mistakes that will lead to inaccurate answers. Therefore, at least part of the problem with the students’ performance on this objective is that many of them did not perform accurate computations while solving the problem. Another reason for the students’ lack of success on this learning goal was that I did not have enough time in the period to allow the students to have independent practice so that I could point out their mistakes. Due to the numerous steps that are involved in solving a system of equations, the lesson was very lecture-heavy with not enough student activity.

My instructional procedures over the course of the summer have varied according to the complexity and number of objectives I was responsible for teaching during a given lesson. A typical lesson involves review of the previous lesson, introduction of the new topic and instruction on the procedures for solving a specific type of problem, guided practice, followed by an activity or independent practice. I typically do a lot of board work and incorporate a lot of verbal repetition into the lesson. For example, I will repeatedly ask the students throughout the lesson about major concepts that they need to understand. I also have students put problems on the board and ask the students questions throughout the lesson to make sure that they are attentive. For the most part, the students appeared to catch on to the concepts that were taught. While my instructional procedures have been somewhat effective, I think that the students would have achieved a better level of mastery on some of the lessons if I were able to spend more time on some of the lessons and design additional activities to give the students more practice. However, due to time constraints of a short summer school session, that was not always possible.

I differentiated instruction by writing important concepts and example problems on the board or overhead (visual); verbally repeating and requesting that students repeat procedures for solving problems (auditory); providing handouts which show step-by-step instructions for solving problems (visual); and allowing students to actively participate in the lessons by going to the board or doing activities individually or as a pair (kinesthetic). Some of the activities included a paper folding activity during which students created study material that showed translations between verbal and algebraic expressions and examples of each; a relay activity involving the order of operations; and matching activities in which students match related mathematical expressions. During guided practice and independent practice, I also went by students’ desks and pointed out errors to them and explained to them where they were making mistakes

As mentioned previously, the students’ performance could be improved if there were additional time for in-class practice exercises and activities for complex objectives. In the context of a brief summer school session, this could possibly have been achieved by combining lessons of easier objectives, thereby creating more time for objectives that students find more difficult. I definitely need to find a way to incorporate more instruction that is geared toward kinesthetic learners. In addition, I would like to more often guide the students toward discovering rules and concepts rather than just telling them directly.

EDCI 602 BLOG # 1

In making decisions regarding which six lessons to teach first in our algebra class, we thought about the basic computational skills that are necessary in order to be successful in algebra and upper level math courses. Both I and the other second year teacher taught algebra two during the school year. We used our knowledge of the weaknesses of our algebra two students to determine what foundational lessons needed to be covered at the beginning of an algebra course. Last year, I learned that one of the most challenging aspects of the class for the students is performing accurate computations. Thus, the first few lessons of the summer school session were designed to give the students the basic foundation to eventually be able to relate a real world problem to an algebraic problem, and to accurately perform the computations that are necessary to solve the algebraic problems.

The lesson on translating between verbal and algebraic expressions is the beginning foundation for being able to translate real world problems to algebraic equations and inequalities. The lessons on simplifying and evaluating expressions by performing operations on integers, rational numbers, and irrational numbers, order of operations, and scientific notation, were aimed at making sure the student is able to correctly perform the computations that may be necessary to solve a specific problem.

Because the ultimate goal of an algebra course is to teach the student how to solve real world problems algebraically, the above objectives are appropriate. The objectives are appropriate in terms of development because a thorough understanding of the above topics is needed in order to be successful in the course. For example, a student will not be able to successfully solve an equation if he/she does not know how to correctly add integers and fractions or does not know the order of operations (when solving an equation, the inverse operations are performed in opposite order).

With regard to instructional decisions, we decided to primarily utilize the following lesson structure: input (lecture), modeling, guided practice, individual or group activity, closure, and time permitting, independent practice (homework). We use the guided practice and independent practice time to individually assist students at their desks as needed. It was important for us to include an activity in the lessons in order to keep the students engaged, especially since the students are attending the same class for four hours. Examples of the types of activities included matching a problem with the appropriate rule to simplify the problem, and a relay process of performing the order of operations such that every student had a particular role in solving the problem. We also decided to incorporate into our lessons review of the prior lessons since the course is very fast-paced. Furthermore, when possible, we included review of topics which were not able to be taught in separate lessons given the brevity of the course. For example, the classifications of real numbers were reviewed during the lesson on integers and fractions.

