Narrative
The lesson I am doing for Lesson 3 is on the Golden Ratio. This topic study provided me with a lot of helpful information on how students should be making connections between different ideas within the broad topic of Numeric Patterns. Many aspects of the topic study have contributed to the ideas I have created for the lesson. A large portion of this topic discussed the relevance of patterns in nature and the real world. This relates to the lesson because the Golden Ratio is famous for its appearance in nature, and its further applications into art, music, architecture and other subjects. Since the topic focuses being able to draw connections between ideas introduced within the topic of numeric patterns and even outside of it, I plan on crafting the lesson in such a way which allows student to discover equivalent ratios among different objects, introducing this idea that multiple objects can have the same ratio. Then, the Golden Ratio can be formally discussed, and the students can learn about its relation to other subjects and objects in nature. Finally, I plan to link to the original concept of the Fibonacci numbers (which will be introduced in the Engage part of the activity) so students can link the Golden Ratio to yet another concept they have been made familiar with. I will do this by showing the students how the ratio of two consecutive numbers in the Fibonacci sequence will produce the Golden Ratio. The readings support this structure for the lesson because if executed correctly, it should link the concept of a pattern found in nature as observed in the Exploration to a ratio representation of this patter, to a number sequence representation of this pattern (the Fibonacci sequence). If the students can learn to see these connections, they may learn to recognize patterns among other things in nature and try to find other places they apply to, which is overall the purpose of mathematics. Mathematics is defined as this study of patterns found in nature and described as continual finding of new connections among topics. A long-term goal would be for students to learn to create these connections on their own, or even discover new connections!
Although time consuming, I have come to appreciate the process of Curriculum Topic Study because it provides everything you could possibly need to know about a topic you plan on teaching. I especially appreciate the Research section because it gives insight on types of misconceptions students may have and the specific ideas research indicates the students will struggle with. This benefits the teacher by providing them with areas to really concentrate on so they are more prepared if students have a lack of understanding or a misconception within that part of the topic. For example, I know that students tend to struggle in making connections between topics, so now I am better prepared mentally to answer questions or guide students thinking in the right direction when it comes to making a necessary connection within the topic. The topic study requires a teacher to devote one-hundred percent to a topic, which will benefit both the teacher and the students in the long run.
My ideas for this lesson have not changed much through this process. The topic study expanded on my initial ideas, reinforcing the structure of the lesson I was interested in designing in the first place. The research was definitely helpful in giving me a better idea of student thinking for this topic, however, and has put me in the frame of mind to create this lesson using information that I have learned along the way. It would be helpful to be able to read more research on this topic in terms of student learning in order to be as prepared as possible for the students.
Although time consuming, I have come to appreciate the process of Curriculum Topic Study because it provides everything you could possibly need to know about a topic you plan on teaching. I especially appreciate the Research section because it gives insight on types of misconceptions students may have and the specific ideas research indicates the students will struggle with. This benefits the teacher by providing them with areas to really concentrate on so they are more prepared if students have a lack of understanding or a misconception within that part of the topic. For example, I know that students tend to struggle in making connections between topics, so now I am better prepared mentally to answer questions or guide students thinking in the right direction when it comes to making a necessary connection within the topic. The topic study requires a teacher to devote one-hundred percent to a topic, which will benefit both the teacher and the students in the long run.
My ideas for this lesson have not changed much through this process. The topic study expanded on my initial ideas, reinforcing the structure of the lesson I was interested in designing in the first place. The research was definitely helpful in giving me a better idea of student thinking for this topic, however, and has put me in the frame of mind to create this lesson using information that I have learned along the way. It would be helpful to be able to read more research on this topic in terms of student learning in order to be as prepared as possible for the students.