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

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

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.

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?

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?

Properties of parallelograms AnnenbErg Media

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: 10 - 12

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.

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

Properties of parallelograms https://www.learner.org/resources/series34.html#

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

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?  

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)?

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.

If time: mathematical vocabulary and vocab vids

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

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

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

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

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

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