Developing a Keen Eye
Video Analysis Lesson Cycle
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 supports 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 focuses teachers' attention on ways to promote students' engagement in mathematically productive practices and key moments when students' opportunities to achieve the intended learning goal occurred in 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 element in the keen eye video analysis cycle includes opportunities to delve deeper (optional prompts to explore) and hear final reflections from the teacher in the video.
BACKGROUND & CONTEXT
INTRODUCE
Interior Angles of Regular Polygons
In this video, the teacher (Kathleen) introduces herself and provides some background knowledge about the lesson she was teaching on the day the video was recorded.
NARRATIVE & GOAL
Interior Angles of Regular Polygons
Students develop strategies for determining the sum of the interior angles of regular polygons by decomposing them into shapes with known angles.
CLASSROOM MATHEMATICS PRACTICES
ANALYZE
Interior Angles of Regular Polygons
Video Analysis: Round One
After engaging in the “Which One Doesn’t Belong?” routine, students explore ways to break up different polygons in order to find the sum of the interior angles. This video features the first share out. Prior to watching the video, anticipate various ways students might decompose their shapes. Review the descriptors on page one of the keen eye template to support your video reflection focus.
Classroom Environment
Teacher
Students
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.
Students
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 develop strategies for determining the sum of the interior angles of polygons by dissecting them into shapes with known angles. This will enable them to discover a relationship between the angles and sides in polygons, with the ultimate goal of generalizing their strategy as a formula.
MATH LEARNING OPPORTUNITIES
ANALYZE
Interior Angles of Regular Polygons
Video Analysis: Round Two
Following round one, review the descriptors from page two of the keen eye template. What do you notice about the focus of these descriptors? Watch the clip a second time, now with a sharper focus on the mathematics and mathematical goal of the lesson. Identify key moments when students’ opportunities to achieve the learning goal occurred. Consider ways the learning opportunities could potentially be enhanced.
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 develop strategies for determining the sum of the interior angles of polygons by dissecting them into shapes with known angles. This will enable them to discover a relationship between the angles and sides in polygons, with the ultimate goal of generalizing their strategy as a formula.
EXTENDING OUR LEARNING
Other Questions to Explore:
- Why did the teacher have the students explore the angle sums of different regular polygons? How did this connect to her learning goal?
- In what ways were the students positioned to make sense of Morgan’s group’s strategy?
- How did Morgan use her understanding of isosceles triangles to find the missing angles in the polygon? What assumptions (if any) were made as part of her explanation?
- Why were the students in groups asked to apply Morgan’s strategy to their shape? What purpose did this serve?
- In the opening video, the teacher (Kathleen) said she was actively working on "shifting the mathematical authority" to the community. What evidence did you see of this goal in the video?
REFLECTIONS FROM THE TEACHER
REFLECT
Interior Angles of Regular Polygons
Discussion Points
- In what ways did opening up the task provide more students with greater access and opportunities to achieve the lesson learning goal?
- How did the plan support evolving students' understanding over time, particularly in light of the team's (teacher and coach) ultimate goal of generalizing the formula for any polygon, regular or not?