## Developing a Keen Eye

Play Video

## Video Analysis Lesson Task

## Explore this resource

### 1. Introduce

The * developing a keen eye* video library provides teachers and coaches with a rich set of resources to support the analysis of teaching with a goal of having productive and transformative discussions about ways to promote more ambitious teaching and learning in their mathematics classrooms. The introduction to each cycle includes background information about the lesson, the teacher, and the context for the classroom video recording.

### 2. Goal

Establishing clear and meaningful learning goals is an essential aspect of planning for effective mathematics instruction. Teachers need focused opportunities to articulate the intended math goals of their lessons as well as the key connections students need to make in order to achieve the intended learning goal. Math learning goals should be situated within a progression of coherent teaching that promotes and deepens student understanding over time.

### 3. Analyze

Research shows that analysis of teaching is one of the most effective levers for improving instruction and student achievement (Roth et al., 2019). The use of short classroom video clips and *keen eye* protocols focus teachers' attention on ways to promote students' engagement in mathematically productive practices and key moments when students' opportunities to make progress toward the intended learning goal occur during the lesson.

### 4. Reflect

Reflection is an essential part of improving planning and instructional practices. No lesson is perfect and whether teachers are new to teaching or have been teaching for many years, learning and growth results from an ongoing focus on teaching from a learning stance. The final elements the keen eye video analysis reflection cycle includes opportunities to delve deeper (optional prompts to explore) and hear final reflections from the teacher in the video.

#### BACKGROUND & CONTEXT

#### INTRODUCE

## Making Sense of Trigonometric Ratios

## Students reason about the ratios of the side lengths within right triangles and use principles of similarity to understand and justify the meaning of trigonometric functions.

## This video introduces the classroom teacher (Shellee Wong) and provides background information about the content of the video. The lesson for the day involves helping students make sense of trigonometric ratios.

#### NARRATIVE & GOAL

## Making Sense of Trigonometric Ratios

## Students reason about why the ratio of the side lengths of different right triangles in which corresponding angles are congruent must be the same value.

## In this* keen eye* video analysis cycle, students are trying to make sense of data they have just collected after drawing a 30º-60º-90º triangle. Using the 60-degree angle as **θ**, the students record the ratio of the adjacent side to the hypotenuse in a table on the board. The video begins with the teacher pulling the class together to discuss their data.

#### Classroom MATHEMATICS PracticES

#### ANALYZE

## Making Sense of Trigonometric Ratios

### Video Analysis: Round One

Prior to watching the classroom video, take a few moments to review the first page of the video analysis protocol. Use the descriptors to focus your attention on the ideas embedded in the guide. Consult with the facilitation guide to help promote a more productive conversation.

Classroom Environment

Teacher

Student Engagement

Classroom Environment

**E1.** Collaborative structures support student-to-student interaction**E2.** Norms for engagement are in place (e.g., Rights of the Learner)**E3.** Evidence of safe learning environment (e.g., mistakes are used as sites for learning, students volunteer explanations)

Teacher

**T1. **Asks questions that elicit students thinking

**T2. **Encourages justification using words, symbols, and visual representations

**T3. **Engages students in listening to and building upon one another’s reasoning (e.g., wait time, restating, re-voicing, adding on, agree/disagree, and why)

**T4. **Promotes connections by focusing students’ attention on key mathematical ideas

Student Engagement

**S1. **Grapple with the mathematics and engage in conversations about key ideas

**S2. **Question one another’s thinking (engage in respectful debate)

**S3. **Justify, clarify, and elaborate on their thinking

**S4.** Discuss and compare approaches

**S5.** Engage in continuous refinement (and revision) of ideas and precision of language

## Students analyze the data they have collected after creating a right triangle with a 60-degree angle and finding the ratio of the adjacent to the hypotenuse of the triangle.

#### MATH Learning opportunities

#### ANALYZE

## Making Sense of Trigonometric Ratios

## Video Analysis: Round Two

### Before watching the video clip a second time, take a few moments to examine the second page of the* keen eye* video analysis protocol. How are these descriptors different from those listed on page one? Use these descriptors to focus your attention on the mathematics and intended learning goal of the lesson. Identify key moments when students’ opportunities to make progress regarding the learning occurred. The given facilitation guide is designed to help you structure a meaningful and productive conversation.

Mathematical Engagement

Mathematical Engagement

**M1.** Teacher elicits students’ ideas and incorporates them to promote key connections related to the identified learning goal.**M2.** Use of representations (student artifacts) promotes mathematical sense making and productive discourse.**M3.** Learning activities promote cognitively demanding mathematics practices by students.**M4.** Students have extended opportunities to describe their reasoning and what they grappled with as part of their exploration.**M5.** Small and whole group conversations are purposefully structured to help students clarify and refine their ideas and make productive progress towards the math learning goal.

## Students analyze the data they have collected after creating a right triangle with a 60-degree angle and finding the ratio of the adjacent to the hypotenuse of the triangle.

## EXTENDING OUR LEARNING

## Questions to Explore:

- The students in this class have explored similarity in a previous unit and applied trig functions in a prerequisite math course. What important conceptual connections did this activity support?
- When did the
*critical*moment(s) occur in the lesson? What made it a*critical*moment? - How might this review enhance the students' understanding about the meaning of trigonometric ratios for other types of right triangles?
- How might this activity help students connect how the inputs and outputs of a trig function are related to the inverse of the trig function?

#### reflections from the teacher

#### REFLECT

## Making Sense of Trigonometric Ratios

## Discussion Points

- How did planning for the
*critical*moment better position the students to take ownership for the mathematics in the lesson? - In what ways were the students afforded a safe space for sharing and building upon one another's thinking?