Teaching and Learning Geometry

“Reasoning” — is the action of thinking about something in a logical, sensible way. As a teacher candidates, I believe that reasoning is one of important part in learning mathematics. The reason for this is, when doing the reasoning, students will know why each mathematics concept be designed. In other words, students will explore and understand more the mathematical concept.
In reading materials this week, I found that there is an interesting part of teaching perimeter and circumference by involving reasoning method. By using open-ended tasks and real problem, the teacher asks students to develop strategies for finding the perimeter of closed regions, and so avoid confusing formula for finding perimeter and area. Based on the reading materials, the process of finding the perimeter of closed regions begin by drawing a rectangle with a perimeter of 18 units on a geoboard, and the student has to draw the other rectangle with the same perimeter. In the process of drawing the rectangle, students have to describe how they find these rectangles? and also give reasoning about the rule to find these rectangles based on their understanding. In my opinion, this kind of learning process is better rather than the teacher just give the formula. The reason is when teacher only gives the formula and students only memorize it, there is a probability that students will forget the formula in the future. However, if students understand and know the reason for the concept, students no longer need to memorize all of the formulae.
In addition, from the learning materials, I just realize that there is different approach to teaching measurement for each level of students. In the primary years of students, the teacher will introduce the concept of measurement by using direct comparison. They place objects each other to see which is bigger or longer. When I was an early primary student, I remember that my teacher ask me to compare several objects and I just realize that it is the part of learning measurement. Then, in the secondary years, teacher introduces the use of measurement in solving real problems including the design and construction of objects and event. That is why it is important to ensure students’ ability in the decimal place value systems, multiplication and division operation system before starting to teach measurement in secondary level.