Santa Cruz County Office of Education Teaching Algebraic Thinking Professional Development Focus on Lesson Study October 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 = and cannot be ) 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. STUDY Consider 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. REFLECT Share data What was learned about students learning, lesson design, this content? What are implications for this lesson and instruction more broadly?

Visible Features 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-Learning Specific Examples: Teaching -Offer high-level task Learning -Student journals reveal thinking re: proportional reasoning

Lesson Study Cycle 1.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 #2  Listen 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 Process How do we keep ourselves on track? Video clip

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