REFLECTIVE PRACTICE

Each day, I looked back at my lesson from my first period of a specific class after I presented it and evaluated how I could improve it, whether this was for my Inclusion sophomores (which I repeated twice a day), my seniors (whom I repeated biweekly), or my freshmen (to whom I often reiterated material for more than a single day). I also focused on what I could learn from it based on what did or did not go necessarily according to plan. During one observation, for example (as every great story of improvisation occurs on an observation day, of course), I originally planned on giving a lesson on new transversal theorems and leading into it with a right angle theorem review as a short Problem of the Day, just to see if my students recalled the material and could apply it later on (as transversals rely on right angles as a special case in many proofs). However, my students did not seem very comfortable with drawing out the right angle theorems and with reiterating them in proofs, and I even had one student sincerely ask me about the mere point behind doing proofs themselves. I had to stop at this moment and reconsider where my lessons were leading and how I was going about my lessons for proofs themselves. Was I simply giving students sentences to spit out in columns on their sheets of paper, or was I conveying the actual concepts behind my proofs? While my students were copying down what I had written for the previous problems, I looked at the remainder of the daily set and evaluated how the rest of the problems were conceptualizing the theorems, such that they made sense logically. I decided to focus on a smaller Problem of the Day that I had extracted from the worksheet, which required diagrams for each theorem, and I invited a group of students up to the board to do it for me. As I suspected, they found it difficult to copy down diagrams to represent each right angle theorem! From then on, I made absolute sure to convey the proofs in a visual light along with their written forms, even though I had originally suspected that a rote memorization approach would be the most effective for these specific students, and I even required visual diagrams as a part of their Proofs Project rubric later in the unit to ensure that this vital component was not surpassed.

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It is important for students to internalize each component of a lesson that makes it truly effective, such as visual diagrams like this. I regularly found myself reflecting on each day's lesson and on which part of it made it the most accessible for students, discussing these ideas with my mentor teacher and with a neighboring teacher in the math department. We found that lessons that synthesized previous information and brought it into perspective through multiple formats, such as with visuals, in a written manner, and even with tangible objects, proved to be the most engaging and memorable lessons. I regularly strived to meet these multiple learning styles, often challenging my own beliefs that learning styles are more of a myth for easier categorization of instruction than a set means by which students learn best. Either way, when I applied a different type of learning element to my lesson or even changed the colors of the markers that I used in a specific visual, students seemed more eager to copy the notes down, to directly ask questions, and to engage during my lectures, suggesting a more effective lesson.