Contexts for Developing Mathematical Thinking in Mathematics Classroom through Lesson Study Maitree Inprasitha Center for Research in Mathematics Education Khon Kaen University, Thailand

A Sociocultural Perspective for Mathematical Thinking However, we can never observe mathematical thinking - we can only observe what we assume to be its products, namely mathematical ideas and processes. We can also observe what conditions and contexts might have been responsible for the products of mathematical thinking, which brings us rather closer to the social context. Bishop (2007)

Today topics Introduction on the Lab School Project Contexts for Developing Mathematical Thinking Results with teachers and students

Introduction to Lab School Project Initiated by Ministry of Education responding to an agenda “Enhance Thinking in Schools” Collaborated with Regional Universities Implementing some innovation into school

A National level Context - a school coordinator - Graduate Students - Teachers - educational supervisors - School Principal Coach - a school coordinator - Graduate Students - Teachers - educational supervisors - School Principal School 1School 2 OBEC+OKMD One university professor Graduate Program Ministry of Education

A Model for Implementing Lesson Study into School Context Preliminary Workshop : 1 day (option) Intensive Workshop : 2-4 days Implementing Lesson Study into School System : 3 yrs Coach School Coordinators Young Researchers Educational Supervisors Teachers Principals Students Parents Participants

Coach, school teachers, school coordinator, and parents shared their understanding on how to implement LS as innovative teaching

School teachers experienced doing open- ended mathematical activities as students do in the classroom Workshop on Open Approach and Lesson Study at Faculty of Education Khon Kaen University, 8-11 May 2006

Do See Plan a university-school level context at the faculty of education KKU and school implementation of the lesson into each school and observation lesson evaluation and reflection every period and once a week Coach, School Coordinator, Teachers, Researcher School Co. Teachers, Researcher, Coach

Process of Lesson Study and Open Approach for Teachers Professional Development Study of teaching materials (Plan) Lesson Study (Do) Lesson Discussion meeting (See) Social and Cultural Context Adapted from: The history of Japan’s Educational Development, 2004 Social and Cultural Context Open- ended Problem Situation

Lesson Study (Plan) School Co. Researcher Teachers

Lesson Study (DO) Coach School Co. Teachers

Lesson Study (See) School Co. Coach Teacher of the class Principal

Students presented their ideas in whole-class discussion Usual class scenario at Kookham Pittayasan School in the first year

In Classroom Context: Students working together Open Forum at Chomchon Ban Chonnabot School in the first year

Results I: What changed with teachers, students after one year passed?

Changed in Teachers’ Beliefs and Values about Teaching Mathematics 1.Collaboratively constructing lesson plan and reflecting regularly made the teachers more understanding with lesson plan, in turn, affecting ways to collect and follow student’s ideas, and how to organize whole class discussion 2.Beginning to value their students and their classes, which in turn, making them happier, more being confident with their pedagogical stance

Changed in Teachers’ Beliefs and Values about Teaching Mathematics 1.Created new culture in working together in school 2.Created in-school supervision 3.Created networking between teachers and supervisors which support constructive critiques

Changed in Teachers’ Beliefs and values about Teaching Mathematics 1.Concerned with the balance between new roles and former roles 2.Concerned with how to construct lesson plan to be opened 3.Concerned with how to record (e.g., journalizing) what happened in their own classrooms 4.Feel difficulty to discuss students’ ideas occurred in the classroom

Results II: What changed with students after one year passed?

Results of the survey at Chumchon Banchonnabot School Khon Kaen 44 of 1 st Grade 87 of 4 th Grade

1 more chance to express themselves 7 feel like independent period 2 more thinking 8 being oneself more valuable in the class 3 more relaxing9 more chance to do hands- on activities 4 using more art knowledge10 be able to summarize thing by themselves 5 more friendly classroom environment11 when think out feel like being genius 6 have a chance to innovate thing12 others The reasons why they like classroom activities

Positive changed with students 1 more reasonable 8 better communication with other people 2 more noticeable 9 more approaches to solving problem 3 more cool hearted 10 be able to connect things 4 Know to work with other people 11 more enthusiastic 5 more confident with questioning 12 better achievement 6 be able to argue according to his/her own reason 13 others 7 be able to reject the idea they do not agree with

Topic: Number larger than 10 Goal To create Number Sense in Student and using handmade wood, block, paper sheet To help students realize the meaning of place value.

Instruction 1.Count pandas and elephants and put them into the base-ten container as fast as you can (first round : count pandas, second round: count elephants) 2.shade in the figure and write down the number of pandas and elephants Language in Classroom: Thai and Dialect

Instructional Materials

20 Counter (handmade) 2 Base-ten Containers

Worksheet

Teaching Scenarios Introduction Greeting Introduce instructional materials Explain instruction to the students

Group Working use the counters to put on the picture and count aloud many times After they finished counting, they put the counter on base- ten (container, block)

Group Working Write down the number in the block under the figure Shade in the figure started from the left

Whole class discussion Each group demonstrates their ideas.

Whole class discussion Why did you write 13 ? Can we write 31 or 10 3

Summary The teacher summarizes what have learned in this period. Observer Teacher