##
* *Reflection: Developing a Conceptual Understanding
Formative assessment over Identities - Section 1: Method for Assessment

Until the last couple of years, I have required my students to memorize trig identities during this unit. Then, I took the time to reflect on whether memorizing met my goals and my students. When they memorize, my students make flashcards and quiz each other. But, they were never able to use the ideas as deeply as they do with the reference sheet. Yes there are some ideas that have to be memorized but how we get our students to memorize the key ideas will make a difference in retention.

Since reducing the amount of memorization required, I have found that my students actually retain more of the concepts and skills that I want them to gain from the unit. At this point in my class, most students can recall the reciprocal identities, the quotient identity, and sin^2 x+cos^2 x=1 from memory. Beyond that, students use their resource sheet. But, as they do the work, they are continuing to learn the material, even on the assessment.

*Why not memorize*

*Developing a Conceptual Understanding: Why not memorize*

# Formative assessment over Identities

Lesson 8 of 14

## Objective: SWBAT use fundamental identities to verify identities.

#### Method for Assessment

*45 min*

For this unit I employ a different process for assessment. Here is the Verifying Identities quiz.

After considering the best way to assess students on this topic for several years, I have designed a new method to assess the students' performance. My goal is to allow students to demonstrate their knowledge, even if they make a mistake early in the process.

At this point in my class, the students are still learning the identities discussed in class. I don't want verifying identities to be about memorizing a lot of rules. I want my students working to learn to use identities to show something is true, meaningfully. Along the way I want the students to understand the structure of the expression, use known identities meaningfully, and demonstrate mathematical practices. With this in mind, I have decided to allow students to use a reference sheet during the quiz. My guidelines for a reference sheet are that a student can include identities, but not examples.

Another technique I use on this quiz is to allow students to get a hint on a question. I sell hints for a point: if I give the students a hint, I deduct a point from their final score. I find that many times students are able to finish a problem once a hint is given. The students respond positively to this policy. And, they use it thoughtfully. Students take the time to determine if they are willing to lower their grade for the hint, or, persevere to solve the problem without taking a deduction.

To help me remember who I have helped I write the hint in red pen on their paper (see help on test example). On this student's paper, I gave assistance working with fractions. In this case, the finding a common denominator was a productive hint.

**Teaching Note**: Some of my students struggle when adding and subtracting fractions is necessary. This issue is a challenge for me in a PreCalculus class. But, I have many important topics to teach, so I try to make decisions that enable students to be successful in my class.

*expand content*

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- UNIT 1: Introduction to Learning Mathematics
- UNIT 2: Functions and Piecewise Functions
- UNIT 3: Exponential and Logarithmic functions
- UNIT 4: Matrices
- UNIT 5: Conics
- UNIT 6: Solving Problems Involving Triangles
- UNIT 7: Trigonometry as a Real-Valued Functions
- UNIT 8: Graphing Trigonometric Functions
- UNIT 9: Trigonometric Identities
- UNIT 10: Solving Equations
- UNIT 11: Vectors and Complex Numbers
- UNIT 12: Parametric and Polar graphs and equations

- LESSON 1: Formalizing Properties Known Informally
- LESSON 2: The Pythagorean Identities
- LESSON 3: Simplifying Expressions
- LESSON 4: Proving Identities
- LESSON 5: Co-Function Identities
- LESSON 6: Even Odd Identities
- LESSON 7: Problem Solving Identities
- LESSON 8: Formative assessment over Identities
- LESSON 9: Sum and Difference Day 1 of 2
- LESSON 10: Sum and Difference Day 2 of 2
- LESSON 11: Double Angle Identities
- LESSON 12: Using Half Angle Identities
- LESSON 13: Review Identities
- LESSON 14: Assessment for Identities