• Describe one “teaching moment” from the past few weeks about which you are proud. In particular, think of a time in which you designed a task or an activity, gave an explanation, asked a question, or answered a student’s question with an example or explanation that really helped the student(s) to make sense of mathematics or to understand a mathematical idea more deeply. This “teaching moment” could have occurred when working with an individual, a small group, or the whole class. How did you know that your actions resulted in student learning?
• Describe one “teaching moment” from the past few weeks in which you felt particularly challenged. What mathematical idea/concept/procedure were you trying to help students understand? What was so difficult about helping them learn it? What obstacles were you encountering? Now that you have had time to think about the situation, what would you do differently the next time if you were in the same situation again?
This week I was teaching an introduction to area of a kite, rhombus, and a trapezoid. I found an activity that would guide the students to find the formulas for figuring the area of each of these shapes by having them cut out one of these shapes and rearrange it into a rectangle or parallelogram. If they did it correctly the base and height of the newly formed rectangle would help them arrive at the formulas because the diagonals, height, and bases were labeled before they cut apart their original shapes. I showed them how to do the first one and let them work together to figure out the other two.
It was great to see how the students worked together to find the formula. I heard several students saying they could understand where the formulas came from. This is why I wanted them to do his activity. They were able to see why the formulas were what they are and how they are formed. It was great to see students excited to “find” the formula. They were able to understand why the formula was what it is, and this gave them an idea of how other formulas might have been formed. One of my students actually used this procedure to show me how he would find the formula to find the area of a regular polygon, and he was correct!
One teaching moment that I was challenged by was when we were learning about the are of a regular polygon. I was trying to help them with the formula, which involved being able to tell the difference between a radius and a apothem (and know what an apothem is). This was a huge struggle because they were not paying attention and putting any effort towards the lesson. I tried to find an engaging activity to do with the students but I was unable to come up with one. This might have been the reason why some of them struggled with it as well. Unlike the lesson with the rhombuses, kites, and trapezoids, they were taking notes and completing examples with me.
Even though I gave them time to ask questions, nobody asked any. I had to change my daily plan and add a day where we worked on this section again. Another reason they might have struggled is because they needed to use trigonometry as well. Even though a majority of my bell work consisted of trigonometry, some students still struggle with this. If I would have done this lesson differently, I would have created an engaging activity, much like the one I used with the trapezoids, rhombuses, and kites. This would help the students see where the formula comes from. I would have also given them more examples to work with, and possibly given a sheet of examples for group work. This would have been something that would benefit their learning.
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