Solving Quadratics by Factoring Lesson Plan
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Lesson ReflectionDuring the card sort warm up, I noticed that most of the students were using the same groupings. They used different names, such as number of solutions, number of times the graph touches the x-axis, but they were all the same categories. After students shared out their sorting methods, I asked the class what other characteristics of parabolas they could use to sort these graphs. My goal was for this activity to help refresh their memory of the previous lessons on concepts like solutions, axis of symmetry, concave up and down, and how narrow or wide the parabola was. Students came up with these characteristics after the card sort, but one student pointed out that they felt that they couldn’t sort them into these categories because they had to have at least three categories. When I made this activity, I had written in this guideline, but I did not realize the number of categories that would be eliminated with this constraint. Next time, I will tell the students to sort the cards into at least two different categories.
The Desmos activity I was using in this lesson had some screens that the students needed to read to understand the lesson. For example, Screen 8 had the following instructions: “Talk with a neighbor about how you might be able to solve this algebraically (e.g., by manipulating the equation instead of graphing it). Once you've talked about it some, move on to the next screen.” I had set up the pacing of the activity so that the students could only go through one section at a time. My intent was to stop the class after each section to review what they had found and make sure there were no questions. The investigation was pretty self explanatory based on the directions in the activity, or so I thought. I realized within the first five minutes of the activity that none of the students were reading the text on the screen. They were guessing at what it said and then continuing on, causing them to miss some important information. Next time, I think it would be better to have more places for students to respond within the Desmos activity instead of just reading a screen to keep them engaged and encourage them to read the information. I would also reduce the amount of text on each screen. Based on my observations during the lesson, I decided to give students a quick summary of what I expected them to do for each set of screens that I gave them access to. I think this helped provide some structure to the lesson and gave them specific tasks to look for in the slides instead of being expected to self guide themselves through the lesson. After implementing this strategy, both classes became more focused and were more productive. I was worried about this lesson because the classes I was implementing this lesson in had struggled with the previous unit on factoring. I was worried about the stress of factoring a quadratic taking away from the lesson itself. For this reason, I tried to keep this lesson as conceptual as possible and only required students to actually factor a quadratic expression a few times near the end of the investigation. In the following class period, I had planned to review factoring methods and have students practice solving quadratics by factoring. Providing students with the factored form of most of the quadratic equations was helpful because they still were able to see how the method worked, and more importantly, why the method worked without having to spend limited class time factoring. Becoming a Reflective PractitionerI believe that this lesson shows that I am a reflective practitioner because there is evidence of my reflections at various stages in planning and implementing the lesson. The list of possible groupings for the card sort in my lesson plan shows that I think about how my students will approach a task and anticipate their solutions. My decision to modify the Desmos activity to include less factoring work shows that I understand the abilities of my students and can modify instruction to fit their needs without changing the learning goals. Both of these decisions required reflection on how my students would approach and handle various tasks.
During the lesson, I also chose to make some decisions that altered the lesson plan. Providing students with a summary of what I expected them to do in each section of the Desmos activity shows that I can recognize during a lesson when improvements need to be made and I am flexible enough in my teaching style to make those changes immediately. During implementation of the lesson, I also asked students what other categories they would have sorted the cards into if they did not have the three category restriction. This shows that I am open to student input and that I recognized during the lesson the need for improvement. Even though I did not make the change in this case, I still was open to suggestions and used my students as a resource. After the lesson was over, I still reflected on how I would change the lesson the next time I implemented it. This shows that I realize that no lesson plan is ever perfect. There is always room for improvement and I have the ability to critically think about my work and the humility to point out when it needs to be changed. In my reflection, I provided a few examples of how I would change the lesson for “next time” and I intend to review my reflections and make these changes in the future. Becoming a reflective practitioner means that I will not accept a fixed mindset. Current standards can always be raised. My ability to reflect on the planning process, the implementation stages of a lesson, and after a lesson show that throughout my entire teaching practice I am reflecting upon my work and looking for ways to improve. |