1. PROMOTING PROBLEM SOLVING AND SENSE-MAKING DAY 3
VIDEO CASES: GEOMETRY
PROMOTING PROBLEM SOLVING AND SENSE-MAKING
DAY 3

2. Video Case Agenda Small Group Discussion and Reflection
Cut, Paste, and Enact
Properties of Parallelograms
Small Group Discussion and Reflection

3. Do Now (in Pairs)
Draw any large scalene triangle and list as many of its properties as you can. Include relationships between angles, sides, and special segments of the triangle.
Visualize how the triangle might be cut to form a parallelogram. Draw a line on the scalene triangle, cut out the shapes, and construct a parallelogram. List as many of the parallelogram's properties as you can. Present your construction to the group and explain your reasoning.

4. Think-Pair-Share
What properties did you use to form the parallelogram?
What questions could you ask to help students understand the relationships between the triangle and the parallelogram formed from the triangle?
How could this activity help students explore the area formulas for these two shapes?
What knowledge do students need to complete this discovery?

5. Group Discussion
How do informal explorations of geometric relationships prepare students to construct formal arguments? How can you encourage them to search for several relationships?
How would you address students' misconceptions or inaccurate conclusions about geometric relationships?

6. Properties of parallelograms
AnnenbErg Media

7. Launch Process Standards: Communication, Problem Solving
School: Arlington High School; 970 students Location: Arlington, Massachusetts Teacher: Carol Martignette Boswell Years Teaching: 21 Students in Classroom: 16 Grade: 

8. Video Overview
Students present homework on changing a right triangle into a rectangle. They evaluate one another's presentations with peer assessment cards numbered 1, 2, 3, or 4 (4 as highest), and explain the scores they give. Then students work in small groups to cut a triangle into pieces to form a parallelogram. During the activity, students explain to Ms. Martignette Boswell how their work illustrates the properties of a parallelogram, and she encourages them to use mathematical vocabulary. At the end of class, students are told they will present their work the following day.

9. Lenses In your small groups, you will focus on two lenses: Task
Power and Participation
Take a few minutes with your group to discuss how you want to organize your viewing

10. Properties of parallelograms

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

12. Small-Group Discussion
Task
Describe the main mathematical task that students are asked to do.
What makes this a good and/or problematic task?
What is/are the central math ideas in this task?
How does the task provide (or not) learning opportunities for students?
Power and Participation
Who participates?? Where does the majority of the math “work” take place in the classroom (e.g., front of room, small group, individual desks) and how does this contribute to participation?
Who holds authority for knowing mathematics? Do some students hold more status than others?
How do issues of participation, authority, and status influence learning?  

13. Whole-Group Discussion
What are the similarities and differences in the ways the two lenses focused your attention on specific aspects of instruction?
How did the use of these resources influence students’ learning?
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)?

14. Focusing on Content
How did students' understanding and misunderstanding of terminology affect their work? How important do you think the relationship is between knowing mathematical vocabulary and understanding mathematical concepts? Explain.

15. If time: mathematical vocabulary and vocab vids

16. 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

17. Selecting Words Tier 1 Tier 2 Tier 3 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

18. 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

19. 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

20. 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

21. 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

22. 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!

23. 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

24. Vocab Vids

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

26. Step 2: Film
Improvise
Redo
Revise

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