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It is important to critically analyze questions such as, what is p’? , And what is the area of a circle? The obvious assumptions would be the numerical approximation 3. 14 and the formula of the area of a circle, pi*raw. However, as we soon learned Pi is the ratio of a circle’s circumference to its diameter or the number of radius squares needed to completely cover a circle exactly. And the area off circle is the unit squares needed to cover a circle exactly, or the space inside the boundaries of a circle.
Such revelations prompted the lessons that were soon to follow. All these lessons had one common factor; they focused on a unit centered on a circle. Lesson one was a common lecture in which the teacher used examples and taught the lesson by simply stating the facts on the board and asking the students to practice. Lesson two was based on interaction. Students learned by watching and interacting with manipulative that a parallelogram formed from pieces of a circle has the area calculated by Pi*r*r which is Pi*raw.
Lesson three focused on the guess and check attempt. Students were asked to find their own ways to approximate the area of a given circle without using the formula. Finally lesson four was investigative, students were given radius squares and asked to discover the area of a circle using fractions. Lesson one and three might have not been my ideal vision of a lesson I would teach, however, lesson two and four inspired me.
Lesson two and four were interesting to me because I learned something new in each approach. I used my previous knowledge to solve a new problem. While lesson one was too boring for me to sit through, and lesson four was open-ended and I did not quite understand the point of the lesson. After we broke into groups and began discussing these lesson, I earned my two favorite lessons might not be the most suited for a student centered classroom that I would hope to achieve.
I learned that in mathematics, although students might be discovering new information on lesson two and four because of the complexity of the lessons, they may not learn what I as well as the math standards would like them to learn. Consequently, I learned that to plan a good lesson, I first have to establish what I want my students to learn, and then plan my lesson around the first step. The two questions that prompted the beginning of the lesson also resonated with e after the lesson was complete.
I began thinking of ways to assess my students’ learning. Although it might be simpler to ask the students to memorize the numerical approximation of Pi and the formula for the area of a circle, I would also like them to learn the definitions of these concepts. After reading chapter one of ‘Teaching Secondary and Middle School Mathematics’ by Daniel Brazier, I learned that with a bit more planning on my part, I can use the five steps of ‘doing’ mathematics to help students grasp these ideas and create their own meaning of such notions.