The inductive strategy of concept attainment was employed in the lesson on scientific notation. The teacher drew a line down the middle of the whiteboard and began writing numbers on either side of the board, pausing every so often to prompt students to articulate the rules of scientific notation. This strategy was selected because in order for the student to master the objective for writing numbers in scientific notation and performing operations in scientific notation, he/she must recall what scientific notation format looks like and must be able to distinguish it from standard notation. The inductive method helps the student to remember the format because the student was engaged in a process that allowed the student to consider for himself/herself the differences between scientific notation and other ways of writing numbers.

YES, THE MONEY DOES MATTER

Prior to becoming a teacher, and even throughout the year, I was convinced that the low pay teachers receive is not a big factor in high teacher turnover and the difficulties school districts experience in recruiting good teachers. However, the truth of the matter is that money is a contributing factor. Perhaps if being a teacher were not so demanding, depressing, and aggravating, (yes, teaching can be all these things at times) the low salary wouldn't matter. However, when you throw in all the negative experiences that come along with being a teacher, it does make a person say, I could be doing something else and making a whole lot more money than this.

I am a very practical person when it comes to money. That means that I do not believe in spending more money than I take home. For the most part, if I don't have the cash to buy something, I won't buy it. This year I have survived without cable, without taking any long distance trips, and without buying many new clothes. Even being this frugal, I would still probably be in the red if it were not for the fact that I eat most meals at my parents' home. So the question that I ask myself is how does someone raise a family like this? (assuming that both parents are teachers) Perhaps those who have the passion to teach kids in the school system are willing to make great sacrifices to do that. However, people like me, who have a passion for kids but not necessarily a passion to teach in the school system, are moved to pursue something else and contribute to education in a different way.

I have never made a decision just on the basis of money. I actually don't think my decision to stop teaching at the conclusion of next year is all about money either. However, I am willing to admit that it is a contributing factor. I think that ultimately I am looking for something to do that is in agreement with my principles, aligned with my personality, and allows me to at least live comfortably. For many reasons, teaching is not it.

GUILT TRIP

Last Friday, the underclassmen's last day at school (the seniors finished last Monday), I received a phone call on my cell phone just as I was pulling into my driveway. Apparently, one of my students had gotten my phone number from her mother's caller id when I called to speak to the mother regarding the student's grades. The student proceeded to ask me whether the grade that she received in the class was correct. I informed her that it was; it was a 69. The student then began to cry and inform me that my class was keeping her from graduating. She wanted to know if there was anything she could do to get an extra point. I told her, with regret in my heart, that there was nothing to be done at this point. I told her that I structured the class such that students would be able to do those extra things all throughout the year so that it would not come down to the wire and a situation where I would have to grade numerous extra papers and tests. I told her that is why I allowed retests, assigned projects to pull up low test grades, provided tutoring services, and even allowed a comprehensive final exam to weigh heavily such that a student who was failing could pass if the student showed on the exam that he/she had mastered the material. Needless to say, the final exam showed that the young lady had not mastered the material, and I felt morally obligated to give her the failing grade that she earned.

After stating her case for a few minutes, the student broke down crying and said that she would call me back. A few minutes later, she called again. At this point, she started laying it on thick. While making herself seem quite sympathetic, she pretty much painted me as an insensitive teacher who was ruining her life. She told me that I don't know what goes on in her home or what's happening in her life that prevents her from coming after school for tutorial or from doing better in the class. She also told me, as if I don't want the same for her, that she wants to be something in life. Furthermore, she insisted, I should consider the fact that she attended class regularly and was never a behavior problem. While, in my mind, I was definitely suffering from a guilt trip, I informed her that this situation would not prevent her from being something in life. I told her that obstacles will always arise in life, and this was just one of them. It was up to her to have the determination and will to overcome the obstacle. I told her that although I understood that she was hurting, she should dust herself off and make up her mind to pass the class in summerschool and go on to reach all of the great goals that she has set for herself.

After our conversation, I was indeed second guessing my decision. But after thinking about it for a few days, I was sure that I had done the right thing. It does students no good to receive things that they have not earned; it gives them an unrealistic view of life that will harm them in the long run.

I attended graduation on Wednesday night. After all that, the student actually walked. Apparently she didn't need the class to graduate!