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

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

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?

Ferris Wheel

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

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.

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

Ferris Wheel https://www.learner.org/resources/series34.html#

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

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?

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)?

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?

If Time: Vocabulary

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

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 http://rfptemplates.technologyevaluation.com/Dale-Chall-List-of-3000-Simple-Words.html

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

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

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

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

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!

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

Vocab Vids

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

Step 2: Film Improvise Redo Revise

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