Santa Cruz County Office of Education

Teaching Algebraic Thinking Professional Development

2010-11

Focus on Lesson StudyOctober 11, 2010

Warm-Up Activity

As 900 students enter a school, they pass lockers that are numbered from 1 to 900. The first student opens every locker; the second student closes every second locker; the third student changes the position of every third locker (by opening the closed lockers and closing the open lockers); and the fourth student changes the position of every fourth locker. This pattern continues for all 900 students. Which lockers are open after all students enter the school?

Turn your first five cards face up to represent 5 lockers. Open and close the lockers for five students. Which lockers are left open?

Which lockers are left open when you have 10 lockers and students? 15? 20?

What conjecture can you make about a rule for 900 lockers and students? n lockers and students?

Which Pay? Task: Jocelyn wanted to make some extra money.

Her father offered to pay her for odd jobs around the home for a week and gave her a choice of two options. The first option was that her father would pay her $1.25 for the week. The second option was that her father would pay her in the following manner for a week: on Monday he would give his daughter $0.01; on Tuesday $0.02; on Wednesday $0.04 and so on through Sunday. What would you tell Jocelyn to do, so she can earn the greatest amount?

Classroom Activity Debrief Share the activity you did with your

students. What strengths did you see? What weaknesses or concerns did you

see? Share your student work to support your

thoughts.

To Use Lesson Study to: Focus instruction on helping students

make sense of Math (e.g. why 9.83 x 7.65 = 75.1995 and cannot be 7519.95)

Help teachers focus on student thinking when planning and teaching

Learn strategies to encourage “student talk” to promote language development and mathematical proficiency

TODAY’S OUTCOMES

Develop an understanding of Lesson Study

Experience how to use “evidence” of student thinking to inform instruction

Plan your ‘dirty lesson’ Decide who will teach lesson, and where

Professional Development model used in Japan (originally to implement student-centered curriculum from U.S.)

Continuous Improvement model Teachers are the experts; others

provide resources

Background about Lesson Study

Lesson Study

1. STUDYConsider long term goals for

student learning and development

Study curriculum and standards 2. PLAN

Select or revise research lesson

Do task

Anticipate student responses

Plan data collection and lesson

3. DO RESEARCH LESSON

Conduct research lesson

Collect data

4. REFLECTShare data

What was learned about students learning, lesson

design, this content?

What are implications for this lesson and instruction more

broadly?

VisibleFeatures of Lesson

Study•Consider Goals

•Study Curriculum and Standards

•Plan and Conduct Research Lesson

•Collect Data

•Debrief Lesson

•Use Debrief to Inform Instruction

•What Else?

How Does Lesson Study Improve Instruction?Cause Changes In:

•Teachers-Knowledge of subject matter and its teaching

-General knowledge of instruction

-Ability to observe students

-Connection of daily instruction to long-term goals

-Motivation/willingness to improve

-Capacity to learn together, collegial networks

•Curriculum-Better lessons-Choice of better curricula•System-Changes in policy-Changes in learning structures

Result in Changes in Teaching-LearningSpecific Examples:

Teaching-Offer high-level task

Learning-Student journals reveal thinking re: proportional reasoning

Lesson Study Cycle1. Collaboratively plan a detailed lesson (including

researching the topic and existing lessons)

2. At least one team member teaches the lesson and other team members observe it (“live” or on video)

3. The team meets to analyze their observations of what students said and did mathematically

4. The team revises the lesson based on their observations

5. (Sometimes another team member teaches the revised lesson and is observed)

How Many Seats? Activity- If triangular tables are lined up side

to side in a row with just one seat allowed on each side…

- What patterns do you notice about how many seats will fit around a given number of tables?

Background for Observing “Planning Meeting #1”

Teachers are in San Mateo for a summer institute and teaching summer school

“Planning Meeting #1”– teachers are deciding between two published lessons to modify for lesson study

Observing Lesson #1 Listen and watch for evidence of students’ mathematical thinking.

What math/strategies are you seeing or hearing?

TAKE NOTES.

After “Lesson #1” video, discuss: What math did you see or hear? Where does the +1 rule come

from and the +2 rule? What do they mean?

How might you change the lesson to help more students find the +2 rule?

Observing Lesson #2Listen and watch for evidence of students’ mathematical thinking.

What math/strategies are you seeing or hearing?

TAKE NOTES

After “Lesson #2” video, discuss: What math did you see or hear? How did the changes to the

lesson promote more student thinking?

What do you think the team of lesson study teachers learned from their participation in this?

Keys of Lesson Study:

When observing, the focus is on the students, not the teacher. The team is judging the effectiveness of their lesson (not the teacher).

It’s not a perfect lesson—teachers’ learning occurs through the process.

Purpose is for teachers to learn about students’ thinking on the topic.

Next Steps for First Cycle of Lesson Study

Next meeting (Dec.) teams present their research lesson

Teachers will analyze the student work Revise lesson for second presentation If time: Observe second taught lesson If no time: teach the revised lesson in

your own classroom and bring resulting student work to Jan. 13th session

Back to Goals of the Series:Think about the videos and discuss: How did or did not this lesson (either

version) promote “reasoning” and “making sense of Math” including building mental images?

What about the lesson made student thinking visible so that we were able to find evidence?

First Steps What mathematical concept/topic are

you going to teach?

Why are you choosing this particular topic?

Planning Session What are the mathematical connections

for the lesson? What standard does the lesson

address? What best practices does the lesson

focus on?

Be Curious

What are we trying to accomplish?

Video clip

Sticking to the ProcessHow do we keep ourselves on track?

Video clip

Plan Your Lesson

Choose a topic Follow the template Review your plan Revise as needed