Week Two Prompt (1/17 - 1/21)

Week 2:
Think about the mathematical content being taught this week in the classes you are observing and/or teaching. Choose the content topic from ONE of these classes and make a list of all the prior knowledge and skills that students need in order to understand both the conceptual and procedural aspects of this content topic. How does the classroom teacher (or how do you) assess the prior knowledge that students bring with them to this new topic? How critical is this prior knowledge/skills to understanding the new content topic? Describe the quality and/or quantity of the necessary prior knowledge that these students seem to have for this topic.

Currently we are working with our geometry classes with the topic of the similar triangles formed when creating an altitude from a right angle to the hypotenuse in a large right triangle. The two smaller right triangles that are formed are similar to the original right triangle. Some of the prior knowledge students need to have to understand this topic is as follows:
-Properties of triangles
-Hypotenuse
-Legs
-Sum of interior angles
-Altitude and what it forms
-Proportions
-Similarity
-Proof why each triangle is similar to one another
-How to multiply radicals
-Square roots

Looking at the prior knowledge the students need, I feel a lot of these topics were covered in the previous lessons. Because this happens, the teacher can assess the students in previous lessons by looking at their homework, quizzes, or asking the students questions. I go over homework every day with the geometry classes. During this time I am able to tell which students understand the concepts, and which students will need more help. I do this by looking at which questions on the homework they did not understand. This will show me what level they are at in their understanding. If my cooperating teacher or myself does not feel the class is ready to move on, based on their homework or questions, we can design learning activities for the students to strengthen these skills. It would make no sense to move onto more complex concepts when the foundation concepts are weak in the students.
For this particular topic, without knowing the prior knowledge the new concepts would be almost impossible to understand. The prior knowledge sets up the new concepts and allows the students to build upon their older concepts. Without the prior knowledge, students would have nothing to build upon. I still find myself explaining to students where the hypotenuse is and how to set up the proportions between the sides of the similar triangles. Other students pick up on the new material quickly because they thoroughly understand what was being taught in previous lessons. A majority of the students fall in between the two extremes. They need reminders every so often on how to start or which sides are being compared in the ratio. I find this rather typical of a high school mathematics class.