Part+III+-+Suggestions+for+teachers

Major ideas teachers need to keep in mind:

The very first thing a teacher needs to keep in mind is to relate the new information to past knowledge. Connecting prior knowledge on the topic of circles will go back to definitions of perimeter and area. You should have a warm up activity that gets students to think about properties of circles and allow them to express any ideas they may have for the future task.

Always when developing new knowledge, teachers should be giving students the opportunity to derive the formulas on their own. Simply expressing the formula or main idea to the students is purely a memory game. By forming their own meaning, students are able to more fully understand and interpret information. This method allows students to have long term connections with these ideas. The area and circumference formulas are to be derived in this lesson, and though pi is a known figure, students should derive pi from the formulas of area and circumference to understand how this number came to be.

In order to avoid "giving away" the formulas for circles, the teacher should use scaffolding to help guide the students thinking in the proper direction. What you should do is show different approaches to thinking about circle properties. Our three samples provided give a few example methods. This is a very challenging aspect of teaching, but asking questions to students rather than giving them answers goes a very long way.

Just as we discussed in focusing on prior knowledge when introducing a topic, we must focus on major concepts during exploration that the students need to understand for future mathematical explorations. Especially in geometry, many of the topics piggy back each other where principles applied in one topic, such as circles and pi, are seen again when we talk about volume. Radius for example, is something that will be used in many constructions and derivations or proofs in the future.