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.