Mathematical Sciences, Secondary Education
ADJUSTMENTS TO PRACTICE
In order to exemplify this element, I must strive to "organize and analyze results from a comprehensive system of assessments to determine progress toward intended outcomes and frequently use these findings to adjust practice and identify and / or implement appropriate differentiated interventions and enhancements for individuals and groups of students and appropriate modifications of lessons and units" (DESE CAP). I must also aim to model this element.
SECOND ESSENTIAL ELEMENT
Any great lesson plan has its flaws initially, and students are ever-unpredictable when it comes to processing the lectures that they receive and asking questions that the teacher may have not previously considered. This was especially true for the classes that I taught during my practicum, particularly my Inclusion Geometry courses, not only because I taught the period lecture twice throughout the day, but since the Special Education students had a tendency to pipe up with ideas and curiosities that had never even crossed my mind to address.
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My first class period of the day was a type of "test-run" for my later lessons. I could prepare for questions that I may receive in the moment or reconsider for later periods, and I could prepare alternate materials or pop quiz assessments if needed. It helped with both geometry, of course (especially as that was the first class that I picked up in my practicum and it consequently became my main source of pedagogical development, plus it was the class period that was most often observed for my periodic evaluations), and with my overall mood for the day and how I was going to feel and run coming into my lessons. I often grabbed specific markers and organized the board slightly differently per the day, just to keep things interesting, and my first period decisions set the tone for how the day was going to go... assuming that everything was running effectively and did not need any momentary tweaks or major overhauls, that is.
Alas, an efficient day is a suspicious day, and I had to pay consistent attention to how students were taking the material that I was throwing at them. I often conducted my lessons based off of instant feedback from students, having the learners choose the direction in which I led our discussions, yet lightly guiding them to getting the correct answers and building their confidence. For example, a very typical lesson would include something like, "this is the Pythagorean Theorem, I'm glad you guys remembered it. I am going to mark this triangle with an a, b, and c. I know that the length of a is --" (waiting for any student to count how many units on the coordinate grid were located between the two plotted points making up side a and to tell me the answer aloud) "and b is --" (waiting for a different student, as the students knew that I preferred wide participation) "so what does that mean about c?" (turning to the class and waiting for someone or a group of students at once to tell me about plugging a and b into the Pythagorean Theorem and solving for c). I am not a big proponent of raising hands or calling on students unless participation begins to grow narrow and more students need recognition or should be encouraged for a chance to speak, so my students knew to speak up when they knew an answer. Thus, if any answers that students shouted out were not necessarily correct, then it helped me to assess and to adapt to my students' participatory moods for the day as well as to address common misconceptions that I may not have foreseen arising when planning lessons.
MY ADJUSTMENTS
In my classroom, students knew that they should openly and honestly participate in their daily lessons as often and as fully as they could. Many of my students respected the fact that I was not hard on them for spending a day just listening or being drowsy from a rough situation at home, although they also knew that I had no issue calling on them specifically if they had spent a few days avoiding input and if I needed to particularly check in on their understanding before moving on. As I mentioned, every question that students asked aided the lesson, and responding to student inquiries gave me invaluable insight into how they were processing the material.
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There were often days when I slightly altered pieces of my lessons from earlier in the day when I was presenting them the next period. I looked back at my lesson from the beginning and figured that some small details, such as easier numbers to work with or a change in marker color, would positively affect the lesson and allow for more productive questions later on, if necessary. This applied both on a daily basis (as with my geometry board reorganization) and on a weekly basis (as with my senior classes when a lesson needed a small tweak to be more effective for the other class), but overall, I attempted to scaffold my lessons so that I could easily pinpoint the specific lesson aspect that was tripping up the students. In my Transformations & Transversals Quiz, for example, I made sure to begin with more basic polygonal transformations and with simpler transversal calculations, later quizzing more difficult processes and applying more problem solving skills (I even added a bisection problem, which we had covered in class but not on an assessment, as extra credit). I used these results to hone in on and to evaluate exactly where my students needed further instruction or even problem drills.
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Some lessons required a major upheaval, as actually occurred during my third formal observation. Upon noticing that my Problems of the Day were just not engaging or motivating my students enough that they completed them on their own rather than fooling around, even while I circulated the classroom to guide with questions and to control the noise level (using various methods, including proximity, verbal suggestions, and explicit commands to focus on the work at hand rather than talk about the latest TikTok trend), I spoke with my advisor, Jackie, about how she supposed I could get the kids to concentrate and to be willing to do independent work. After all, the students became engaged and worked hard the second that I began to speak and to go over the problem on the board, and they seemed to respect my instruction rather than my direction. She suggested that, during the same class fifth period, I try a "pop quiz"-type approach and collect the problems for participation points before discussing them, simply to aid with accountability and to establish a little bit stronger of a results-based classroom expectation for the future. Thus, even though Jackie was not able to watch the plan go into action, I later gave my students ten minutes to complete the problems on a sheet of paper and collected them before covering them. It was surprisingly less effective than I thought that it would be, as I had to keep prompting the students to work and I collected many half-completed papers... during that particular lesson, at least. In further lessons, however, I actually noticed my students acting more eager and focused to complete their work, as well as finishing their homework worksheets more frequently and completely, both with a small anxiety that I would collect their work and hopefully with a wish that I would see their best work. I tried this tactic with my Algebra I students the following day to gauge if they understood our previous day's work, as shown. I tried to cover any topics that they may have had trouble with and to see how they would work under a time pressure as opposed to my procrastinating geometry students, so I tried to scaffold the expectations and improve upon my usual format.