Reflection of Goals: Highest and Lowest Levels

Objective 5: Highest Performance

               For the Transformation Unit I found that the students did best on Objective 5: Given two 2-dimensional shapes on a Cartesian plane, students will correctly identify the transformation performed 75% of the time. With the time used from the previous days preparing to be familiar with the vocabulary and using the vocabulary for more than a week, gave a firm foundation for identifying transformations. Although the students did do graphing on this formative assessment as well, as a whole assessment they did very well, 75% of the student got higher than a 76.5%. I believe that one reason they student did so well on this assessment is the placement on which it was taught in the lesson. This objectives advantage was that two of the four transformations were covered over a period of three days with the review of vocabulary each day for all the transformations. Another reason I feel the students did so well on this assessment was because this was a simpler objective with just identifying not constructing. Looking at the blooms taxonomy and this type of identifying pertains to knowledge and comprehension, the two lowest levels. So overall, the instruction placement (where in the unit it was taught), and the level of difficulty within the blooms taxonomy I feel are the two main reasons the student did better with this goal. The of the students that performed lower than a 76.5% scored, 0, 45, 53, 60, and 73.

Objective 4: Lowest Performance

For this same unit I found that the students did least well on Objective 4: Given at least 4, 2-dimensional shapes or their coordinates, students will be able to plot and/or reflect and determine their new transformed coordinates given a horizontal or vertical line of reflection with 75% accuracy. I expected the students overall achievement too have been higher than what it was. I knew this one was going to be difficult but I did not think that so many of the students would have struggled with this objective. This data displayed the largest interquartile range than any other goal. Only 25% of the students scored lower than a 32.5%. While there were students that did do very well, 25% of the class had higher than 82%. I believe this was mostly a struggle because of the lack in prior knowledge of lines on the coordinate plane. Although the line of reflections that they had to find were y= 0 and x= 0, it was really confusing going back and forth from x-axis and y-axis. The other lines of reflections were given to them if it was not the x or y-axis. Another reason I feel that the students did not do as well as they could have is they did not use the cheat sheet I gave them. This consisted of x= 0 is the y-axis and y=0 is the x-axis. I struggle with students closing their journals once the lecture/note-taking time is over and not opening them back up to do the assignment. I need to do better at making sure the students not only have notes but efficient notes to be more successful in their independent study and making sure that the students are actually using them and not closing them. I have a tendency to pamper them and leave enough notes on the board that would get them through the lesson, but that only hinders them from being self-reliable and accountable with their journals. Another reason I feel like the students did not do as well is because I did not spend as much time breaking down the assignment as I did in the first two days. When I tend to go slower and take baby steps I see the student perform better. I would next time break this assignment into two days or sections where the students are just graphing y= 0 and x= 0 or x and y-axis. Doing this would give them a chance to master that prior to having to simultaneously graph the line of reflections as well as reflect polygons on the Cartesian plane.  So overall I feel the student do as well because the lack of prior knowledge and confidence in graphing lines of reflections, not breaking the lesson down into smaller parts instead of teaching graphing the lines of reflections simultaneously, and the level of blooms was higher, with graphing (illustrating) and identify the reflected points with the line of reflections, which reaches analysis and synthesis.

Daily Schedule

               Daily Schedule for Lesson 3, each lesson has the same layout but the times change per lesson usually in preparation. My class always starts off with my paraprofessional passing out the journals and name plates. Bell work is then done in their journals (10-15 minutes for Lesson 3). Within this 10-15 minutes, I take roll on the computer and tend to anything that always arises at the beginning of a class, for example phone calls, emails from the office, introducing the bell work, and getting messages to students that I have written about past assignments or assessments incomplete or missed. Every 3^rd class of the day 5 minutes is reserved for announcements and the pledge of allegiance. Once class gets started, I have students put backpacks down, pencils, journals, assignments, and name plates out/displayed. Class starts with reviewing answers from the bell work. For Lesson 3 I reserved 20 minutes for direct instruction. Within the direct instruction, guided practice is started with the eight online multiple choice questions that the student vote on to answers, but then an extra 20 minutes is reserved for just guided practice with the guided practice worksheet attached to the assessment plan. Independent practice mostly always runs this way in my class: I start off assigning certain problems to do with a partner or a group, making sure I assign groups or allow them to choose and then changing the groups I need to in order to maintain good classroom management along with productive learning groups; then the remainder of the paper gets done independently. Once the independent assignment/formative assessment is passes out I turn on Pandora, keeping a variety of music on depending on season and activity. Most all work is done with no vocal music unless there is a math art activity that the students are allowed to talk softly during the work as well.  For Lesson 3 I reserved 30-40 minutes for the independent practice. Each day the closing varies but usually takes no longer than 10 minutes. The only day I usually do not have a formal closing is on assessment days or certain activities. But even then, I allow for cleanup and the transition from class to leaving with a warning of time or instruction to clean up. In Lesson 3 I reserved 5 minutes to go over one problem pre-selected or selected based on student struggle to go over and answer at the board or have students compare answers and then a student or myself give an explanation. 

