## Reflection: Student Ownership Double Angle Identities - Section 2: Other double angle problems

Today, I used video to capture two students working on verifying the identities. The students are not particularly engaged in working on the identities, but in the video they demonstrate the importance of student ownership of the concepts and skills in the Common Core curriculum. Without student ownership, which would be evidenced by fluent application when learning new concepts, students are not achieving the goals of the Common Core.

Student 1 does not substitute using a correct expression from the Pythagorean Identity.  In response, I ask the student to check his formula sheet. When he is unable to remedy his error, I ask a student in his group to help him find the mistake.  The student applies his peer's suggestion, but the next step that he chooses to take lacks mathematical meaning for him. In this example, I recognize that I need to work with the student on his algebra techniques. He is not yet fluent enough with operations on algebraic expressions to work with trig functions.

Student 2 also demonstrates an error when writing down each step.  I have to remind the student about using parenthesis correctly.  Some students will distribute the negative as they write the problem, which is fine, but many of my students fail to take the opposite of all of the terms in the expression. In this instance, if you listen closely, you can hear that the student does not appreciate the importance of the parenthesis in the expression. She simply ignores that parenthesis, which is sometimes allowable, but in this case it is consequential.

Both of these students do not yet own the algebraic skills required to complete the Common Core curriculum successfully. This fact makes it difficult for me to move forward at an appropriate pace in Pre-Calculus. I hope that as the Common Core advances in my school, students will gain more ownership over the concepts in the curriculum. If so, it will surely be the students who benefit.

Student Ownership: Students solving

# Double Angle Identities

Unit 9: Trigonometric Identities
Lesson 11 of 14

## Big Idea: Trigonometric sum formulas are used to find double angle formulas for sine, cosine and tangent.

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Standards:
Subject(s):
Math, double angle formulas, Trigonometric identities, PreCalculus
40 minutes

### Katharine Sparks

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