Week Three Prompt (1/24 - 1/28)

Week Three Prompt:
Think about the lessons that you are teaching or observing this week. Usually the primary way teachers describe lessons is by their content topic, which is easily tied to a content standard (or maybe two content standards if the lesson merges algebra and geometry, for instance.) But there are (hopefully) process standards that are also being addressed, even though they might not be explicit in a lesson’s description. Obviously not all process standards need to be incorporated in all lessons, but over time students should experience aspects of these process standards in the mathematics classroom.

Describe/discuss ways that the five NCTM process standards are being addressed (or not addressed, if that is the case) in the lessons you teach or observe.

On Friday I took over all three Geometry classes at the beginning of the new chapter. The lesson I taught on Monday focused on The Pythagorean Theorem, how to find missing sides of a right triangle, and classifying triangles using the properties of The Pythagorean Theorem.
Problem Solving:
The problem solving process standard is being used when the students and myself work through word problems involving the Pythagorean Theorem together and individually. These students have to apply what they know about the Pythagorean Theorem to a real life situation to arrive at the correct answer. Students are challenged with several different types of problems so they can use their problem solving skills to solve the problem.
Communication:
There is plenty of communication during these lessons. While I teach these lessons I try to get the students involved with the learning process. After teaching the necessary concepts, I have students verbalize the steps they took on different examples I give them. This helps them communicate mathematics between themselves, the rest of the class, and me. It helps them gain a better understanding on the new concepts.
Connections:
This particular lesson has a lot of connections to the previous chapter. The previous chapter dealt with similar triangles and proportions between sides. The next couple sections have students learn about special right triangles (45°-45°-90° and 30°-60°-90°) and the ratios between their sides. This also leads into right triangle trigonometry where students will use their knowledge of proportions between sides to help find angles and missing side lengths. There are a lot of connections between the topics the students have already learned, and what they will be learning in the near future.
Reasoning and Proof:
The way the book teaches the Pythagorean Theorem seems to leave out why it works. There are no proofs offered on the Pythagorean Theorem and students are not required to know why it works, but only required to know how to use it and apply it in different situations. I would love to have the students explore the many different proofs, but because of time restraints placed on the class I have to pick and choose what they are spending their time on.
Representations:
In this chapter, students have the ability to see multiple representations of how to use the Pythagorean Theorem. They have been able to use real life situations and multiple representations of different problems. I can still try to present them with different representations throughout my lessons. This will deepen their understanding of the concepts being taught.