3/22/2023 0 Comments Reflection geometry![]() It is extremely important as a teacher to be able to adapt and find new ways to teach concepts, but direct instruction is the one that I feel most comfortable with, and I know that will never change for me. I really enjoyed this portion of the lesson because it allowed me some time for direct instruction. The properties of the special cases of right triangles allow for shortcuts to be used to find information, and only one side length is needed to determine more information. I personally believe that while sometimes are multiple ways to do math problems, efficiency in math is very important. Next in the lesson was an extension of the previous activity by examining special cases of right triangles and Pythagorean triples. Overall, I think this activity was very effective. This activity also had the students do a non-example and show that the Pythagorean Theorem does not hold for non-right triangles. There are no special technical skill required for this activity except the use of a laptop. It is purposeful in that the students can find the measurements of the sides and calculate the squares of the sides to see the relationship. Because of this, mathematical representations are 100% accurate. Another benefit is that this takes and human error in measurement out of the equation but still has them doing the triangle construction. If gives a great, accurate visual representation for the students. The technology was a Geometer’s Sketchpad activity that lead the students through constructing a right triangle and discovering the side length relationship. This was my technology component of the lesson, and I thought it was very effective in helping to represent the concept. ![]() The main activity of the lesson had the students discover the relationship between the side lengths of right triangles. I thought this was a nice introduction and lead-in to the discussion of right triangles and exploration of the Pythagorean Theorem. The last two questions I thought did a good job of having the students think conceptually in applying the ideas of equilateral, isosceles, and scalene triangles to right triangles. I made sure to give clear explanations about the distinctions between the different types of triangles. I was able to test each student’s understanding as there were enough problems on it to hear from everyone. ![]() It had the students do some fairly simple calculations to demonstrate the properties. The opening of the lesson I felt was beneficial in reviewing the different types of triangles and the properties of each. This lesson and also the opportunities we’ve had to teach a class of Geometry students this semester has helped me grow and improve tremendously as a teacher. It surprised me then that the most effective lesson I designed out of the four major ones was my Geometry lesson. Coming into this year, Geometry would have been the area that I would have said I was least comfortable teaching since I hadn’t seen most of the material formally since high school. ![]() I think the overall content of the material that I taught in this lesson was very well organized and ordered in a way that allowed for each activity and concept to build off of the previous one. Above anything else, I had a lot of fun doing in, and this speaks to the comfort level that I’ve developed over the course of the semester with my own teaching, as well as my comfort level with what I was teaching in this lesson. Of everything that I’ve done this semester in both Math Education courses, I think I was most satisfied with how this particular lesson went. ![]()
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