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### Camarena Elementary School

July 18, 2013

Agenda

- Overview of CCSS and 8 SMPs
- Review of Math Discourse
- Talking About Mathematical Concepts
- Math Proficiency
- Lunch
- Align Pacing Guide and EnVision
- Planning a Lesson Focused on Math Discourse

Objectives

PWBAT:

- Review the five talk moves in math discourse
- Watch math discourse in action
- Discuss the purposes and benefits of talking about math concepts
- Discuss Camarena’s vision of a proficient math student
- Align Pacing Guide with EnVision
- Plan a Lesson(s) Focused on Math Discourse

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Standards for Mathematical PracticeWhat is Mathematical Proficiency?

- Conceptual Understanding- comprehension of concepts, operations, and relations--supports retention and preventscommon errors
- Procedural Fluency-carrying out procedures flexibly, accurately, efficiently, and appropriately
- Strategic Competence-ability to formulate, represent, and solvemathematical problems
- Adaptive Reasoning-capacity for logical thought, reflection, explanation, and justification
- Productive Disposition-inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

4 Rules for Successful Video Viewing

- Assume that there are many things you don’t know about the students, the classroom, and the shared history of the teacher and students on the video.
- Assume good intent and expertise on the part of the teacher. If you cannot understand his or her actions, try to hypothesize what might have motivated him or her.
- Keep focused on your observations about what students are getting out of the talk and interaction.
- Keep focused on how the classroom discourse is serving the mathematical goals of the lesson.

Why Use Talk in Mathematics Classrooms?

5 Major Reasons That Talk is Critical to Teaching and Learning

- Talk can reveal understanding and misunderstanding.
- Talk supports robust learning by boosting memory.
- Talk supports deeper reasoning.
- Talk supports language development.
- Talk supports development of social skills.

Discussion Questions

- Talk about your own students and their learning strengths and difficulties. Which of the five reasons for using classroom talk and discussion seem most relevant to your current teaching?
- Is there an example from your experience that might support one of the five claims?

Talking About Mathematical Concepts

Thinking about number patterns…

What number patterns are explored in grades K-2?

- How do you use the hundreds chart to help students learn these counting patterns?
- What difficulties do young students have with learning them?
- What types of knowledge do you want students to gain?
- What is the learning trajectory for a counting pattern? Namely, what do students learn first, second, and so on?

Talking About Mathematical Concepts

What are the purposes and benefits of talking about math concepts?

- Video clip 3.1a: Number Patterns on the Hundreds Chart (Grade 1)

In this clip, a number of students count to one hundred using different patterns.

- Video clip 3.1b: Magnet Man-on the Move! (Grade 1)

In this clip, students play Magnet Man-on the Move!, where they identify a number and use counting patterns to reach it.

Talking About Mathematical Concepts

First Viewing: 3.1a

Second Viewing: 3.1a

- What number patterns did students use to count to one hundred?
- What do you think were the benefits of asking students to restate the number pattern that was used?

- Were you surprised that first graders were able to repeat another student’s response? Why or why not?
- How does the hundreds chart support the talk about the different number patterns?
- Some students are grappling with counting by tens starting at a number other than ten. How does this type of activity coupled with talking about counting help them learn to count by tens starting at any number?

Talking About Mathematical Concepts

First Viewing: 3.1B

Second Viewing: 3.1B

- What did you see happening here?

- What is the purpose of activity?
- What talk moves did you notice the teacher using during this activity?

Talking About Mathematical Concepts

Review Lesson Plan

- How might you adapt this lesson for your students?

Summary Points

- Even young students can talk about mathematical concepts.
- We can plan our lessons by creating questions that will guide student talk and bring them more deeply into considering the mathematical concepts in the lesson.

Talking About Mathematical Concepts

Draw or create as many rectangles as possible using exactly twenty squares.

Record the dimensions, area, and the perimeter for each rectangle.

- In groups…
- List concepts associated with area and perimeter.

Talking About Mathematical Concepts

Video clip 3.2a:

Finding Rectangles with a Specific Area

(Grade 4)

In this clip, students work in small groups to find all possible rectangles using exactly twenty square tiles and then have a discussion about the perimeters of the rectangles.

Video clip 3.2b:

Examining Area and Perimeter

(Grade 4)

In this clip, students discuss in small groups and as a class some of their thoughts about why the perimeters of rectangles with the same area are different.

Talking About Mathematical Concepts

First Viewing: 3.2a

Second Viewing: 3.2a

- Students used different strategies to determine the perimeter of the rectangles. What were the three strategies students used to find the perimeter of the 5-by-4 inch rectangle?

- How are students justifying that they have found all possible rectangles using exactly twenty square tiles?
- How does Ms. Luipold use small group work to support the development of students’ abilities to talk about math concepts?
- Sometimes a student’s response is not completely accurate. What might teachers do in those circumstances?

Talking About Mathematical Concepts

First Viewing: 3.2B

Second Viewing: 3.2B

- What talk moves were used?

- How is the use of technology (interactive whiteboard) supporting students’ reasoning and talk about perimeter?
- Students are asked to explain what happens to the perimeter when the shape changes from a 1 by 20 inch to either a 2 by 10 inch or 4 by 5 inch rectangle. Are students listening to each other? How do you know?
- A concept is built on relationships. What relationship does the teacher want her students to grasp? How does she facilitate the learning?
- What are the benefits of letting many students participate in the summary of the lesson?

Talking About Mathematical Concepts

Review Lesson Plan

- How might you adapt this lesson for your students?

Summary Points

- Talking about the mathematical concepts helps students understand more deeply how the perimeters of rectangles with a fixed area are affected by the dimensions of the rectangles.

Talking About Mathematical Concepts

- Chapter 3: Mathematical Concepts

- Jigsaw
- Everyone reads p 49 – 50 Exploring a Math Concept.
- K-3 teachers read p. 50 Exploring a Math Concept – p. 55 Building Relationships
- 4th Grade teachers read p. 55 Building Relationships to p. 60
- 5th/6th grade teachers read p. 61-64

Talking About Mathematical Concepts

- What is a math concept?
- How are concepts different from skills?
- For each teacher/student vignette, discuss the concepts that were discussed.

- One of the benefits of talking about concepts is that students’ misconceptions or confusions often are revealed.
- Describe some examples from your own teaching experience in which you learned about a student’s misconception.
- How might talk be used to help students address the misconception?

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Standards for Mathematical PracticeWhat SMPs are addressed with Math Discourse?What is Mathematical Proficiency?

- Conceptual Understanding- comprehension of concepts, operations, and relations--supports retention and preventscommon errors
- Procedural Fluency-carrying out procedures flexibly, accurately, efficiently, and appropriately
- Strategic Competence-ability to formulate, represent, and solvemathematical problems
- Adaptive Reasoning-capacity for logical thought, reflection, explanation, and justification
- Productive Disposition-inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

What is Camarena’s vision for a proficient math student?

- What does a proficient Camarena math student look like and sound like?
- Discuss with your group
- Draw
- Everyone participates
- Assigned color per person

Pacing Guides

- Look for focus, coherence, and rigor
- Change McGraw-Hill heading to EnVision
- In grade level teams, identify chapters/lessons

Planning Time

- Use lesson planning template
- Create a lesson for your 1st topic

Did we meet our objectives?

PWBAT:

- Review the five talk moves in math discourse
- Watch math discourse in action
- Discuss the purposes and benefits of talking about math concepts
- Discuss Camarena’s vision of a proficient math student
- Align Pacing Guide with EnVision
- Plan a Lesson(s) Focused on Math Discourse

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