1. Video Cases: Trigonometry
PROMOTING PROBLEM SOLVING AND SENSE-MAKING
DAY 4

2. Video Case Agenda Trigonometric Functions
Ferris Wheel
Small Group Discussion and Reflection

3. Think-Pair-Share
What real-world phenomena could be used to demonstrate relationships involving trigonometric functions?
How could a physical model of a Ferris wheel help students to explore properties in trigonometric functions?

4. Ferris Wheel

5. Launch
Content Standards: Functions, Algebra, Geometry from an Algebraic Perspective, Trigonometry
Process Standards :Problem Solving, Communication, Reasoning, Connections
School: North Carolina School of Science and Mathematics, 550 students Location: Durham, North Carolina Teacher: Helen Compton Years Teaching: 26 Students in Classroom: 16 Grade: 11

6. Video Overview
The class reviews homework in which students wrote a function describing a rider's height on a single Ferris wheel. Then students work in groups, using graphing calculators to write a function for a rider who travels from the bottom to the top of a double Ferris wheel. At the end of the class, Ms. Compton reconvenes the students and presents that evening's homework on writing a function for the rider's horizontal position on a double Ferris wheel.

7. Lenses In your small groups, you will focus on two lenses: Teaching
Learning
Take a few minutes with your group to discuss how you want to organize your viewing

8. Ferris Wheel

9. Reflection and Note-Writing
Take 2-3 minutes to finish your video notes before you discuss your lenses in your group

10. Small-Group Discussion
Teaching
How does the teacher elicit and respond to students’ thinking?  
What opportunities does the teacher create for diverse learners to communicate their mathematical understandings - show what they know?  
What resources and knowledge does the teacher use/draw upon to support students’ math understanding?  
How do the teacher’s actions support student learning?
Power and Participation
What specific math understandings and/or confusions are indicated in students’ work, talk, and/or behavior?  
How do students communicate their understandings and sense making of others’ thinking? 
In what ways does student engagement reflect conceptual and/or procedural learning?
What resources or knowledge do students draw upon to understand and solve the math task?

11. Whole-Group Discussion
What are the similarities and differences in the ways the two lenses focused your attention on specific aspects of instruction?
What are other opportunities or ways that the teacher and/or students might have integrated students’ knowledge bases and resources in this lesson? Why might you choose to pursue these alternatives (or why not)?

12. Focusing on Content
How does Ms. Compton help students investigate their assumptions?
What affect would a different set of assumptions - such as a different starting point or the Ferris wheel moving clockwise - have on the way students approach the problem?
What are the advantages and disadvantages of establishing assumptions with the class before beginning work on a problem?

13. If Time: Vocabulary

14. A Continuum of Word Knowledge
No knowledge
A vague sense of the meaning
Narrow knowledge with aid of context
Good knowledge but shaky recall
Rich, decontextualized knowledge,
connected to other word meanings

15. Tier 1 Tier 2 Tier 3 Selecting Words Basic Words Dale Chall List
High frequency words for mature language users
Low frequency words limited to specific domains
clock
baby
happy
coincidence
absurd
industrious
isotope
lathe
peninsula
Note: Link to the Dale Chall List

16. Examples: book, girl, dog Around 8,000 word families
Tier 1 Words
Basic words
Rarely require direct instruction and usually don’t have multiple meanings
Examples: book, girl, dog
Around 8,000 word families

17. High-frequency words for mature language users
Tier 2 Words
High-frequency words for mature language users
Important for reading comprehension, used across a variety of environments, often contain multiple meanings
Instructional potential: words that can be worked with in a variety of ways so that students can build rich representations
Examples: measure, analyze, synthesize, effect
7000 word families

18. Examples: isotope, lathe, crepe
Tier 3 Words
Found in specific domains: subjects in school, hobbies, occupations, geographic regions, technology, weather, etc.
Learning these words occurs when a specific need arises, such as learning amino acid during a chemistry lesson.
Examples: isotope, lathe, crepe
Estimate: The remaining 400,000 words in English

19. Selecting Words Words that are important for understanding a text.
Select words that have cost/efficiency—words that appear frequently enough and across multiple contexts that they are worth the teaching time investment.
Select words that students will encounter while reading content material
Key words
Useful words
Interesting words
Vocabulary-building words

20. How do you currently select vocabulary words?
Discussion
How do you currently select vocabulary words?
How is the tiered system similar to or different from what you already do?
Hint: Search for “academic vocabulary list”
Berkeley Unified School District has a good one!

21. Groups
Think about vocabulary terms in geometry that have caused issues or surfaced misconceptions in your classroom in the past
As a group, select one Tier II vocabulary term—a word that has multiple meanings, that students will encounter again and again, and that they need to know to access disciplinary content

22. Vocab Vids

23. Step 1: Plan Research your chosen word
Brainstorm possible concepts/places where you might see the word
Props
Location
Sign showing the word?

24. Step 2: Film
Improvise
Redo
Revise

25. Step 3: Share (or Publish)
Use as review of vocabulary terms
Do Nows
Projects