Maximizing Class Time

I try to maximize time by knowing each class and knowing their level of performances and being over prepared. If I feel the students might struggle with an assignment but then find out they thrived I am always prepared with giving teacher made on the moment assignments. I use these times mostly to encourage writing in math. I have student usually write one to two paragraph summary or explanation of the assignment. I also try to maximize class time by pacing myself, but not to the fault that I lose the student just because I am trying to stay on time but it allows me to stay on track and progress through the lesson. I also try to have students be prepared as they come to class and I or the paraprofessional passes out needed material in order to start the class in a timely manner. Before class if I need the starboard and websites I try to make sure they are all set up prior to class starting because sometime the technology can take longer to start and it stalls the lesson greatly, especially when the whole lesson has to be changed due to technology malfunctions. This has happened a few times where the network was down or my teacher computer could not get online.  In these events I am already mentally prepared so the lesson will be taught will just the white board and anything else I can find and throw in like white boards etcetera to compensate. In this event I have had to alter my class times a lot usually. The concepts seem to take longer to teach without the use of technology, and yet there are some lessons with activities and games that take longer with the technology. I have found what helps me the most to maximize the time I have with my students though, is to know the material. Knowing the material and mentally being prepared for the lesson takes anxiety and stress out of teaching regardless of what happens, and staying as flexible and easy going as possible has also been my friend.

Class Time Adjustments

            Within these two weeks of the Transformation Unit I found there were several times I adjusted the time to meet the students needs and skill level. One constant activity I do during ever direct instruction is integrating guided practice. This helps the students with their attention spans when they are actively involved in the lesson as well as allowing me to monitor comprehension levels throughout the lesson. Being able to integrally monitor student comprehension and performance in the direct instruction as saved me a lot of time of the years. When I was not doing this I found myself during the actually time allotted for guided practice having to re-teach and remind a lot more. When I have integrally inputted guided practice I catch their mistakes before the lesson progresses and causes more confusion.

               This happens usually on a daily basis. I have never had a lesson go exactly as planned and stay exactly on time with each section. I have learned to regulate time in my class when one section is taking longer, even it is bell work, to adjust the rest of the time accordingly by just making sure I check the clock, knowing how much time before the end of class, how much time I need to give the students to reach the goal, and perform the tasks assigned.  During Lesson 3 I found that I needed to help the students more and spend more time than allotted for finding the line of reflection than expected. I did not originally reserve time teach graphing lines, but I found myself once I got some of the guided practice problems that even though I gave the student a key to determine where x= 0 and y=0 is and I gave the student any other lines of reflections that I had to go back and explain more on graphing lines with one variable equations such as x= 2 or y= -4. I was very happy to see the curiosity with the questions coming from graphing the lines but had to adjust the lesson. At that time I stopped and showed many examples of points on a vertical line and showed that all the x values were the same. I then did this as well for a horizontal line. Then I moved the points to being on the axis which was causing most of the confusion. (3, 0), (6, 0), (0, 0) all have the same y value but they are all on the x-axis. I then graphed the line and had students come up with more points on the line to check if all the points on this line will have y= 0. They came to the conclusion that all the points on this line will have y= 0. I then did the same for a few more lines, one being x= 0, y= -3, and x= 6.

               After taking a step back in the lesson and spend more time on finding lines of reflection on the Cartesian plane the student did better finding the reflections on the website with the guided practice problems with the virtual graph that displayed reflections step by set or all at once. Although the students did well with the guided practice I saw that Objective 4 still was more difficult for them. This might also have to do with having to redirect the lesson instead of flowing nicely like the other lessons did. I adjusted the amount of questions that needed to be done with partners by lessening the amount of questions to be done independently and increasing the pair work.